Answers
The corresponding sides and angles of the similar and congruent triangles indicates that we get the following approximate and exact values;
Page 1;
5. [tex]\overleftrightarrow{AC}[/tex] = 4.3. 6. [tex]\overline{BP}[/tex] ≈ 7.5 7. [tex]\overline{YV}[/tex] ≈ 8
Page 2
5. [tex]\overline{DF}[/tex] = [tex]11\frac{1}{4}[/tex], 6. [tex]\overline{ED}[/tex] = 5, 7. [tex]\overline{BC}[/tex] = 22, 8. [tex]\overline{EF}[/tex] = 8
Page 3;
8. m∠ABC = 30°, 9. m∠XYP = 44°, 10. [tex]\overline{AC}[/tex] = 14
What are congruent triangles?Congruent triangles are triangles that have all three corresponding sides of the same length and all three angles of the same measure.
First Page
5. The distance from the vertex B to the line segment [tex]\overleftrightarrow{AC}[/tex] in the triangle ΔABC is the altitude of the triangle, which is 4.3
6. The distance from the vertex B to [tex]\overleftrightarrow{AC}[/tex] = [tex]\overline{BP}[/tex]
Pythagorean theorem indicates that the length of the segment [tex]\overline{BP}[/tex] can be found as follows;
[tex]\overline{BP}[/tex] = √(13.5² - 11.2²) ≈ 7.5
7. The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] is the altitude of the triangle ΔXYZ, which indicates;
The distance from Y to [tex]\overleftrightarrow{XZ}[/tex] = [tex]\overline{YV}[/tex]
The Pythagorean theorem indicates that we get;
[tex]\overline{YV}[/tex] = √(13.34² - 10.67²) ≈ 8
Second page;
5. The scale factor from ΔABC to ΔDEF = 3/4
Therefore, the length of [tex]\overline{DF}[/tex] = (3/4) × 15 = 45/4 = [tex]11\frac{1}{4}[/tex]
6. The scale factor of (1/3) indicates that we get;
[tex]\overline{ED}[/tex] = (1/2) × 10 = 5
7. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 18/9 = 10/5 = 2
The corresponding side to [tex]\overline{BC}[/tex] is [tex]\overline{EF}[/tex]
[tex]\overline{EF}[/tex] = 11, therefore, the length of [tex]\overline{BC}[/tex] = 2 × 11 = 22
8. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 4/6 = 10/15 = 2/3
The corresponding side to [tex]\overline{EF}[/tex] is [tex]\overline{BC}[/tex]
[tex]\overline{BC}[/tex] = 12, therefore [tex]\overline{EF}[/tex] = (2/3) × 12 = 8
Third page;
8. The triangles ΔABV and ΔCVB are congruent triangles by the Leg Hypotenuse congruence theorem.
The angles ∠ABV and ∠CBV are corresponding triangles, therefore;
∠ABV ≅ ∠CBV
m∠CVB = m∠ABV = 15° (Definition of congruent triangles and symmetric and substitution property)
∠ABC = ∠ABV + ∠CBV
Therefore; m∠ABC = 15° + 15° = 30°
9. The angles ∠YXP and ∠YZP are right triangles, therefore;
m∠YXP = m∠YZP = 90°
The right triangles ΔYXP and ΔYZP are congruent by the LH congruence theorem
∠XYP ≅ ∠ZYP (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
m∠XYP = m∠ZYP (Definition of congruent triangles)
m∠XYZ = m∠XYP + m∠ZYP (Angle addition property)
m∠XYZ = 2 × m∠XYP
2 × m∠XYP = m∠XYZ = 88°
m∠XYP = 88°/2 = 44°
10. The angles ∠ACP and ∠ABP are right angles, according to the indicated markings, therefore;
∠ACP ≅ ∠ABP (All right angles are congruent)
ΔACP ≅ ΔABP by SAA congruence theorem
[tex]\overline{AC}[/tex] ≅ [tex]\overline{AB}[/tex] (CPCTC)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] (Definition of congruent segments)
[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] = 14
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Related Questions
(2x5)(10x−2) simplified
Answers
Answer:
200x - 40 (5x-1)
Step-by-step explanation:
2 x 10 = 20
20 x 10 = 200
20 x -2 = -40
200 - 40 = 100 - 20, 50 - 10, 20 - 4, 10 - 2, 5 -1
so the answer is either 5x - 1 or 200x - 40
what are the three arithmetic means between 10 and 130
Answers
The three arithmetic means between 10 and 130 are 40, 70, and 100.
To find the three arithmetic means between 10 and 130, we need to calculate the common difference between consecutive terms.
The common difference (d) can be found using the formula:
d = (last term - first term) / (number of terms - 1)
In this case, the first term is 10, the last term is 130, and we need to find three arithmetic means.
d = (130 - 10) / (3 + 1) = 120 / 4 = 30
Now, we can calculate the three arithmetic means by adding the common difference to the previous term:
First arithmetic mean = 10 + 30 = 40
Second arithmetic mean = 40 + 30 = 70
Third arithmetic mean = 70 + 30 = 100
So 40, 70, and 100 are the three arithmetic means between 10 and 130.
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NO LINKS!! URGENT HELP PLEASE!!
Please help with 37
Answers
Answer:
Step-by-step explanation:
all circles have same round shape with no edges and corners so they all are similar in terms of their shape and appearance but not all the circles are congruent.
two circles are congruent if they have the same measurements of radius, circumference, diameter as well as the surface area. So, to determine whether the two circles are congruent or not we have to perform the calculations.
find the volume of a cube whose diagonal is 4√2
Answers
The volume of the cube with a diagonal of 4√2 is 64 cubic units.
To find the volume of a cube, we need to know the length of its side. In this case, we are given the length of the diagonal, which we can use to find the side length.
Let's assume the side length of the cube is represented by "s". We know that the diagonal of a cube forms a right triangle with two sides of equal length, which are the sides of the cube.
Using the Pythagorean theorem, we can set up the equation:
s² + s² = (4√2)²
Simplifying the equation:
[tex]2s² = 32[/tex]
Dividing both sides by 2:
[tex]s² = 16[/tex]
Taking the square root of both sides:
[tex]s = 4[/tex]
Now that we have the side length of the cube, we can find the volume by cubing the side length:
Volume = s³ = 4³ = 64 cubic units.
Therefore, the volume of the cube with a diagonal of 4√2 is 64 cubic units.
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The volume of the cube whose diagonal is 4√2 is 128√2 cubic units.
To find the volume of a cube, we need to know the length of its side. Given that the diagonal of the cube is 4√2, we can use this information to determine the side length.
In a cube, the diagonal is related to the side length (s) by the equation:
diagonal = s√3
The given diagonal is 4√2. So we can set up the equation:
4√2 = s√3
To find s, we can divide both sides of the equation by √3:
s = (4√2) / √3
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √3:
s = (4√2 ׳ √3) / (√3 × √3)
s = (4√6) / √3
Now, let's calculate the value of s:
s = (4√6) / √3
s = (4/√3) × √6
s = (4/√3) × (√3 × √2)
s = 4√2
So the side length of the cube is 4√2.
Now, to calculate the volume of the cube, we use the formula:
Volume = side^3
Volume = (4√2)³
Volume = 4³ × (√2)³
Volume = 64 × 2√2
Volume = 128√2
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Which model represents a percent error of 25%?
A- A model with 12 squares labeled exact value and 3 squares labeled error.
B- A model with 10 squares labeled exact value and 5 squares labeled error.
C- A model with 9 squares labeled exact value and 3 squares labeled error.
D- A model with 8 squares labeled exact value and 4 squares labeled error.
Answers
The correct answer is A- A model with 12 squares labeled exact value and 3 squares labeled error.
To determine which model represents a percent error of 25%, we need to compare the number of squares labeled "exact value" and "error" in each model and calculate the ratio between them.
Let's calculate the ratio for each model:
Model A: 3 squares labeled error / 12 squares labeled exact value = 0.25 or 25%.
Model B: 5 squares labeled error / 10 squares labeled exact value = 0.5 or 50%.
Model C: 3 squares labeled error / 9 squares labeled exact value ≈ 0.3333 or 33.33%.
Model D: 4 squares labeled error / 8 squares labeled exact value = 0.5 or 50%.
From the calculations, we can see that only Model A represents a percent error of 25%. The other models have ratios of 50% and 33.33%, which do not match the desired 25% error.
Consequently, the appropriate response is A- A model with 12 squares labeled exact value and 3 squares labeled error.
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3. Pi is defined as the ratio of the circumference of a circle to the diameter of that circle. Which of the following correctly explains why the formula for the circumference of a circle is 2 mr 7 (1 point)
Two times equals the distance from one side of the circle to the other. When you multiply that by r, you get the distance around the circle, or the circumference.
Pi times requals the diameter of the circle. The diameter is half the circle, so when you multiply it by 2, you get the distance around the entire circle, or the circumference.
Two times requals the diameter of the circle. Pi is needed for all circle formulas, so you multiply by since you are finding the circumference.
Two times requals the diameter of the circle. Pi equals the circumference divided by the diameter. When you multiply, the diameter is in both the numerator and the denominator, which cancels out, leaving the circumference.
Answers
Answer:
The correct answer is "Two times r equals the diameter of the circle. When you multiply that by pi, you get the distance around the circle, or the circumference." This is because the circumference of a circle is equal to the distance around it, which is the same as the length of its perimeter. The diameter of a circle is the straight line that passes through the center of the circle and touches both sides. Therefore, if you multiply the diameter by pi, which is the ratio of the circumference to the diameter of a circle, you get the circumference. Alternatively, you can also use the formula C = 2πr, where C is the circumference and r is the radius of the circle. Since the radius is half the diameter, the formula can also be stated as C = πd, where d is the diameter of the circle.
Step-by-step explanation:
3
Which expression is equivalent to -x--xy?
2x-xy?
4
x(3-y)
4x(3-y)
x(3+y)
4x(3 + y)
Answers
The expression equivalent to -x--xy is 4x(3 + y).
To simplify the expression -x--xy, we can apply the rules of combining like terms and distribute the negative sign.
-x - (-xy)
Removing the double negative:
-x + xy
Factoring out the common factor of x:
x(-1 + y)
Now, let's compare the simplified expression with the given options:
Option 1: 2x - xy
This expression is not equivalent to -x - (-xy) as it includes an additional term of 2x.
Option 2: x(3 - y)
This expression is equivalent to the simplified expression x(-1 + y), as it represents the distribution of x over the terms inside the parentheses.
Option 3: 4x(3 - y)
This expression is not equivalent to -x - (-xy) as it includes the constant term 4.
Option 4: x(3 + y)
This expression is not equivalent to -x - (-xy) as it includes the positive sign before the y term.
Option 5: 4x(3 + y)
This expression is not equivalent to -x - (-xy) as it includes the constant term 4 and the positive sign before the y term.
From the given options, the expression that is equivalent to -x - (-xy) is:
Option 2: x(3 - y).
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What is the square root of m^6?
m²
m³
m^4
m^5
Answers
The square root of m^6 is always positive.
The square root of m^6 can be calculated by dividing the exponent 6 by 2, since taking the square root is equivalent to raising a number to the power of 1/2.
In this case, m^6 divided by 2 gives us m^3.
Thus, the square root of m^6 is m^3.
This means that if we square m^3, the result will be m^6.
It is important to understand that the square root operation yields the positive root, so the square root of m^6 is always positive.
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Suppose that the relation H is defined as follows. H = {(9, 3), (8, p), (3, q), (8, 0)) Give the domain and range of H. Write your answers using set notation.
Answers
Answer:
See below
Step-by-step explanation:
Domain would be all the x-values, so this is {3, 8, 8, 9}
Range would be all the y-values, so this is {0, 3, p, q}
A scatterplot includes data showing the relationship between the value of a painting and the age of the painting.
Which graph displays the line of best fit for the data?
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit is too steep.
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit is not steep enough.
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit is not steep enough.
A graph has age (years) on the x-axis and value (dollars) on the y-axis. A line with best fit goes through the points.
Mark this and return
Answers
The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.
To determine which graph displays the line of best fit for the data, we need to analyze the provided options and identify the one that represents the relationship between the value of a painting and the age of the painting accurately.In a scatterplot, the line of best fit represents the trend or relationship between the two variables. It aims to summarize and capture the general pattern of the data points. The line of best fit should pass through the data points in a way that represents the overall trend.Analyzing the options, we see that three of them mention that the line with the best fit is either too steep or not steep enough. These options suggest that the line does not accurately capture the trend of the data.However, the remaining option states that the line with the best fit goes through the points. This implies that the line accurately represents the relationship between the value of a painting and the age of the painting by passing through the data points.Based on this analysis, we can conclude that the graph where the line of best fit goes through the points is the one that displays the most accurate representation of the relationship between the value of a painting and the age of the painting.For more such questions on graph, click on:
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Tell whether the information in the diagram allows you to conclude that c is on the perpendicular bisect of ab
Answers
11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.
12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector divides or bisects a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.
Question 11.
By critically observing the geometric shape, we can logically deduce that there is enough information to conclude that C is on the perpendicular bisector of AB because CE bisects AB:
AC ≅ BC
CD ≅ CD
AE ⊥ EC
Question 12.
By critically observing the geometric shape, we can logically deduce that there is enough information to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The cost to buy p pounds of potatoes at $0.32 per pound and n
pounds of onions at $0.48 per pound can be determined by using
the expression 0.32p + 0.48n. How much will it cost to buy 4.5
pounds of potatoes and 2.5 pounds of onions?
Answers
$1.44 for potatoes
$1.22 for onions
help please its due in 50 minutes ill mark brainliest answer too and no need to show work
Answers
The height, h, of the cylinder is approximately 1.27 centimeters when the volume is 100 cm^3 and the radius is 5 cm, rounded to the nearest tenth.
To find the height, h, of the cylinder, we can rearrange the formula for the volume of a cylinder:
V = πr^2h
Given that the volume, V, is 100 cm^3 and the radius, r, is 5 cm, we can substitute these values into the formula:
100 = π(5^2)h
Simplifying further:
100 = 25πh
To solve for h, divide both sides of the equation by 25π:
100 / (25π) = h
To calculate the value, we'll use an approximation for π as 3.14:
100 / (25 * 3.14) ≈ h
Simplifying:
100 / 78.5 ≈ h
h ≈ 1.27 cm
Therefore, when the volume is 100 cm3 and the radius is 5 cm, the cylinder's height, h, is about 1.27 centimetres, rounded to the closest tenth.
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The shaded part of the circle represents the part of gas used to fill up the gas tank of a lawn mower what part of the container is needed to fill up the gas tank of the lawn mower 4 times is the answer 8/48 8/12 6/16 or 6/12
Answers
The fraction of the container needed to fill up the gas tank of the lawn mower four times is 6/12. Option D.
The shaded part of the circle represents the fraction of gas needed to fill up the gas tank of the lawn mower once. To determine the fraction needed to fill it up four times, we can simply multiply the fraction by 4.
Let's assume that the shaded part of the circle represents x part of the whole container. Therefore, the fraction needed to fill up the gas tank of the lawn mower once is x.
To fill up the gas tank four times, we need to multiply x by 4. Therefore, the fraction needed to fill up the gas tank four times is 4x.
Now, we can compare this to the answer choices given:
8/48: This can be simplified to 1/6, which is not equal to 4x.
8/12: This can be simplified to 2/3, which is not equal to 4x.
6/16: This can be simplified to 3/8, which is not equal to 4x.
6/12: This can be simplified to 1/2, which is equal to 4x.
Therefore, the correct answer is 6/12, which represents the fraction of the container needed to fill up the gas tank of the lawn mower four times. so Option D is correct.
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Note the complete question is
Estimate the variation (strength) of the correlation of the scatter plot shown.
a.
moderate correlation
b.
no correlation
c.
strong correlation
d.
weak correlation
need now mamayang 11pm na pasahan
Answers
The strength of the correlation as shown in the scatter plot can be concluded to be: b) no correlation.
How to Estimate the variation (strength) of the correlation of a scatter plot shown?To estimate the strength of the correlation in a scatter plot, visually assess the clustering and linearity of the data points. If the points cluster tightly around a linear trend, it indicates a strong correlation, whereas dispersed and non-linear points suggest a weak correlation.
However, if the points on a scatter plot do not exhibit a discernible pattern (as shown in the image given above), it can be concluded that there is no correlation between the variables being plotted.
Therefore, the answer is: b. no correlation.
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hmm this is tricky help
Answers
The diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm (option e).
Given that the diameter of the engine cylinder needs to be 5 cm wide with a tolerance of ± 0.005 cm.
To determine the permissible range of the diameter, we need to consider both the upper and lower limits.
Upper limit: Add the tolerance to the desired diameter.
Upper limit = 5 cm + 0.005 cm = 5.005 cm.
Lower limit: Subtract the tolerance from the desired diameter.
Lower limit = 5 cm - 0.005 cm = 4.995 cm.
Therefore, the permissible range for the diameter of the engine cylinder is between 4.995 cm and 5.005 cm.
Hence, the final answer is that the diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm.
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recursive formula for an=1/8(2)n-1
Answers
Answer:
The recursive formula for an=1/8(2)n-1 is:
a1=1/8 an+1=1/8(2)(n)
This formula defines a sequence where each term is equal to 1/8 of the previous term multiplied by 2.
Step-by-step explanation:
B
C
W
A
E
Use the given diagram to answer the question,
Which line is the intersection of two of the planes
shown?
Which line intersects one of the planes shown?
Which line has points on three of the planes shown?
G
Answers
The line that intersects two of the planes is : Line X
The line that intersects one of the planes is : Line Z
The line that that has points on three of the planes shown is Line Y
How to find the intersection line on the plane?From this figure you can see that there are 3 different levels and 3 different lines. One line intersects two planes (line X), another line intersects only one plane (line Z). Line Y, on the other hand, has points in all three planes.
A line y has points A and B in all three planes.
A plane is simply a plane that can be intersected by a straight line connecting any two points on the plane.
Therefore, we can conclude from the figure
A line that intersects two planes is: line x
A line that intersects one of the planes is: line Z
A line with points on the three planes shown is Line Y.
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PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS)
Identify the arc length of MA◠ in terms of a and rounded to the nearest hundredth.
Answers
The length of the arc in terms of π and the actual length is as follows;
8.17π m²
25.68 m²
How to find arc length?Let's find the length of the arc of the circle as follows:
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 180 - 88 = 92 degrees
r = 16 m
length of an arc MA = 92 / 360 × 2 × π × 16
length of an arc MA = 2944π / 360
length of an arc MA = 8.17π
Therefore,
length of an arc MA = 25.68 m²
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Please answer ASAP I will brainlist
Answers
Answer:
Step-by-step explanation:
(a) To find the linear cost function C(x), we need to consider the fixed cost and the marginal cost. The fixed cost is $100, and the marginal cost is $8 per pair of earrings.
The linear cost function can be represented as C(x) = mx + b, where m is the slope (marginal cost) and b is the y-intercept (fixed cost).
In this case, the slope (m) is $8, and the y-intercept (b) is $100. Therefore, the linear cost function is:
C(x) = 8x + 100.
(b) The average cost function (AC) can be found by dividing the total cost (C(x)) by the number of units produced (x):
AC(x) = C(x) / x.
Substituting the linear cost function C(x) = 8x + 100, we have:
AC(x) = (8x + 100) / x.
(c) To find C(5), we substitute x = 5 into the linear cost function:
C(5) = 8(5) + 100
= 40 + 100
= 140.
Interpretation: C(5) = 140 means that when the artist produces 5 pairs of earrings, the total cost (including fixed and variable costs) is $140.
(d) To find C(50), we substitute x = 50 into the linear cost function:
C(50) = 8(50) + 100
= 400 + 100
= 500.
Interpretation: C(50) = 500 means that when the artist produces 50 pairs of earrings, the total cost (including fixed and variable costs) is $500.
(e) The horizontal asymptote of C(x) represents the cost as the number of units produced becomes very large. In this case, the marginal cost is constant at $8 per pair of earrings, indicating that as the number of units produced increases, the cost per unit remains the same.
Therefore, the horizontal asymptote of C(x) is $8, indicating that the average cost per pair of earrings approaches $8 as the number of units produced increases indefinitely.
In practical terms, this means that for every additional pair of earrings produced beyond a certain point, the average cost will stabilize and remain around $8, regardless of the total number of earrings produced.
Determine the domain of the following graph:
Answers
Answer:
-9 is less than x, which is less than or equal to 11
Step-by-step explanation:
Answer:
Step-by-step explanation:
Domain is where the function exists for x.
The functions domain goes in terms of x goes from -9 to 11 not including -9 and including 11.
Interval notation:
-9 < x ≤ 11
Set notation:
(-9, 11]
The length of ribbons found at a seamstress are listed.
3, 11, 11, 13, 13, 21
What is the appropriate measure of variability for the data shown, and what is its value?
The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.5.
The range is the best measure of variability and equals 18.
The IQR is the best measure of variability and equals 2.
Answers
What is the solution to the equation below In X=3.1
Answers
Answer:
the solution would be X=3 as 3.1 represents 3×1.
Please answer ASAP I will brainlist
Answers
(a) The average cost in 2011 is $2247.64.
(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.
(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.6Inx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2011 - 2006) + 6
x = 5 + 6
x = 11 years.
Next, we would substitute 11 for x in the function:
g(11) = -1736.7 + 1661.6In(11)
g(11) = $2247.64
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
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NO LINKS!! URGENT HELP PLEASE!!
Please help with #4
Answers
Step-by-step explanation:
Let the statement be:
"If p, then q"The converse of a statement is:
"If q, then p"Let's try it for each statement and see if the converse is true.
a) The converse is:
If the interior angles sum to 180°, then my shape is a triangle.It is true.
b) The converse is:
If alternate interior angles are equal, the two lines are parallel.It is true.
c) The converse is:
If I have a Rhombus, then I also have a Square.It is false, since not all rhombus have four right angles.
d) The converse is:
If I have a shape with four right angles, then I have a rectangle.It is false, since it could be a square.
a. Converse: If the interior angles sum to 180°, then my shape is a triangle. (Converse is not true)
b. Converse: If alternate interior angles are equal, then the lines are parallel. (Converse is true)
c. Converse: If I have a Rhombus, then I also have a Square. (Converse is not true)
d. Converse: If I have a shape with four right angles, then I have a rectangle. (Converse is true)
a. Converse: If the interior angles of a shape sum to 180°, then the shape is a triangle.
The converse of this statement is not true. There are many shapes other than triangles whose interior angles sum to 180°, such as quadrilaterals and polygons with more than four sides.
b. Converse: If alternate interior angles of two lines are equal, then the lines are parallel.
The converse of this statement is true. If the alternate interior angles of two lines are equal, then the lines are parallel. This is a property of parallel lines and can be proven using the corresponding angles postulate.
c. Converse: If I have a Rhombus, then I also have a Square.
The converse of this statement is not true. While all squares are rhombuses (a square is a special type of rhombus), not all rhombuses are squares. A rhombus is a quadrilateral with all sides of equal length, but its angles can be anything other than 90°.
d. Converse: If I have a shape with four right angles, then I have a rectangle.
The converse of this statement is true. If a shape has four right angles, then it is a rectangle. This is a defining characteristic of rectangles, as all rectangles have four right angles.
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The complete question is :
Write the converse of each statement and determine if the converse is true.
a. If my shape is a triangle, then the interior angles sum to 180°.
b. If two lines are parallel, then alternate interior angles are equal.
c. If I have a Square, then I also have a Rhombus.
d. If I have a rectangle, then I have a shape with four right angles.
pls pls pls help
Based on the graph of F(x) below, which of the following statements is true
about F(x)?
Answers
The correct statement regarding the relative extremas of F(x) is given as follows:
F(x) has a relative maximum at x = -1 and a relative minimum at x = -0.8.
What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing.Hence the extremas for this problem are given as follows:
Maximum: x = -1.Minimum: x = 0.8.More can be learned about relative minimums of a function at https://brainly.com/question/9839310
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Please awnser asap I will brainlist
Answers
The result of the row operation on the matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
How to apply the row operation to the matrix?The matrix in this problem is defined as follows:
[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
The row operation is given as follows:
[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]
The first row of the matrix is given as follows:
[2 0 0 16]
The meaning of the operation is that every element of the first row of the matrix is divided by two.
Hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]
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What is the radius of a circle that has a circumference of 68 cm
Answers
Step-by-step explanation:
The formula to calculate the circumference (C) of a circle is C = 2πr, where r represents the radius of the circle.
In this case, the given circumference is 68 cm. Plugging this value into the formula, we can solve for the radius (r):
68 = 2πr
To find the radius, we can divide both sides of the equation by 2π:
r = 68 / (2π)
Using an approximate value of π ≈ 3.14159, we can calculate the radius:
r ≈ 68 / (2 × 3.14159) ≈ 10.8419 cm
Therefore, the radius of the circle, which has a circumference of 68 cm, is approximately 10.8419 cm.
Therefore, The Radius of the Circle is 10.8 cm.
Evaluate the following expression when a = 5 and b = 1. Then, plot the resulting value on the provided number line. 12+2 (4 a²) ÷ 7 + 8
Answers
Answer:
To evaluate the expression when a = 5 and b = 1, we substitute the values into the expression:
12 + 2(4(5)²) ÷ 7 + 8
= 12 + 2(4 * 25) ÷ 7 + 8 (Note: 5² means 5 raised to the power of 2)
= 12 + 2(100) ÷ 7 + 8 (Note: 4 * 25 = 100)
= 12 + 200 ÷ 7 + 8
= 12 + 28.57 + 8 (Note: ÷ means divide)
= 48.57
To plot the resulting value on the provided number line , we would need to know the scale and range of the number line. Without this information, we cannot accurately plot the value.
Step-by-step explanation:
```
12 + 2(4a^2)÷7 + 8
= 12 + 2(4(5)^2)÷7 + 8 (substituting a=5)
= 12 + 2(4(25))÷7 + 8 (evaluating 5^2 = 25)
= 12 + 2(100)÷7 + 8
= 12 + 28.57 + 8 (evaluating 2(100)÷7 = 28.57)
= 48.57
```
So the value of the expression when `a=5` and `b=1` is `48.57`.
To plot this value on a number line, we first need to determine the appropriate scale for the number line. Since the value we obtained is between 40 and 50, we can use a scale of 1 unit per tick mark. We then draw a number line and label it with tick marks at appropriate intervals. Finally, we plot the value `48.57` on the number line:
```
|-------------------------------------------
40 50
x=48.57
```
Therefore, the value of the given expression when `a=5` and `b=1` is `48.57` and we have plotted it on the number line.
A given city is at 35°S and 200°W. How far is it from this city to A. the North Pole and B. the Equator C. the south pole
Answers
The distance from the given city to the South Pole is 125 degrees of latitude.
To determine the distance from the given city to various locations, we need to consider the latitude and longitude coordinates.
Distance to the North Pole:
The North Pole is located at 90°N latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the North Pole.
Distance to the North Pole = 90° - 35° = 55°
The distance from the given city to the North Pole is 55 degrees of latitude.
Distance to the Equator:
The Equator is located at 0° latitude. To determine the distance from the city to the Equator, we need to calculate the absolute value of the latitude of the city.
Distance to the Equator = |35°| = 35°
The distance from the given city to the Equator is 35 degrees of latitude.
Distance to the South Pole:
The South Pole is located at 90°S latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the South Pole.
Distance to the South Pole = 35° - (-90°) = 35° + 90° = 125°
The distance from the given city to the South Pole is 125 degrees of latitude.
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