What is the first step in solving ab -c = d for a
Answer:
See below
Step-by-step explanation:
To solve for "a", you would first isolate ab on the right-hand side by adding "c" on both sides:
[tex]ab-c=d\\ab-c+c=d+c\\ab=d+c[/tex]
Next, you would divide both sides by "b" to isolate "a":
[tex]ab=d+c\\ab\div b=(d+c)\div b\\a = \frac{d+c}{b}[/tex]
The solution is:
[tex]\large\boldsymbol{a = \dfrac{d + c}{b}}[/tex]Work/explanation:
To solve the given expression for a, we should isolate it by using basic algebraic operations.
The first step is to add c to each side:
[tex]\sf{ab-c=d}[/tex]
[tex]\sf{ab=d+c}[/tex]
Now, divide each side by b:
[tex]\sf{a=\dfrac{d+c}{b}}[/tex]
I have solved the equation for a.
Thrrefore, the answer is a = d + c / b.What’s the value of each variable in the parallelogram
Answer:
m = 5
n = 12
Step-by-step explanation:
The parallel sides of a parallelogram are equal.
m +1 = 6 so m = 6 -1 = 5, and n = 12
Answer:
m = 5 , n = 12
Step-by-step explanation:
the opposite sides of a parallelogram are congruent , then
m + 1 = 6 ( subtract 1 from both sides )
m = 5
and
n = 12
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
The coordinate of the fourth vertex is (9,11)
What is coordinate?Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space is called coordinate
For example (6,3) is a coordinate on a plane where 6 represent the value on x axis and 3 represent the value on y axis.
Since the shape is parallelogram;
√ -3-1)² + 8-0)² = √ x-5)² + y-3)²
= √4² +8² = √ x-5)² + y -3)²
therefore, relating the two values;
4 = x-5 and 8 = y -3
x = 4+5 = 9
y = 8+3 = 11
Therefore the coordinate of the fourth vertex = ( 9,11)
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Please answer ASAP I will brainlist
(a) The amount for total expenditures in 2015 was about $63.2 billion.
(b) The first full year in which expenditures exceeded $110 billion was 2027.
(a) To find the amount for total expenditures in 2015, we need to substitute x = 20 into the function h(x) = [tex]23.4(1.08)^{(x-5)[/tex].
h(x) = 23.4(1.0[tex]8)^{(20-5)[/tex]
= 23.4(1.0[tex]8)^{15[/tex]
≈ 23.4(2.717)
Rounding to the nearest tenth, the total expenditures in 2015 were about $63.2 billion.
(b) To determine the first full year in which expenditures exceeded $110 billion, we need to find the value of x when h(x) is greater than $110 billion.
110 = 23.4(1.0[tex]8)^{(x-5)[/tex]
Dividing both sides by 23.4:
4.7008547... = (1.0[tex]8)^{(x-5)[/tex]
Taking the logarithm base 1.08 of both sides:
log₁.₀₈(4.7008547...) = x - 5
Using a logarithm calculator or software, we find:
x - 5 ≈ 11.75
Adding 5 to both sides:
x ≈ 16.75
Rounding to the nearest whole number, the first full year in which expenditures exceeded $110 billion was 2027.
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CAPM Elements
Value
Risk-free rate (rRF
)
Market risk premium (RPM
)
Happy Corp. stock’s beta
Required rate of return on Happy Corp. stock
An analyst believes that inflation is going to increase by 2.0% over the next year, while the market risk premium will be unchanged. The analyst uses the Capital Asset Pricing Model (CAPM). The following graph plots the current SML.
Calculate Happy Corp.’s new required return. Then, on the graph, use the green points (rectangle symbols) to plot the new SML suggested by this analyst’s prediction.
Happy Corp.’s new required rate of return is .
The new required rate of return for Happy Corp. can be calculated using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:
Required rate of return = Risk-free rate + Beta * Market risk premium
Since the analyst believes that the market risk premium will be unchanged, the only factor that will affect the new required return is the risk-free rate.
Given that the analyst predicts a 2.0% increase in inflation, the risk-free rate will also increase by that amount. Therefore, the new required rate of return for Happy Corp. will be the current risk-free rate plus the product of Happy Corp.'s beta and the market risk premium.
To plot the new Security Market Line (SML) on the graph, we would use the new required return calculated above and plot it against the corresponding beta values. The SML represents the relationship between risk (beta) and return (required rate of return).
By incorporating the new required return, we can determine the new expected returns for various levels of beta and create the updated SML.
It is important to note that without specific values provided for the risk-free rate, market risk premium, and Happy Corp.'s beta, it is not possible to calculate the exact new required return or plot the new SML accurately.
These values are crucial in determining the precise position of the SML on the graph.
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B
A
C
Intro
y
-6
4
3
2
+
1
2 3
x
Suppose quadrilateral ABCD has been transformed by
Ty=x. What are the coordinates for the vertices of the
reflected quadrilateral A'B'C'D'?
A' =
B' =
C' =
D'=
The coordinates of the reflected quadrilateral A'B'C'D' are:
A' = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
To find the coordinates of the reflected quadrilateral A'B'C'D', we need to apply the transformation Ty = x to each vertex of the original quadrilateral ABCD. The transformation Ty = x reflects each point across the y-axis.
Given the coordinates of the original quadrilateral ABCD as:
A = (-6, 4)
B = (3, 2)
C = (+1, 23)
D = (x, 12)
Applying the transformation Ty = x to each vertex, we can determine the coordinates of the reflected quadrilateral A'B'C'D':
A' = (-(-6), 4) = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
The reflected quadrilateral A'B'C'D' thus has the following coordinates:
A' = (6, 4)
B' = (-3, 2)
C' = (-1, 23)
D' = (-x, 12)
Therefore, the x-coordinate for point D' will be represented as -x in the reflected quadrilateral.
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Prove the following?
The given statement proposition is a that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
The given statement is a logical proposition involving the concept of induction. Let's break it down and analyze its components.
"If x is inductive..."
This implies that x is a concept or object that possesses the property of being inductive. In mathematics, the term "inductive" typically refers to the property of being a natural number or belonging to the set of natural numbers.
"...then so is (x ∈ X : x = Ф or x = y ∪ {y} for some y)"
Here, we have a set X that consists of elements satisfying a certain condition. The condition states that an element x in X can either be equal to the empty set (Ф) or the union of a set y with itself ({y}). This construction represents a recursive definition, where each element in X is defined in terms of a base case (Ф) and a recursive step ({y}).
"...hence each n ≠ 0 is m + 1 for some m."
This conclusion states that for every natural number n that is not equal to 0, there exists another natural number m such that n can be expressed as m + 1. In other words, any non-zero natural number is the successor of some other natural number.
Overall, the given statement is a proposition that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.
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Jessica and Barry squeezed oranges for juice. Jessica squeezed 23
5
cups of juice. Barry made 1
4
cup less than Jessica. Barry estimated that Jessica squeezed about 21
2
cups of juice.
Which is the best estimate for the amount of juice Barry made?
Jessica squeezed 235 cups of juice, Barry made 221 cups of juice, and the best estimate for the amount of juice Barry made is 198 cups.
Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. The best estimate for the amount of juice Barry made is 198 cups.
There are different ways to approach this problem, but one possible method is to use subtraction to find out how much juice Barry actually made, and then compare it to the estimated amount. If Jessica squeezed 235 cups of juice and Barry made 14 cups less, then Barry made 235 - 14 = 221 cups of juice.
This is the exact amount of juice that Barry made, but it may not be a convenient answer if we are looking for an estimate that is close to Barry's estimate of 212 cups of juice. One way to get such an estimate is to round 221 to the nearest ten or hundred. For example, if we round to the nearest ten, we get 220, which is only 8 cups away from Barry's estimate.
Alternatively, if we round to the nearest hundred, we get 200, which is only 12 cups away from Barry's estimate. Therefore, the best estimate for the amount of juice Barry made is 198 cups, which is obtained by rounding down to the nearest ten. This estimate is only 14 cups away from Barry's estimate, and it is also easy to compute mentally.
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What is the formula?
What do the V’s equal?
Answer:
60 cm³
Step-by-step explanation:
volume of a rectangular pyramid
v = ( l * w * h ) / 3
v = ( 4 * 5 * 9 ) / 3
v = 60
Which of the following functions is graphed below?
Answer: C
Step-by-step explanation:
the x - 2 means go right 2
the +3 means go up 3
HELP PLEASE AND HURRYY
Answer:
Part A: Answer: D.
Part B:
true
false
true
Step-by-step explanation:
Part A:
Use a tree.
Round 1 Round 2 Round 3
W W W
W W L
W L W
W L L
L W W
L W L
L L W
L L L
All possibilities are:
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
Answer: d.
Part B:
Winning 3 games is WWW.
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
Out of the 8 possible outcomes shown above, only 1 of them is WWW.
p(WWW) = 1/8
Answer: true
Winning exactly 2 games happens when there are exactly 2 W's:
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
p(exactly 2 wins) = 3/8
Answer: false
Wining at least 2 games means winning exactly 2 or exactly 3 times.
WWW, WWL, WLW, WLL, LWW, LWL, LLW, LLL
p(winning at least 2 games) = 4/8 = 1/2
Answer: true
I dont understand these can someone help?
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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Tyrone places a carton of milk and a box of cookies together. The carton of milk has a length of 6 inches, a width of 4 inches, and a height of 8 inches. The box of cookies has a length of 5 inches, a width of 4 inches, and a height of 2 inches. What is the combined volume of the boxes?
Therefore, the combined volume of the carton of milk and the box of cookies is 232 cubic inches.
To find the combined volume of the carton of milk and the box of cookies, we need to calculate the volume of each object and then add them together.
The volume of an object can be found by multiplying its length, width, and height. Let's calculate the volume for each item:
Carton of milk:
Volume = Length × Width × Height
= 6 inches × 4 inches × 8 inches
= 192 cubic inches
Box of cookies:
Volume = Length × Width × Height
= 5 inches × 4 inches × 2 inches
= 40 cubic inches
Now, we can find the combined volume by adding the volumes of the carton of milk and the box of cookies:
Combined Volume = Volume of Carton of milk + Volume of Box of cookies
= 192 cubic inches + 40 cubic inches
= 232 cubic inches
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. Initially 100 milligrams of a radioactive substance was present.
After 6 hours the mass had decreased by 3%. If the rate of
decay is proportional to the amount of the substance present at
time t, nd the amount remaining after 24 hours.
Answer:
Incomplete Question
Simplify 15a6 bc4/ 35a2 c4
The simplified value of the expression given is 3a⁴b/ 7
Given the fraction :
15a⁶bc⁴/ 35a²c⁴divide the coefficients by 5
3a⁶bc⁴/ 7a²c⁴From division rule of indices, subtract the powers of values with Equivalent coefficients.
Hence,
coefficient of of a = 6-2 = 4coefficient of c = 4-4 = 0coefficient of b = bFinally we have :
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The parallel gram shown below has an area of 72 units^2
Answer:
h = 12 units
Step-by-step explanation:
The formula for the area of a parallelogram is given by:
A = bh, where
b is the base of the parallelogram,and h is an altitude (i.e., a perpendicular line that connects the two bases of a parallelogram).Thus, the base is 6 units. We can find the height by dividing the area by 6:
A = bh
72 = 6h
72/6 = h
12 = h
Thus, the height of the parallelogram is 12 units.
Evaluate. -15 +7-(-8)
The answer options are
16
0
-16
-3
Answer:
To evaluate -15 + 7 - (-8), we can simplify the expression by first removing the double negative.
-15 + 7 + 8 = 0
Therefore, the answer is 0.
Step-by-step explanation:
The answer is:
0Work/explanation:
Remember the integer rule,
[tex]\bullet\phantom{4444}\sf{a-(-b)=a+b}[/tex]
Similarly
[tex]\sf{-15+7-(-8)}[/tex]
[tex]\sf{-15+15}[/tex]
Simplify fully.
[tex]\sf{0}[/tex]
Therefore, the answer is 0.A spinner has five sectors of equal size the sectors are labeled 1, 2, 3, 4 and five the spinner is spun twice X is the number of times three is fun drag each bar on the horizontal axis to the correct location to create a probability distribution for X
The probability distribution for X is given as follows:
P(X = 0) = 0.64.P(X = 1) = 0.32.P(X = 2) = 0.04.How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
The distribution gives the probability of each possible outcome, hence it is given as follows:
P(X = 0) = 0.64.P(X = 1) = 0.32.P(X = 2) = 0.04.Learn more about the concept of probability at https://brainly.com/question/24756209
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Solve the system of equations. 8 � + 5 � = 24 � = − 4 � 8x+5y=24 y=−4x
The solution to the system of equations is x = 2 and y = -8.
To solve the system of equations, we'll use the substitution method. The given equations are:
Equation 1: 8x + 5y = 24
Equation 2: y = -4x
We'll substitute Equation 2 into Equation 1 to eliminate one variable:
8x + 5(-4x) = 24
8x - 20x = 24 [Distribute the -4]
-12x = 24 [Combine like terms]
x = 24 / -12 [Divide both sides by -12]
x = -2
Now that we have the value of x, we can substitute it back into Equation 2 to find the value of y:
y = -4(-2)
y = 8
Therefore, the solution to the system of equations is x = -2 and y = 8.
However, let's double-check the solution by substituting these values into the original equations:
Equation 1: 8(-2) + 5(8) = 24
-16 + 40 = 24
24 = 24 [LHS = RHS, equation is satisfied]
Equation 2: 8 = -4(-2)
8 = 8 [LHS = RHS, equation is satisfied]
Both equations are satisfied, confirming that x = -2 and y = 8 is indeed the solution to the given system of equations.
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4x+y20
find the value of y when x =6
Answer:
y= -4
Step-by-step explanation:
To find the value of y when x = 6, we can substitute x = 6 into the equation and solve for y:
4(6) + y = 20
24 + y = 20
y = 20 - 24
y = -4
Therefore, when x = 6, y is equal to -4.
what is $2^{-3}\cdot 3^{-2}$.
Answer:
[tex]\frac{1}{72}[/tex]
Step-by-step explanation:
[tex]2^{-3}\cdot 3^{-2}=\frac{1}{2^3}\cdot\frac{1}{3^2}=\frac{1}{8}\cdot\frac{1}{9}=\frac{1}{72}[/tex]
87,959 to the nearest hundred
which equation could use the find the length of the hypotenuse
0 6² + 11² - c²
0 6²+c² - 11²
Oc²-6²-11²
0 11²-6²-c²
Answer:
A. 6² + 11² = c²
Step-by-step explanation:
The correct equation to find the length of the hypotenuse in a right triangle is the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, if we assume that the length of one side is 6 and the length of the other side is 11, the correct equation would be:
A. 6² + 11² = c²
This equation can be simplified as follows:
36 + 121 = c²
157 = c²
Therefore, the correct equation to find the length of the hypotenuse in this case is A. 6² + 11² = c².
An architect is designing a swimming pool with a base in the shape of a right triangle according to the architect the pools depth should be 6 feet less than It’s length x and it’s width should be 8 feet less than it’s length the volume of water in the pool cannot exceed 1680 cubic feet which statement
Find the measure of the indicated angle.
45°
65°
55°
135°
270°
T
Why do we define
a curvature in terms of tha arc length?
i.e.
why do we put 's' into this definition?
(where s(t) is arc length function)
The inclusion of the arc length function in the definition of curvature provides a consistent and intrinsic measure of the rate of deviation from a straight line.
Incorporating arc length allows for the calculation of various geometric properties associated with curvature, such as the radius of curvature or the osculating circle.
The definition of curvature in terms of arc length is used to describe the rate at which a curve deviates from being a straight line. By incorporating the arc length function, denoted as 's(t)', into the definition, we can measure the curvature at different points along the curve.
Curvature, represented by 'k', is defined as the derivative of the unit tangent vector 'T' with respect to the arc length 's'. This definition has several advantages.
Firstly, it eliminates the dependency on the parametrization of the curve. Different parametrizations can yield the same curve, but their tangent vectors may differ. By using arc length as the parameter, we obtain an intrinsic measure of curvature that remains consistent regardless of the chosen parametrization.
Secondly, arc length provides a natural way to measure distance along the curve. By considering the derivative of the tangent vector with respect to arc length, we obtain a measure of how quickly the curve is turning per unit distance traveled.
Lastly, incorporating arc length allows for the calculation of various geometric properties associated with curvature, such as the radius of curvature or the osculating circle. These properties provide insights into the shape and behavior of the curve.
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The times taken for a group of people to
complete a race are shown below.
Estimate the number of people who took
longer than 325 minutes to complete the
race.
Cumulative frequency
250-
200-
150-
100-
50-
0
Time to complete a race
100 200 300 400 500
Time (minutes)
An estimate of 20 people took longer than 325 minutes to complete the race.
To estimate the number of people who took longer than 325 minutes to complete the race, we need to use the cumulative frequency distribution.
The cumulative frequency of a class interval is obtained by adding up the frequencies of all the class intervals up to and including that interval. The sum of the frequencies for each class interval is known as the cumulative frequency.In this case, the cumulative frequency distribution is given as follows:
Class Interval | Frequency | Cumulative Frequency250 - 200 | 5 | 5200 - 150 | 12 | 12150 - 100 | 18 | 30100 - 50 | 11 | 4050 - 0 | 4 | 44Total: 50
Now, to estimate the number of people who took longer than 325 minutes to complete the race, we need to look at the cumulative frequency that corresponds to 325 minutes.
From the table, we can see that the cumulative frequency of the class interval 300-400 minutes is 30. This means that 30 people took between 100 and 400 minutes to complete the race.
Therefore, the number of people who took longer than 325 minutes is the difference between the total number of people who took between 100 and 500 minutes and the number of people who took between 100 and 325 minutes. This can be calculated as follows:50 - 30 = 20.
Hence, an estimate of 20 people took longer than 325 minutes to complete the race.
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The probable question may be:
Estimate the number of people who took longer than 325 minutes to complete the race, given the following cumulative frequency distribution:
Cumulative frequency:
250-
200-
150-
100-
50-
0
Time to complete a race:
100 200 300 400 500
Time (minutes).
Question #2
Solve for x
2
O Saved 1
4
3
Q
69x + 2
R
70°
Which is a valid prediction about the continuous function f(x)? • f(x) ≥ 0 over the interval [5, ∞). • f(x) ≤ 0 over the interval [-1, ∞). • f(x) > O over the interval (-0, 1). • f(x) < O over the interval (-0. -1).
Answer:
The valid prediction about the continuous function f(x) is : f(x) ≥ 0 over the interval [5, ∞).
Step-by-step explanation:
Which of the following pairs show(s) two congruent triangles?
O B only
OB and C only
O A, B, and C
O A and C only
Answer:
B only
Step-by-step explanation:
Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.
Therefore, only B is correct
The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.
Explanation:The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.
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