Answers
There is just one solution to this system. The answer is (460/7), (-13/7), and (-24/7). The correct answer is option A.
Given the system of equations as X+ y- z=63x- y+ z=2x- 4y+ 2z-34.We have to use row operations to solve this system of equations. Let us start by writing down the augmented matrix of the given system of equations. [1, 1, -1 | 6][3, -1, 1 | 2][1, -4, 2 | -34]
The first step is to change the first element of the second row to zero. For that, we subtract three times the first row from the second row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][1, -4, 2 | -34]
Now, we need to change the first element of the third row to zero. For that, we subtract the first row from the third-row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, -5, 3 | -40]
The next step is to change the second element of the third row to zero. For that, we add 5/4 times the second row to the third row to get the following: [1, 1, -1 | 6][0, -4, 4 | -16][0, 0, 7 | -24]
Now, we solve the system of equations using back-substitution. We have 7z = -24 ⇒ z = -24/7
Substituting this value of z in the second equation, we get -4y = 4 - z = 4 + 24/7 = 52/7⇒ y = -13/7
Substituting these values of y and z in the first equation, we get x = 63 - y + z = 63 + 13/7 - 24/7 = 460/7Thus, the solution of the given system of equations is (x, y, z) = (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
The given system of equations is solved using row operations. It is found that this system has exactly one solution which is (460/7, -13/7, -24/7). Therefore, the correct choice is A. This system has exactly one solution. The solution is (460/7, -13/7, -24/7).
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Related Questions
What are the coordinates of the midpoint of the line segment whose end points are (2, 6) and (10, 4)?
Answers
The midpoint of the line segment with endpoints (2, 6) and (10, 4) is (6, 5).
To find the midpoint of a line segment, we can use the midpoint formula, which states that the coordinates of the midpoint are the average of the coordinates of the endpoints.
Let's denote the coordinates of the first endpoint as (x1, y1) and the coordinates of the second endpoint as (x2, y2).
In this case, the first endpoint is (2, 6) with coordinates (x1, y1) = (2, 6), and the second endpoint is (10, 4) with coordinates (x2, y2) = (10, 4).
To find the midpoint, we use the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Plugging in the values, we have:
Midpoint = ((2 + 10) / 2, (6 + 4) / 2)
= (12 / 2, 10 / 2)
= (6, 5)
As a result, (6, 5) is the point on the line segment where the endpoints are (2, 6) and (10, 4) respectively.
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6. Juan y Roberto son dos hermanos que juegan Piedra, Papel y Tijera para determinar quien hace el aseo de su cuarto. ¿Cuántos serán los posibles resultados que podemos tener?, ¿Cuál es la probabilidad de que Juan no haga el aseo? *
Answers
Given, Juan y Roberto is two brothers who play Rock, Paper, and Scissors to determine who does the cleaning in their room. The total number of possible outcomes is 3. The possible outcomes are rock, paper, and scissors. So, the probability of Juan not doing the cleaning is 1/2 or 50 percent.
The probability that Juan will not do the cleaning is 1/2 or 50 percent. The possible outcomes for playing the game Rock, paper, and Scissors are given as follows. Rock can break scissors, Paper can cover rock, and Scissors can cut paper. Therefore, there are three possible outcomes in this game. The possible outcomes are rock, paper, and scissors.
The probability that Juan will not do the cleaning is 1/2 or 50 percent since there are two possible outcomes where Juan does not do the cleaning. The two possible outcomes are paper and scissors. Juan can pick the paper or scissors to win. Therefore, the probability of Juan not doing the cleaning is 1/2 or 50 percent.
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What is the degree in leading coefficient of f(x) equals 3X -5
Answers
Answer:
1
Step-by-step explanation:
The degree of a polynomial is the exponent of the varieble x. So the exponent of x in that function is 1.
A national dog show had two types of poodles. This table
shows height data, in inches, for the two types of poodles.
Heights of Poodles
Type of Poodle
Miniature
Standard
Number of Dogs
18
24
Mean Height Variation in Height
(inches)
(inches)
13
23
2
2
What number completes the sentence?
The difference in inches, between the mean height for the two
types of poodles is
times the variation for
either type.
Enter your answer in the space provided.
Answers
Here's how to calculate it:
- For the miniature poodles, the mean height is 13 inches and the variation is 2 inches.
- For the standard poodles, the mean height is 23 inches and the variation is also 2 inches.
- The difference between the mean heights is 23 - 13 = 10 inches.
- We want to express this difference in terms of the variation for either type. Since the variation for either type is 2 inches, we can divide the difference by 2 to get the answer:
```
10 ÷ 2 = 5
```
So the difference in inches is 5 times the variation for either type.
6 + 9x^2 + 3x^3 + 2x^4 - 12x
how many positive, negative, and complex zeros are there?
Answers
There are no positive or negative zeros, and the number of complex zeros cannot be determined without further information.
To determine the number of positive, negative, and complex zeros of the given polynomial [tex]6 + 9x^2 + 3x^3 + 2x^4 - 12x,[/tex] we need to analyze its behavior and apply the properties of polynomial functions.
Positive Zeros:
Positive zeros are the values of x for which the polynomial evaluates to zero.
To find positive zeros, we set the polynomial equal to zero and solve for x.
However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.
Therefore, there are no positive zeros.
Negative Zeros:
Negative zeros are the values of x for which the polynomial evaluates to zero.
Similar to positive zeros, we set the polynomial equal to zero and solve for x.
However, in this case, we can see that all the coefficients of the terms in the polynomial are positive.
Therefore, there are no negative zeros.
Complex Zeros:
Complex zeros occur when the polynomial has complex roots. Since the given polynomial has only real coefficients, complex zeros will occur in conjugate pairs.
To determine the number of complex zeros, we need to examine the degree of the polynomial.
In this case, the highest power of x is [tex]4 (x^4),[/tex] indicating a fourth-degree polynomial.
A fourth-degree polynomial can have at most four complex zeros. However, we cannot determine the exact number of complex zeros without further information or solving the polynomial explicitly.
In conclusion, the given polynomial has no positive or negative zeros due to all coefficients being positive.
The number of complex zeros cannot be determined without additional information.
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10. Consider the quadratic function f(x)=x² +6x. Solve the inequality for f(x) > -5.
Answer: x<-5
x>-1
Answers
The solution to the inequality f(x) > -5 is x < -5 or x > -1.
To solve the inequality f(x) > -5 for the quadratic function f(x) = x^2 + 6x, we need to find the values of x that satisfy the inequality.
First, set up the inequality:
x^2 + 6x > -5
Next, move all terms to one side of the inequality to get a quadratic expression:
x^2 + 6x + 5 > 0
To solve this quadratic inequality, we can factor it:
(x + 5)(x + 1) > 0
Now, we need to determine the sign of the expression for different intervals on the x-axis.
a) When x < -5:
If x is less than -5, both (x + 5) and (x + 1) are negative, so their product is positive.
Thus, the inequality is satisfied for x < -5.
b) When -5 < x < -1:
If x is between -5 and -1, (x + 5) is positive, but (x + 1) is negative. The product of a positive and a negative number is negative.
Thus, the inequality is not satisfied for -5 < x < -1.
c) When x > -1:
If x is greater than -1, both (x + 5) and (x + 1) are positive, so their product is positive.
Thus, the inequality is satisfied for x > -1.
Therefore, x -5 or x > -1 is the answer to the inequality f(x) > -5.
In summary:
x < -5 or x > -1.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The value of x in ΔSTU is in the range (2, 32).
Given that ΔSTU is a triangle,
ST = 15,
US = x,
UT = 17.
We need to find the length of x in the triangle STU.
To solve this question, we need to apply the triangle inequality theorem.
According to the theorem, the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Therefore, using this theorem, we get:
ST + US > UT => 15 + x > 17
=> x > 17 - 15
=> x > 2US + UT > ST
=> x + 17 > 15 => x > 15 - 17
=> x > -2UT + ST > US
=> 17 + 15 > x
=> 32 > x
In this case ST = 15, US = x, UT = 17. Let's apply the triangle inequality to the sides of the triangle STU:
ST + US > UT
15 + x > 17
Simplify the inequality:
x > 17 - 15
x > 2
Triangle STU is valid The length of US(x) must be greater than 2 to be a perfect triangle.
However, without further information, we cannot determine the exact value of x.
You can specify any value greater than 2.
Therefore, from the above conditions, we conclude that 2 < x < 32.
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What is the volume of the following triangular prism?
A. 380 m³
B. 398 m³
C. 351 m³
D. 327 m³
Answers
Answer:
C-351
Step-by-step explanation:
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
PLS HELP WILL GIVE BRAINLIEST IF ANSWER IS CORRECT (NO LINKS )
Find the measure of arc GW.
Answers
Answer:c
Step-by-step explanation:
which of the following will form the composite function G(F(x)) shown below G(F(x)) = 4√x
Answers
Pls help I am stuck Tysm
Answers
The perimeter of the figure is 30 cm.
How to find the perimeter of a figure?The perimeter of the figure is the sum of the whole sides of the figure. Therefore, the perimeter of the figure can be found as follows:
perimeter of the figure = sum of the whole sides
Therefore,
perimeter of the figure = 6 cm + 9 cm + 2 cm + 3cm + 2cm + 3cm + 2cm + 3cm
Hence,
perimeter of the figure = 15 cm + 5 cm + 5cm + 5 cm
perimeter of the figure = 30 cm
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Does the mapping diagram represent a function? Why or why not?
-5
8
9
y
-8
A. Yes; each input pairs with only one output.
B. No; the input value x = -5 pairs with two output values.
C. No; each input pairs with only one output.
D. No; each output value pairs with two input values.
Answers
The correct answer is: A. Yes; each input pairs with only one output.
To determine whether the given mapping diagram represents a function, we need to analyze the relationship between the input values (x) and the corresponding output values (y).
Looking at the mapping diagram, we can see that the input value -5 is paired with the output value 8. This implies that when x = -5, the corresponding y value is 8. Similarly, when x = 9, the corresponding y value is -8.
Since each input value has a unique and specific output value, we can conclude that the mapping diagram represents a function. In other words, for every input value, there is only one output value associated with it.
This is consistent with the definition of a function, where each input has a single and distinct output. Therefore, the mapping diagram satisfies the criteria for a function, and the correct answer is:
A. Yes; each input pairs with only one output.
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The mapping diagram does not represent a function that reflects this is: No; each output value pairs with two input values. D.
To determine whether the mapping diagram represents a function, we need to assess whether each input value pairs with only one output value.
Looking at the given mapping diagram:
-5 -> 8
9 -> y
-8 -> y
We can see that the input value -5 maps to the output value 8.
There are two different input values, 9 and -8, that map to the same output value, y.
In a function, each input should correspond to exactly one output, but in this case, the output value y is associated with two different input values.
In this case, y, the output value, pairs with both 9 and -8, indicating that the diagram does not meet the criteria for a function.
We must examine if each input value couples with only one output value in order to evaluate whether the mapping diagram reflects a function.
Observing the provided mapping diagram:
-5 -> 8 9 -> y -8 -> y
As can be seen, the input value of -5 corresponds to the output value of 8.
The identical output value, y, is mapped to two distinct input values, 9 and -8.
A function should have only one output for each input, however in this situation, the output value y is connected to two separate input values.
This figure does not fit the definition of a function because the output value, y, couples with both 9 and -8.
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NO LINKS!! URGENT HELP PLEASE!!
Use the parallelogram ABCD to find the following.
8. part 2
b. AE=
d. m<DCB=
f. m<ADC=
Answers
Answer:
b. 7
d. 120°
f. 60°
Step-by-step explanation:
The properties of a parallelogram are:
Opposite sides are parallel and congruent.Opposite angles are equal.Adjacent angles are supplementary.The diagonals bisect each other.The sum of the interior angles is 360 degrees.For Question:
b.
AE=CE=7 since diagonals of parallelogram bisect each other
d.
m ∡ DCB= m ∡DAB=120° Opposite angle in a parallelogram is congruent or equal.
f.
m ∡ ADC=?
Here
m ∡ADC+ m ∡DAB=180° being co interior angle
m ∡ADC+120°=180°
m ∡ADC=180°-120°=60°
m ∡ADC=60°
Answer:
b) AE = 7
d) m∠DCB = 120°
f) m∠ADC = 60°
Step-by-step explanation:
Part bThe diagonals of a parallelogram always bisect each other.
Therefore, point E (the point of intersection of the two diagonals) is the midpoint of diagonal AC. So AE = EC.
As EC = 7, then AE = 7.
[tex]\hrulefill[/tex]
Part dAs the measure of the opposite angles of a parallelogram are equal, then m∠DCB is equal to m∠DAB. From inspection of the given parallelogram, we can see that m∠DAB = 120°. Therefore:
m∠DCB = 120°
[tex]\hrulefill[/tex]
Part fAdjacent angles of a parallelogram are supplementary (sum to 180°).
Angle DAB and angle ADC are adjacent angles, so their sum is 180°.
Therefore:
⇒ m∠ADC + m∠DAB = 180°
⇒ m∠ADC + 120° = 180°
⇒ m∠ADC + 120° - 120° = 180° - 120°
⇒ m∠ADC = 60°
HELP ME PLS I'LL MARK BRAINLIEST AND GIVE U 13 POINTS
Answers
Answer:
The answer is number 3
Y =-3/7X + 3
Step-by-step explanation:
Substitue with the value of the two points in all answers
The value of the left side must equal the value or the right side
For instance,
The two points are (0,3) & (7,0)
Substitue in the first answer with the point (0,3)
3 = - 3 (rejected)
Second answer
3 = 3 works for the point (0,3) then also Substitue with the other point (7,0)
0 = 6 (rejected)
The third answersub. With point (0,3).
3 = 3 it worksSub. With point (7,0)
0= - 3+3 0=0 it worksThen that's the right one
Jenny is watching her favorite soccer team playing a match. The odds against her favorite team winning are 7/10. What is the probability of her favorite team winning?
Answers
Answer:
70%
Step-by-step explanation:
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.
En la tabla se muestra la cantidad de zapatos vendidos en 1 almacén durante una semana, calcula las medidas de tendencia central y realiza el análisis correspondiente
Answers
Based on the information, we can infer that the mean is 14.28, the median is 15, and there is no unique mode (several repeated values).
How to calculate measures of central tendency?To calculate the measures of central tendency, we will use the data provided in the table. The pairs of shoes sold on each day are as follows: 10, 14, 15, 12, 16, 18, 16.
Mean:
The mean is calculated by adding all the values and dividing by the total number of items.
Mean = (10 + 14 + 15 + 12 + 16 + 18 + 16) / 7 = 101 / 7 = 14.28
Median:
The median is the value in the middle of an ordered data set. To calculate it, we first order the values from smallest to largest.
10, 12, 14, 15, 16, 16, 18
Since there are an odd number of values, the median is the value in the middle position, which in this case is 15. Therefore, the median is 15.
Mode:
The mode is the value that occurs most frequently in a data set. In this case, there is no value that is repeated more times than the others. The values 16 and 12 are repeated twice each, but there is no single mode. Therefore, there is no single mode in this data set.
Note: Here is the question in English:
The table shows the number of shoes sold in 1 store during a week, calculates the measures of central tendency, and perform the corresponding analysis.
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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
NO LINKS!! URGENT HELP PLEASE!!
Please help with 23a and 24a
Answers
Answer:
perimeter = 75 cm , area ≈ 28.3 in²
Step-by-step explanation:
23 (a)
since the figure is being enlarged by a scale factor of 5
then the perimeter is increased by a factor of 5.
perimeter of larger shape = 5 × 15 = 75 cm
24
the area (A) of the sector is calculated as
A = area of circle × fraction of circle
= πr² × [tex]\frac{90}{360}[/tex]
= π × 6² × [tex]\frac{1}{4}[/tex]
= 36π × [tex]\frac{1}{4}[/tex]
= 9π
≈ 28.3 in² ( to 1 decimal place )
(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
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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Find the local and absolute maximum and minimum points in (x, y) format for the
function f(x) = 3/5x^5 - 9x^3 + 2 on the closed interval [-4,5]. Answer the following
questions.
a) Find all critical numbers (x- coordinates only)
b) Find the intervals on which the graph is increasing Mark critical numbers
Answers
f'(x) = 15/5x^4 - 27x^2 = 3x^4 - 27x^2
a) To find the critical numbers (x-coordinates), we need to solve the equation 3x^4 - 27x^2 = 0 for x:
3x^2(x^2 - 9) = 0
This equation factors as 3x^2(x + 3)(x - 3) = 0. Setting each factor to zero gives us three critical numbers: x = 0, x = -3, and x = 3.
b) To find the intervals on which the graph is increasing or decreasing, we can use the critical numbers and test points within each interval. However, since the interval is already specified as [-4, 5], we can determine the intervals based on the critical numbers and endpoints.
The critical numbers divide the interval [-4, 5] into four smaller intervals: [-4, -3], [-3, 0], [0, 3], and [3, 5].
We can determine if the function is increasing or decreasing within each interval by evaluating the derivative (f'(x)) at a test point in each interval:
For the interval [-4, -3], let's evaluate f'(-4) = 3(-4)^4 - 27(-4)^2 = 768, which is positive. Therefore, the function is increasing in this interval.
For the interval [-3, 0], let's evaluate f'(-3) = 3(-3)^4 - 27(-3)^2 = 0, which is neither positive nor negative. We need to test another point in this interval, such as f'(-2) = 3(-2)^4 - 27(-2)^2 = -96, which is negative. Therefore, the function is decreasing in this interval.
For the interval [0, 3], let's evaluate f'(0) = 3(0)^4 - 27(0)^2 = 0, which is neither positive nor negative. We need to test another point in this interval, such as f'(1) = 3(1)^4 - 27(1)^2 = -24, which is negative. Therefore, the function is decreasing in this interval.
For the interval [3, 5], let's evaluate f'(3) = 3(3)^4 - 27(3)^2 = 0, which is neither positive nor negative. We need to test another point in this interval, such as f'(4) = 3(4)^4 - 27(4)^2 = 768, which is positive. Therefore, the function is increasing in this interval.
Based on these calculations, the intervals on which the graph of the function f(x) = (3/5)x^5 - 9x^3 + 2 is increasing are [-4, -3] and [3, 5]. The intervals on which the graph is decreasing are [-3, 0] and [0, 3].
Please note that this analysis gives us information about the increasing and decreasing behavior of the function, but it doesn't provide specific local or absolute maximum and minimum points.
6. For each final matrix, state the solution.
Please answer this picture
Answers
The solutions associated with the final matrices representing a system of linear equations are listed below:
First case: x = 3, y = 1, z = 8
Second case: No solution
Third case: No solution
What are the solutions contained in each final matrix?
In this problem we find three of final matrices, each of them representing a system of linear equations. There are two rules to be considered:
A system has no solution if there is a row with only zeroes in the dependent coefficients matrix.A system has a solution if there is a singular matrix, there is, the dependent coefficients matrix has only ones in the main diagonal and the rest of elements are zeroes.Now we proceed to determine the solution associated with each matrix:
First matrix:
x = 3, y = 1, z = 8
Second matrix:
No solution
Third matrix:
No solution
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Step-by-step explanation:
For the left matrix, since the matrix is already in reduced row form,
The solutions to the matrix is (3,-1,8)
For the middle matrix, we need to convert the -6 to a zero,
notice how in the third row, every entry except the last one is 0, this implies that
0=-2, which is not the case thus the middle matrix has no solution.
For the last one, notice that we have 3 colums but only two non zero rows, this means that this matrix has infinite solutions.
Show 2x -6 in a line graph
Answers
The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.
To plot the line graph of the equation 2x - 6, we need to assign values to the variable x and calculate the corresponding values of y.
Let's choose a range of x-values and calculate the corresponding y-values:
For example, let's choose x = -3, -2, -1, 0, 1, 2, and 3.
Substituting these values into the equation 2x - 6, we get:
For x = -3: y = 2(-3) - 6 = -12
For x = -2: y = 2(-2) - 6 = -10
For x = -1: y = 2(-1) - 6 = -8
For x = 0: y = 2(0) - 6 = -6
For x = 1: y = 2(1) - 6 = -4
For x = 2: y = 2(2) - 6 = -2
For x = 3: y = 2(3) - 6 = 0
Now, we can plot these points on a graph with x as the horizontal axis and y as the vertical axis:
(-3, -12), (-2, -10), (-1, -8), (0, -6), (1, -4), (2, -2), (3, 0)
We can then connect these points with a straight line. Since the equation is in the form y = 2x - 6, the line will have a slope of 2 and a y-intercept of -6. The line will have a positive slope, meaning it will slant upwards from left to right.
The resulting line graph will be a straight line that starts below the y-axis, crosses it at the point (0, -6), and continues upwards as the x-values increase.
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NO LINKS!! URGENT HELP PLEASE!!
Please help me with #11. I plotted the points, the rest of the questions I need help with
Answers
Answer:
Not parallelogram
Step-by-step explanation:
points A(-4, 1), B(1,3), C(8, -1) and D(4, -3).
The slope of a line can be found using the following formula:
Slope [tex]m= = \frac{(y_2 - y_1) }{(x_2 - x_1)}[/tex]
where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the formula above,
Side AB: Slope =[tex]\frac{3-1}{1-(-4)}=\frac{2}{5}[/tex]
Side BC: Slope =[tex]\frac{-1-3}{8-1}=\frac{-4}{7}[/tex]
Side CD: Slope =[tex]\frac{-3 - (-1)}{4 - 8}= \frac{1}{2}[/tex]
Side DA: Slope =[tex]\frac{-3 - 1}{4 - (-4)}= \frac{-1}{4}[/tex]
Since The slopes of opposite sides are equal,
Therefore ABCD is not Parallelogram:
B
E
7
4
3
1
-2 -1 0
D
Determine the line of reflection.
O Reflection across x = 4
Reflection across y = 4
Reflection across the x-axis
Reflection across the y-axis
3
4
C
D'
8
E'
9
10
B'
A'
11
Answers
Answer: 10
Step-by-step explanation: it is a 5+ 5 =
There are 29 students in a homeroom. How many different ways can they be chosen to be elected President, Vice President, and Treasurer?
Answers
Since the positions of President, Vice President, and Treasurer are distinct, we can consider them as three separate positions to be filled.
The number of ways to choose a President from 29 students is 29.
After choosing the President, there are 28 students remaining.
The number of ways to choose a Vice President from the remaining 28 students is 28.
After choosing the Vice President, there are 27 students remaining.
The number of ways to choose a Treasurer from the remaining 27 students is 27.
To find the total number of different ways, we multiply the number of choices for each position:
29 * 28 * 27 = 21,924
Therefore, there are 21,924 different ways to choose the President, Vice President, and Treasurer from a homeroom of 29 students.
Which equation best shows that 45 is a multiple of 15?
Choose 1 answer:
A45-15 = 30
B
45 x 3 = 15
48= 45 +3
45÷3= 15
Answers
The correct Option is D. 45÷3= 15 . The equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
A multiple is a product that results from multiplying two or more numbers.
A common multiple is a multiple that is common to two or more numbers.
A multiple of a number can be expressed as an integer multiple of the number.
If the result is a whole number, the first number is a multiple of the second.
An equation that shows 45 is a multiple of 15 is as follows: 45 ÷ 3 = 15.
A multiple is a number that can be divided by another number without leaving a remainder.
As a result, we divide 45 by 3 to find out whether 45 is a multiple of 15.
If the result is a whole number, 45 is a multiple of 15.
Here is the equation that shows this: 45 ÷ 3 = 15
Thus, we can conclude that the equation that best shows that 45 is a multiple of 15 is 45 ÷ 3 = 15.
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What is the sum of the series?
∑k=36(−2k+5)
Enter your answer in the box.
Answers
Hello !
Answer:
[tex]\large \boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]
Step-by-step explanation:
We want to calculate the following sum :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)[/tex]
Let's remember the following property :
[tex]\fbox{\begin{tabular}{1\textwidth}\star\ \underline{\sf Linearity:}\\ \sf \sum\limits^n_{k=n_0}(\alpha a_k+\beta b_k)=\alpha\sum\limits^n_{k=n_0} a_k+\beta \sum \limits^n_{k=n_0}b_k\end{tabular}}[/tex]
Now we can apply this property to our formula :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2\sf \sum\limits^6_{k=3}(k)+\sum\limits^6_{k=3}5[/tex]
Now we can calculate :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2(3+4+5+6)+(6-3+1)5\\=-2\times18+4\times 5\\=-36+20\\\boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]
Have a nice day ;)