Answer:
Average rate of change: [tex]-3[/tex]
Step-by-step explanation:
We are asked to find average rate of change for our given function [tex]f(x)=-3x+2[/tex].
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{Average rate of change}=\frac{f(2)-f(-1)}{2-(-1)}[/tex]
[tex]\text{Average rate of change}=\frac{(-3(2)+2)-(-3(-1)+2)}{2-(-1)}[/tex]
[tex]\text{Average rate of change}=\frac{(-6+2)-(3+2)}{2+1}[/tex]
[tex]\text{Average rate of change}=\frac{(-4)-(5)}{3}[/tex]
[tex]\text{Average rate of change}=\frac{-4-5}{3}[/tex]
[tex]\text{Average rate of change}=\frac{-9}{3}[/tex]
[tex]\text{Average rate of change}=-3[/tex]
Therefore, the average rate of change for our given function from [tex]x=-1[/tex] to [tex]x=2[/tex] is [tex]-3[/tex].
Alison wants to construct the perpendicular bisector of MN¯¯¯¯¯¯¯. What should Alison do for her first step? A.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is equal to 1/2MN . B.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN. C.) Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is less than 1/2MN. D.) Use the straightedge to draw a line that intersects MN¯¯¯¯¯¯¯ at a point between M and N.
Answer:
Place the point of the compass on point M and draw an arc, using a width for the opening of the compass that is greater than 1/2MN.
Step-by-step explanation:
The site told me that correct answer was B., so it was greater than.
The equation of line m is 4x+5y=−2. What is the slope of a line that is perpendicular to line m?
The required slope of a line will be 5/4 which is perpendicular to line m.
What are the perpendicular lines?Perpendicular lines are two lines that cross one other and create a 90-degree angle. Two lines are perpendicular if the product of their slopes is -1.
The equation of line m is given in the question below as:
⇒ 4x + 5y = −2
We have to determine the slope of a line that is perpendicular to line m
First, we need to find the slope of line m
To convert to slope-intercept form
⇒ 4x + 5y = -2
⇒ 5y = - 4x - 2
⇒ y = -4/5 x - 2/5
So the slope of this line is -4/5 and the slope of a line perpendicular to it is
⇒ - 1 / (-4/5)
Reciprocal the terms in the numerator,
⇒ 5/4
Therefore, the required slope of a line will be 5/4 which is perpendicular to line m.
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is 2x-5y=10 a function ------is it linear or nonlinear?
It is linear when 2x- 5y = 10. A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 Or 1.
How can we tell whether a function is linear or not?Looking at a function’s graph will reveal if it is linear or not with the greatest ease. When a linear function is plotted on a graph, a straight line is formed.
A nonlinear function Is curved in some way; it does not form a straight line.
How is a function defined as linear?The graph of a linear function is a straight line. One independent variable and one dependent variable make up a linear function.
X and Y are the independent and dependent variables, respectively. The constant term, or a, is the y-intercept.
Is a function 2x-5y=10 real? Is it nonlinear or linear?Given that a linear equation is an equation of a straight line, its degree must be either 0 or 1.
For every one of its elements. In this instance, both the degree of the variables Y and X is 1.
Resolve the Y equation.
2x-5y=10
Y=-2+2x/5
Hence Given that a linear equation is an equation of a straight line, its degree must be either 0 or 1. For every one of its elements. The degree of the variable Y in this instance is 1, while the degree of the variable X is linear at 1.
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What is solution to the system of equations? Y=5×+2 3×=-y+10
Chloe draws three parallelograms. In each figure, she measures a pair of angles, as shown.
What is a reasonable conjecture for Chloe to make by recognizing a pattern and using inductive reasoning?
In a parallelogram, all angles are congruent
In a parallelogram, consecutive angles are congruent.
In a parallelogram, consecutive angles are supplementary.
In a parallelogram, all angles are supplementary.
Solution-
1st statement- In a parallelogram, all angles are congruent.
If all the angels are congruent then all angles will be 90° (as summation of all the angles are 360° and 360/4= 90°), then it will be either a rectangle or a square, not a parallelogram.
2nd statement- In a parallelogram, consecutive angles are congruent.
If consecutive angles are congruent, then it will be rectangle or a square, not a parallelogram. In a parallelogram, opposite angles are congruent not consecutive angles.
4th statement- In a parallelogram, all angles are supplementary.
In a parallelogram, all the consecutive angles are supplementary or summation of measurements consecutive angles is 180°, not all the angels are supplementary, because opposite angles can't be supplementary.
3rd statement- In a parallelogram, consecutive angles are supplementary.
This is the reasonable conjecture for a parallelogram, because always the summation of measurement of consecutive angles are 180°.
A plumber charges $70 per hour plus $40 dollars for the call. What does he charge for 4 hours of work
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15
we have
[tex]x<9[/tex] ------> inequality A
The solution of the inequality A is the interval--------> (-∞,9)
All real numbers less than [tex]9[/tex]
[tex]x\geq14[/tex] -----> inequality B
The solution of the inequality B is the interval--------> [14,∞)
All real numbers greater than or equal to [tex]14[/tex]
The solution Inequality A or Inequality B is equal to
Solution A+Solution B
(-∞,9)U[14,∞)
The solution of the compound system of inequalities must satisfy inequality A or inequality B
we're going to verify every case
case A) [tex]\$8[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]8<9[/tex] -------> is true
Therefore
[tex]\$8[/tex] is a possible value for x
You don't need to check for inequality B
case B) [tex]\$9[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]9<9[/tex] -------> is not true
Verify inequality B
[tex]9\geq14[/tex] ------> is not true
Therefore
[tex]\$9[/tex] is not a possible value for x
case C) [tex]\$11[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]11<9[/tex] -------> is not true
Verify inequality B
[tex]11\geq14[/tex] ------> is not true
Therefore
[tex]\$11[/tex] is not a possible value for x
case D) [tex]\$13[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]13<9[/tex] -------> is not true
Verify inequality B
[tex]13\geq14[/tex] ------> is not true
Therefore
[tex]\$13[/tex] is not a possible value for x
case E) [tex]\$14[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]14<9[/tex] -------> is not true
Verify inequality B
[tex]14\geq14[/tex] ------> is true
Therefore
[tex]\$14[/tex] is a possible value for x
case F) [tex]\$15[/tex]
Substitute the value of x in the inequality A and in the inequality B to verify
Verify inequality A
[tex]15<9[/tex] -------> is not true
Verify inequality B
[tex]15\geq14[/tex] ------> is true
Therefore
[tex]\$15[/tex] is a possible value for x
therefore
the answer is
[tex]\$8[/tex]
[tex]\$14[/tex]
[tex]\$15[/tex]
In how many games did the team score at least 70 points?
Answer: the answer is 5
Step-by-step explanation:
b
50 POINTS!! + BRAINLIEST
Find the measure of ∠AED
What does .9999 rounded to the thousandths?
Write each mixed number as an improper fraction. 1 7/8 1 7/12 2 1/2 NEED BRAINLIEST!!!
How many 1-cm squares would it take to construct a square that is 3 m on each side?
Which equation can be used to find the answer? sharifa spends $51 on the first day of her vacation. this leaves her with $127 to spend during the rest of her vacation. how much money did sharifa bring to spend during her vacation?
a. t = 127 · 2 t = 254 $254
b. t – 51 = 127 t = 178 $178
c. t + 51 = 127 t = 76 $76
d. t = 127 ÷ 2 t = 63.5 $63.5?
How many ways can i distribute 3 slices of pizza to 3 people of fairness doesn't matter?
Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates to a rectangle as shown. Then she uses the coordinates to write and simplify expressions for the lengths of the diagonals.
What is the length of one of the diagonals of the rectangle?
Enter an expression in the box for the length of the diagonal.
The length of a line with known end point coordinates is given by Pythagoras's theorem
The expression for the length of the diagonal [tex]\overline{PR}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]
The expression for the length of the diagonal [tex]\overline{QS}[/tex], is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]
Reason:
The given coordinates of the vertices are; P(0, b), Q(a, b), R(a, 0), and S(0, 0)
Diagonals of the rectangle are segments; [tex]\overline{PR}[/tex], and [tex]\overline{QS}[/tex]The lengths of the diagonals are given by the equation for finding the length, l, of a line given the coordinates which is [tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Where:
(x₁, y₁) = P(0, b), and (x₂, y₂) = R(a, 0), we get;
[tex]Length \ of \ diagonal \ segment \ \overline{PR} = \sqrt{\left (0-b \right )^{2}+\left (a-0 \right )^{2}} = \sqrt{b^2 + a^2}[/tex]Where:
(x₁, y₁) = Q(a, b), and (x₂, y₂) = S(0, 0), we get;
[tex]Length \ of \ diagonal \ segment \ \overline{QS} = \sqrt{\left (0-b \right )^{2}+\left (0-a \right )^{2}} = \sqrt{b^2 + a^2}[/tex]Therefore,
The expression for the length of the diagonal is [tex]\underline{\sqrt{b^2 + a^2}}[/tex]Learn more here:
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what is the advantage of multiplying both sides of the equation by the least common multiple of the denominators in the first step?
Raise to the power:
(–0.2xy)4
Does the graph represent the function?
for a different pizza dough recipe, the equation f=2.5w represents the number of cups of flour, f, that you need for w cups of water. what is the constant of proportionality? explain what it means in this context.
For any direct variation, the equation is of the form y = kx, where k is the constant of proportionality.
Given the equation: f = 2.5wThe constant of proportionality is 2.5.
This means that the ration of the cups of flour to the cups of water used in the recipe is 2.5
Final answer:
The constant of proportionality in the equation f=2.5w is 2.5, representing the ratio of cups of flour to cups of water for the recipe.
Explanation:
Proportionality Constant:
The constant of proportionality in the equation f=2.5w is 2.5. In this context, the constant of proportionality represents the ratio of cups of flour to cups of water needed for the pizza dough recipe.
Explanation:
The constant 2.5 indicates that for every cup of water (w), you will need 2.5 cups of flour (f) in the pizza dough recipe.
What are the x and y-intercepts of the line described by the equation?
3x−9y=10.8
Enter your answers, in decimal form, in the boxes.
x-intercept =
y-intercept =
The x-intercept and the y-intercept of the line described by the equation 3x - 9y = 10.8 are 3.6 and -1.2
The x-intercept of a line is the point where y-coordinate is zero while the y-intercept of the line is the point where the x-coordinate is zero
Given the expression 3x - 9y = 10.8
Get the x-intercept. If y = 0
3x - 9(0) = 10.8
3x = 10.8
x = 10.8/3
x = 3.6
Get the y-intercept. If x = 0
3(0) - 9y = 10.8
-9y = 10.8
y = -10.8/9
y = -1.2
Hence the x-intercept and the y-intercept of the line described by the equation 3x - 9y = 10.8 are 3.6 and -1.2
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A car is traveling at a rate of 50 miles per hour. what is the car's rate in kilometers per hour? how many kilometers will the car travel in 3 hours? in your computations, assume that 1 mile is equal to 1.6 kilometers.
Final answer:
To convert 50 miles per hour to kilometers per hour, multiply by 1.6 to get 80 km/h. In 3 hours, the car will travel 240 kilometers.
Explanation:
The student is asking how to convert a car's speed from miles per hour (mi/h) to kilometers per hour (km/h), and then calculate the distance traveled in kilometers over a period of 3 hours.
Conversion from mi/h to km/h
To convert the car's speed from miles per hour to kilometers per hour, you can use the conversion factor that 1 mile is equal to 1.6 kilometers. Given the car's speed of 50 miles per hour, the calculation would be:
Speed in km/h = Speed in mi/h imes Conversion factor = 50 mi/h imes 1.6 km/mi = 80 km/h.
Distance Traveled in 3 Hours
Now, to compute the distance the car will travel in 3 hours at 80 km/h, use the formula:
Distance = Speed imes Time = 80 km/h imes 3 h = 240 kilometers.
How do i graph y= 2x
Given that the rectangle above has a perimeter of 34 units, find . round the answer to the nearest hundredth.
A cotton candy vendor has 11 cones of blue cotton candy to sell. if the blue cotton candy is 25% of the total number of cones, how many total cotton candy cones does he have
7.9×10^-6 in standard notation.
Which phrase describes an unknown or changeable quantity?
NEED HELP! Thanks!
Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the other train travels at 80 mph.
How much time passes until the trains are 600 mi apart?
Enter your answer in the box.
The length of a rectangular jewelry box is 3 in. more than twice the width. the perimeter is 36 in. find the length and the width.
Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the link to learn key facts about the economics of organic produce and answer a few questions. Which is a reason that organic farming is more expensive than conventional farming? How many years must a farm be run organically before its produce can be labeled as “organic”? Why do most small organic farms pay a higher percentage of their profit for farming equipment than conventional farms?
Answer:
Which is a reason that organic farming is more expensive than conventional farming?
Organic farmers must pay for a costly certification process
How many years must a farm be run organically before its produce can be labeled as “organic”?
3
What is a benefit of crop rotation?
Rotating crops can help build healthy soil.
Step-by-step explanation:
Just took the test!
Answer:
Economists study the way society uses its resources. One important resource studied is agriculture. The recent increase in demand for organic produce has created some interesting economic scenarios for both farmers and consumers. Click the article to learn key facts about the economics of organic produce and answer a few questions.
Which is a reason that organic farming is more expensive than conventional farming?
✔ Organic farmers must pay for a costly certification process.
How many years must a farm be run organically before its produce can be labeled as “organic”?
✔ 3
What is a benefit of crop rotation?
✔ Rotating crops can help build healthy soil.
Step-by-step explanation:
just got it on edge
What is the japanese poetry of a pattern of 5 7-5 syllables?