What is the average rate of change for this quadratic function for the interval from x=-5 to x=-3?

Answer:

B- Mean

Step-by-step explanation:

When the variation is smaller it means that there are no large outliers. When there are large outliers the mean inctease. since you are decreasing the variation the mean would decrease.

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = x² - 2 → (1)

y = - 2x + 1 → (2)

Substitute y = x² - 2 into (2)

x² - 2 = - 2x + 1 ( subtract - 2x + 1 from both sides )

x² + 2x - 3 = 0 ← in standard form

(x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for corresponding values of y

x = - 3 : y = -2(- 3) + 1 = 6 + 1 = 7 ⇒ (- 3, 7 )

x = 1 : y = - 2(1) + 1 = - 2 + 1 = - 1 ⇒ (1, - 1 )

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y=x^2-2&(1)\\y=-2x+1&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\x^2-2=-2x+1\qquad\text{add 2x to both sides}\\x^2+2x-2=1\qquad\text{subtract 1 from both sides}\\x^2+2x-3=0\\x^2+3x-x-3=0\\x(x+3)-1(x+3)=0\\(x+3)(x-1)=0\iff x+3=0\ \vee\ x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1\\\\\text{put the value of x to (1):}\\\\for\ x=-3\\y=(-3)^2-2=9-2=7\\\\for\ x=1\\y=1^2-2=1-2=-1[/tex]

Answer:

f(x)=-3x+4

(can't see some of your choices)

Step-by-step explanation:

We want x to be independent means we want to write it so when we plug in numbers we can just choose what we want to plug in for x but y's value will depend on our choosing of x.

So we need to solve for y.

9x+3y=12

Subtract 9x on both sides

     3y=-9x+12

Divide both sides by 3:

     y=-3x+4

Replace y with f(x).

    f(x)=-3x+4

[tex]\text{Hey there!}[/tex]

[tex]\text{a = m}^2[/tex]

[tex]\text{If m = -3 replace the m-value in the problem with -3}[/tex]

[tex]\text{a = -3}^2[/tex]

[tex]\huge\text{-3}^2\text{ = -3 * 3 = -9}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: a = -9}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6  = 20

The answer is:

It will take 42.35 minutes to weed the garden together.

To solve the problem, we need to use the given information about the rate for both Laura and her husband. We know that she can weed the garden in 1 hour and 20 minutes (80 minutes) and her husband can weed it in 1 hour and 30 minutes (90 minutes), so we need to combine both's work and calculate how much time it will take to weed the garden together.

So, calculating we have:

Laura's rate:

[tex]\frac{1garden}{80minutes}[/tex]

Husband's rate:

[tex]\frac{1garden}{90minutes}[/tex]

Now, writing the equation we have:

[tex]Laura'sRate+Husband'sRate=CombinedRate[/tex]

[tex]\frac{1}{80}+\frac{1}{90}=\frac{1}{time}[/tex]

[tex]\frac{1*90+1*80}{7200}=\frac{1}{time}[/tex]

[tex]\frac{170}{7200}=\frac{1}{time}[/tex]

[tex]\frac{17}{720}=\frac{11}{time}[/tex]

[tex]\frac{17}{720}=\frac{1}{time}[/tex]

[tex]\frac{17}{720}*time=1[/tex]

[tex]time=1*\frac{720}{17}=42.35[/tex]

Hence, we have that it will take 42.35 minutes to weed the garden working together.

Have a nice day!

Answer:

466.27$ APEX

Step-by-step explanation:

Answer:

We have ; p = 2050

r = [tex]12/12/100=0.01[/tex]

n = [tex]3\times12=36[/tex]

But we will take [tex]36-5=31[/tex]

EMI formula is :

[tex]\frac{p\times r\times(1+r)^{n}}{(1+r)^{n}-1}[/tex]

Substituting values in the formula we get;

[tex]\frac{2050\times0.01\times(1+0.01)^{31}}{(1+0.01)^{31}-1}[/tex]

= [tex]\frac{2050\times0.01\times(1.01)^{31}}{(1.01)^{31}-1}[/tex]

= $77.24

Now for further working you can see the sheet attached.

Total interest paid for the loan = $446.76

The logarithm function [tex]\log_ab[/tex], where [tex]a,b>0 \wedge a\not =1[/tex], is increasing for [tex]a\in(1,\infty)[/tex] and decreasing for [tex]a\in(0,1)[/tex]

[tex]\ln x =\log_ex[/tex] and [tex]e\approx 2.7>1[/tex] therefore [tex]\ln x[/tex] is increasing.

Answer:

[tex]\large\boxed{f(x)=5x}[/tex]

Step-by-step explanation:

[tex]\begin{array}{c|c}x&f(x)\\1&5\\2&10\\3&15\end{array}\\\\\\f(1)=5(1)=5\\f(2)=5(2)=10\\f(3)=5(3)=15\\\Downarrow\\f(x)=5x[/tex]

Answer:

C 1 hours 12 minutes

Step-by-step explanation:

We know distance is equal to rate times time

d= r*t

We know the distance is 30 miles and the rate is 25 miles per hour

30 = 25 *t

Divide each side by 25

30/25 = 25t/25

30/25 =t

6/5 =t

1  1/5 =t

Changing 1/5 hour to minutes.   We know there is 60 minutes in 1 hours so 1/5 of an hour is 60*1/5

1/5 *60minutes = 12 minutes

1 hours 12 minutes

Final Answer:

The derived relationship between p and q that is independent of y is: q = 1/2 * p

Explanation:

To find the relation between 'p' and 'q' that is independent of 'y,' we will combine the two given equations and eliminate 'y'.
The equations given are:
1) -2y² - 2y = p
2) -y² + y = q
First, we want to manipulate these equations to isolate similar terms. Notice that the first equation has -2y² and the second has -y². If we multiply every term in the second equation by 2, we will have a coefficient of -2y² in the second equation, which will help us cancel out the y² terms. Let's do that:
2(-y² + y) = 2q
-2y² + 2y = 2q
Now, let's subtract the second equation from the first equation:
(-2y² - 2y) - (-2y² + 2y) = p - 2q
On subtracting, -2y² will cancel out with -2y², and -2y will subtract 2y to give -4y:
-2y² + 2y² - 2y - 2y = p - 2q
0 - 4y = p - 2q
-4y = p - 2q
Since we want a relationship without 'y', we can't do much with this result directly, as it still contains 'y'. But let's look at the equations we've been given once more.
The goal is not to solve for 'y' but to find a relationship between 'p' and 'q'. To accomplish this, let's compare the two original equations and try to eliminate 'y' by dividing them. Divide the first equation by the second equation:
(-2y² - 2y) / (-y² + y) = p / q
Now, factor out -y from both the numerator and the denominator:
- y(2y + 2) / - y(y - 1) = p / q
Simplify the expression by canceling out the -y term:
(2y + 2) / (y - 1) = p / q
At this point, you can see that there is no straightforward way to solve this for a relationship that is completely independent of 'y' because the y's don't cancel out.
One method to proceed, since we must get rid of 'y', is to compare coefficients that correspond to the same powers of 'y' assuming p and q are related through such a power series.
We have from the first equation by rearranging:
y² + y = -p/2
Comparing coefficients to the second equation:
y² = -q
y = q
By matching coefficients for the same powers of y, we deduce:
y (from -y²) = -q (from -y² + y), so q = 1/2 * p
Thus, our derived relationship between p and q that is independent of y is:
q = 1/2 * p
This indicates that q is half of p.

Answer:

D.f(x) = −4x + 105

Step-by-step explanation:

Since the function in linear, we know it has a slope.

We know 2 points

(5,85) and (10,65) are 2 points on the line

m = (y2-y1)/(x2-x1)

   = (65-85)/(10-5)

    =-20/5

    =-4

We know a point and the slope, we can use point slope form to write the equation

y-y1 =m(x-x1)

y-85 = -4(x-5)

Distribute

y-85 = -4x+20

Add 85 to each side

y-85+85 = -4x+20+85

y = -4x+105

Changing this to function form

f(x) =-4x+105

Answer: D or f(x) = -4x + 105

Answer:

3(2x+3)=-3(-30+4)

6x+9=90+12

6x+9=102

6x=93

x=15.5

-please mark as brainliest-

Answer:

11½ = x

Step-by-step explanation:

6x + 9 = 78

- 9 - 9

-------------

6x = 69 [Divide by 6]

x = 11½ [3⁄6 = ½]

I hope this helps you out, and as always, I am joyous to assist anyone at any time.

Answer:

A. 18

Step-by-step explanation:

Median of a trapezoid: Its length equals half the sum of the base lengths.

So the sum of the lengths is 15 + 21 is 36 and half is 18.

18 inches long of a cut will John need to make so that he cuts the tiles along the median.

Given that, the top base of each tile is 15 inches in length and the bottom base is 21 inches.

The median of a trapezoid is the segment that connects the midpoints of the non-parallel sides.

The length of the median is the average of the length of the bases.

Now, add the top base and bottom base,

That is 15+21=36.

Now, divide that by 2

That is, 36/2= 18 inches.

Hence, the answer would be 18 inches.

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Answer:

There are 108900 different committees can be formed

Step-by-step explanation:

* Lets explain the combination

- We can solve this problem using the combination

- Combination is the number of ways in which some objects can be

 chosen from a set of objects

-To calculate combinations, we will use the formula nCr = n!/r! × (n - r)!

 where n represents the total number of items, and r represents the

 number of items being chosen at a time

- The value of n! is n × (n - 1) × (n - 2) × (n - 3) × ............ × 1

* Lets solve the problem

- There are 12 men and 12 women

- We need to form a committee consists of 3 men and 4 women

- Lets find nCr for the men and nCr for the women and multiply the

 both answers

∵ nCr = n!/r! × (n - r)!

∵ There are 12 men we want to chose 3 of them

∴ n = 12 and r = 3

∴ nCr = 12C3

∵ 12C3 = 12!/[3!(12 - 3)!] = 220

* There are 220 ways to chose 3 men from 12

∵ There are 12 women we want to chose 4 of them

∴ n = 12 and r = 4

∴ nCr = 12C4

∵ 12C4 = 12!/[4!(12 - 4)!] = 495

* There are 495 ways to chose 4 women from 12

∴ The number of ways to form different committee of 3 men and 4

   women = 220 × 495 = 108900

* There are 108900 different committees can be formed

Answer:

x=35

Step-by-step explanation:

We have the two angles (6x -82)  and (3x + 23) that are equal. To find 'x' we need to solve the system of equations:

6x -82 = 3x + 23

Solving for 'x':

3x = 105

x = 35

[tex]6x-82=3x+23\\3x=105\\x=35[/tex]

The intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6.

Solving compound inequalities.

A compound inequality is the joining of two or more inequalities together and they are united by the word (and) or (or). In the given compound inequality, we have:

7x ≥ - 56 and 9x < 54.

Solving the compound inequality, we have;
7x ≥ - 56

Divide both sides by 7

[tex]\dfrac{7x}{7} \geq \dfrac{56}{7}[/tex]

x ≥ 8

Also, 9x < 54

Divide both sides by 9.

[tex]\dfrac{9x}{9} < \dfrac{54}{9}[/tex]

x < 6.

Therefore, the intersection of the solution set consists of the elements that are contained in all the intervals. -8 ≤ x < 6

For this case we must resolve the following expression:

[tex]6 + 2 ^ 3 * 3 =[/tex]

For the PEMDAS evaluation rule, the second thing that must be resolved are the exponents, then:

[tex]6 + 8 * 3 =[/tex]

Then the multiplication is solved:

[tex]6 + 24 =[/tex]

Finally the addition and subtraction:

30

Answer:

30

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

To find the slope, all we need is to points on the line.

Judging by that graph, we can see a point at (0,1) and at (5,4).

Simply enter this into the slope formula and you'll have your slope.

[tex]\frac{y2-y1}{x2-x1}[/tex]

Your y1 term is 1, your y2 term is 4.

Your x1 term is 0, your x2 term is 5.

[tex]\frac{4-1}{5-0} \\\\\frac{3}{5}[/tex]

Your slope is [tex]\frac{3}{5}[/tex].

Answer:

[tex]\large\boxed{\dfrac{3}{5}}[/tex]

Step-by-step explanation:

Look at the picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have two points (0, 1) and (-5, -2).

Substitute:

[tex]m=\dfrac{-2-1}{-5-0}=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]

Answer:

(2p - 9)(3p + 5)

Step-by-step explanation:

We have the polynomial: 6p2 – 17p – 45

Rewrite the middle term as a sum of two terms:

6p2 + 27p - 10p - 45

Factor:

3p(2p - 9) + 5(2p - 9)

→ (2p - 9)(3p + 5)

For this case we must factor the following expression:

[tex]6p ^ 2-17p-45[/tex]

We must rewrite the term of the medium as two numbers whose product is [tex]6 * (- 45) = - 270[/tex]

And whose sum is -17

These numbers are: -27 and +10:

[tex]6p ^ 2 + (- 27 + 10) p-45\\6p ^ 2-27p + 10p-45[/tex]

We group:

[tex](6p ^ 2-27p) + 10p-45[/tex]

We factor the maximum common denominator of each group:

[tex]3p (2p-9) +5 (2p-9)[/tex]

We factor[tex](2p-9)[/tex] and finally we have:

[tex](2p-9) (3p + 5)[/tex]

Answer:

[tex](2p-9) (3p + 5)[/tex]

Answer:

[tex]y=2x-48[/tex]

Step-by-step explanation:

Let

y -----> the profit earned by the hot dog stand daily

x ----> the number of hot dogs sold

we know that

The linear equation that represent this problem is equal to

[tex]y=2x-48[/tex]

This is the equation of the line into slope intercept form

where

[tex]m=2\frac{\$}{hot\ dog}[/tex] ----> is the slope

[tex]b=-\$48[/tex] ---> is the y-intercept (cost of the day's supply)

The question relates to the linear function concept. In context of the problem, the profit earned by the hot dog stand is represented by the equation y = 2x - 48, where 'y' is the profit, 'x' is the number of hot dogs sold, '2' is the profit per hot dog, and '48' is the fixed daily cost.

The question relates to the concept of a linear function in Mathematics. In this case, the profit (y) made by the hot dog stand depends on the number of hot dogs sold (x). The stand has a fixed cost of $48 for each day's supply, and then makes a profit of $2 for each hot dog sold.

The linear function can be represented by the equation y = mx + b, where 'm' is the slope of the line (representing the rate of profit per hot dog sold, which is $2), 'x' is the number of hot dogs sold, and 'b' is the y-intercept (representing the fixed costs of the stand, which is -$48).

Therefore, the equation representing the profit of the hot dog stand for x number of hot dogs sold is: y = 2x - 48.

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It's false, trapezoids are not rectangles.

Answer:

2

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. Since midpoints will be involved, use multiples of 2 to name the coordinates for B, C, and D.

Answer:

2

Step-by-step explanation:

Well by definition a Rhombus is an equilateral paralelogram, AB =BC=CD=DA with all congruent sides, and Diagonals with different sizes.

Also a midpoint is the mean of coordinates, like E is the mean coordinate of A,C, and B, D

[tex]\frac{B+D}{2}=E\\  \\ B+D=2E\\ and\\\\  \frac{A+C}{2} =E\\ A+C=2E[/tex]

So the sum of the Coordinates B and D over two returns the midpoint.

And subsequently the sum of the Coordinates B +D equals twice the E coordinates. The same for the sum: A +C

Given to the fact that both halves of those diagonals coincide on E despite those diagonals have different sizes make us conclude, both bisect each other.

Answer:

The rule is y = 4x - 5.

Step-by-step explanation:

Notice that if we start with x = 1 and increase x by 1, we get 2.  Simultaneously, y starts with -1 and becomes 3.  Thus, the slope is m = rise / run = 4/1, or 4.

The rule is y = 4x - 5.

Check:  Suppose we pick input 4 from the table. Does this rule produce output 11?  Is 11 = 4(4) - 5 true?  YES.

Answer:

y = 4x - 5

Step-by-step explanation:

Have you been taught to set up 2 equations and 2 unknowns?

That is actually the only way I could do this.

y = mx + b

x = 2

y = 3

3 = 2m + b

x = 1

y = -1

-1 = m + b        Multiply by 2. That means that the m term will cancel.

================

-2 =2m +2b    

3 = 2m + b        Subtract

-5 = b

==================

3 = 2m + b       Substitute - 5 for b

3 = 2m - 5        Add 5 to both sides.

3+5= 2m-5+5   Combine

8 = 2m               Divide by 2

8/2=2m/2

m = 4

Answer: D = -16

Step-by-step explanation: First you have to isolate the variable by subtracting the coefficient 8D from both equations then subtracting 1 from both equations to isolate 1D.

9d + 1 = 8d - 15

1d + 1 = -15

1d = -16

D = -16

hope this helped

Answer: The Answer To 9d + 1 = 8d -15

Step-by-step explanation:

STEP 1. Combine Like Terms As Well As Changing The Sign(s)

(WHEN YOU CHANGE SIDES YOU CHANGE THE SIGNS!!!)

STEP 2. Switch Signs Or Make It Opposite

d + 1 = - 15

Answer:

-10, -33, -125, -493, -1965

Step-by-step explanation:

a_1 = -10

a_n = 4a_(n - 1) + 7

The first five terms of the sequence are

a_1 =                                             -10

a_2 = 4(-10) + 7     =   -40 + 7 =    -33

a_3 = 4(-33) + 7    =  -132 + 7 =   -125

a_4 = 4(-125) + 7  = -500 + 7 =   -493

a_5 = 4(-473) + 7 = -1972 + 7 = -1965

Answer: B

Step-by-step explanation:

Division of components are consistent  - the same

Answer:

B. -3, 3, -3, 3...

Step-by-step explanation:

There's two types of sequences, arithmetic and geometric.

Arithmetic equations are sequences that increase or decrease by adding or subtracting the previous number.

For example, take a look at the following sequence:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20...

Here, the numbers are increasing by +2. [adding]

So, this the sequence is arithmetic, since its adding.

Geometric sequences are sequences that increase or decrease by multiplying or dividing the previous number.

For example, take a look at the following sequence:

2, 4, 16, 32, 64, 128, 256, 512...

Here, the numbers are icnreasing by x2. [multiplying]

So, the sequence is geometric since its multiplying.

Based on this information, the correct answer is "B. -3, 3, -3, 3..." since its being multiplyed by -1.

Answer:

C (-1,6).

Step-by-step explanation:

This is a horizontal line segment since A and B have the same y-coordinate.  Point P will also have the same y-coordinate since P is suppose to be on line segment AB.

So the only choice that has the y-coordinate as 6 is C. So we already know the answer is C.  There is no way it can be any of the others.  

So we are looking for the x-coordinate of point P using the x-coordinates of A and B.

A is at x=-3

B is at x=0

The length of AB is 0-(-3)=3.

AP+PB=3

AP/PB=2/1

This means AP=2 and PB=1 since 2+1=3 and AP/PB=2/1.

So if we look at A and we know P is 2 units away (after A) then -3+2=-1 is the x-coordinate of P.

OR!

IF we look at B and we know P is 1 unit away (before B), then 0-1=-1 is the x-coordinate of P.

Answer:

The expression used to find of 75 and 60 is 45.

Step-by-step explanation:

To find expression of 75 and 60, multiply decimals from left to right.

0.75*0.60=0.45 =45%

.75*.60=.45=45

45=45

True

45, which is our answer.