What is the average rate of change for the following graph over the interval 1 ≤ x ≤ 3?

A. 4

B. -4

C. 3

D. -3

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Explanation:

The ratio QR : RS : ST  is equal to 1 : 4 : 5

This means we have the following three equations

For some positive number x.

Note the ratio QR : RS : ST turns into x : 4x : 5x, which reduces to 1 : 4 : 5 when we divide all three parts by x .

Along with those three equations, we'll also use QT = 40 as well.

Now turn to the segment addition postulate. Plug in the equations mentioned earlier, and solve for x .

QT = QR + RS + ST

40 = x+4x+5x

40 = 10x

10x = 40

x = 40/10

x = 4

So we know that

QR = x = 4

RS = 4x = 4*4 = 16

ST = 5x = 5*4 = 20

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As a check,

QR + RS + ST = 4 + 16 + 20 = 40

which is the same as QT = 40

Therefore, we've confirmed that QR + RS + ST = QT is correct and we've confirmed our answers.

Answer:

109 is 63% of 173.02

Step-by-step explanation:

Let 109 = 63% of x

Thus;

63/100 * x = 109

63x = 10900

x = 10,900/63

x = 173.02

Answer:

1. [tex] x \ge -4 [/tex]

2. [tex] x < -2 [/tex]

Step-by-step explanation:

1. [tex] 10^{2x - 4} \le 1000^x [/tex]

Make both sides of the same base

[tex] 10^{2x - 4} \le (10^3)^x [/tex]

[tex] 10^{2x - 4} \le 10^{3x} [/tex]

Both bases will cancel each other

[tex] 2x - 4 \le 3x [/tex]

Subtract 2x from each side

[tex] - 4 \le 3x - 2x [/tex]

[tex] -4 \le x [/tex]

Rewrite

[tex] x \ge -4 [/tex]

2. [tex] (\frac{1}{5})^{3x + 10} > (\frac{1}{25}^{x + 4} [/tex]

Apply the inverse law of exponents

[tex] (5^{-1})^{3x + 10} > (25^{-1})^{x + 4} [/tex]

[tex] (5^{-1})^{3x + 10} > (5^{-2})^{x + 4} [/tex]

[tex] 5^{-3x - 10} > 5^{-2x - 8} [/tex]

Both bases will cancel each other

[tex] -3x - 10 > -2x - 8 [/tex]

Collect like terms

[tex] -3x + 2x > 10 - 8 [/tex]

[tex] -x > 2 [/tex]

Divide both sides by -1.

(Note: since we are dividing by a negative number, the inequality sign would change)

[tex] x < -2 [/tex]

Answer:

32 pounds of almonds

Step-by-step explanation:

Monique sells nut mixes . She uses * 1/4 of her supply of almonds to make a nut mix and of her 5/8 supply to make a fruit and nut mix.

The total fraction of almonds that Monique used both for her but mix and fruit and nut mix =

1/4 + 5/8

Lowest common denominator is 8

1 × 2 + 5 × 1/8

2 + 5/8

= 7/8

If Monique uses 28 pounds of almonds

Let the total number of almonds = x

7/8 × x = 28

7x /8 = 28

Cross Multiply

7x = 8 × 28

x = 8 × 28/7

x = 32 pounds

Therefore, Monique initially had 32 pounds of almonds in her supply.

I hope help for you ......

Answer:

x=

[tex] - \frac{1}{3} [/tex]

Step-by-step explanation:

y=-4x+2

-1 -4*-1= 4 y=4

0 -4*0=y y=0

1 -4*1=y y=-4

2 -4*2=y y=-8

Answer:

AE = 26 units

Step-by-step explanation:

Given that ABC is congruent to EDC, therefore, the corresponding angles and corresponding lengths of ∆ABC and ∆EDC are equal to each other in measure.

AE = 2(AC) = 2(CE) or

AE = AC + CE

Let's find the AC using Pythagorean Theorem, since the ∆s are both right triangles.

BA is congruent to DE.

Since DE = 12 units, therefore, BA = 12 units.

BC = 5 units (given)

Using Pythagorean Theorem:

AC² = BA² + BC²

AC² = 12² + 5² (substitution)

AC² = 144 + 25 = 169

AC = √169

AC = 13 units

Since ∆ABC = ∆EDC, therefore:

AE = 2(AC)

AE = 2(13)

AE = 26 units

Answer:

99.25

Step-by-step explanation:

3 times 25.50 = 76.5

2 times 4.75 =

3 times 2.25 = 6.75

3.5 + 3 + 76.5 + 9.5 + 6.75 = 99.25

In total, they spent $99.25 at the football game.

Answer:

Answer: x=2 (third option)

Step-by-step explanation:

Equation of a line

Being m is the slope and (h,k) is a point through which the line passes, the point-slope form of the equation of a line is:

y - k = m ( x - h )

We have the function f passes through the point (-1,9) and has a slope of m=-3. The point-slope equation of the line is:

y - 9 = -3 ( x - (-1) )

Operating:

y - 9 = -3 ( x + 1 )

y - 9 = -3x - 3

Adding 9:

y = -3x + 6

To calculate the zero of the function we set y=0 and solve for x:

-3x + 6 = 0

Subtracting 6:

-3x = - 6

Dividing by -3

x = - 6 / ( - 3 )

x = 2

Answer: x=2 (third option)

Answer:

-22

Step-by-step explanation:

(Is that Aleks?)

Plug it in.

(-2)^2 + 9(-2) - 8

= 4 + (-18) - 8

= -14 - 8

= -22

Given:

The sum of three numbers is 12 .

The sum of twice the first​ number, 3 times the second​ number, and 4 times the third number is 37 .

The difference between 7 times the first number and the second number is 25.

To find:

The three number.

Solution:

Let the three numbers are x, y and z respectively.

According to the question,

[tex]x+y+z=12[/tex]           ...(i)

[tex]2x+3y+4z=37[/tex]         ...(ii)

[tex]7x-y=25[/tex]           ...(iii)

From (iii), we get

[tex]-y=25-7x[/tex]

[tex]y=-25+7x[/tex]

Put [tex]y=-25+7x[/tex] value in (i).

[tex]x+(-25+7x)+z=12[/tex]

[tex]8x-25+z=12[/tex]

[tex]8x+z=12+25[/tex]

[tex]8x+z=37[/tex]        ...(iv)

Put [tex]y=-25+7x[/tex] value in (ii).

[tex]2x+3(-25+7x)+4z=37[/tex]

[tex]2x-75+21x+4z=37[/tex]

[tex]23x+4z=37+75[/tex]

[tex]23x+4z=112[/tex]          ...(v)

Now, Multiply equation (iv) by 4 and subtract the result from (v).

[tex]23x+4z-4(8x+z)=112-4(37)[/tex]

[tex]23x+4z-32x-4z=112-148[/tex]

[tex]-9x=-36[/tex]

[tex]x=4[/tex]

Put x=4 in (iv).

[tex]8(4)+z=37[/tex]

[tex]32+z=37[/tex]

[tex]z=37-32[/tex]

[tex]z=5[/tex]

Put x=4 in [tex]y=-25+7x[/tex].

[tex]y=-25+7(4)[/tex]

[tex]y=-25+28[/tex]

[tex]y=3[/tex]

Therefore, the three numbers are 4, 3 and 5 respectively.

Answer:

x^2+5x-14

Step-by-step explanation:

you multiply both equations so that you get:

x^2-2x+7x-14

and then you simplify it to:

x^2+5x-14

If you found this helpful please give it a thanks

I would also appreciate it if you give me a brainliest

Answer:

commutative property

Step-by-step explanation:

it is

Answer:

34

Step-by-step explanation:

Ohio had 20

14 votes less than Texas (20 + 14)

34 electoral votes Texas had in 2004.

~~~Hope this helps~~~

Answer:

No

Why he is not correct is because the y-intercept is the coordinate of the point where the graph meets or crosses the y-axis, which is equivalent to a point on the graph where the x-coordinate value reduces to zero, or to put it in a mathematical form x = 0

Step-by-step explanation:

From the given data, we have;

x     [tex]{}[/tex]       y

2     [tex]{}[/tex]      -2

4     [tex]{}[/tex]       0

6      [tex]{}[/tex]      2

8      [tex]{}[/tex]      6

The given data is linear because it has a constant first (common) difference of 2

The general form of the straight line equation is y = m·x + c

Where;

m = The slope

c = The y-intercept

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

The slope of the graph of the data from any two points, (x₁, y₁) = (4, 0) and (x₂, y₂) = (4, 0)) is m = (2 - 0)/(6 - 4) = 1

The equation representing the data in point and slope form is therefore;

y - 4 = 1 × (x - 0)

Which gives;

y = x + 4

Therefore, the y-intercept = 4.

Answer:

x = 110° ; y = 49°

Step-by-step explanation:

m∠ABD = m∠ADB = 35° ⇒ x = 180° - 2 × 35° = 110°  

m∠CDB = m∠CBD = 2y ⇒ y = (180° - 82°) ÷ 2 = 49°

Answer:

B and C

Step-by-step explanation:

Option B and Option C

Expand it and you'll get 12 + 12 * 0.25 and the question says she ran 0.25 of the distance she ran before.

Hence, Option B and Option C would be correct

Answer: i got 394

Step-by-step explanation:

9514 1404 393

Answer:

  0.579

Step-by-step explanation:

You can consider what the offered numbers are when they are rounded to hundredths:

  0.574 ⇒ 0.57

  0.579 ⇒ 0.58 . . . matches your requirement

  0.585 ⇒ 0.59

  0.681 ⇒ 0.68

The only number on the list that matches your rounding requirement is 0.579.

Answer:

Use the algorithm method.

 9 6 0

2 1 | 2 0 1 6 8

1 8 9  

1 2 6

1 2 6

8

960

Step-by-step explanation:

May I have brainliest plz

Answer:

P(A)=0.75

Step-by-step explanation:

I think you already have your answer. If this is all the information given in the problem, there is nothing more to do.

Answer: XD You have Among Us

Step-by-step explanation:

$1972.00 is what I got

Mark me as brainliest, Among Us User

Answer:

Step-by-step explanation:

Their is no answer sorry

Answer:

[tex]0W = 32yd[/tex]

Step-by-step explanation:

See attachment for complete question.

From the attachment, we have:

[tex]0N = 30yd[/tex]

[tex]NW = 12yd[/tex]

Required

Determine 0W

To solve this , we apply Pythagoras theorem as follows:

[tex]0W^2 = 0N^2 + NW^2[/tex]

[tex]0W^2 = 30^2 + 12^2[/tex]

[tex]0W^2 = 900 + 144[/tex]

[tex]0W^2 = 1044[/tex]

Take square roots

[tex]0W = \sqrt{1044}[/tex]

[tex]0W = 32.31[/tex]

[tex]0W = 32yd[/tex] (approximated)

Hence, she walked 32 yards

Answer:

3,564

Step-by-step explanation:

324

11

×___. if you multiply this way it might help

Answer:

54

Step-by-step explanation: