Louie drove 50 1/8 miles and used 2.5 gallons
of gas. find the number of miles driven per
gallon of gas.

Based on the given graph, the average rate of change from x=1 to x = 4 is - ²/₃

To find the average rate of change which is the slope, the formula is:

= (Y₂ - Y₁) / (x₂ - x₁)

The coordinates of x = 1 and x = 4 are:

(1, 5) and (4, 3)

Average rate of change is:
= (3 - 5) / (4 - 1)

= -2 / 3

= - ²/₃

In conclusion, the average rate of change is - ²/₃.

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Answer:

6x²+11x

Step-by-step explanation:

1. Group like terms

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

2. Add like terms

[tex]6x^2+3x+8x-10+10[/tex]

3. Add the numbers

[tex]6x^2+11x[/tex]

Answer:

$3.00

Step-by-step explanation:

The values that satisfy the inequality are -3 , 0 , 14 .

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. On the number line, size comparisons between two numbers are typically conducted. Different notations can be used to represent various kinds of inequalities, including:

The symbol a <b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered.

Now the given inequality is of the form  -a < 4

solving we get:

a > - 4

Therefore the number which will satisfy this inequality are:

 -3 , 0 , 14 .

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Answer:

-1

Step-by-step explanation:

2 – (9 ÷ 3)

divide 9 and 3

2 - 3

subtract 2 from 3 and you get

-1

Answer:

-1

Step-by-step explanation:

Its just the answer.

The distance value of the BD, CE, AC is 2 cm, 2 cm, 9cm.

According to the statement

We have to find that the distance between the given points.

So, For this purpose, we know that the

The distance between two points is the length of the path connecting them.

From the given information:

The given values of the points are:

Ab = 5 cm and AD = 7 cm and AE = 11 cm

Then we know that the

BD = AD -AB and

And the BD = CE and AC = AE - CE

Here we have to find the value of the BD, CE, AC .

Then

BD = AD -AB

BD = 7 -5

BD = 2

And

BD = CE

2 = CE

CE =  2cm

And

AC = AE - CE

AC = 11- 2

AC = 9cm.

So, The distance value of the BD, CE, AC is 2 cm, 2 cm, 9cm.

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Using the segment addition postulate, we have that:

5. The graph is given at the end of the answer.

6. The value of x is of x = 9.

7. The length is of PQ = 46.

8. The length is of QR = 46

9. The length is of PR = 92.

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For item 5, the diagram is given at the end of the answer.

For item 6, due to the congruence, Q is the midpoint, that is:

PQ = QR.

Hence:

6x - 8 = 10x - 44

4x = 36

x = 9

For the remaining items, the lengths are given as follows:

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If scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score you would need to be in the top 2% is equal to 88.929.

This type of problem can be referred to as a normal distribution problem.

It can be solved by using the z-score.

Formula;

Z = x - μ / σ

Here,

Z represents the standard score

x represents the observed value

μ represents the mean

σ represents the standard deviation

The z- score can be found by using the p-value on a standard table.

As the minimum score to be in the top 2% is needed to be found, p-value = 0.02

z- score that corresponds to the p-value of 0.02 in the standard table is equal to 2.054

Hence,

2.054 = x - 76.4 / 6.1

2.054(6.1) = x - 76.4

12.529 = x - 76.4

x = 12.529 + 76.4

x = 88.929

Hence the minimum score needed to be in the top 2% is calculated to be 88.929

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Answer:

C. b || c

Step-by-step explanation:

Answer:

c) b // c

Step-by-step explanation:

Two lines are said to be parallel when one of the conditions is true.

1) Corresponding angles are equal.

2) Alternate interior angles are equal.

3) Co interior angles are supplementary.

∠1 =115°   {Vertically opposite angles}

∠1 = ∠2 = 115°

If corresponding angles are equal, then the lines are parallel. So, b // c

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter is 20 unit and area is 21 unit² for vertices of a polygon W(5,−1), X(5, 6), Y(2,−1), Z(2, 6).

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.

All four angles of a rectangle are 90°.

The opposite sides of a rectangle are equal in measure.

The Perimeter of a rectangle = 2(l + w).

given coordinates:

W(5,-1), X(5,6), Y(2,-1), Z(2,6).

Now, considering the coordinates we will find the width and length of rectangle :

Taking points (2,6) and (5,6):

w=5-2=3

Taking  points (5,6) and (5,-1):

l=6-(-1)=7

Now, perimeter of rectangle

= 2x(3+7)

= 20 unit

Hence, area rectangle is : 3x7=21 unit²

Therefore area is 21 unit² and perimeter is 20 units of polygon with the given vertices W(5,−1), X(5, 6), Y(2,−1), Z(2, 6).

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Answer:

3h-6=d

Step-by-step explanation:

h=d/3 +2

take away 2 on both side this gives

h-2=d/3

multiply by 3 on each side which gives

3(h-2) =d

expand the brackets this gives

3h-6=d

so final answer is

3h-6=d

Answer:

The answer is d = 3h - 6........

Answer:

Step-by-step explanation:

Explanation:

I would write the growth function as:

y

=

100

e

k

t

So that at

t

=

0

we get:

y

=

100

e

0.02

⋅

0

=

100

bacteria.

At

t

=

5

hours we will get:

y

=

100

e

5

⋅

0.02

=

110

bacteria.

To double the initial number we need to solve:

200

=

100

e

0.02

t

e

0.02

t

=

2

Apply natural logs to both sides:

ln

(

e

0.02

t

)

=

ln

(

2

)

0.02

t

=

ln

(

2

)

t

=

ln

(

2

)

0.02

=

34.65

≈

34.6

34

hours and 36 minutes approx.

On the outside to the left of the L shape is K, then the synthetic division used to represent the dividend is[tex]2x^{3} +10x^{2} +x+5[/tex].

A more straightforward method of dividing a polynomial using a degree one polynomial equation is known as synthetic division.

a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.

Here,

An L shape is created when a vertical line and a horizontal line are combined.

Within the form, there are two rows of entries.

Entries 2, 10, 1, and 5 are in row 1.

Row 2 has the entries -10, 0 and blank.

On the outside, to the left of the form, is entry number five.

The entry stands for the divisor's zero.

This entry for the variable, let's say x, is [tex]2x^{3} +10x^{2} +x+5[/tex].

Therefore, the Synthetic division of the dividend is [tex]2x^{3} +10x^{2} +x+5[/tex].

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Answer: Step 1: K=2, Step 2: A=1, Step 3: B=2, C=-1, D=-2 LAST QUESTION is A on edge.

Step-by-step explanation:

The function that represents the distance from the fountain is:

Number of minutes  Distance

0                                     50

2                                      60

4                                      70

6                                       60

8                                        50

A circle is a bounded figure which points from its center to its circumference is equidistant.

If Brady jogs around the circular park with a fountain at its center, it means that at a point as he runs he would be further away from the fountain. And with time, he would be approaching the fountain since the park is circular. Thus, the function that represents the distance Brady runs from the fountain would be increasing at a point and then start to decrease.

If the park were a straight line, the function would be increasing with time.

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Answer:

Step-by-step explanation:

C on edge

For the given equation 10x=1/100, the value of x is 0.001

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

Given,

10x = 1/100

x = 1/1000

x = 0.001

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According to the question given that 6x +7 if x = 5 .If we put x=5 then we get the final answer i.e 37.

= 6x + 7

= 6×5 + 7 putting ( x=5)

= 30 + 7

= 37.

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, [tex]3^4[/tex] indicates that we are multiplying 3 by 4 times. Its full form is 3 3 3 3. Exponent is another name for a number's power.

How many times we must multiply the reciprocal of the base is indicated by a negative exponent. For instance, if a-n is provided, it may be stretched to 1/an. It implies that we must multiply 1/a 'n' times, which is the reciprocal of a. When writing exponentiated fractions, negative exponents are employed.

A fractional exponent is one where the exponent of a number is a fraction. Parts of fractional exponents include square roots, cube roots, and nth roots. The square root of a base is a number having a power of half. The term "cube root of the base" is also used to describe a number with a power of 3.

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The solution to the system of equations is x = 7 and y = -3

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

5x + 2y = 29

5x - 2y = 41

Add both equations

So, we have

10x = 70

Divide the equation by 10

So, we have

x = 7

Substitute x = 7 in 5x - 2y = 41

5 x 7 - 2y = 41

This gives

35 - 2y - 41

Evaluate

2y = -6

Divide by 2

y = -3

Hence, the solution to the system of equations is x = 7 and y = -3

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If the binomial (x−7) is a factor of the polynomial function f(x), then the true statement is f(-7) = 0

The given parameters are

The binomial (x + 7) is a factor of the polynomial function f(x)

The above means that

When the function f(x) is divided by x + 7, it has no remainder

So, we have

x + 7

Set to 0

x + 7 = 0

Add -7 to both sides

x = -7

Substitute x = -7 in f(x) = 0

f(-7) = 0

Hence, if the binomial (x−7) is a factor of the polynomial function f(x), then the true statement is f(-7) = 0

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Answer: m<2 = 18°

Step-by-step explanation:
m<1 + m<2 = 90°

7x - 19 + x + 5 = 90°
     First add common variables; 7x + x = 8x || -19 + 5 = -14
8x - 14 = 90°
     Second add 14 on both sides;

8x - 14 = 90°

     +14   +14

8x = 104°
      Third divide 8 to 104
[tex]\frac{8x}{8} = \frac{104}{8}[/tex]

x = 13

m<1 7(13) - 19 + m<2 (13) + 5 = 90°
13 * 7 = 91
91 - 19 = 72
72 + 13 = 85
85 + 5 = 90°

m<2 = 13 + 5 = 18°

Hope this helps! :]
--Blu

Step-by-step explanation:

Select the correct answer from each drop-down menu. A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt. He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true. The conclusion drawn from the study is because the sample is . In this instance, an study was

Using the distance formula, the perimeter of triangle EFG = 25.7 units

The perimeter of triangle EFG = EF + FG + EG

Using the distance formula, d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex], find the lengths of EF, FG, and EG:

Find EF:

E(-8,1) = (x1, y1)

F(1,1) = (x2, y2)

Plug in the values

EF = √[(1−(−8))² + (1−1)²]

EF = √[(9)² + (0)²]

EF = √81

EF = 9 units

Find FG:

F(1,1) = (x1, y1)

G(-3,8) = (x2, y2)

Plug in the values

FG = √[(−3−1)² + (8−1)²]

FG = √[(−4)² + (7)²]

FG = √65

FG ≈ 8.1 units

Find EG:

E(-8,1) = (x1, y1)

G(-3,8) = (x2, y2)

Plug in the values

EG = √[(−3−(−8))² + (8−1)²]

EG = √[(5)² + (7)²]

EG = √74

EG ≈ 8.6 units

Perimeter of triangle EFG = 9 + 8.1 + 8.6

Perimeter of triangle EFG = 25.7 units

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Answer:

50.27 ft

Step-by-step explanation:

hope this helps :)

Answer:

6n-2

Step-by-step explanation:

Write the expression

subtracted from  means it comes after

product of 6 and a number means multiply

6n

2 is subtracted from

6n-2

Answer:

It can be expressed as:

6x-2

6(coefficient)

x(variable)

2(constant)

Answer: Im not sure but have a wonderful day god bless you.

Step-by-step explanation:

The values of the variables in the ordered pair are as follows;

18. y = 10

19. x = 6

20. y = -14

21. x = -4

22. x = -5

23. x = 40

24. y = -30

25. y = 5

Ordered pairs are points located on the graph of a function.

In a direct variation, we have;

y = m•x

Where;

m = The slope of the line joining the points

18. (2, -4), (-5, y) the ordered pair is a direct variation

The slope = (y + 4)/((-5) - 2) = (y + 4)/(-7)

y = (y + 4)/(-7) × (-5)

7•y/5 = y + 4

7•y/5 - y = 4

2•y/5 = 4

19. (4, 16), (x, 24)

m = (24 - 16)/(x - 4) = 8/(x - 4)

y = 24

Which gives;

24 = (8/(x - 4))×x

24 × (x - 4) = 8•x

16•x = 96

x = 96/16 = 6

20. (12, y), (4, 7)

m = (7 - y)/(4 - 12) = (7 - y)/(-8)

y = ((7 - y)/(-8)) × 12

12•y/(-8) = 7 - y

12•y = -56 + 8•y

4•y = -56

y = -56/4 = -14

21. (x, -16), (6, 24)

m = (24 - (-16))/(6 - x) = 40/(6 - x)

-16 = (40/(6 - x))×x

16•x - 96 = 40•x

24•x = -96

x = -96/24 = -4

22. y = -18, x = 3

-18 = m×3

m = -18/3 = -6

When y = 30

x = 30/(-6) = -5

23. y = 80 when x = 32

m = 80/32 = 10/4 = 2.5

When y = 100, we have;

x = 100/2.5 = 40

24. y = 10 when x = -4

m = 10/(-4) = -2.5

When x = 12, y = 12 × (-2.5) = -30

25. y = -7 when x = -28

m = -7/(-28) = 1/4 = 0.25

When x = 20, y = 0.25 × 20 = 5

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Answer:

Slope or (m) = 1           Give Brain

Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 2}{log \\7}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

[tex]log_7{2}[/tex]

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

[tex]log_7{2}[/tex] =  [tex]\frac{log \ 2}{log \ 7}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log \\2}{log \\7}[/tex]

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Answer:

5.67

Step-by-step explanation:

The quotient was 5.6671 and rounded to the nearest hundredth is 5.67. Hope it helps.

Tonya's total earnings are the sum of the basic pay and other commissions so Tonya's earnings for a month including all incentives will be $5450.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Basic pay of Tonya = $650

3% of 32000 ⇒

3 × 32000 / 100 = $960

Now 8% on higher of $32000

Amount higher of $32000 ⇒ 80000 - 32000 = $48000

So,

8% on 48000 ⇒

8 × 48000/100 = $3840

Total earning = 650 + 960 + 3840 = $5450

Hence "Tonya's total earnings for a month including all incentives will be $5450".

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