Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile. If she continue this pattern, when was the first time she ran more than one mile explain

Answers

Answer 1

Answer:

In seventh time she ran more than one mile from first time she ran.

Step-by-step explanation:

Given Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile.

We have to find when was the first time she ran more than one mile.

The sequence followed is

[tex]\frac{3}{16}, \frac{6}{16}, \frac{9}{16}, \frac{12}{16}, \frac{15}{16}, \frac{18}{16}, \frac{21}{16}....[/tex]

First time she ran more than 1 mile is [tex]\frac{3}{16}+1=\frac{19}{16}[/tex]

In the seventh time she ran [tex]\frac{21}{16}[/tex] miles which is more than one mile from the first time.

Hence, in seventh time she ran more than one mile from first time she ran.

Related Questions

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners? S = {FGI, GFI, IFG} S = {FGI, FIG, GFI, GIF} S = {FGI, FIG, GFI, GIF, IFG, IGF} S = {FGI, FIG, GFI, GIF, HFG, HGI, IFG, IGF}

Answers

the Different possibilities in which the three players are placed are as follows ;
F can come first then the possibilities of other 2 players are ;
FGI and FIG
G can come first then the possibilities of other 2 players are ;
GIF and GFI
Next If I comes first then the possibilities are
IGF and IFG

Therefore sample space for all the possibilities as noted above are;
S = {FGI, FIG, GFI, GIF, IFG, IGF}

The sample space or sets showing the possible orders of the other three runners is S = {FGI, FIG, GFI, GIF, IFG, IGF}.

What are Sets?

Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team.

Haley is the first runner in the relay. The other runners can run in any order.

The sample space or sets showing the possible orders of the other three runners will be

S = {FGI, FIG, GFI, GIF, IFG, IGF}

Thus, the correct option is C.

More about the sets link is given below.

https://brainly.com/question/8053622

A circle is divided into parts. Which sum could represent the angle measures that make up the circle?

Answers

360 degrees. all the way around the circle is 360 degrees!

A circle is always going to be 360°.

Write, and show on a number line, the set of all the numbers that are:

greater than (−3) and less than 3.

Answers

-2, -1, 0, 1, 2. 3 and -3 don't count because it isn't less than or equal to.

which method could be used to factor 4x^2-50

Answers

The correct factorization for [tex]$4x^2 - 50$ is $2(x\sqrt{2} - 5)(x\sqrt{2} + 5)$[/tex], where [tex]$\sqrt{2}$[/tex] is included in each term.

The given quadratic expression [tex]$4x^2 - 50$[/tex] can be factored using the difference of squares method.

The difference of squares formula is[tex]$a^2 - b^2 = (a + b)(a - b)$.[/tex]

In this case, a = 2x and [tex]$b = \sqrt{50}$.[/tex]

1. Identify the expression as a difference of squares: [tex]$4x^2 - 50 = (2x)^2 - (\sqrt{50})^2$.[/tex]

2. Apply the difference of squares formula:[tex]$4x^2 - 50 = (2x + \sqrt{50})(2x - \sqrt{50})$.[/tex]

3. Further simplify by factoring out 2: [tex]$4x^2 - 50 = 2(2x + \sqrt{50})(2x - \sqrt{50})$.[/tex]

The correct factorization for [tex]$4x^2 - 50$ is $2(x\sqrt{2} - 5)(x\sqrt{2} + 5)$[/tex], where [tex]$\sqrt{2}$[/tex] is included in each term.

Let j and k stand for two different rational numbers. If ∣j∣>∣k∣, then what else must be true?
A) j is farther from 0 than k is. B) j is less than k. C) On a number line, j is to the right of k.
D) the opposite of j is less than the opposite of k

Answers

A is the correct answer trust me

Answer:

A) j is farther from 0 than k is

Step-by-step explanation:

Find the 5th partial sum of the arithmetic sequence an=2n–3.

Answers

this would be -1 + 1 + 3 + 5 + 7 = 15

Which logarithmic equation is equivalent to 3^2 = 9?

Answers

the law of logarithms is
㏒ₓᵃ =n and a=x^n
we have ㏒₃ 9=2
3 is the base

Answer:

[tex]log_3(9)=2[/tex]

Step-by-step explanation:

[tex]3^2 = 9[/tex]

Logarithmic form is the reverse of exponential form

To convert exponential form in to log form we use a rule

[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]

WE apply the same rule in our exponential equation to convert it into log form

[tex]3^2 = 9[/tex]

The base of exponent is the base of log

[tex]log_3(9)=2[/tex]

How to find A? help please and thanks

Answers

This problem exercises the concept of "similar triangles."

With similar triangles, we can compare the sides using ratios.
The equation we can use to find side A is stated below.

Side 1A / Side 1B = Side 2A / Side 2B

The number refers to the triangle, and the letter refers to the side of each triangle. Side A in both triangles must be the base of the triangle, and side B in both triangles can be either of the other sides. The only restriction is that once we pick a side B on triangle 1, we must pick that same side on triangle 2.

A / 7 = 3 / 2

Then we can solve for the length of side A.

A = 7*3/2 = 21/2 = (E) None of These

select all expressions thr equal 3.15/0.45

Answers

Select all expressions equal 3.15/0.45

let's analyze case by case
case A) 3.15*0.45---------> is not (3.15/0.45)
case B) 3.15/0.45-----------> is correct
case C) 3.15*(1/0.45)=(3.15*1)/0.45--------> 3.15/0.45----------> is correct
case D) 3.15/(45/100)=3.15*100/45=315/45-------------> is not (3.15/0.45)
case E) 0.45/3.15------------> is not (3.15/0.45)

the answers are
case B) 3.15/0.45-----------> is correct
case C) 3.15*(1/0.45)=(3.15*1)/0.45--------> 3.15/0.45----------> is correct

Which model shows the correct factorization of x2 + 2x - 8

Answers

To factor x^2 + 2x - 8 follow these steps

1) Write to factors, with x as the first term, this way:
(x )(x )

2) The sign to the right of the x in the first factor is the same sign of the coeficient of x in the polynomial.
That is +.

The sign to the right of the x of the second factor is the product of the sign of the coefficent of x (this is +) and the sign of the independent term (this is - ).
So that is (+).(-) + -.
Now the two factors have this form:
(x + ) (x - )

3) Now find two numbers whose product is - 8 and whose difference is +2

Those numbers are + 4 and -2.

Then the two factors are:
(x + 4) (x - 2).

So the answer if that the correct factorization is (x + 4) (x - 2)

The correct answer is D.

I just took the test.

margaret purchased a doormat measuring 1/2 yard by 2/3 yard for her back door step. If the step is 1/4 square yard, will the mat fit? explain

Answers

we know that
[the area of a doormat]=(1/2)*(2/3)---------> 2/6 --------> 0.33 yd²
[the area of the step]= 1/4 --------> 0.25 yd²

[the area of a doormat] > [the area of the step]
0.33 yd² is > 0.25 yd²
therefore
the doormat will not fit because it is too large

the answer is
the doormat will not fit

Final answer:

The doormat measuring 1/2 yard by 2/3 yard will not fit on a step that is 1/4 square yard because the doormat's area, 1/3 square yard, is larger than the step's area.

Explanation:

The question "Will a doormat measuring 1/2 yard by 2/3 yard fit on a step that is 1/4 square yard?" involves understanding of measuring areas in yards and comparing the area of the doormat with that of the step. First, we calculate the area of the doormat by multiplying its length and width (1/2 yard * 2/3 yard = 1/3 square yard).

Next, we compare the area of the doormat, which is 1/3 square yard, to the area of the step, which is 1/4 square yard. Since 1/3 square yard is larger than 1/4 square yard, the doormat will not fit perfectly on the step as it is too big.

Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept.
The Choices are
F(x)=2x^2-4x-3
G(x)= -x^2+x+1
H(x)= -2x^2+3x-1
M(x)=x^2-9
N(x)= -3x^2+7

Answers

Hello there!

The only thing you need to do is look at the leading coefficient for each choice to decide which ones open down and have a maximum. If the leading coefficient is negative, then they open down and have a maximum.

F(x) is out of our choices because the leading coefficient is positive.

G(x) and H(x) are still options.

M(x) is gone for the same reason we won't choose F(x).

N(x) is still an option.

Now our choices are between G(x), H(x), and H(x). To decide which ones have a positive y-intercept, look at the constant term. If it's negative, then it has a negative y-intercept and it's out of our choices.

G(x) and H(x) remain our only options and since the question can have multiple answers, G(x) and H(x) are the answers!

I really hope this helps!
Best wishes:)

Final answer:

Out of the options provided, only G(x) = -x^2 + x + 1 fits the conditions asked in the question. It is a quadratic function that opens downward, has a vertex that is a maximum, and a positive y-intercept.

Explanation:

The key features of a quadratic function are determined by its equation: f(x) = ax2 + bx + c. The sign of 'a' determines whether the function opens up or down. If 'a' is positive, the graph opens up, and if 'a' is negative, it opens down. The vertex of a quadratic function is given by the formula (-b/2a , f(-b/2a)). If 'a' is negative, this vertex will be a maximum. The y-intercept of the function is the value of 'c' in the quadratic equation. According to the conditions provided, we can classify the given functions.

f(x) = 2x2 - 4x - 3 opens upward and has a negative y-intercept; it’s not in the selection.G(x) = -x2 + x + 1 opens downward, has a maximum vertex, and a positive y-intercept. It fits the conditions.H(x) = -2x2 + 3x - 1 opens downward and has a maximum vertex, but has a negative y-intercept, so it’s not in the selection.M(x) = x2 - 9 opens upward and has a negative y-intercept; it’s not in the classification.N(x) = -3x2 +7 opens downward and has a maximum vertex, but it does not mention whether there is a positive y-intercept; so it’s unclear.

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How many x intercepts appear on the graph of this polynomial function? F(x)=x^4-5^2.
1 x intercept
2 x intercepts
3 x intercepts
4 x intercepts

Answers

x-intercepts are the points where the graph crosses the x-axis. Along the x-axis value of y-coordinate is zero. So if we equate the given equation to 0, we can find the points where y-coordinate is zero and thus we can find the x-intercepts of F(x).

[tex]0= x^{4}- 5^{2} \\ \\ 25= x^{4} \\ \\ [/tex]

Taking square root of both sides we get:

[tex](5) = x^{2} , \\ -5= x^{2} [/tex]

The square root of -5 will result in a complex number. So we reject this value and only consider [tex]5= x^{2} [/tex]

Taking the square root again, we get:
[tex]+- \sqrt{5}=x [/tex]

Thus the F(x) has two x-intercepts at [tex]x= \sqrt{5} [/tex] and [tex]x= -\sqrt{5} [/tex]

Find the first five non-zero terms of taylor series centered at x=3x=3 for the function below. f(x)=6x−x2−−−−−−√ f(x)=6x−x2

Answers

Try the suggested solution for f(x)=6x-x².
Note, that because of simple function (parabola) almost all the members of the series are '0'.

A punch recipe requires 4/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?

Answers

we know that
2 1/2----------> (2*2+1)/2-----------> 5/2

[unit rate of soda to pineapple juice]=[quantity of soda]/[quantity of pineapple]
[unit rate of soda to pineapple juice]=[5/2]/[4/5]----> 25/8-------> 3.125---> 3 1/8

the answer is 3.125 (3 1/8)

The graph below shows the solution to a system of inequalities
Which of the following inequalities is modeled by the graph?
A. x + 4y ≥ 15; y ≥ 0
B.x − 4y ≥ 15; y ≥ 0
C.x + 4y ≤ 15; y ≥ 0
D.−x − 4y ≥ 15; y ≥ 0

Answers

we have that

using a graph tool
I proceed to graph each of the cases to verify the answer
see the attached figures

the solution is the option C) x + 4y ≤ 15; y ≥ 0

an automobile radiator contains 20 L of antifreeze and water. this mixture is 20% antifreeze. how much of this mixture should be drained and replaced with pure antifreeze so that the mixture will be 50% antifreeze.

Answers

Try this solution (this suggested way is not short, but pure):
1. to make up the scheme of changes; 2. to make up the system of the equations according to the scheme.

Note, that antifreeze is marked by black in the picture.

Final answer:

To make a 20L mixture 50% antifreeze, 7.5L of the mixture should be drained and replaced with pure antifreeze. This calculation is based on the original 20% antifreeze concentration and the goal of reaching a 50% concentration without changing the total volume.

Explanation:

The question asks how much of a 20L mixture, which is 20% antifreeze, needs to be drained and replaced with pure antifreeze so the mixture will be 50% antifreeze. To solve this, first calculate the current amount of antifreeze in the mixture: 20L * 20% = 4L. Let's say x liters are drained and replaced with pure antifreeze. The volume of the solution does not change, the remaining 20L. After replacement, the quantity of antifreeze is (4 - 0.2x + x) liters (since we subtract the antifreeze drained, which is 20% of x, and add back x liters of pure antifreeze), and we require this to be 50% of the total, which is 10L (50% of 20L).

Setting up the equation: 4 - 0.2x + x = 10. Simplifying gives 0.8x = 6, so x = 7.5. Therefore, 7.5L of the mixture should be drained and replaced with pure antifreeze to achieve a 50% concentration.

Each term in a binomial expansion has degree n; therefore, the product of the exponents of each term is n.

true
or
false

Answers

False. The SUM of the exponents of each term is n.

(a+b)^n = a^n b^0 + a^(n-1) b^1 + ......

Answer:

False

Step-by-step explanation:

In any binomial expansion of the form

[tex](x+a)^n = \Sigma_0^n nCr x^{n-r} a^{r}[/tex]

We find that each term has decreasing powers of x by 1 and increasing powers of a by 1, such that the sum of exponents is always n

Hence product of exponents of each term cannot be n.

The given statement is false.

Only the sum of the exponents of each term in a binomial expansion has degree n

Click on ALL the values for n that make this inequality true. There maybe more than one answer.

[tex]120 \geq 10n + 20[/tex]

Possible Answers:

Answers

You can divide by 10 and subtract 2.

12 ≥ n + 2 . . . . . . divide by 10

10 ≥ n . . . . . . . . . subtract 2

The values that will make the inequality true are those that are 10 or less, including 0 and all negative numbers.

A hotel is in the shape of a square pyramid. Each side of the base is 183 meters long and the height is 110 meters. What is the hotel's volume? Enter your answer in the box

Answers

Answer:

1,227,930 m²

Step-by-step explanation:

We are given that,

Base of the pyramid = 183 meter

Height = 110 meter.

Since, we know,

Volume of a square pyramid = [tex]Base^2\times \frac{Height}{3}[/tex]

We have,

Volume of the square pyramid = [tex]183^2\times \frac{110}{3}[/tex]

i.e. Volume of the square pyramid = [tex]33489\times 36.667[/tex]

i.e. Volume of the square pyramid = 1,227,930 m²

Hence, the volume of the square pyramid is 1,227,930 m².

The city transportation commission surveys a random sample of licensed drivers, asking the question, "Do you favor increasing the number of bus routes within the city limits?" Which shows how bias might have affected the results of the survey? A. The question is biased in favor of bus riders. B. The question is biased against bus riders. C. Surveying only licensed drivers creates a bias against people who don't have driver's licenses. D. Since the survey used random sampling, it is unlikely to be biased.

Answers

C) this shows bias against people without a license.

It stands to reason that someone without a driver's license is more likely to ride the bus; therefore their input should be received as well.

Finn imagines 1 more row of nines to find the total area of 9 * 9 rectangle. explain how this could help him solve 9 * 9

Answers

im confused by the question.

but i would say imagining nine rows of nine

the area would be 81.

Hope this helps :)

How many ways can Hannah give three of her eight T-shirts to her younger sister?

Answers

If Hannah gives her younger sister 3 shirts, it does not matter what order she hands them to her. No matter the order, it will still be the same group of 3 shirt. Since order is not important this problem can be solved using a combination.

Specifically we are asked to find 8C3 (sometimes called "8 choose 3"). This is a fraction. In the numerator we start with 8 and count down 3 numbers. In the denominator we start with 3 and count all the way down to 1. Thus we obtain,

[tex] \frac{(8)(7)(6)}{(3)(2)(1)}=(8)(7)=56 [/tex]

How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number. The large tire has a diameter of 60 inches. The small tire has a radius of 9 inches.

Answers

Final answer:

For the large tire with a diameter of 60 inches, it would make 38 rotations after traveling 600 feet. The small tire with a radius of 9 inches would make 127 rotations in the same distance.

Explanation:

First, let's convert the feet into inches since the tire measurements are given in inches. There are 12 inches in a foot, so 600 feet is equal to 7200 inches. Now, we need to determine the circumference of each tire, which we can find using the formula for the circumference of a circle which is 2πr (twice the product of pi and the radius).

For the large tire, the diameter is 60 inches, so the radius (r) is half the diameter, which is 30 inches. Thus, the circumference of the large tire would be 2π*30, which is about 188.5 inches. The large tire would therefore make about 7200/188.5 = 38 rotations.

The small tire has a radius (r) of 9 inches, so its circumference is 2π*9, which is about 56.55 inches. The small tire would hence make about 7200/56.55 = 127 rotations.

Please note that the numbers are rounded off to the nearest whole number as requested.

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Final answer:

The large tire makes approximately 38 rotations, and the small tire makes approximately 128 rotations when each travels a distance of 600 feet.

Explanation:

To find the number of rotations a tire makes, you first need to know the circumference of the tire, which represents the distance the tire would cover in one full rotation. The circumference of a circle (or tire, in this case) is calculated as 2πr, where r is the radius of the circle.

For the large tire with a diameter of 60 inches (which makes the radius 30 inches because the radius is half the diameter): The circumference is 2π × 30 = 188.5 inches. Convert this to feet because the distance given is in feet. So, 188.5 inches is about 15.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 15.7 feet = approximately 38 rotations.

For the small tire with a radius of 9 inches: The circumference is 2π × 9 = 56.5 inches, which is about 4.7 feet. Divide the total distance by the circumference to find the number of rotations: 600 feet / 4.7 feet = approximately 128 rotations.

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The figures shows the show the dimension of a tennis court and a basketball court given in term of the width x in feet.

Answers

------------------------------------------------------------------------------
Formula
------------------------------------------------------------------------------
Perimeter = 2(Length + Width)

------------------------------------------------------------------------------
Perimeter of the Tennis Court
------------------------------------------------------------------------------
Perimeter of the Tennis Court = 2(Length + Width)
Perimeter of the Tennis Court = 2 (2x + 6 + x)
Perimeter of the Tennis Court = 2 (3x + 6)
Perimeter of the Tennis Court = 6x + 12

------------------------------------------------------------------------------
Perimeter of the Basketball Court
------------------------------------------------------------------------------
Perimeter of the Basketball Court = 2(Length + Width)
Perimeter of the Basketball Court = [tex]2(3x -14 + \dfrac{1}{2}x + 32)[/tex]
Perimeter of the Basketball Court = [tex]2( 3\dfrac{1}{2}x+ 18)[/tex]
Perimeter of the Basketball Court = [tex]7x + 36[/tex]

------------------------------------------------------------------------------
Answer: Tennis Court = 6x + 12 ; Basketball Court = 7x + 36
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Difference in the two perimeter
------------------------------------------------------------------------------
(7x + 36) - (6x + 12)
= 7x + 36 - 6x - 12
= x + 24

------------------------------------------------------------------------------
Answer: Basketball Court is (x + 24) unit greater than Tennis Court
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Tennis Court is 36 feet wide. Find dimension
------------------------------------------------------------------------------
Width of Tennis Court = x = 36 ft
Length of Tennis Court = 2x + 6 = 2(36) + 6 = 78 ft
Perimeter of Tennis Court = 6x + 12 = 6(36) + 12 = 228 ft

Width of Basketball Court = 1/2x + 32 = 1/2(36) + 32 = 50 ft
Length of Basketball Court = 3x - 14 = 3(36) - 14 = 94 ft
Perimeter of Basketball Court = 7x + 36 = 7(36) + 36 = 288 ft

------------------------------------------------------------------------------
Answer:
Tennis Court is 36 ft by78 ft and its perimeter is 228 ft.
Basketball Court is 50 ft by 94 ft and its perimeter is 288 ft
------------------------------------------------------------------------------

Patricia pays $1.19 each to download songs to her MP3 players. If n is the number of downloaded songs, which equation represents the cost C in dollar?

Answers

C=1.19n or C=1.19 X n
Because each song costs 1.19, you just multiply it by the number of songs downloaded. So if I downloaded 2 songs the cost would be $2.38.

Hope this Helps

what is community property and associative property

Answers

It's "commutative property," which says that (for addition/multiplication) order of the operator doesn't matter. For eg, 3 * 5 = 5 * 3.

Associative property (again, of multiplication and addition) means that it doesn't matter how you solve an expression if the same operand is used and some numbers are grouped. For eg. 3 * (5 * 4) = (3 * 5) * 4.

Final answer:

The associative property in mathematics states that the way in which numbers are grouped or associated does not affect the result of the operation. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership.

Explanation:

The associative property is a property in mathematics that states that the way in which numbers are grouped or associated does not affect the result of the operation. For example, for addition, the associative property states that (a + b) + c = a + (b + c). This property holds true for addition and multiplication, but not for subtraction and division.

Community property, on the other hand, is a concept in the field of law, specifically property law. Community property refers to the legal framework in which the ownership of property is divided equally between spouses in a marriage or a domestic partnership. It is most commonly associated with community property states in the United States.

Using the tables found in the textbook, determine the difference between the monthly payments on a $120,000 home at 6½% and at 8% for 25 years.

Answers

the answer is in the question

Answer:115.20

Step-by-step explanation:

A container shape as a rectangular prism can hold 840 wooden cube blocks with edge lengths of 1/2 feet. What is the volume of the container?

Answers

we know that
volume of one wooden cube blocks=(1/2)³=1/8 ft³

volume rectangular prism=840*(1/8)=105 ft³

the answer is 105 ft³

The first thing we should know is that the volume of a cube by definition is:
V = L ^ 3
Where:
L: side.
We have then that the volume of a cube is:
V = (1/2) ^ 3
V = 1/8
Then, the prism volume is:
Vtotal = 840 * V
Vtotal = 840 * (1/8)
Vtotal 105 feet ^ 3
Answer:
the volume of the prism is:
Vtotal 105 feet ^ 3

Use the zero product property to find the solutions to the equation 6x^2-5x=56

Answers

Answer:x ∈ {-8/3, 7/2}Step-by-step explanation:

6x² -5x -56 = 0 . . . . . subtract the constant

(3x +8)(2x -7) = 0 . . . .factor*

The zero product property says the product will be zero only when one (or both) of the factors is zero.

First Factor

... 3x +8 = 0

... x + 8/3 = 0 . . . . divide by the coefficient of x

... x = -8/3 . . . . . . subtract 8/3

Second Factor

... 2x -7 = 0 . . . . . . set the factor to zero

... x -7/2 = 0 . . . . . divide by the coefficient of x

... x = 7/2 . . . . . . . add 7/2

_____

*Comment on factoring

There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.

... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)

Answer:

B. x = -8/3, or x= 7/2

Step-by-step explanation:

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