There were 15 girls and 25 boys in the Science club. What percent of the members were girls?

Answers

Answer 1

Answer: 37.5

Step-by-step explanation:

15 15 3

___ = ___ = ___ = 0.375 = 37.5

15+25 40 8


Related Questions

PLEASE HELP ME

The results of a random sample of 1000 people are recorded in table one use this data to answer the questions that follow What percentage of Americans would you predict wear glasses

Answers

Answer:

63,8%

Step-by-step explanation:

Assuming the sample is a good representation of the people from the United States.

Since there were 1,000 surveyed... and 638 of them were wearing glasses,  that makes a proportion of 638 out of  1,000 people, or 63,8 / 100 people... so 63.8%

I would say the sample is not representative of the reality.... because I don't think so many people wear glassed.

30 POINTS PLEASE ANSWER ASAP. The Diagram shows the front wooden wall of the warehouse in the shape of a trapezoid with a rectangular section cut out for the steel door. What is the area of the front wooden wall of the warehouse?

Answers

Answer:

900 sq ft

Step-by-step explanation:

The area of a trapezoid is (Base 1 + Base 2) * height/2. So to plug the numbers in...

(30+60)20/2

90*20/2

1800/2

900 sq ft

The correct answer is: 708 square feet

the area of the full shape is 900^2 feet and the area of the door is 192^2 feet therefore 900 - 192 = 708.

Which statements are true about the curve? Check all
that apply.
O The standard deviation of the data is 64.
O The variance of the data is 49.
O The median is 64.
O
The data point 75 is less than one standard
deviation from the mean.
The data point 50 is two standard deviations away
from the mean.

Answers

Answer:

B, C, E

Step-by-step explanation:

trust me ;)

The correct statements are true about the curve are as follows;

The variance of the data set is 49.

The median is 64.

The data point 50 is two standard deviations away from the mean.

What is the standard deviation?

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The correct statements are true about the curve are as follows;

1. The variance of the data set is;

σ ² = 7²

σ ² = 49

The variance of the data set is, 49.

2. The median is the middle value of the data set.

The median is 64.

3. The data point 50 is two standard deviations away from the mean.

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-102=-6-2(6-7x) answer ​

Answers

Add 6 to both sides

-102 + 6 = -2(6 - 7x)

Simplify -102 + 6 to -96

-96 = -2(6 - 7x)

Divide both sides by -2

-96/-2 = 6 - 7x

Two negatives make a positive

96/2 = 6 - 7x

Simplify 96/2 to 48

48 = 6 - 7x

Simplify 48 - 6 to 42

42 = -7x

Divide both sides by -7

-42/7 = x

Simplify 42/7 to 6

-6 = x

Switch sides

Answer: x = -6

write an inequality, use n as a variable, and then solve the inequality.

an auto mechanic estimates that the cost to repair Brett’s car will be no more than $200. the parts will cost $49.23. what is the estimated cost for the labor?

Answers

Answer:

The estimated cost for the labor is less than or equal to [tex]\$150.77[/tex]

Step-by-step explanation:

Let

n -----> the estimated cost for the labor

we know that

The inequality that represent this situation is equal to

[tex]49.23+n\leq 200[/tex]

Solve for n

[tex]n\leq 200-49.23[/tex]

[tex]n\leq \$150.77[/tex]

Which equations is 8 a solution? Check all that apply. A. x+6=2 B. x+2=10 C. x-4=4 D. x-2=10 E. 2x=4 F. 3x=24 G. x/2=16 H. x/8 = 1

Answers

Answer:

B, C, F, H

Step-by-step explanation:

Just search up how to solve equations

Answer: B. x+2=10

C. x-4=4

F. 3x=24

H. [tex]\dfrac{x}{8}=1[/tex]

Step-by-step explanation:

To check whether 8 is a solution of the given equation or not , we need to substitute the value of 8 in the place of x check whether equation is truw or not.

A. [tex]x+6=2[/tex]

At x= 8, we have

[tex]8+6=2\Rightarrow\ 14=2[/tex] , which is not true , it means 8 is not a solution of this equation.

B. x+2=10

At x= 8, we have

[tex]8+2=10\Rightarrow\ 10=10[/tex] , which is true , it means 8 is a solution of this equation.

C. x-4=4

At x= 8, we have

[tex]8-4=4\Rightarrow\ 4=4[/tex],  which is true , it means 8 is a solution of this equation.

D. x-2=10

At x= 8, we have

[tex]8-2=10\Rightarrow\ 6=10[/tex] , which is not true , it means 8 is not a solution of this equation.

E. 2x=4

At x= 8, we have

[tex]2(8)=4\Rightarrow\ 16=4[/tex] , which is not true , it means 8 is not a solution of this equation.

F. 3x=24

At x= 8, we have

[tex]3(8)=24\Rightarrow\ 24=24[/tex],  which is true , it means 8 is a solution of this equation.

G. [tex]\dfrac{x}{2}=16[/tex]

[tex]\dfrac{8}{2}=16\Rightarrow\ 4=16[/tex], which is not true , it means 8 is not a solution of this equation.

H. [tex]\dfrac{x}{8}=1[/tex]

At x= 8, we have

[tex]\dfrac{8}{8}=1\Rightarrow\ 1=1[/tex],  which is true , it means 8 is a solution of this equation.

Hence, the required equations :

B. x+2=10

C. x-4=4

F. 3x=24

H. [tex]\dfrac{x}{8}=1[/tex]

Solve for x: x^2 + 28x = 60

Answers

For this case we have a quadratic equation, [tex]x ^ 2 + 28x-60 = 0[/tex], of the form [tex]ax ^ 2 + bx + c = 0[/tex]

Where:

[tex]a = 1\\b = 28\\c = -60[/tex]

We can solve the equation by factoring, that is, we bias two numbers that multiplied give as a result -60 and added as a result 28.

These numbers are:

[tex]+30\ and\ -2\\+ 30-2 = + 28\\+ 30 * -2 + -60[/tex]

Then, the factorization is given by:

[tex](x-2) (x + 30) = 0[/tex]

The roots are:

[tex]x_ {1} = 2\\x_ {2} = - 30[/tex]

Answer:

[tex]x_ {1} = 2\\x_ {2} = - 30[/tex]

I need help please???):

Answers

Hello There!

The Y-intercept Of this line is -4 because it’s subtracting 4 that’s me as it’s going down on y axis

Answer: -4

y=mx+b

b=y intercept
m=slope of line

insert 0 for y and you will find the coordinate value of x

and vice versa, insert 0 for x and you have what the y coordinate value

Any questions feel free to ask. Thanks

Emily, Jean, and Amanda live in apartments on the 5th, 6th and 7th floors. One girl likes basketball, one likes football, and the other likes soccer.

The girl on the 6th floor is the football fan
The girl on the fifth floor thinks soccer is boring
Jean is a baseball fan

Which floor does Jean live on?

Answers

Answer:

Assuming you mean baseball in stead of basketball, if must be the 5th floor.

Step-by-step explanation:

"The girl on the fifth floor thinks soccer is boring" implies that on the 5th floor lives the football or baseball fan. However, it cannot be the football fan since it is already known that she lives on 6th.

So the baseball fan, which is Jean, lives on 5th.

Find the sum of the following infinite geometric series.

Answers

Answer:

Final answer is [tex]\frac{80}{3}[/tex].

Step-by-step explanation:

We have been given an infinite geometric series.

Now we need to find it's sum.

common ratio [tex]r=-\frac{1}{5}[/tex].

plug n=1 to get the first term

[tex]a_n=32\left(-\frac{1}{5}\right)^{\left(n-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(1-1\right)}[/tex]

[tex]a_1=32\left(-\frac{1}{5}\right)^{\left(0\right)}[/tex]

[tex]a_1=32\left(1\right)[/tex]

[tex]a_1=32[/tex]

Now plug these values into infinite sum formula

[tex]S_{\infty}=\frac{a_1}{1-r}=\frac{32}{1-\left(-\frac{1}{5}\right)}=\frac{32}{1.2}=\frac{320}{12}=\frac{80}{3}[/tex]

Hence final answer is [tex]\frac{80}{3}[/tex].

The sum of the infinite geometric series given in the problem is 26.6

7.

A geometric series is a sequence of terms in which each term is obtained by multiplying the previous term by a constant ratio. It is a specific type of series where the terms follow a geometric progression.

Formally, a geometric series is expressed as:

a, ar, a[tex]r^2[/tex], a[tex]r^3[/tex], ...

To solve the geometric series sum of the form:

S = a + ar + a[tex]r^2[/tex] + a[tex]r^3[/tex] + ...,

where a is the first term and r is the common ratio, we can use the formula for the sum of an infinite geometric series:

S = [tex]\frac{a}{1 - r}[/tex].

In this case, the given series is:

S = 32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

Comparing this to the standard geometric series form, we can identify that the first term a is 32, and the common ratio r is [tex]\frac{-1}{5}[/tex].

Substituting these values into the formula, we get:

S =  32[tex]\times \frac{-1}{5}^(^n^ -^ 1^)[/tex],

S = [tex]\frac{32}{(1 +\frac{1}{5})}[/tex],

S = [tex]\frac{32}{\frac{6}{5} }[/tex],

S = 32 [tex]\times \frac{5}{6}[/tex],

S = [tex]\frac{160}{6}[/tex]

S = [tex]\frac{80}{3}[/tex] = 26.67.

Therefore, the sum of the given geometric series is 80/3 or approximately 26.67.

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What is the least common multiple of the two denominators
6/8 4/32

Answers

Answer:

32

Step-by-step explanation:

To find the lcm of 8 and 32 by listing

multiples of 8 are : 8, 16, 24, 32, 40, ....

multiples of 32 : 32, 64, 96, ....

The least common multiple of 8 and 32 is 32

Transform the standard form of the following quadratic function into vertex form and into intercept form.: f(x)= - 3x^2 - 6x + 24 What is the vertex? What are the x-intercepts?

Answers

Answer:

f(x)=-3(x+1)^2+27

Step-by-step explanation:

Forst, simplify the expression by pulling out -3, but leave 24 out.

=-3(x^2+2x)+24

Then complete the square of the equatio inside the parenthesis (remember to subtract from the outside what you add to the inside times -3).

=-3(x^2+2x+1)+24+3

=-3(x+1)^2+27

The equation is now in vertex form.

from that, we now know that the vertex is (-1,27).

Set this equation equal to 0 to find the x intercepts:

0=-3(x+1)^2+27

-27=-3(x+1)^2

9=(x+1)^2

3 and -3=x+1

x=2 and -4

According to the stem and leaf plot how many trees are more than 640 inches tall? CANT MISS ANYMORE PLEASE GIVE THE FOR SURE ANSWER!!

Answers

Answer:

9

Step-by-step explanation:

Because every number next to 64 is over

Which of the following is a true

A. -9<-4

B. |-10| >| 2 |

C. | -3 | < | 2 |

D.6< - 12

Answers

Answer:

A and B

Step-by-step explanation:

A. -9<-4  ....TRUE

B. |-10| >| 2 |  => 10 > 2 ...TRUE

C. | -3 | < | 2 |   => 3 > 2  ....FALSE

D. 6< - 12 ....FALSE

Answer A and B

PLSSSSSSSSS HELP!!!! ALGEBRA NATION TEST
consider the following polynomial.


-2xy^5+3x^7-10x^3y^6+8x^6+4


which of the following statements are true? select all that apply


A)The polynomial has 5 terms.

B)The leading coefficient is -2.

C)The degree of the polynomial is 7.

D)The constant term is 4.

E)The polynomial is in decreasing degree order.

Answers

Answer:

[A.] and [D.]

Step-by-step explanation:

Before we even solve to see which options are true and false, write the polynomial in descending order.

To do this, break the polynomial into terms.

1. -2xy^5

2. 3x^7

3. -10x^3y^6

4. 8x^6

5. 4

To write this in descending order, look at the exponents or degrees.

We have 5 terms [So A. is already a correct option choice] so look at the exponents or degrees for each term

1. -2xy^5  [degree: 6 (x has an exponent, 1)]

2. 3x^7 [degree: 7]

3. -10x^3y^6 [since there are 2 exponents, add them together (degree: 9)]

4. 8x^6 [degree: 6]

5. 4 [degree: 1 (even though it doesn't look like it, 4 actually has an exponent, 1, along with other numbers like 1, 2, 3, 4, 5 etc.)]

-10x^3y^6 has the largest degree, then 3x^7, then 8x^6 and -2xy^5, and lastly 4.

Now, rewrite the polynomial

-2xy^5 + 3x^7 -10x^3y^6 + 8x^6 + 4 = -10x^3y^6 + 3x^7 + 8x^6 -2xy^5 + 4

We already established A.) is a correct answer.

B.) is not correct since our leading term is -10x^3y^6 and -10 would be the leading coefficent.

C.) Is not correct since the degree of the polynomial is 9, since the highest degree is 9

D.) Is correct since 4 has no variables attached to it

E.) Is not correct since the polynomial was not in descending form, we had to do it for them.

Thus, A.) and C.) are the correct answers.

I hope this helps! Let me know if I did something wrong or you have any questions! Thanks! :)

A boy and girl ran towards each other. The boy ran at 1 mph and the girl ran at
2 mph. The distance between them when they started was 50 meters. After how much time did they meet each other?

I will give brainliest to whoever answer first!!!!!!!!!! And 99 points!!!!!!!!!!!!!!!! I PROMISE THIS

Answers

Step-by-step explanation:

Firstly to facilitate the conversion we need to convert mph to km/h.

50 m= 0.05 km

1 mph= 0.001 km/h

2 mph= 0.002 km/h

For the girl

D=0.05 km

S= 0.002 Km/h

T= 25 h

For the Boy

D=0.05

S= 0.001

T= 50 h

Now to find after how many time they will meet each other, we simply have to add the two times.

So,

25 h + 50 h= 75 h

ANS: 75 h

Can someone help with this question?

Answers

Answer:

w = 4 m

Step-by-step explanation:

The volume (V) of a cuboid is

V = lwh ( l is length, w is width and h is height )

Given V = 144 m³, then

lwh = 144 ( substitute l = 3 and h = 12 )

3 × w × 12 = 144

36w = 144 ( divide both sides by 36 )

w = 4

The volume of a rectangular prism is given by the product of its dimension: let w, h, l be the width, height and length of the prism, we have

[tex]V = whl[/tex]

In your case, everything is given except the width:

[tex]144 = w\cdot 3 \cdot 12 \iff 144 = 36w \iff w = \dfrac{144}{36} = 4[/tex]

PLEASE HELP QUICK I WILL GIVE BRAINLIEST THIS IS A UNIT TEST!!!!
What is the value of x?

Enter your answer in the box.

x =
A right triangle. The legs are labeled x and 12, and the hypotenuse is labeled 13.

Answers

You appear to be missing side A. Here is the equation for that:

a = √(c² - b²)

So do c squared (13 squared) - b squared (12 squared)

= 25

However, the answer is not c squared - b squared, but the SQUARE ROOT of c squared - b squared.

In other words, we want the square root of 25, so your answer is...

5!

Consider the following function:y=1/(x+5)+2
How does the graph of this function compare with the graph of the parent function, y=1/x
It is shifted right 5 units and up 2 units from the parent function.
It is shifted left 5 units and up 2 units from the parent function.
It is shifted right 5 units and down 2 units from the parent function.
It is shifted left 2 units and down 5 units from the parent function.
It is shifted right 2 units and up 5 units from the parent function.
It is shifted left 2 units and up 5 units from the parent function.

Answers

Answer:

Step-by-step explanation:

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.  That +2 shifts this result UP by 2 units.

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.

We have given that function

y=1/(x+5)+2

We have to determine,

The graph of this function compares with the graph of the parent function, y=1/x.

Starting with the parent function, x was replaced by (x + 5), indicating that the graph of the new function is that of the old function shifted 5 units to the LEFT.

That +2 shifts this result UP by 2 units.

Therefore the graph of the y=1/x is given below.

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What is 8 3/4 - 7 1/2

Answers

let's firstly convert the mixed fractions to improper fractions and then subtract, bearing in mind that the LCD of 4 and 2 is 4.

[tex]\bf \stackrel{mixed}{8\frac{3}{4}}\implies \cfrac{8\cdot 4+3}{8}\implies \stackrel{improper}{\cfrac{35}{4}}~\hfill \stackrel{mixed}{7\frac{1}{2}}\implies \cfrac{7\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{15}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{35}{4}-\cfrac{15}{2}\implies \stackrel{\textit{using the LCD of 4}}{\cfrac{(1)35~~-~~(2)15}{4}}\implies \cfrac{35-30}{4}\implies \cfrac{5}{4}[/tex]

The life spans, in years, of some plants in a nursery are shown below:

5, 3.2, 4.1, 3.8, 3.1, 3.2, 5.8, 3.8, 4.2, 4.3

Jack made the following box plot to represent the life spans:

box plot shows minimum at 3.1, first quartile at 3.2, median at 3.95, third quartile at 4.8 and maximum at 5.8

Which of the following did Jack show incorrectly on his box plot?

Median
Minimum
First quartile
Third quartile

Answers

Jack incorrect plotted the third quartile.

Explanation:

A box plot has 5 data descriptions. The option that Jack marked incorrectly is Median.

How does a boxplot show the data points?

A box plot has 5 data descriptions:

The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called the second quartile.The last line of the box shows the third quartile.

In the given box plot, the median is plotted wrongly, because the median of the box plot is not 3.9.

Hence, the option that Jack marked incorrectly is Median.

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please help (10 points)

Answers

a. addition

b. multiplication

c. division

d. distributive property

Answer:

six plus y

five times j

h divided by eight / h over eight

x plus seven times four

Step-by-step explanation:

Measure the width of the paper clip to the nearest eighth of an inch.

A. 1/2
B. 1/8
C. 3/8
D. 1/4

Answers

Answer:

Step-by-step explanation:

d. 1/4

width of clip is 1/4 to the 1 inch

The width of the paper clip to the nearest eighth of an inch is 1/2 inch.

What is Scale division?

The smallest subdivision or unit that a scale's digital display can display is a scale division. It's a phrase that's frequently used synonymously with readability or resolution. The scale's capacity can be calculated by dividing it by its readability.

We have to find the width paper clip.

Here, the scale is having 4 division each of marked as 1/4.

So, the paper clip covers

= 1/4 + 1/4

= 2/4

= 1/2

Thus, the width of paper clip in 1/2 inch.

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5.) A contractor is building a deck around a rectangular swimming pool. The deck is x feet from every side of
the pool. Write an expression for the total area of the pool and deck, if the pool is 25 feet long and 20 feet
wide. Find the area of the pool and deck.​

Answers

The Answer is in the picture below...

the area of the pool and deck can be calculated by using the expression [tex]500 + 90x + 4x^2[/tex]

The dimension of the pool are:

25 ft long and 20 ft wide

We know that the deck extends x ft away from every side of the pool.

Thus, the total length of the pool and deck together is 25 + 2x ft, and the total width is 20 + 2x ft

Area of rectangle can be found using the formula:

[tex]Area = length \times breadth[/tex]

Putting in values we get:

[tex](25 + 2x) \times (20 + 2x)[/tex]

On simplifying we get:

[tex](25 + 2x) (20 + 2x) = 500 + 50x + 40x + 4x^2 \\\\(25 + 2x) (20 + 2x) = 500 + 90x + 4x^2[/tex]

Thus the area of the pool and deck can be calculated by using the expression [tex]500 + 90x + 4x^2[/tex] ft²

Choose the single logarithm expression that is equivalent to the one shown!!! Help needed !!
A. Log 64
B. Log 12
C. Log 20
D. Log 10

Answers

Answer:

log 64

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ nlogx

• logx + logy ⇔ log xy

Given

2 log 4 + log 2 + log 2

= log 4² + log (2 × 2)

= log 16 + log 4

= log (16 × 4) = log 64

 

Answer:

A, log 64

Step-by-step explanation:

your answer A, log 64 is correct. i will explain why below:

2 log 4, log 2 and log 2 have the same bases (10), meaning they are able to be added easier. but before we add, we use the Power Rule of Logarithms on 2 log 4

the Power Rule says that we can move an exponent in a logarithm to the front then solve. this also applies to the reverse, as we can move 2 back as an exponent of 4 and solve

2 log 4 ---> log 4² < simplify the exponent and we get log 16

we can now use the Product Rule of Logarithms where log x + log y = log(xy)

we can use that on the first two terms of the addition

log 16 + log 2 ----> log (16 × 2) = log 32

now we can apply the other log 2 to the rule but instead with log 32

log 32 + log 2 ---> log (32 × 2) = log 64

our answer is log 64

What values of a and b make the equation true? Screenshots attached, please help!

Answers

Answer:

Option C is Correct

Step-by-step explanation:

Given:

[tex]\sqrt{648}= \sqrt{2^a.3^b}[/tex]

We need to check the values of a and b such that the given equation remains true

1. a= 3 and b=2

[tex]\sqrt{648}= \sqrt{2^3.3^2}\\25.4 = \sqrt{72}\\25.4 \neq 8.4[/tex]

So, Option A is incorrect

2. a=2 and b= 3

[tex]\sqrt{648}= \sqrt{2^2.3^3}\\25.4 = \sqrt{108}\\25.4 \neq 10.3[/tex]

So, Option B is incorrect

3. a=3, b=4

[tex]\sqrt{648}= \sqrt{2^3.3^4}\\25.4 = \sqrt{648}\\25.4= 25.4[/tex]

So, Option C is correct.

4. a= 4, b=3

[tex]\sqrt{648}= \sqrt{2^4.3^3}\\25.4 = \sqrt{432}\\25.4 \neq 20.7[/tex]

So, Option D is incorrect.

Find the value of y.
Please Help Needed Badly!!

Answers

Answer:

The measure of angle y is 90°

Step-by-step explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

m∠y=(1/2)[180°] -----> because the diameter divide the circle into two equal parts

so

m∠y=90°

m∠x=(1/2)[148°]

m∠x=74°

Answer:

Y = 90

Step-by-step explanation:

A line passes through A(3, 7), and B(-4, 9). Find the value of a if C(a, 1) is on the line.

Answers

ANSWER

a=-32

EXPLANATION

If C(a,1) is on the line that passes through A(3, 7), and B(-4, 9), then the three points are collinear.

This implies that, when we find the slope using any two points, we should get the same result.

[tex] \frac{9 - 1}{ - 4 - a} = \frac{9 - 7}{ - 4 - 3} [/tex]

We simplify to obtain;

[tex] \frac{8}{ - 4 - a} = \frac{ - 2}{ - 7 } [/tex]

[tex]\frac{8}{ - 4 - a} = \frac{ 2}{ 7 } [/tex]

We cross multiply to get;

[tex]8 \times 7 = 2( - 4 - a)[/tex]

This implies that,

[tex]56 = - 8 - 2a[/tex]

[tex]56 + 8= - 2a[/tex]

[tex]64 = - 2a[/tex]

Divide both sides by -2

[tex]a = \frac{64}{ - 2} [/tex]

[tex]a = - 32[/tex]

Answer:

a=-32

Step-by-step explanation:

What percent of the total players scored 31-40 points during November

Answers

Answer:

40%

Step-by-step explanation:

4÷10x100=40

As you have 10 players total and 4 players scored between 31 and 40 points

Solving equations, thank you!

Answers

Answer:

x = -4 or x = 1

Step-by-step explanation:

[tex]\dfrac{x}{2x-3}-\dfrac{8-3x}{4x^2-9}=0\\\\\bold{DOMAIN:}\\\\2x-3\neq0\ \wedge\ 4x^2-9\neq0\\\\2x-3\neq0\qquad\text{add 3 to both sides}\\2x\neq3\qquad\text{divide both sides by 2}\\\boxed{x\neq1.5}\\\\4x^2-9\neq0\qquad\text{add 9 to both sides}\\4x^2\neq9\qquad\text{divide both sides by 4}\\x^2\neq2.25\\x\neq\pm\sqrt{2.25}\\\boxed{x\neq-1.5\ \wedge\ x\neq1.5}[/tex]

[tex]\dfrac{x}{2x-3}-\dfrac{8-3x}{4x^2-9}=0\\\\\dfrac{x}{2x-3}-\dfrac{8-3x}{(2x)^2-3^2}=0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{x}{2x-3}-\dfrac{8-3x}{(2x-3)(2x+3)}=0\\\\\dfrac{x(2x+3)}{(2x-3)(2x+3)}-\dfrac{8-3x}{(2x-3)(2x+3)}=0\\\\\dfrac{x(2x+3)-(8-3x)}{4x^2-9}=0[/tex]

[tex]\text{The fraction is equal to 0 if the numerator is equal to 0. Therefore}\\\\\dfrac{x(2x+3)-(8-3x)}{4x^2-9}=0\iff x(2x-3)-(8-3x)=0\\\\\text{use the distributive property}\\\\(x)(2x)+(x)(3)-8-(-3x)=0\\\\2x^2+3x-8+3x=0\qquad\text{combine like terms}\\\\2x^2+(3x+3x)-8=0\\\\2x^2+6x-8=0\qquad\text{divide both sides by 2}\\\\x^2+3x-4=0\\\\x^2+4x-1x-4=0\\\\x(x+4)-1(x+4)=0\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\x+4=0\qquad\text{subtract 4 from both sides}\\x=-4\in D\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]

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