Solve the following system using substitution. 1/3 x+2y=1 y=2/3 x-4

Answer:

y = 2/5x + 4/5

Step-by-step explanation:

We'll begin by calculating the slope of the equation: y = 2/5x – 1/2

The slope of the above equation can be obtained as follow:

y = mx + c

Where m is the slope.

c is the y-intercept.

y and x are the coordinate.

Comparing:

y = 2/5x – 1/2 with y = mx + c

The slope of y = 2/5x – 1/2 is 2/5.

Now, let us determine the equation parallel to y = 2/5x – 1/2.

This is illustrated below:

The coordinate of the line => (–7, 2)

x1 = –7

y1 = 2

Slope (m) = 2/5 => Since the lines are parallel, their slope are equal.

y – y1 = m (x – x1)

y – 2 = 2/5(x – –7)

y – 2 = 2/5(x + 7)

Clear bracket

y – 2 = 2/5x + 14/5

Rearrange

y = 2/5x + 14/5 + 2

y = 2/5x + 4/5

Therefore, the equation is:

y = 2/5x + 4/5

Answer:

Option D. f(x) = 6^x

Step-by-step explanation:

To know which of the function is increasing, let us obtain f(1) and f(2) for each function.

This is illustrated below:

f(x) = (1/6)^x

f(1) = (1/6)¹ = 1/6

f(2) = (1/6)² = 1/36

Therefore, f(x) = (1/6)^x is decreasing.

f(x) = (0.6)^x

f(1) = (0.6)¹ = 0.6

f(2) = (0.6)² = 0.36

Therefore, f(x) = (0.6)^x is decreasing.

f(x) = (1/60)^x

f(1) = (1/60)¹ = 1/60

f(2) = (1/60)² = 1/3600

Therefore, f(x) = (1/60)^x is decreasing.

f(x) = 6^x

f(1) = 6¹ = 6

f(2) = 6² = 36

Therefore, f(x) = 6^x is increasing.

Answer:

Option D

Step-by-step explanation:

The reason why it is D is because if it was something below 1, such as 0.6, it would be decreasing. That is why 6 is the answer.

Answer:

153.

Step-by-step explanation:

If the second part is 34 units, then the 2 of the ratio is equal to 34 / 2 = 17.

That means the first part will be 7 * 17 = 119.

119 + 34 = 153.

Hope this helps!

Answer:

The length of longest piece is 105 cm.

Step-by-step explanation:

Given:

Rope is 245 cm long.

Ratio of lengths of first to second piece = 2:3.

Ratio of lengths of second to third piece = 4:5.

To find:

Length of longest piece = ?

Solution:

We are given the ratio of first and second pieces AND

ratio of second and third pieces.

Common link is second piece.

We need to make the ratio of second piece equal in both the ratio to find the ratio of all three pieces.

2:3

  4:5

Multiply 1st ratio by 4 and 2nd ratio by 3:

Now, the ratio becomes:

8:12 and 12:15

And the ratio of three pieces can be represented as:

8: 12: 15, this ratio is the first piece: second piece: third piece

[tex]\Rightarrow 8x+12x+15x = 245\\\Rightarrow 35x = 245\\\Rightarrow x = \dfrac{245}{35}\\\Rightarrow x = 7[/tex]

So, the pieces lengths will be

First piece = [tex]8 \times 7 = 56[/tex] cm

Second piece = [tex]12 \times 7 = 84[/tex] cm

Third piece = [tex]15 \times 7 = 105[/tex] cm

So, the length of longest piece is 105 cm.

Answer:

a. 7.5 minutes

b. 4 and one-half toothpicks

Step-by-step explanation:

a. an hour = 60 minutes

Allotted time for the exam = 1/2 hour = 1/2 * 60 = 30 minutes

He used 3/4 of this time, so the time left in fraction would be 1-3/4 = 1/4

So the time left in minutes is 1/4 * 30 = 7.5 minutes

b. The total length he has here is 14 3/5 inches

Now he wants to cut toothpicks of 3 1/5

To know the number of toothpicks he can cut, we simply divide the total length by the length of each toothpick

14 3/5 divided by 3 1/5

= 73/5 divided by 16/5

= 73/5 * 5/16 = 73/16 = 4.5625

which is closer to 4 and one-half toothpicks

Answer:

18 multiplied by 2/9 = 4

Step-by-step explanation:

To determine the number of almonds that Pete grabbed, you have to multiply how much of the nuts were almonds by the total number of nuts that he grabbed. So,

   2/9 × 18

= 0.2222 × 18

= 4

Pete grabbed 4 almonds out of the 18 mixed nuts that he grabbed.

Hope that helps.

Answer:

Amount of almonds = 18 × [2/9]

Amount of almonds =  4 almonds

Step-by-step explanation:

Given:

Number of mixed nuts = 18

Probability of almonds = 2/9

Find:

Amount of almonds

Computation:

Amount of almonds = Number of mixed nuts × Probability of almonds

Amount of almonds = 18 × [2/9]

Amount of almonds = 36 / 4

Amount of almonds =  4 almonds

Answer:

[tex]\large \boxed{\sf \ \ \ \dfrac{\sqrt{4025}-5}{2}=29.22144... \ \ \ }[/tex]

Step-by-step explanation:

Hello

Let's note the original speed of the car v

it means that in 1 hour he is going v miles

so to go 200 miles it takes ( in hour)

[tex]\dfrac{200}{v}[/tex]

If the speed of the car is v+5 than to go 200 miles it takes (in hour)

[tex]\dfrac{200}{v+5}[/tex]

and this time is one hour less so we can write

[tex]\boxed{\sf \ \ \dfrac{200}{v+5}=\dfrac{200}{v}-1 \ \ }[/tex]

We can multiply by v(v+5) both parts of the equation so

[tex]200v=200(v+5)-v(v+5)\\\\<=>200v=200v+1000-v^2-5v\\\\<=>v^2+5v-1000=0[/tex]

[tex]\Delta=b^2-4ac=5^2+4*1000=4025\\\\ \text{There are potential solutions }\\\\\ \ \ \ \ x_1=\dfrac{-5-\sqrt{4025}}{2}\\\\\ \ \ \ \ x_2=\dfrac{-5+\sqrt{4025}}{2}[/tex]

Only one is positive and this is is

[tex]x_1=\dfrac{\sqrt{4025}-5}{2}=29.22144...[/tex]

So the original speed is 29.22144... mph

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: 215,820 ways

Step-by-step explanation:

There are 110 applicants for three cosmetology positions. How many different ways can the three positions be filled?

Number of positions = 110

Number of applicants = 3

Number of way in which the positions can be filled ;

This is a combination problem

nCr = n! ÷ (n-r)! r!

110C3 = 110! ÷ (110 - 3)! 3!

110C3 = 110! ÷ 107! 3!

110C3 = (110 * 109 * 108) / (3 * 2 * 1)

110C3 = 1294920 / 6

= 215820 ways

Answer:

Option (A)

Step-by-step explanation:

Two bases of the the given cylinder are circular in shape in the given picture.

When we take a cross-section of the cylinder parallel to the bases or perpendicular to the height, we get a circle exactly same as the bases (As shown on the rectangular slide).

Cross-section will have the same radius as the bases of the cylinder.

Therefore, Option (A) will be the answer.

Answer:

2675 +2V10

Step-by-step explanation:

Answer:

D :)

Step-by-step explanation:

did on edge 2021

Answer:

Both the relations are functions, the correct answer is a.

Step-by-step explanation:

In order to solve this problem we will first find the inverse relation as shown below:

[tex]y = 3x^2 + 5\\x = 3y^2 + 5\\3y^2 = x - 5\\y^2 = \frac{x - 5}{3}\\y = \sqrt{\frac{x - 5}{3}} = \frac{\sqrt{x - 5}}{\sqrt{3}}\\y = \frac{\sqrt{x - 5}\sqrt{3}}{\sqrt{3}\sqrt{3}} = \frac{\sqrt{3x - 15}}{3}[/tex]

Functions are relations between two groups of numbers, for which the input must generate only one output. Using this definition we can classify both the relation and its inverse as a function, therefore the correct answer is a.

Answer:

The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].

Step-by-step explanation:

Let suppose that one side of the rectangular area to be fence coincides with the contour of the river, so that only three sides are needed to be enclosed. The equations of perimeter ([tex]p[/tex]) and area ([tex]A[/tex]), measured in feet and square feet, are introduced below:

[tex]p = 2\cdot w + l[/tex]

[tex]A = w\cdot l[/tex]

Where [tex]w[/tex] and [tex]l[/tex] are the length and width of the rectangle, measured in feet.

Besides, let suppose that perimeter is equal to the given amount of fencing, that is, [tex]p = 500\,ft[/tex]. The system of equations is:

[tex]2\cdot w + l = 500\,ft[/tex]

[tex]A = w\cdot l[/tex]

Let is clear the length of the rectangle and expand the area formula:

[tex]l = 500\,ft-2\cdot w[/tex]

[tex]A = w\cdot (500\,ft-2\cdot w)[/tex]

[tex]A = 500\cdot w -2\cdot w^{2}[/tex]

To determine the maximum area that can be enclosed, first and second derivatives to obtain the critical values that follow to an absolute maximum.

First derivative

[tex]A' = 500 - 4\cdot w[/tex]

Second derivative

[tex]A'' = -4[/tex]

Now, let equalize the first derivative to zero, the only critical value is:

[tex]500-4\cdot w = 0[/tex]

[tex]4\cdot w = 500[/tex]

[tex]w = 125\,ft[/tex]

Since the second derivative is a negative constant function, then, the previous outcome follows to an absolute maximum. The length of the rectangular area is: ([tex]w = 125\,ft[/tex])

[tex]l = 500\,ft - 2\cdot (125\,ft)[/tex]

[tex]l = 250\,ft[/tex]

The dimensions of the rectangular pen that maximize the area are [tex]w = 125\,ft[/tex] and [tex]l = 250\,ft[/tex].

Answer:

$17,028.06

Step-by-step explanation:

Given that :

Kaylee's down payment = $4500

monthly payment = $300

If he can finance a vehicle with a 7%, 4-year loan (assume a 0% tax rate).

the  maximum amount Kaylee can afford to spend on the car is being calculated as the present value for all the payments.

= [tex]=\$4,500 +\dfrac{\$300}{(1+\frac{0.07}{12})} + \dfrac{\$300}{(1+\frac{0.07}{12})^2} +\dfrac{\$300}{(1+\frac{0.07}{12})^3} + ....+ \dfrac{\$300}{(1+\frac{0.07}{12})^{46}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{47}}+ \dfrac{\$300}{(1+\frac{0.07}{12})^{48}}[/tex]

Using the online desmos calculator to determine the maximum amount Kaylee can afford to spend on the car; we have:

= $17,028.06

Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Find the angle between the given vectors to the nearest tenth of a degree.

u = <8, 7>, v = <9, 7>

we will be using the formula below to calculate the angle between the two vectors;

[tex]u*v = |u||v| cos \theta[/tex]

[tex]\theta[/tex] is the angle between the two vectors.

u = 8i + 7j and v = 9i+7j

u*v = (8i + 7j )*(9i + 7j )

u*v = 8(9) + 7(7)

u*v = 72+49

u*v = 121

|u| = √8²+7²

|u| = √64+49

|u| = √113

|v| = √9²+7²

|v| = √81+49

|v| = √130

Substituting the values into the formula;

121= √113*√130 cos θ

cos θ = 121/121.20

cos θ = 0.998

θ = cos⁻¹0.998

θ = 3.6° (to nearest tenth)

Hence, the angle between the given vectors is 3.6°

Answer:

>There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.

>There is no correlation between playing time and number of goals.

Hope this helps....

Have a nice day!!!!

Answer:

q = 4 mi

Step-by-step explanation:

Using the sine or cosine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{q}{4\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

[tex]\sqrt{2}[/tex] × q = 4[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )

q = 4

Answer:

x= -4   x= 3

Step-by-step explanation:

x2 + x-12 = 0

Factor

What 2 numbers multiply to -12 and add to 1

4 * -3 = -12

4+3 = 1

( x+4) ( x-3) =0

Using the zero product property

x= -4   x= 3

Answer:

E, F

Step-by-step explanation:

x² + x - 12 = 0

Let’s factor left side.

Find 2 numbers that multiply to get -12 and add to get 1

4 ×  -3 = -12

4 + 3 = 1

x² - 3x + 4x - 12 = 0

x(x - 3) + 4(x - 3) = 0

(x + 4)(x - 3) = 0

Set factors equal to 0.

x + 4 = 0

x = -4

x - 3 = 0

x = 3

Answer:

D. 4√2

Step-by-step explanation:

A triangle with 45°, 45°, and 90° is a special right triangle.

hypotenuse = √2 · leg

1. Set up the equation

8 = √2 · x

2. Divide by √2 and solve

x = [tex]\frac{8}{\sqrt{2} }[/tex] · [tex]\frac{\sqrt{2} }{\sqrt{2}}[/tex] = [tex]\frac{8\sqrt{2} }{2}[/tex] = 4√2

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 ​minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72​, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N([tex]\mu=72, \sigma^{2} =23^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 ​minutes is given by = P(X > 82 min)

       P(X > 82 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{82-72}{23}[/tex] ) = P(Z > 0.43) = 1 - P(Z [tex]\leq[/tex] 0.43)

                                                           = 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{13} } }[/tex] ) = P(Z > 1.57) = 1 - P(Z [tex]\leq[/tex] 1.57)

                                                           = 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let [tex]\bar X[/tex] = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

                            Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 72 minutes

           [tex]\sigma[/tex] = standard deviation = 23 minutes

           n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 ​minutes is given by = P([tex]\bar X[/tex] > 82 min)

       P([tex]\bar X[/tex] > 82 min) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{82-72}{\frac{23}{\sqrt{34} } }[/tex] ) = P(Z > 2.54) = 1 - P(Z [tex]\leq[/tex] 2.54)

                                                           = 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 ​minutes, then we conclude that the population mean must be more than 72​, since the probability is so low.

Answer:

Step-by-step explanation:

From the given data

mean, u = 72

Standard deviation [tex]\rho[/tex] = 23

A) Probability that a randomly selected time interval between eruptions is longer than 82​minutes

[tex]P (x > 82) = P[\frac{x-u}{\rho} > \frac{82-72}{23}]\\\\P (x > 82) = P[z > 0.43]\\\\P (x > 82) = 0.3336[/tex]

B)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{13}}}]\\\\P (x > 82) = P[z > 1.5676]\\\\P (x > 82) = 0.0594[/tex]

C)

[tex]P (x > 82) = P[\frac{x-u}{\frac{\rho}{\sqrtn}} > \frac{82-72}{\frac{23}{\sqrt{34}}}]\\\\P (x > 82) = P[z > 2.5351]\\\\P (x > 82) = 0.0057\\\\[/tex]

D) If the mean is less than 82minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes decrease because the variability in the sample mean decrease as the sample size increases

For more information on this visit

https://brainly.com/question/17756498

Answer:

The points of the image are;

E'(5, 1), D'(5, -1), C'(1, 0), E'(-2, -3)

Step-by-step explanation:

The coordinates of the preimage are E(-5, -1) D(-5, 1) C(-1, 0) B(-2, -3)

Rotation of a point 180° about the origin gives;

Coordinates of the point of the preimage before rotation = (x, y)

The coordinates of the image after rotation = (-x, -y)

Therefore, the coordinates of the points EDCB after 180° rotation about the origin are;

E(-5, -1) rotated 180° becomes E'(5, 1)

D(-5, 1) rotated 180° becomes D'(5, -1)

C(-1, 0) rotated 180° becomes C'(1, 0)

B(-2, -3) rotated 180° becomes E'(-2, -3).

Answer:  y = 23x - 62

Step-by-step explanation:

Parallel lines have the same slope.

y = 23x + 4

  m=23   b=4

Input x = 3, y = 7, & m = 23 into the Point-Slope formula to find the equation or the Slope-Intercept formula to find b (you already have m).  I will choose the latter.

 y = mx + b

 7 = 23(3) + b

 7 = 69 + b

-62 = b

m = 23, b = -62  -->  y = 23x - 62

Answer: x=30

Step-by-step explanation: if you were looking for the value of x, hope this helps!

first, you have to make sure that the correct values are on the right side to allow us to find the answer faster and easier. your modified formula should look like this: 4x-3.2x=11+13

if you do the operations on each side, it will look like this: 0.8x=24, from here, all you have to do now is divide 24 by 0.8 to get the X value, which will result in 30!

Step-by-step explanation:

An algebraic expression haa atleast one variable and operator sign such as (+,-,×,÷)

According to the question, an algebraic expression should be made from difference of 'a' and 'b'

so, the expression is (a - b) or a - b.

Hope it helps!!!!

Answer:

last answer

Step-by-step explanation:

P' (2, -4)

Q' (-2, -5)

R' (1, -8)

Answer:

C. P'(2, -4) Q'(-2, -5) R'(1, -8)

Step-by-step explanation:

When you reflect something across the y-axis you change (x,y) to (-x,y).

For each point, change the x to a negative x.

P(-2, -4) --> P'(2, -4)

Q(2, -5) --> Q'(-2, -5)

R(-1, -8) --> R'(1, -8)

Hope this helps. If you have any follow-up questions, feel free to ask.

Have a great day! :)

Answer:

y = -5x - 9.

Step-by-step explanation:

(-2, 1)

(0, -9)

(1 - -9) / (-2 - 0) = (1 + 9) / (-2) = 10 / (-2) = 5 / (-1) = -5

Since -5 is the slope, and the y-intercept is at (0, -9), we have an equation of y = -5x - 9.

Hope this helps!

Answer:

y=-5x-9

Step-by-step explanation:

Change in x = +2

Change in y=-10

-10/2=-5

m=-5

plug in an point

example:

1=-5(2)+B

B=-9

To check your answer:

y=-5x-9

plug in an point for x given on the chart:

-5(0)-9=-9

Answer:

12-5=7

unless it's not a prank or a joke question

Answer:

7

Step-by-step explanation:

Original number of monkeys = 12

Number taken away = 5

So, number left = 12-5 = 7.

Hope this helps.

Answer:

X = 5

Y = 7

Step-by-step explanation:

First we will find x

4x + 2 = 3x + 7

x + 2 = + 7

x = 5

Next we will find y

2y + 9 = 4y - 5

-2y + 9 = -5

-2y = -14

y = 7

Answer;

The relevant probability is 0.136 so the value of 56 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05

Step-by-step explanation:

The complete question is as follows;

For 100 births, P(exactly 56 girls = 0.0390 and P 56 or more girls = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less V so 56 girls in 100 birthsa significantly high number of girls because the relevant probability is The relevant probability is 0.05

Solution is as follows;

Here. we want to know which of the probabilities is relevant to answering the question and also if 56 out of a total of 100 is sufficient enough to provide answer to the question.

Now, to answer this question, it would be best to reach a conclusion or let’s say draw a conclusion from the given information.

The relevant probability is 0.136 so the value of 56 girls in 100 births is not a significantly high number of girls because the relevant probability is greater than 0.05

Answer:3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

AHH! Geometry!

Thanks for this problem. Needed to refresh my skill for similarity and rations.

First, notice the lines that are on sides of the triangles. Lines with the same number of marks are the same measure. You may have already known this, but I'll just tell you for reference.

That means both of those pair of sides have equal length. What does this mean though?

Imagine that each of the line segments(the ones with two marks) are... 1 cookie (Their lengths, also, I really want a cookie.)

Now, this is where ratios come into play. Consider only the top triangle to the entire triangle. The Top Triangle has a side with the length of one cookie. That corresponding side on the entire large one is 2 cookies (because they are the same measure, and 1*2=2).

Thus, we can make a ratio, comparing the lengths of a corresponding sides.

(BTW, these are similar triangles, meaning that they have all the same angle measures, but different side lengths.)

[tex]\frac{1Cookie}{2Cookies}[/tex]

Now. (Refer to above) Similar triangles have ratios of similarity. Meaning that: Corresponding sides have a 1/3 ratio. This means, also, that all the other corresponding sides have a 1/3 ratio. Neat, huh?

Putting into other words, we can compare CB and RT with the same 1/2 ratio!(Just cancel out the cookies, its still the same ratio)

Now, that we have all our needed information, let's solve!(Also, remember to match it up properly, or else it won't work: Small triangle side/Small Triangle side=Large Triangle Side/Large Triangle Side, or something like that).

[tex]\frac{1}{3x-8} =\frac{2}{2x+4} \\2x+4=6x-16\\4x=20\\x=5[/tex]

^ ANSWER

So there you go! X is equal to 5. I'm sure you can solve the rest on your own!

Hope this helps!

Stay Safe! I'm going to get that cookie now...