Use the given information to prove that ΔRST ≅ ΔVUT.
Given: ST ≅ UT
∠SRT ≅ ∠UVT
Prove: ΔRST ≅ ΔVUT

The simplified expression is  c²a³ - 3[tex]a^4[/tex]c +  a²bc² - a³bc  - 3[tex]a^4[/tex]b+ 4ab²c² - 22a²b²c + 36a³b + 12a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²).

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

c +6b/(-2bc-6ab- 3a²) + 2b/(a² + 2ab) - b/(ac - 3a²)

Now, simplifying

(c+ 6b) (a² + 2ab)(ac - 3a²) + 2b(-2bc-6ab- 3a²)(ac - 3a²)- b (-2bc-6ab- 3a²)(a² + 2ab) / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= ca² + abc + 6a²b + ab² (ac - 3a²) + (4b²c - 12ab² - 6a²b)(ac - 3a²) - ( -2b²c - 6ab² - 3a²b)(a² + 2ab) / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= c²a³ - 3[tex]a^4[/tex]c + a²bc² - 3a³bc + 6a³bc - 18[tex]a^4[/tex]b + 4ab²c² - 12a²b²c - 12 a²b²c+ 36a³b - 6a³bc + 18[tex]a^4[/tex]b + 2a²b²c +  4a³bc + 6a³b² + 12a²b³  - 3[tex]a^4[/tex]b + 6a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

= c²a³ - 3[tex]a^4[/tex]c +  a²bc² - a³bc  - 3[tex]a^4[/tex]b+ 4ab²c² - 22a²b²c + 36a³b + 12a³b² / (-2bc-6ab- 3a²)(a² + 2ab)(ac - 3a²)

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Answer: 3m+4=6m is the false equation

Step-by-step explanation:

Substitute 5 into the 4 equations to find whether they are true or false

3(5)+4=6(5)

15+4=30

19[tex]\neq[/tex]30 False

-5(5-7)=10

-5(-2)=10

10=10 true

17=4(5)-3

17=20-3

17=17 True

5+9=14

14=14 True

3m+4=6m is the false equation

We reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

Given that,

Consider an NFL team that says the average weight of its defensive players is 315 pounds. A opposing team believes that their defensive players' average weight is lower than the 315 pounds they state. Consider that they take 15 defensive players as a sample and discover that the average weight of the players is 300 pounds, with an 8-pound sample standard deviation.

We have to create a suitable hypothesis test, draw conclusions at significance level 0.08, and then. Suppose that the weights are evenly distributed.

We know that,

Weights are normally distributed.

We are given μ = 315 , n= 15 , x = 300, s = 8, α = 0.08

The hypothesis are :

H₀ : μ = 315   v/s  H₁ : μ ≠ 315

The test statistic is given by,

z=x-μ/σ/√15

=300-315/8/√15

=-7.26

The critical value = z(α)  = z(0.04) = -1.75 and z(1-α)  = z(1-0.04)  = 1.75

Here calculated value of z > critical value of z

Therefore, we reject null hypothesis when hypothesis test, draw conclusions at significance level 0.08.

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Answer:

Answer:

Below

Step-by-step explanation:

Domain is the set of values x can be for a function .....it looks like this one goes from -2 to 2 with asymptopes at these values:

-2< x < 2  

Range is the 'y' values a graph can have...this one goes from -1.5 -ish to 5.5 ish    

-1.5 <= y <= 5.5

Here is the graph with some lines on it:

The doubling time is approximately 83 years. This means that it will take approximately 83 years for the squirrel population to double from its initial size of 450 squirrels.

What is an exponential function?

An exponential function is a function in which the variable appears in the exponent. Exponential functions have the form y = ab^x, where a and b are constants and x is the variable. The constant b is called the base of the exponential function.

The given information states that the squirrel population P(t) follows a logistic growth model with a growth constant k = 0.8 yr-1 and a carrying capacity of 1800 squirrels. The formula for the squirrel population P(t) can be found using the logistic growth model:

P(t) = K / (1 + (K/P0 - 1) * e^(-kt))

where P0 is the initial population of squirrels, K is the carrying capacity, and t is time in years.

Substituting the given values into the formula, we get:

P(t) = 1800 / (1 + (1800/450 - 1) * e^(-0.8t))

Simplifying the equation, we get:

P(t) = 1800 / (1 + 3e^(-0.8t))

This is the formula for the squirrel population P(t).

To find the doubling time (the time it takes for the squirrel population to double), we need to find the time t at which the squirrel population reaches twice the initial population of 450 squirrels. This can be represented by the equation:

2 * 450 = 1800 / (1 + 3e^(-0.8t))

Solving for t, we get:

0.8t = ln(3)

t = ln(3) / 0.8

Hence, the doubling time is approximately 83 years. This means that it will take approximately 83 years for the squirrel population to double from its initial size of 450 squirrels.

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To compare the sampling distribution, first I would simulate the machine by randomly generating n number of samples between 8 and 10 oz with a uniform distribution and calculate the 4th spread for each sample size. I would then repeat this experiment multiple times and take the average of the fourth spread values for each sample size to compare the sampling distributions.

To compare the sampling distributions of the fourth spread for sample sizes n = 5, 10, 20, and 30, I would simulate the machine by randomly generating samples between 8 and 10 oz with a uniform distribution. For each sample size, I would calculate the fourth spread for each sample and then repeat the experiment multiple times. Finally, I would take the average of the fourth spread values for each sample size to compare the sampling distributions. This way, I would be able to see how the fourth spread changes as the sample size changes. It would also allow me to see how the fourth spread is affected by the uniform distribution of the machine's output.

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Although part of your question is missing, you might be referring to this full question: Write an expression that describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. –1, 0, 1, 2, ...

The expression that describes the given sequence is: aₙ = –2 + n

This is an arithmetic sequence. Arithmetic sequence is a sequence of numbers in which every term (except the first term) is provided by adding a constant number to the previous term.

An arithmetic sequence can be defined by an explicit formula in which aₙ = d (n – 1) + c, where d is the common difference between consecutive terms, and c = a₁.

In this case, the given sequence is –1, 0, 1, 2, ...

This is an arithmetic sequence with common difference.

Because of:

0 – (–1) = 1

1 – 0 = 1

2 – 1 = 1 …

Then, a₁ = –1

Now, substitute the value of a₁ = –1, d = 1 into the formula.

aₙ = d (n – 1) + c

aₙ = 1 (n – 1) + (–1)

aₙ = n + (–2)

aₙ = –2 + n

Hence, the expression that describes the given sequence is: aₙ = –2 + n.

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The table with constant of proportionality between x and y is table A

We should be able to know that constant of proportionality shows a type of relationship between two variables that shows a constant relationship or same ratio.

The given fraction is 8/5

Rewrite 8/5 as a ratio of two numbers

8:5

Constant of proportionality is written as

y=k/x

Making k the subject, k=y/x

Where k is a constant.

From table A,

The constant  (K) is 4/1 = 4:1

Now multiply 4*8=32

8*1=5

Therefore 32/5 is a proportion of 8/5

Also using the constant k=10

⇒10:1   Then 10*8=80

And 1*5=5

⇒ 80/5=16

Also in the last constant K=11, we have 11:1

⇒[tex]\frac{11*8}{1*5}[/tex] =88/5

In conclusion option A gives the table that has constant of proportionality to 8/5

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The answer is √7.

What is Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Step-by-step explanation:

Using the pythagorean theorem, we know that

     a^2 + b^2 = c^2

In this case,

c = 4, which means that a^2 + b^2 = 16

Since we know that a = 3, this means that a^2 is also 9. So, we know that b^2 = 16-9

Therefore, b^2 = 7

So, the answer is √7.

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The quadrilateral abcd is a parallelogram because the slopes of opposite sides are equal.

In the given figure we have a quadrilateral  ABCD with A (-2,-2) , B(-3,4), C(2,2)

and D(3,-4).

We know that when the slope of two lines are equal then they are parallel.

In the given figure, Slope of BC= Slope of AD =

⇒ BC and AD are parallel .

Also, Slope of CD= Slope of BA =-6

⇒ CD and BA are parallel .

ABCD is a parallelogram because both pairs of opposite sides are parallel.

Hence, the correct reason for the given space is "slopes of opposite sides are equal"

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Answer:

Step-by-step explanation:

what is your question?

y = mx + b where m is the rate of change and b is the y-intercept, describes the linear relationship between rise in temperature (y) and change in time (x) from 6 to 24 minutes.

To calculate the linear equation, we can use the Point-Slope Form of a Line formula, y = mx + b. To find the slope (m), we must calculate the rise (change in the y-value) over the run (change in the x-value). We must calculate the temperature difference between 6 minutes (T1) and 24 minutes (T2). Then, divide the temperature difference by the time difference of 18 minutes. The y-intercept (b) can be found by plugging in the known x and y values of 6 minutes and T1 respectively into the equation y = mx + b. Once we have the slope and y-intercept, we can plug them into the equation y = mx + b to calculate the equation that describes the linear relationship between the rise in temperature (y) and change in time (x) from 6 to 24 minutes.

y = mx + b, where

m = (T2 - T1)/(24 - 6) = (T2 - T1)/18

b = T1 - (m*6)

Therefore,

y = (T2 - T1)/18 * x + (T1 - (m*6))

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The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 foot

The surface area of the box = [tex]225[/tex] [tex]ft^{2}[/tex]

Weight of the metal = 1125 kg

According to the question,

Given value = [tex]500[/tex] [tex]ft^{3}[/tex] tanks is to be built which has to be a square-based rectangle steel holding tank.

For this, we have to know the total surface area of the box,

Surface area (A) = 4 x sides of the rectangle + square base -- equation 1

Let's take the width of the square base = p

And let height = h

Since we know that,

Rectangle sides = p x h

Square base ⇒ p x p = [tex]p^{2}[/tex]

Substituting these values in equation 1,

Surface area ( A ) = 4 x ( p x h ) + [tex]p^{2}[/tex] ---- equation 2

The formula for calculating the volume of the box,

V = p x p x h

V = [tex]p^{2}[/tex] x h --- equation 3

Referring to the question that the value of the volume is already given such that volume = [tex]500[/tex] [tex]ft^{3}[/tex]

So, V = [tex]500[/tex] [tex]ft^{3}[/tex]

Putting the value of V in equation 3,

500 = [tex]p^{2}[/tex] x h

h = [tex]\frac{500}{p^{2} }[/tex] ---- equation 4

Substituting the value of h from equation 4 to equation 2,

A = 4 x ( p x [tex]\frac{500}{p^{2} }[/tex] ) + [tex]p^{2}[/tex]

⇒ A = [tex]\frac{2000}{P}[/tex] + [tex]p^{2}[/tex]

We will be taking the derivative of the above equation,

⇒ A' = - [tex]\frac{2000}{p^{2} }[/tex] + 2p

Now we will be minimizing A,

⇒ 0 = - [tex]\frac{2000}{p^{2} }[/tex] + 2[tex]p[/tex]

⇒ [tex]\frac{2000}{p^{2} }[/tex] = 2[tex]p[/tex]

⇒ 2000 = 2[tex]p^{3}[/tex]

⇒ 1000 = [tex]p^{3}[/tex]

⇒ p = [tex]\sqrt[3]{1000}[/tex]

⇒ p = 10 foot

Substituting the value of p in equation 4,

⇒ h = [tex]\frac{500}{10^{2} }[/tex]

⇒ h = [tex]\frac{500}{100}[/tex]

⇒ h = 5 foot

Substituting values in the area of the square box,

A = 4 x (10 x 5) + [tex]5^{2}[/tex]

A = 200 + 25

A = 225 [tex]ft^{2}[/tex]

The weight of the metal,

⇒ weight = A x weight per square foot

⇒ weight = 225 x 5

⇒ weight = 1125 kg

Therefore, The dimensions we will tell the shop to use are ⇒ Volume =  10 x 10 x 5 feet

The surface area of the box = 225 [tex]ft^{2}[/tex]

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The probability is 0.7888.

Standard error of the mean [tex]$\sigma_{\bar{x}}=20$[/tex]

The population standard deviation (σ)=500

Standard deviation of [tex]$\bar{x}$[/tex] is given by:

[tex]\sigma_{\bar{x}} & =\frac{\sigma}{\sqrt{n}} \\\\\Rightarrow 20 & =\frac{500}{\sqrt{\mathrm{n}}} \\\\\Rightarrow n & =\left(\frac{500}{20}\right)^2 \\[/tex]=625

Probability that the point estimate [tex]$\bar{x}$[/tex] was within ±25 of the population mean is: [tex]$$p(\mu-25 < \bar{x} < \mu+25)$$[/tex]

At [tex]$\bar{x}[/tex]=μ-25, we have

[tex]z & =\frac{-25}{20} \\[/tex]=-1.25

Z=-1.25

At [tex]$\bar{x}[/tex]=μ+25, we have

[tex]z & =\frac{25}{20} \\[/tex]=1.25

Z=1.25

So the required probability is:

[tex]$$\begin{aligned}p(\mu-25 < \bar{x} < \mu+25) & =p(-1.25 < z < 1.25) \\& =p(z < 1.25)-p(z < -1.25) \\\end{aligned}$$[/tex]

                                     =0.8944-0.1056

                                     =0.7888

Therefore, probability that point estimate is within ±25 population mean is 0.7888.

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A researcher reports survey results by stating that the standard error of the mean is 20 . The population standard deviation is 500 . How large was the sample used in this survey

a. What is the probability that the point estimate was within ±25 of the population mean?

6 + 12^2

12 squared would be 12 to the second power

since the directions say "the sum"

you would use addition to add 6 and 12^2

The value of x in the equation, 3/4x + 6 - 1/4x = 2/4x + 9, is: x = -2.

Solving an equation involves finding the value of the variable in the equation. The value, when plugged into the equation would make it true.

The equation given is, 3/4x + 6 - 1/4x = 2/4x + 9, to solve for the value of x, follow the steps below:

3/4x + 6 - 1/4x = 2/4x + 9 [given]

Combine like terms:

3/4x - 2/4x - 1/4x = 9 - 6

(3 - 2 - 1)/4x = 3

-6/4x = 3

Simplify

-3/2x = 3

Multiply both sides by -2/3:

-3/2x × -2/3 = 3 × -2/3

x = -6/3

x = -2

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The money left is $5000 - $2000 = $3000 will be earned through an internship.

To subtract in mathematics is to take something away from a group or a number of objects.

In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.

As per the given,

Money earned in award = $2000

Money had at the end of saving account = $5000

Money earned by internship = $5000 - $2000 = $3000

Hence "$3000 of the remaining $5000 will be earned through an internship".

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According to the statement above, The Hamden board of education called every tenth person on the registration list. The sample is not randomly chosen (FALSE)

Given that the statement doesn't tell us anything about the way they choose the sample, it is reasonable to conclude that this is a randomly chosen. They called every tenth person on the registration list until the number of people was 40.

The sample should be larger to give more reliable information (TRUE)

We did not have to use mathematics to determine that you would need more information to get a conclusion. You must increase the sample, that is, the sample must be larger to give a reliable information.

The sample size is too large to make inferences (False)

This is explained in the previous item. If the sample should be lager is because the size is not too large.

The sample size is too small to represent the population (TRUE

This is true because 40 voters represent barely 0.5% of the entire list. This list has 7300 voters, so getting the conclusion from this sample doesn't provide with a strong conclusion.

The sample size is too small and will show larger variation. (FALSE)

Although the sample size is too small, the sample size not necessarily will show variation. In fact, it is possible that it does not show any variation and most of the people feel well about building a new media center for the middle school but it doesn't mean that the whole community does.

The sample is invalid because it randomly chooses voters. (FALSE)

It is false because in probability studies the sample is chosen randomly, so you get conclusions about the whole population always taking samples that represent the population as a whole.

The sample size is too small and can lead to false inferences (TRUE)

We can get false conclusions given that the sample size is too small. It's important to note that the sample size supports the conclusion of the study, so the sample must increase to have a reliable study.

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The charge for cutting a board into 8 equal pieces is $1.2

Equate charges for cutting board : Number of equal pieces

0.60 : 4 = x : 8

0.60/4 = x / 8

cross product

0.60 × 8 = 4 × x

4.8 = 4x

divide both sides by 4

x = 4.8 / 4

x = 1.2

Therefore, it will cost $1.2 for cutting a board into 8 equal pieces.

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With regards to the function model then the true statement as per first and second derivatives is: (C) dw/dt = 1/100 W  (70 - W),

When, W = 10 then dw/dt = 6

When W = 35 then d²w/d²t = 0

where the point influx occurs, the weight of the carrying capacity is half

Therefore, 35 = a/2

Then the carrying capacity (a) = 35 x 2

a = 70

A function's sensitivity to change with respect to a change in its argument is measured by the derivative of a function of a real variable. Calculus's core tool is the derivative. It is a crucial idea that is incredibly helpful in a variety of contexts: in daily life, the derivative can inform you how fast you are driving or assist you in predicting stock market changes; in machine learning, derivatives are crucial for function optimization.

Therefore, with regards to the function model then the true statement as per first and second derivatives is: (C) dw/dt = 1/100 W  (70 - W), because the carrying capacity is 70 and the rate of change of the weight is 6 grams per hour when the weight is 10 grams.

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The ordered pair for the vertices for r(90°, s)(QRST) include the following:

Q' = (-5, 1)

R' = (-3, -1)

S' = (0, 0)

T' = (-3, -2)

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

Note: The point S represents the center (origin) of this geometric figure.

By applying a rotation of 90° counterclockwise to the vertices for r, the coordinates of the vertices of the image point r' are as follows:

(x, y)                               →            (-y, x)

Ordered pair Q  = (1, 5) → Ordered pair Q' = (-5, 1)

Ordered pair R = (-1, 3) → Ordered pair R' = (-3, -1)

Ordered pair S = (0, 0) → Ordered pair S' = (0, 0)

Ordered pair T = (-2, 3) → Ordered pair T' = (-3, -2)

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The method that would be the most straight forward for her to use would be the substitution method because you can easily solve one equation for a variable. That is option A.

The substitution method for solving equations is the method that can be used in a quadratic equation whereby one equation is solved and substituted into the next equation.

The given equation such as;

4x - 5y = 7 ---> eq 1

4X -9y = -4---> eq 2

From eq1 make 4x the subject of formula

4x = 7 + 5y

Substitute for 4x in equation 2;

7 + 5y - 9y = -4

7 - 4y = -4

7+4 = 4y

11 = 4y

y = 11/4

y = 2.75

Then substitute y = 2.75 into equation 1;

4x - 5y = 7

4x - 5(2.75) = 7

4x - 13.75 = 7

4x = 7 + 13.75

4x = 20.75

X = 20.75/4

X = 5.2

Therefore with the substitution method the value of X and y can be determined.

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Answer:  [tex]5.8\times 10^4[/tex]

Reason:

Place the decimal point between the 5 and the 8. So we have the value 5.8

To get back to 58000, we need to move the decimal point 4 spots to the right. This is why we have 4 as the exponent over 10.

All scientific notation values are of the form [tex]a \times 10^b[/tex]

where [tex]1 \le a < 10[/tex] or [tex]-10 < a \le 1[/tex]

The b value is an integer.

Answer:

6*3 + 6*2

6*5

6(3+2)

Step-by-step explanation:

All of these equations lead to the same answer which is 30.

The two diagrams are basically the same but they are just separated apart. When you look for the area of both diagrams, it leads to the same answer.

Answer:

Step6x3 = 18. And. 2x6 = 12. Then you add the amounts, 18+12 = 30-by-step explanation:

Answer:

y- intercept = - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{5}{3}[/tex] x - 6 ← is in slope- intercept form

with y- intercept c = - 6

The value of b must be equal to -14, so that the function has at least one inflection point. Hence, option B is correct.

Expressions are mathematical operations that involve at least two terms connected by an operator and can be either integers, variables, or both. The operations with reflection coefficients are addition, subtraction, multiplication, and division. 

As per the instruction given in the question,

The given function,

f(x) = x⁴ + bx² + 1

Differentiate with respect to x,

f'(x) = 4x³ + 2xb

Again differentiate with respect to x,

f''(x) = 12x² + 2b

For inflection point, f''(x) = 0

12x² + 2b = 0

2b = -12x²

b = -6x²

x = √-b/6, x ∈ [1, 2]

Let's assume that b = -28

x = √-(-28)/6

x = √28/6

x = √14/3, here x ∉ [1, 2], hence it is incorrect.

If b = -14

x = √-(-14)/6

x = √14/6

x = √7/3 ≈ 1.82, here x ∈ [1, 2], hence it is correct.

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The answer is false. The covariance statistic gauges how closely two variables are related to one another.

a connection between two quantitative variables in which the corresponding values of the second variable tend to rise when the value of the first variable tends to rise (or fall) (or decrease).

The direction of the link between two variables is measured by covariance. A positive covariance indicates that both variables frequently exhibit high or low values together. While two variables have a negative covariance, they are often low when one is high.

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The regular polygon has 20 sides.

The regular pentagon is a regular polygon with five sides

The regular decagon is a regular decagon with ten sides

The angle sum around a point adds to 360 degrees.

Each interior angle of the square is 90 degrees

Each interior angle of the regular pentagon is 108 degrees.

The Interior angle of our unknown polygon is 360 - 108 - 90 = 162 degrees.

A quick calculation shows us that the exterior angle of this polygon is 18 degrees.

The sum of the external angles of any regular polygon is 360 degrees

Divide 360 by 18 and you get 20 times.

Thus our unknown polygon has 20 sides.

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Answer:

D

Step-by-step explanation:

6^(4+0) = 6^4

6^(-10) : 6^4

6^(-10-4)

6^(-14)

1/6^(14)

Answer:

y = -4/3x + 10

Step-by-step explanation:

A line with a slope of -4 over 3 that passes through the point (6,2) can be written in slope-intercept form as:

y = (-4/3)x + b

To find the value of b, we can plug in the coordinates of the given point (6,2) into the equation and solve for b:

2 = (-4/3)(6) + b

2 = -8 + b

b = 10

Therefore, the equation of the line in slope-intercept form is:

y = (-4/3)x + 10