Radical word problem help

Answer:

15. x = -3.

16. x = -2.

17 x = 2.

Step-by-step explanation:

To solve the equation 7x + 5 = 12x - 10, we want to isolate the variable x on one side of the equation. We can do this by adding or subtracting terms from both sides of the equation until we have x by itself.

First, let's simplify both sides of the equation by combining like terms:

7x + 5 = 12x - 10

-7x -7x (subtracting 7x from both sides)

5x + 5 = -10

Next, let's isolate the term with x by subtracting 5 from both sides of the equation:

5x + 5 = -10

-5 -5 (subtracting 5 from both sides)

5x = -15

Finally, let's solve for x by dividing both sides of the equation by 5:

5x = -15

x = -3

Therefore, the solution to the equation 7x + 5 = 12x - 10 is x = -3.

26 = 24 - x

-24 -24 (subtracting 24 from both sides)

2 = -x

Next, let's isolate the variable x by multiplying both sides of the equation by -1:

2 = -x

-1 -1 (multiplying both sides by -1)

-2 = x

Therefore, the solution to the equation 26 = 24 - x is x = -2.

2(6x - 7) = 10

12x - 14 = 10

Next, let's isolate the term with x by adding 14 to both sides of the equation:

12x - 14 = 10

+14 +14 (adding 14 to both sides)

12x = 24

Finally, let's solve for x by dividing both sides of the equation by 12:

12x = 24

x = 2

Therefore, the solution to the equation 2(6x - 7) = 10 is x = 2.

Answer:

$29.34.

Step-by-step explanation:

To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:

Current balance = previous balance + new charge

Current balance = $319 + $170

Current balance = $489

The minimum payment is 6% of the current balance:

Minimum payment = 6% x current balance

Minimum payment = 6% x $489

Minimum payment = $29.34

Therefore, the minimum payment on the credit card would be $29.34.

Answer:

$29.34.

Step-by-step explanation:

To calculate the minimum payment, we need to find the current balance, which is the sum of the previous balance and the new charge for the Christmas presents:

Current balance = $319 + $170 = $489

Minimum payment = 6% x $489 = $29.34

The minimum payment on the credit card would be $29.34.

Hope this helped, have a GOOD DAY!!!!!

The value of the variable(s) in the figure is  60°, explaination is given below.

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that function at those values of the considered variables.

We are given that;

The variables; (5y)⁰,(2x)°,120⁰,1080

Now,

The first two expressions are both equal to 1, because any number raised to the power of 0 is always 1.

The third expression, 120°, is an angle measurement in degrees. In a triangle, the sum of the interior angles is always 180°. So, if we let x and y be the other two angles in the triangle, we have:

x + y + 120° = 180°

Simplifying this equation, we get:

x + y = 60°

Therefore, the answer of the given function will be  60°.

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Answer:

11° 33'

Step-by-step explanation:

[tex]21' = \left(\dfrac{21}{60}\right)^\circ = \left(\dfrac{7}{20}\right)^\circ \\50^\circ 21' = 50 \dfrac{21}{60}\; degrees\\\\38^\circ 48' = 38 \dfrac{48}{60} \;degrees[/tex]

Break
[tex]50 \dfrac{21}{60} = 49 + 1 \dfrac{21}{60}\\[/tex]

[tex]1 \dfrac{21}{60} = \dfrac{1 \times 60 + 21}{60} = \dfrac{81}{60}[/tex]

Therefore
[tex]50^\circ21' - 38^\circ48' = 49\dfrac{81}{60} - 38\dfrac{48}{60}[/tex]

Subtract the whole numbers:
49 - 38 = 11

Subtract the fractions:
[tex]\dfrac{81}{60} - \dfrac{48}{60} = \dfrac{33}{60} = 33'[/tex]

So

50°21' - 38°48' = 11° 33'

Answer:

17.24

Step-by-step explanation:

find the difference between 29 and 34. Then divide by 29 and multiply by 100. 34-29=5/29=0.1724 multiply by 100 =17.24%

The sum of their 3 prime numbers is 24.

Let's start by finding the prime numbers that Jimmy, Kimmy, and Timmy are thinking of.

We know that the product of Jimmy's and Kimmy's prime is 34. Since 34 is not a prime number, it must be the product of two prime factors.

The only way to factor 34 as a product of two primes is 2 x 17.

So we know that Jimmy's prime is either 2 or 17, and Kimmy's prime is the other one. We also know that Kimmy's and Timmy's primes multiply to 85. Again, 85 is not a prime number, so it must be the product of two prime factors.

The only way to factor 85 as a product of two primes is 5 x 17.

Therefore, we know that Timmy's prime is 5.

So the three primes are 2, 17, and 5.

The sum of these three primes is 2 + 17 + 5 = 24.

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Answer:

x = [tex]\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]7-2(3-8x)=7-6-16x[/tex]

Add/subtract like terms

[tex]5(3-8x)=1-16x[/tex]

Distribute 5

[tex]15-40x=1-16x[/tex]

Simplify

[tex]-40x+15=-16x+1[/tex]

Add -16x to both sides

[tex]-24x+15=1[/tex]

Subtract 15 on both sides

[tex]-24x=-14[/tex]

Divide by -24

[tex]x=\frac{7}{12}[/tex]

Answer:

So, Fatima's curtain company needs to purchase 248 feet of fabric to make the curtains for the local hotel.

Step-by-step explanation:

To find out how many feet of fabric Fatima's curtain company needs, we first need to calculate the total length of fabric required for all 62 curtains.

Each curtain is 48 inches long, so the total length of fabric required for one curtain is:

48 inches = (48/12) feet = 4 feet

Therefore, the total length of fabric required for 62 curtains is:

62 curtains x 4 feet/curtain = 248 feet of fabric

So, Fatima's curtain company needs to purchase 248 feet of fabric to make the curtains for the local hotel.

The value of y is given as follows:

y = 4.3 cm.

The value of y is obtained applying the two secant segment theorem, which means that the following equation will hold true:

3(3 + y) = 2(2 + 9).

(a secant is a segment that crosses the circumference of the circle twice, and the product has to be equal for each).

Then we apply the distributive property to each side of the equality, and then isolate the variable y, as follows:

9 + 3y = 22

3y = 13

y = 13/3

y = 4.3.

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Allison purchased lemons for $0.75 each.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is showing.

Now, Two point on the line are (4, 3) and (8. 6)

Hence, Equation of line is,

⇒ y - 3 = (6 - 3) / (8 - 4) (x - 4)

⇒ y - 3 = 3/4 (x - 4)

⇒ 4 (y - 3) = 3 (x - 4)

⇒ 4y - 12 = 3x - 12

⇒ 4y = 3x

⇒ y = 3/4x

⇒ y = 0.75x

Where, y is cost and x is number of lemons.

Hence, Allison purchased lemons for $0.75 each.

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Therefore , the solution of the given problem of domain comes out to be the appropriate domain for p(w) would be [1, 1000]

The domain of a function is the range of possible arguments that it can accept. The cross of the an f-like functional is represented by these numbers (x). The range of potential values to which a function can be applied is known as its domain. The value that the procedure returns after inserting the x value is part of this set. An equation for a function is Y = f, where y and x are predictor variables (x). When a given value of x can produce a single value of y, a parameter is said to be in the scope of a function.

Here,

Given :

1 kilogram to 1000 kilograms.

He charges $5 for 1 kilogram and $2000 for 1000 kilograms.

So,

The appropriate domain for p(w) would be [1, 1000]

since

Aiden sells any amount of cumin seeds from 1 kilogram to 1000 kilograms.

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The complete question is "Aiden is a spice trader. He sells any amount of cumin seeds from 1 kilogram to 1000 kilograms. He charges $5 for 1 kilogram and $2000 for 1000 kilograms.

p(w) models the price (in dollars) of w kilograms of cumin seeds in Aiden's shop. What's the appropriate domain?"

Answer:

A

Step-by-step explanation:

hope this helps

All the probabilities are solved and are mentioned below.

In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value

Given is that there is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by -

Pr(X = 0) = 0.55

Pr{X = 1) = 0.22

Pr(X = 2) = 0.13

Pr(X = 3) = 0.08

Pr(X = 4) = 0.02

We can find the probabilities as -

{ 1 } - the probability that two or fewer bits are transmitted in error :

P{E} = P(0) + P(1) + P(2)/∑P{n}

P{E} = 0.9/1

P{E} = 0.9

{ 2 } - the probability that at least one bit is transmitted in error -

P{E} = P(1) + P(2) + P(3) + P(4)/∑P{n}

P{E} = 0.45/1

P{E} = 0.45

{ 4 } - the expected value of the number of bits transmitted in error -

n = 0 + 1 + 2 + 3 + 4

n = 10

{ 4 } - the standard deviation of the number of bits transmitted in error -

σ = 1.0677

Therefore, all the probabilities are solved and are mentioned above.

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An expression for e[z] by the given data is  E[z] = (n-1)/n * H_n-1.

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_nT_{n+1} - T_n

for all positive integer values of n.

We are given that;

Balls are thrown uniformly and independently in all bins

Now,

We can express z as the sum of these binary random variables:

[tex]z = z_1 + z_2 + ... + z_{n-1}[/tex]

The random variables z_i are not independent, since the probability of throwing a ball into a bin that already has at least one ball in it depends on the number of balls already in the bin.

However, we can still use the linearity of expectation to calculate the expected value of z:

[tex]E[z] = E[z_1 + z_2 + ... + z_{n-1}][/tex]

By the linearity of expectation, we can distribute the expectation over the sum:

[tex]E[z] = E[z_1] + E[z_2] + ... + E[z_{n-1}][/tex]

Using these probabilities, we can calculate the expected value of each z_i:

[tex]E[z_i] = 1 * P(z_i=1) + 0 * P(z_i=0)= P(z_i=1)[/tex]

= (i-1)/n-i+1

Substituting this into the expression for E[z], we get:

[tex]E[z] = (1-1/n) + (2-1/n-1) + ... + (n-1-1/2)= (n-1)/n + (n-1)/n-1 + ... + 1/2[/tex]

This is a finite arithmetic series with n-1 terms, with first term (n-1)/n and common difference -1/n. Using the formula for the sum of an arithmetic series, we get:

[tex]E[z] = (n-1)/n + (n-2)/n + ... + 1/n= (n-1)/n * (1 + 1/2 + ... + 1/(n-1))[/tex]

This sum is known as the n-th harmonic number, denoted H_n.

Therefore, by arithmetic sequence the answer will be E[z] = (n-1)/n * H_n-1

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Answer:

3.5841 x 10^7

Step-by-step explanation:

358.41 / 100

and add 2 powers of 10

Answer:

x = -3/5

Step-by-step explanation:

Given the equation:
[tex]\displaystyle{8x+9=3x+6}[/tex]

Solve for the variable x by isolating x-term, first move subtract both sides by 3x:

[tex]\displaystyle{8x+9-3x=3x+6-3x}\\\\\displaystyle{5x+9=6}[/tex]

Subtract both sides by 9:

[tex]\displaystyle{5x+9-9=6-9}\\\\\displaystyle{5x=-3}[/tex]

Divide both sides by 5:

[tex]\displaystyle{\dfrac{5x}{5}=\dfrac{-3}{5}}\\\\\displaystyle{x=-\dfrac{3}{5}}[/tex]

Therefore x = - 3/5

Answer:

x = -3/5 (or) x = -0.6

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 8x + 9 = 3x + 6

Then the value of x will be,

→ 8x + 9 = 3x + 6

→ 8x - 3x = 6 - 9

→ 5x = -3

→ x = -3 ÷ 5

→ [ x = -3/5 ]

Hence, the answer is -3/5.

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

The surface area of the solid is 28 square inches.

The surface area of a given object is the sum or total area of all shapes forming its external surfaces. This implies calculating the area of each surface and adding them up.

In the given question, the net has a surface area of;

Area of a square = length*length

                    = 2*2

Area of the square base = 4 [tex]in^{2}[/tex]

Area of a triangle = 1/2 base*height

              = 1/2*2*6

Area of each triangular surface = 6 [tex]in^{2}[/tex]

Surface area of the solid = (4*6) + 4

                                   = 24 + 4

                                   = 28

Surface area of the solid is 28 [tex]in^{2}[/tex].

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Answer:

Surface area of the solid is 28 .

Step-by-step explanation:

Answer:

Step-by-step explanation:

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by an external force.

If you are standing on separate sheets of paper and start running, your body will experience a forward motion. However, the sheets of paper under your feet will initially resist the motion due to friction. The force of friction will create an equal and opposite force, causing the sheets of paper to slide backwards. As you continue to run, the friction between your feet and the paper will decrease, and the sheets of paper may eventually stop sliding and you will continue running with a constant velocity.

This is an example of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force you apply to the ground when running is the action, and the force of the ground pushing back on you is the reaction.

On solving the provided question we can say that The average rate equation of change of g(x) from x = -3 to x = 3 is -27.

A math equation is a procedure that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the calculation 3x + 5 = 14, the equal sign places a space between the values 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The logo and the specifically software are frequently the same. as in, 2x - 4 Equals 2, for instance.

Average Rate of Change = (g(b) - g(a)) / (b - a)

In this case, [tex]g(x) = -3x^3 + 3[/tex], and we need to find the average rate of change from x = -3 to x = 3.

So, we plug in the values of a=-3 and b=3 into the formula:

Average Rate of Change =[tex](g(3) - g(-3)) / (3 - (-3))[/tex]

[tex]= (-3(3)^3 + 3) - (-3(-3)^3 + 3)) / (6)\\= (-81 + 3) - (81 + 3)) / 6\\= (-78 - 84) / 6\\= -162 / 6\\= -27[/tex]

The average rate of change of g(x) from x = -3 to x = 3 is -27.

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Total snacks

15

Initially, cashews are 2x the amount of almonds

After 10 cashews are eaten, there are still 5 more cashews than almonds.

this gives us an insight into the amount eaten before they are equal

cashew eaten = 10

cashews left = almonds + 5

Therefore the almondds are 10 + 5 = 15

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Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform a simple linear regression. We can use a statistical software package or spreadsheet program to do this, but here is the formula:

y = b0 + b1x

where:

y = price per share

x = annual dividend

b0 = y-intercept (constant)

b1 = slope (regression coefficient)

Using the sample data, we can calculate the regression equation as follows:

mean(x) = 9.8567

mean(y) = 53.0357

SSxx = Σ(x - mean(x))² = 7569.6844

SSxy = Σ(x - mean(x))(y - mean(y)) = 4542.4061

b1 = SSxy / SSxx = 4542.4061 / 7569.6844 = 0.6004

b0 = mean(y) - b1 * mean(x) = 53.0357 - 0.6004 * 9.8567 = 47.4759

Therefore, the regression equation is:

y = 47.4759 + 0.6004x

b. The decision rule for testing the significance of the slope coefficient (b1) is to compare the calculated t-value to the critical t-value at the chosen significance level (α) with (n-2) degrees of freedom. For this problem, we will use α = 0.05 and n = 30, so the degrees of freedom is 28. The null hypothesis is that the slope coefficient is equal to zero (i.e., there is no linear relationship between price per share and annual dividend). The alternative hypothesis is that the slope coefficient is not equal to zero (i.e., there is a linear relationship).

c. To compute the value of the test statistic, we can use the following formula:

t = b1 / (SEb1)

where:

SEb1 = standard error of the slope coefficient

SEb1 = sqrt(MSE / SSxx)

MSE = mean squared error

MSE = SSres / (n - 2)

SSres = residual sum of squares

Using the sample data, we can calculate the test statistic as follows:

SSres = Σ(y - ŷ)² = 583.8319

MSE = SSres / (n - 2) = 20.8518

SEb1 = sqrt(MSE / SSxx) = 0.0798

t = 0.6004 / 0.0798 = 7.526

d. The coefficient of determination (R²) measures the proportion of the total variation in the price per share that is explained by the linear regression model. We can calculate it using the following formula:

R² = SSreg / SStot

where:

SSreg = regression sum of squares

SSreg = b1² * SSxx

SStot = total sum of squares

SStot = Σ(y - mean(y))²

Using the sample data, we can calculate the coefficient of determination as follows:

SSreg = b1² * SSxx = 1707.4612

SStot = Σ(y - mean(y))² = 1866.6219

R² = SSreg / SStot = 0.9145

Therefore, 91.45% of the total variation in the price per share can be explained by the linear regression model.

(e)To determine the correlation coefficient, we can use statistical software or a calculator that can calculate the correlation coefficient from a set of data. Using a software or calculator, we get:

Correlation coefficient (r) = 0.7709

Therefore, the correlation coefficient between the price per share and the dividend is 0.7709. This indicates a strong positive correlation between these two variables.

Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform linear regression analysis. We can use a statistical software or spreadsheet to do this. The results are:

Regression equation: price per share = 14.393 + 1.201(dividend)

Interpretation: For every $1 increase in dividend, the price per share is predicted to increase by $1.201, holding all other variables constant.

b. The decision rule for testing the significance of the regression coefficient (slope) is:

H0: β1 = 0 (the slope is not significantly different from 0)

Ha: β1 ≠ 0 (the slope is significantly different from 0)

Test statistic: t = (b1 - 0) / SE(b1)

Rejection region: t < -tα/2,n-2 or t > tα/2,n-2, where α = 0.05 and n-2 = 28 degrees of freedom

c. The value of the test statistic is:

t = (1.201 - 0) / 0.177 = 6.79 (rounded to two decimal places)

d. The coefficient of determination (R-squared) is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variable(s). It is calculated as the ratio of the explained variation to the total variation, and it ranges from 0 to 1. The formula is:

R-squared = explained variation / total variation

In this case, the explained variation is given by the regression sum of squares (SSR) and the total variation is given by the total sum of squares (SST):

SSR = Σ(y-hat - y-bar)^2 = 6418.95

SST = Σ(y - y-bar)^2 = 12345.44

Therefore, the coefficient of determination is:

R-squared = SSR / SST = 6418.95 / 12345.44 = 0.52 (rounded to two decimal places)

Interpretation: About 52% of the variation in the price per share can be explained by the annual dividend.

e. The correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger relationship. The formula is:

r = cov(x,y) / (SD(x) * SD(y))

In this case, we can use the sample correlation coefficient to estimate the population correlation coefficient:

r = cov(price, dividend) / (SD(price) * SD(dividend))

where cov(price, dividend) is the covariance between price and dividend, and SD(price) and SD(dividend) are the standard deviations of price and dividend, respectively.

Using the formula or a spreadsheet, we get:

cov(price, dividend) = Σ[(price - mean price)*(dividend - mean dividend)] / (n - 1) = 417.25

SD(price) = 18.14

SD(dividend) = 6.10

Therefore, the correlation coefficient is:

r = 417.25 / (18.14 * 6.10) = 0.73 (rounded to two decimal places)

Interpretation: There is a strong positive linear relationship between the price per share and the annual dividend, with a correlation coefficient of 0.73.

Therefore, it will take approximately 4.2 years for the television set to be worth half of its original value.

All of your revenues and expenses are listed in your profit and loss statements. They also show whether operating expenses have been covered by profits earned by your business. In that case, you could claim that your business has made money. The profit and loss statement displays the profitability of a company.

We can start solving this problem by setting up an equation for the value of the TV over time. Let V be the value of the TV in dollars and t be the time in years. Then, we have:

V(t) = 1900 - 225t

We want to find the time it takes for the TV to be worth half of its original value, which means we want to find t when V(t) = 950. So, we can set up the following equation:

950 = 1900 - 225t

Solving for t, we get:

t = (1900 - 950) / 225

t = 4.22 years (rounded to two decimal places)

Therefore, it will take approximately 4.2 years for the television set to be worth half of its original value.

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The values of x are 3 or 0. 3 and 0 will satisfy the equation |2x-3| +7 =10.

What is an absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The parent function with an absolute value is defined as f(x)=| x |.

Given equation is

|2x-3| +7 =10

Subtract 7 from both sides:

|2x-3| +7 - 7 = 10 - 7

|2x-3| = 3

Applying absolute function:

Either, 2x-3 = 3         or, 2x-3 = -3

Add 3 on both sides:

2x = 6                         2x = 0

Divide both sides by 2:

x = 3      or     x = 0

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Answer:

D: [-4, ∞) and R: [0, ∞)

Step-by-step explanation:

The answer is D: [-4, ∞) and R: [0, ∞)

Answer:

(g ￮ h)(t) = 8t

Step-by-step explanation:

to find (g ￮ h)(t) substitute t = h(t) into g(t)

(g ￮ h)(t)

= g(h(t))

= g(4t - 2)

= 2(4t - 2) + 4

= 8t - 4 + 4

= 8t

Imagine you draw a straight line down the middle of a piece of paper. This line is the line of symmetry. Anything you draw on one side of the line is going to have a mirror image on the other side of the line that looks exactly the same.

Now, if you have a point on the line of symmetry, that means the point is exactly in the middle of the line. And since the line is the same on both sides, that means the point is going to be the same on both sides too! So, the point on the line of symmetry stays in the same place and looks the same on both sides of the line.

- Dante

Answer:

y = 4x + 3

Step-by-step explanation:

See picture below :)