Write the function whose graph is the graph of y=x², but is translated 4 units to the left.
y=
Help plss

For the given systems of equations, we have that:

1) The infinite solutions have the following format: (3y - 12, y, 10y - 31).

2) There is one solution: (1.58, -3.45, 3.89).

3) There is one solution: (3, 2, 4).

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For item 1, the system is:

From the first equation, we have that:

z = 3x + y + 5.

Replacing on the second equation, we have that:

-4x + 2y + 3x + y + 5 = 17

-x + 3y = 12

x = 3y - 12.

Replacing on the third equation, we have that:

-2x - 4y + 3x + y + 5 = -7

x - 3y = -12

Since x = 3y - 12:

3y - 12 - 3y = -12

0 = 0.

Free variable, hence:

The infinite solutions have the following format: (3y - 12, y, 10y - 31).

For item 2, the system is:

From the first equation:

x = -4 - 5y - 3z.

Replacing on the second equation:

-4 - 5y - 3z + 2y - 3z = 9.

-3y -6z = 13.

3y + 6z = 13.

Replacing on the third equation:

-3(-4 - 5y - 3z) + 2y + 3z = -12

12 + 15y + 9z + 2y + 3z = -12

17y + 12z = -14.

From the second equation, we have that:

z = (13 - 3y)/6.

Hence, replacing on the third again:

17y + 2(12 - 3y) = -14

11y + 24 = -14.

y = -3.45.

z = (13 - 3 x (-3.45))/6 = 3.89.

x = -4 - 5(-3.45) - 3(3.89) = 1.58.

Hence:

There is one solution: (1.58, -3.45, 3.89).

For item 3, the system is:

From the second equation:

z = 5x + 2y - 15.

Replacing on the first:

-4x - 2y + 5(5x + 2y - 15) = 4

-4x - 2y + 25x + 10y - 75 = 4

21x + 8y = 79.

Replacing on the third:

5x - 2y - 3(5x + 2y - 15) = -1

5x - 2y - 15x - 6y + 45 = -1.

-10x - 8y = -46.

Adding both resulting equations, we have that:

11x = 33.

x = 3.

Then

21x + 8y = 79.

63 + 8y = 79

8y = 16

y = 2.

z = 5x + 2y - 15 = 5(3) + 2(2) - 15 = 4.

There is one solution: (3, 2, 4).

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The Lateral surface of the triangular pyramid = 6 cm²

The lateral surface of a triangular pyramid is the area of the three triangular surfaces of the triangular pyramid, which excludes the area of the base.

The area of each triangular face = area of triangle = 1/2(base)(height).

Given the following as shown in the diagram:

Height of the triangular face = 7.2 cm

Base length of the triangular face = 5 cm

Lateral surface of the triangular pyramid = 3(1/2 × base × height)

Plug in the values

Lateral surface of the triangular pyramid = 3(1/2 × 5 × 7.2)

Lateral surface of the triangular pyramid = 3(18)

Lateral surface of the triangular pyramid = 6 cm²

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The area of the circular section is 3.14 square units

The given parameters are:

Radius, r = 1 kilometre

Rewrite the above properly as follows

So, we have

r = 1 kilometre

The area of the circular section is:

A = πr^2

So, we have

A = 3.14 * 1^2

Evaluate the exponent

So, we have

A = 3.14 * 1

Evaluate the product

So, we have

A = 3.14

Hence, the area of the circular section is 3.14 square units

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Answer:

n² p²r³

Step-by-step explanation:

n ⋅ n ⋅ p ⋅ p ⋅ r ⋅ r ⋅ r

Write using exponents

There are 2 n terms

n²⋅ p ⋅ p ⋅ r ⋅ r ⋅ r

There are 2 p terms

n² p²⋅ r ⋅ r ⋅ r

There are 3 r terms

n² p²r³

Answer:

8

Step-by-step explanation:

I attached my answer........

Answer:45

Step-by-step explanation:

5n²

5(3)²

5(9)

∴ The third term in the sequence 5n² is 45

P = 180 - (125 + 30)

P = 180 - 155

P = 25 degrees

Thus :

P = 25/180 n radian

P = 5/36 n

Which mean the first option is the correct answer.

Answer:

[tex] - 2x - h[/tex]

Step-by-step explanation:

We are given a function [tex]g(x)=2-x^2[/tex]. We want to find [tex](g(x+h)-g(x))/h[/tex] To do so, first we need to work out the numerator

[tex]g(x+h)=2-(x+h)^2[/tex]. Therefore

[tex]g(x+h)-g(x)\implies 2-x^2-2xh-h^2-2x-x^2[/tex]

like terms cancel out leaving us with

So,

[tex] \displaystyle\frac{g(x + h) + g(x)}{h} = \frac{ h( - 2x - h )}{h} = \boxed{ - 2x - h}[/tex]

The value of (gof)(-2) for the given values of f(x) and g(x) is 60.

A Composite function may be defined as a function which is formed from the operation of combination of two functions. If f(x) and g(x) are two functions, then the composite functions of the given functions are fog(x) that is f(g(x)) and gof(x) that is g(f(x)).

It is given in the question that f(x) = -2x + 7 and g(x) = x² - 6x + 5.

Now, gof(x) = g(f(x)) = (-2x + 7)² - 6(-2x + 7) + 5

gof(x) = 4x² + 49 - 28x + 12x - 42 + 5

gof(x) = 4x² - 16x + 12

gof(-2) = 4(-2)² - 16(-2) + 12

gof(-2) = 16 + 32 + 12

=>gof(-2) = 60

Therefore, the value of gof(-2) is equal to 60.

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The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex]  .

In the question,

the given expression is [tex]-24\frac{1}{2} +16.15-4[/tex] , solving further we get

= -49/2 + 16.15 - 4       ...(as [tex]24\frac{1}{2} = \frac{49}{2}[/tex]  )

= -24.5 + 12.15

= -12.35

In option(A) we have ,

=[tex]24\frac{1}{2} -16.15+4[/tex]

= 49/2 -16.15 +4

= 24.5 -16.15 +4

= 8.35 + 4

= 12.35

In option(B) we have ,

= 16.15 - 28.5

= -12.35

In option(C) we have ,

= -28.5 + 16.15

= -12.35

In option(D) we have ,

[tex]=-20\frac{1}{2} +16.5[/tex]

= -41/2 + 16.5     ...( as [tex]20\frac{1}{2} = \frac{41}{2}[/tex] )

= -20.5 + 16.5

= -4

In option(E) we have ,

[tex]=12.15-24\frac{1}{2}[/tex]

= 12.15 - 49/2

= 12.15 - 24.5

= -12.35

As we can see that from all the option , only option(B), option(C) and option(E) matches with the given expression .

Therefore , The expressions that are equivalent to [tex]-24\frac{1}{2} +16.15-4[/tex] are (B)16.15 - 28.5 , (C)-28.5 + 16.15 and (E)[tex]12.15-24\frac{1}{2}[/tex]  .

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Answer:

Step-by-step explanation:

Answer is in the pic.

Answer:

See below for proof.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Trigonometric Identities}\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\ \\$\sin^2 \theta + \cos^2 \theta=1$\\\end{minipage}}[/tex]

Use the trigonometric identities to prove the given equation:

[tex]\begin{aligned} \implies \cos 4 \theta & = \cos (2 \theta +2 \theta)\\& = \cos 2 \theta \cos 2 \theta - \sin 2 \theta \sin 2 \theta\\& = \cos^2 2 \theta - \sin^2 2 \theta\\& = \cos^2 2 \theta - (1-\cos^2 2 \theta)\\& = 2\cos^2 2 \theta - 1\\ & = 2\left(\cos 2 \theta \right)^2-1\\& = 2\left(\cos\theta \cos\theta-\sin \theta\sin \theta\right)^2-1\\& = 2\left(\cos^2\theta-\sin ^2\theta\right)^2-1\\& = 2\left(\cos^2\theta-(1-\cos^2\theta)\right)^2-1\\& = 2\left(2\cos^2\theta-1\right)^2-1\\\end{aligned}[/tex]

                 [tex]\begin{aligned}& = 2\left(4\cos^4\theta-4\cos^2\theta+1\right)-1\\& =8\cos^4\theta-8\cos^2\theta+2-1\\ & =8\cos^4\theta-8\cos^2\theta+1 \end{aligned}[/tex]

Answer:The answer would be 8

Step-by-step explanation:You would have to do 8/-2+2 and that would leave you with 8 because -2+2 is 0.

Answer:

$448.766754 per week or $448

Step-by-step explanation:

i gotchu

theres 52.1429 weeks

divide 23,400 by 52.1429

u get $448.766754 per week

After using distributive property we find the solution of 5 × 198 is 990.

What is Distributive property?

By the rule of distributive property, multiplying the sum of two or more addends by a number gives the same result as when each addend is multiplied individually by the number and the products are added together.

The expression is given as;

5 × 198

Now, By using distributive property we calculate as;

5 × 198 = 5 × ( 200 - 2 )

           = (5 × 200) - (5 × 2)

           = 1000 - 10

           = 990

Hence, After using distributive property we find the solution of 5 × 198 is 990.

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Answer:

i think the answer is 0.00263157895

Answer:its a

Step-by-step explanation:

7.5% = 0.075

0.075 x 123.28 = 9.246

So, the tax will be $9.20.

Total cost would be $132.48.

Answer:

x = -6

Step-by-step explanation:

Distribute where possible

5x - 30 + 8 = 7x - 10

Combine like terms

5x - 22 = 7x - 10

Subtract 7x from both sides and add 22 to both sides

-2x = 12

x = -6

Answer:

The distance would be 118

Step-by-step explanation:

The easiest way I solve the distance between a negative number and a positive number is by adding the negative (but making it a positive) and the positive together. If you add 55 and 63 you would get 118. And 118 is the distance between -55 and 63.

I hope this helps!! :)

The value of equation for x is x > 0.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

|5-2x| > 5

To solve for let us take x on one side.

So, Subtracting 5 both the side we get,

|5 - 2x - 5| > 5 - 5

Simplifying we get,

|-2x| > 0

Extracting mod we get,

2x > 0

Now since 2 > 0 which is true,

Thus, x > 0

So, the value of equation for x is x > 0.

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Answer:

5

Step-by-step explanation:

Every number from the absolute sign will be positive.

The value of the Z - Score is a -1.5.

According to the statement

We have to find that the z-score of the company.

So, For this purpose, we know that the

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

From the given information:

The annual salaries of all employees at a financial company are normally distributed with a mean Mu = $34,000 and a standard deviation Sigma = $4,000.

Then

Let X = annual salaries of all employees at a financial company

And

The z score probability distribution for the normal distribution is given by:

Z - Score = Annual salary - mean / s.d.

Then substitute the values

Z - Score = 28,000 - 34,000/ 4000

Z -Score = -6/4

Z -Score = -1.5.

So, The value of the Z - Score is a -1.5.

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According to the statement Donald is using Stratified sampling to collects data from the sample.

The correct option is A.

A simple random sample is then taken from each separate or subgroup using the stratified sampling survey method, which first divides the population being studied into distinct subgroups or groups known as strata.

The ability to reduce the sample size needed to obtain reliable results is one of the main benefits of stratified sampling.

When attempting to evaluate data from various subgroups or strata, researchers frequently use stratified random sampling. They can quickly find a population sample that most accurately reflects the entire population they are studying.

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I understand that the question you are looking for is:

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

a. Systematic sampling

b. Convenience sampling

c. Stratified sampling

d. Cluster sampling

Answer
(-3) - (-10) = 7

|7| = 7

7

Answer:3/7

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation:

change all denominators to 21

{21 is the lcd of all the numbers)

17/21 x 1= 17/21

1/3 x 7 = 7/21

5/7 x 3 = 15/21

17/21 + 7/21 - 15/21

24/21-5/21

9/21

reduce by three

9/21÷3

3/7

The dimensions of original lawn are a. 4 feet by 4 feet.

As per the equation and information mentioned in question, x represents the dimension of original lawn. The equation in question represents the relation between area of lawn at side of reduced lawn and it's area. We will solve this equation to find the value of x.

[tex](x - 8)^{2} = 144[/tex]

The expression on Left Hand Side is same as [tex](a - b)^{2}[/tex]. We know, on expansion, we write it as [tex]a^{2} + b^{2} - 2ab[/tex]. Thus, new equation will be -

[tex]x^{2} + 8^{2} - 2*x*8 = 144[/tex]

[tex]x^{2} + 64 + 16x = 144[/tex]

[tex]x^{2} + 16x + 64 - 144 = 0[/tex]

[tex]x^{2} + 16x - 80 = 0[/tex]

[tex]x^{2} + 20x - 4x - 80 = 0[/tex]

x (x + 20) -4 (x + 20) = 0

(x + 20) (x - 4) = 0

So, the two values of x that we get are:

x = 4 and -20.

The dimensions of lawn can not be negative. Hence, the value of x will be x.

Therefore, the dimensions of original lawn are a. 4 feet by 4 feet.

The complete question is -

Jillian is trying to save water, so she reduces the size  of her square grass lawn by 8 feet on each side. The area of the smaller lawn is 144 square feet. In the equation [tex](x - 8)^{2} = 144[/tex], x represents the side measure of the original lawn. What were the dimensions of the original lawn?

a. 4 feet by 4 feet

b. 8 + [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

c. 8 - [tex]6\sqrt{2}[/tex] feet by 8 + [tex]6\sqrt{2}[/tex] feet

d. 20 feet by 20 feet

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Answer:

[tex]\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex]

to rationalise the denominator multiply numerator/ denominator by [tex]\sqrt{5}[/tex]

= [tex]\frac{\sqrt{15} }{\sqrt{5} }[/tex] × [tex]\frac{\sqrt{5} }{\sqrt{5} }[/tex]

= [tex]\frac{\sqrt{75} }{5}[/tex]

= [tex]\frac{\sqrt{25(3)} }{5}[/tex]

= [tex]\frac{5\sqrt{3} }{5}[/tex]

= [tex]\sqrt{3}[/tex]

Answer:

2,440 acres of old-growth trees.

Step-by-step explanation:

61,000*0.04=2,440

There are 2,440 acres of old-growth trees.

Hope this helps!

Please mark as brainliest if correct!

The regions is represented as :

   A = p - p ∩ q ,  B = p ∩ q  and   C = q - p ∩ q

According to the question we have been given the Venn diagram with two regions p and q.

We need to find the representation of regions A, B and C.

As we can from the diagram,

  region A is the area where the only p statement is there which exclude the B region . That is A is area of difference.

So it can be represented as

                   A = p - p ∩ q

  region B is the intersection of p and q.

So it can be represented by

                  B = p ∩ q

region C is the area where only q statement is there and excludes the intersection region. That is C is area of difference

So it can be represented as

                  C = q - p ∩ q

Hence the regions is represented as

                  A = p - p ∩ q

                  B = p ∩ q

                  C = q - p ∩ q

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