14 What are the solutions to the equation 3(x − 4)² = 27?
(1) 1 and 7
(3) 4 ± √24
(2) −1 and -7
(4) − 4 ± √24

Monetary policy is the actions taken by the reserve banks to influence the real GDP and the inflation rate in the economy.

These are actions done by the central bank of a country and involves adjusting money supply so as to achieve economic growth.

This influences the real gross domestic product and inflation rate of the country .

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Answer: Monetary and Reserve Bank

Step-by-step explanation:

;)

Answer:

Step-by-step explanation:

x² - 3x - 28

What factors multiply to -28 and add to -3?

-7 and 4.

(x - 7) (x + 4)

Answer:

(x - 7)(x + 4)

Step-by-step explanation:

To find the factors, you just need to ask yourself the question: Which two numbers multiply to -28 but add to -3?

Simple guess-and-check will lead you to the numbers -7 and 4.

-7 x 4 = -28

-7 + 4 = -3

These numbers will make up the factored equation.

x² - 3x - 28

(x - 7)(x + 4)

You can check your answer by re-expanding the factored expression. This is done by multiplying each term in the first parentheses by each term in the second parentheses.

(x - 7)(x + 4)  ---->  x² - 7x + 4x - 28  ---->  x² - 3x - 28

Answer

I don’t quite understand what your asking but I hope this helps

y=3x-13

Step-by-step explanation:

Answer:

I would think that it would be 8

Step-by-step explanation:

1-2= (-1)= -1+2=1

I think it's 8. 8 times the number of 1 is well...8.

Step-by-step explanation:

x = the number

x * 2 = 1  

soooo   x = 1/2

then   8 * 1/2  = 4

The coordinates of the point that divides the segment into a 3:2 ratio is (-2.2, -1.2)

The points are given as:

G = (-4,3)

H = (-1,-4)

Ratio, m : n = 3 : 2

The coordinate of the point is calculated using:

[tex](x,y) = \frac{1}{m + n} * (mx_2 + nx_1, my_2 + ny_1)[/tex]

This gives

[tex](x,y) = \frac{1}{3 + 2} * (3 * -1 + 2 * -4, 3 * -4 + 2 * 3)[/tex]

Evaluate

[tex](x,y) = \frac{1}{5} * (-11, -6)[/tex]

Evaluate the product

(x,y) = (-2.2, -1.2)

Hence, the coordinate of the point is (-2.2, -1.2)

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Answer:

The graph does show a linear function

Step-by-step explanation:

The line is decreasing at a constant rate that keeps the line straight.

The volume of the cylindrical can of ground coffee is 19.6 inches cube.

volume of the can ground coffee = πr²h

where

Therefore,

r = 1 inches

h = 6 1 / 4 = 25 / 4 inches

volume of the can ground coffee = 3.14 × 1² × 25 / 4

volume of the can ground coffee = 78.5 / 4

volume of the can ground coffee = 19.6 inches³

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Answer:

[tex]C)~ 10.06~ m[/tex]

Step-by-step explanation:

[tex]~~~~~~\sin 8^{\circ} = \dfrac{1.4}{y}\\\\\implies y = \dfrac{1.4}{\sin 8^\circ}\\\\\implies y \approx 10.06~ m[/tex]

Answer:

a. {(0, 7), (-1, 6)}

Step-by-step explanation:

[tex]y = x^{2} +2x+7\\y=x+7[/tex]

subtract the equations

[tex]y = x^{2} +2x+7 \\- \ \ \ \ \ y=x+7\\y - y =x^{2} +2x+7-(x+7)\\0=x^{2} +x\\x = 0 \ and \ x= -1[/tex]

for [tex]y = x^{2} +2x+7[/tex], substitute x = 0

[tex]y = (0)^{2} +2(0)+7\\y = 0 +0+7\\y=7[/tex]

for [tex]y = x^{2} +2x+7[/tex], substitute x = 0

[tex]y = (-1)^{2} +2(-1)+7\\y = 1 -2+7\\y=6[/tex]

Answer:

A

Step-by-step explanation:

There are different kinds of polygon. The number of sides that this polygon have is 5.

Note that the side of each polygon = 3.5

The parameter of  polygon  =17.5

Therefore the number of sides =  parameter of  polygon /  parameter of  polygon  

So =      [tex]\frac{17.5}{3.5}[/tex]

=5

Therefore, The number of sides that this polygon have is 5.

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Answer:

So first we substitute -2 for x

f(-2) = 10(-2)^2 - 4(-2) - 5

f(-2) = 400 + 8 - 5

f(-2) = 400 + 3

f(-2) = 403

Step-by-step explanation:

An estimate of the number of defective televisions that are made each day is 150.

The first step is to determine the ratio of the televisions sampled to the total number of televisions produced each day.

1000 / 40 = 25

The second step is to multiply, 25 by 6: 25 x 6 = 150

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Answer:

[tex]\{4,-4\}[/tex]

Step-by-step explanation:

[tex]~~~~x^2 = 16\\\\\implies x = \pm\sqrt{16}\\\\\implies x =\pm 4\\\\\implies x = 4 ,~ x = -4[/tex]

Answer:

x = 4

Step-by-step explanation:

x² = 16

We do the opposite of x² , so we [tex]\sqrt{x}[/tex] (square root) both sides

[tex]\sqrt{x}[/tex] = [tex]\sqrt{16}[/tex] = 4

to confirm this, we can square 4, which gets us 16.

Hope this makes sense! Feel free to ask anything further if need be.

- profparis

By critically observing the scatter plot (see attachment), the type of relationship that would best model this data is positive nonlinear.

In Statistics, there are four (4) main types of relationship (association) in a scatter plot and these include the following:

By critically observing the scatter plot shown in the image attached below, we can logically deduce that the type of relationship that would best model this data is positive nonlinear because the change in one of the variables doesn't result in a constant change in other variables.

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Answer:

8^5

Step-by-step explanation:

division is just minusing exponents

The correct value of this expression is 8⁵

A fraction is also a division. When we divide power with equal bases - we subtract the exponents and keep the base.

Therefore, the answer correct is 8⁵

Answer:

29.44

Step-by-step explanation:

Since we know the both the measure of the angle and the adjacent line of the angle, we can use tan to find x.

tan is (Opposite/Adjacent Line)

[tex] \tan(31) = \frac{x}{49} \\ 49 \tan(31) = x \\ 29.44 = x[/tex]

That is the answer

- Kan Academy Advance

[tex]~~~~~~x^2 -10x +10 =0\\\\\implies x^2 -2 \cdot 5 \cdot x +5^2 -5^2 +10 = 0\\\\\implies (x-5)^2 -25+10 = 0\\\\\implies (x-5)^2 -15=0\\\\\implies (x-5)^2 = 15[/tex]

Answer:

BC ≈ 11.8 m

Step-by-step explanation:

using the tangent ratio in the right triangle

tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] , that is

tan32° = [tex]\frac{x}{BC}[/tex] = [tex]\frac{7.4}{BC}[/tex] ( multiply both sides by BC )

BC × tan32° = 7.4 ( divide both sides by tan32° )

BC = [tex]\frac{7.4}{tan32}[/tex] ≈ 11.8 m ( to 3 sf )

Answer:

Step-by-step explanation:

Simplify in steps, using below properties of exponents:

Correct choice is D

Answer:

[tex]4x^2y^3\sqrt[3]{x^2y}[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(8x^4y^5\right)^{\frac{2}{3}}[/tex]

Rewrite 4 as (3 + 1) and 5 as (3 + 2):

[tex]\implies \left(8x^{(3+1)}y^{(3+2)}\right)^{\frac{2}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies \left(8x^3xy^3y^2}\right)^{\frac{2}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 8^{\left(\frac{2}{3}\right)}x^{\left(3 \times\frac{2}{3}\right)}x^{\left(\frac{2}{3}\right)}y^{\left(3 \times \frac{2}{3}\right)}y^{\left(2 \times \frac{2}{3}\right)}}[/tex]

[tex]\implies 4x^2x^{\frac{2}{3}}y^2y^{\frac{4}{3}}[/tex]

[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\frac{4}{3}}[/tex]

Rewrite 4/3 as 1 + 1/3:

[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^{\left(1+\frac{1}{3}\right)}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]

[tex]\implies 4x^2y^2x^{\frac{2}{3}}y^1y^{\frac{1}{3}}[/tex]

[tex]\implies 4x^2y^2y^1x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\implies 4x^2y^{(2+1)}x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]

[tex]\implies 4x^2y^3x^{\frac{2}{3}}y^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies 4x^2y^3\left(x^2\right)^{\frac{1}{3}}y^{\frac{1}{3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot c^b=ac^b:[/tex]

[tex]\implies 4x^2y^3\left(x^2y\right)^{\frac{1}{3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]

[tex]\implies 4x^2y^3\sqrt[3]{x^2y}[/tex]

Answer:

First is b; because [B1] is [A1] multiplied by -4

Second is c; because [C2] = 7[B1] + [B2]

Step-by-step explanation:

One hundred is 10 tens. Using this information, you can divide 90 by 10 to calculate the hundreds, and get 9 hundreds, or 900

Answer:

1:19

2:20

3:21

4:22

Step-by-step explanation:

I think that's the answer

Answer:

The one in the right top hand corner. It shows one arrow pointing up and one to the right.

Step-by-step explanation:

I can't really explain it.

Answer:

1/12

Step-by-step explanation:

Answer:

They use collected data to recognize trends, predict outcomes, and plan for the future.

Step-by-step explanation:

By identifying the largest exponent in each expression, we see that the answers are:

a) D = 3.

b) D = 5.

c) D = 0.

The degree is just the largest exponent of the variable in an expression.

First, we have:

a) √3xyz - 5

The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.

b)  y² - 3y⁵ -y + 2y³ - 4

Here the largest exponent is on the second term, so we can see that the degree is 5.

c) -10³

Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:

-10³*x⁰

Where we use the fact that x⁰ = 1

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Answer: Heyaa! ~

Your Answer in simplified form is... −19√2

Step-by-step explanation:

2√2-7√18 = −19√2

Hopefully this helps you! ~