Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8?
A.
It is the graph of y = x translated 8 units down.
B.
It is the graph of y = x translated 8 units up.
C.
It is the graph of y = x translated 8 units to the left.
D.
It is the graph of y = x where the slope is decreased by 8.

Answer:

  (x, y) = (-1/6, 1/4)

Step-by-step explanation:

This is a system of equations in expressions of two variables. You could solve it by expanding the expressions to the base variables, or you could solve it by first finding the values of the expressions.

Let's see what happens when we expand the equations all the way.

First equation:

  [tex]\dfrac{1}{2}(x +2y)+\dfrac{5}{3}(3x-2y)=-\dfrac{3}{2}\\\\3(x+2y)+10(3x-2y)=-9\qquad\text{multiply by 6}\\\\3x+6y+30x-20y=-9\qquad\text{eliminate parentheses}\\\\\boxed{33x-14y+9=0}\qquad\text{collect terms, add $9$ to get general form}[/tex]

__

Second equation:

  [tex]\dfrac{5}{4}(x+2y)-\dfrac{3}{5}(3x-2y)=\dfrac{61}{60}\\\\75(x+2y)-36(3x-2y)=61\qquad\text{multiply by 60}\\\\75x+150y-108x+72y=61\qquad\text{eliminate parentheses}\\\\-33x +222y = 61\qquad\text{collect terms}\\\\\boxed{33x-222y+61=0}\qquad\text{write in general form}[/tex]

__

The solution process looks like it might be messy for either substitution or elimination, so we choose to solve these equations using the cross-multiplication method.

  Δ1 = (33)(-222) -(33)(-14) = -6864

  Δ2 = (-14)(61) -(-222)(9) = 1144

  Δ3 = (9)(33) -(61)(33) = -1716

  x = Δ2/Δ1 = 1144/-6864 = -1/6

  y = Δ3/Δ1 = -1716/-6864 = 1/4

The solution is (x, y) = (-1/6, 1/4).

_____

Additional comment

The weird numbers notwithstanding, the solution by elimination might be easily achieved by subtracting the second equation from the first. This would give ...

   208y -52 = 0   ⇒   y = 52/208 = 1/4

Direct substitution of this into either equation will require arithmetic with fractions to obtain the solution for x.

This system can be directly solved by a graphing calculator using the equations as given.

__

You can read more about the cross multiplication method of solving a system of linear equations here:

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Step-by-step explanation:

Given equation are: [1/{2(x+2y)}] + [5/{3(3x-2y)}] = -3/2 →Eqn(1)

[5/{4(x+2y)}] - [3/{5(3x-2y)}] = 61/60 →Eqn(2)

Let {1/(x+2y)} = a ; {1/(3x-2y)} = b then

{1/(2a)} + {5/(3b)} = -3/2 →Eqn(3) * 5/2

{5/(4a)} - {3/(5b)} = 61/60 →Eqn(4) * 1

__________________________________

{5/(4a)} + {25/(6b)} = -15/4

{5/(4a)} - {3/(5b)} = 61/60

(-) (+) (-)

______________________

{23/(6b)} + {3/(5b)} = -(15/4) - (61/60)

⇛{(125b + 18b)/(30b²)} = {(-225 - 61)/60}

⇛{(143b)/(30b²)} = -286/60

⇛{143/(30b)} = -286/60

⇛1/b = -1

Therefore, b = -1

Substitute the value of b in equation (3) then we have

{1/(2a)} + (5/3) = -3/2

⇛{1/(2a)} = -(3/2) - (5/3)

= (-9-10)/6

⇛{1/(2a)} = -19/6

⇛1/a = -19/3

a = -3/19

Now, {1/(x+2y)} = a ⇛-3/19

⇛x+2y = -19/3. ⇛3x + 6y = -19 →Eqn(5)

{1/(3x-2y)} = 1⇛ 3x - 2y = 1 →Eqn(6)

(-) (+) (-)

______________

8y = -20

y = -20/8

From equation (6)

3x - 2 * (-5/2) = 1

⇛3x - 5 = 1

⇛3x = 1+5

⇛3x = 6

⇛x = 6/3

Answer: Hence, the required value of x and y with be -5/2 and 2 respectively.

also read similar questions: 1/2x+1/3y=2 1/3x+1/2y=13/6 (x is not equal to 0, y is not equal to 0) by substitution method, step by step https://brainly.com/question/17171235?referrer

Answer:

B and D

Step-by-step explanation:

Distributive property on 3(c-3) is 3c-12=20. D is the same. Divide instead.

Answer:

the 2nd and 4th one

Step-by-step explanation:

4( c - 3 ) = 8

you can either distribute the 4 which means multiply whats inside of the parenthesis by 4 , 4 * c = 4c and 4 * -3 = -12 to get 4c - 12 = 8

or you can divide both sides by 4 which will get you c - 3 = 2

4(c-3)/4 = c - 3

8/4 = 2

c - 3 = 2

Your answer would be 98086.

The value of money Brianna need to invest is,

⇒ P = $99,259

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

Brianna is going to invest in an account paying an interest rate of 5.2% compounded continuously.

Here, We have;

Final amount (A) = $134,000

Time (n) = 6 years

Rate (r) = 5.2%

We know that;

⇒ Amount = P (1 + r)ⁿ

Substitute the values we get;

⇒ 134,000 = P (1 + 0.052)⁶

⇒ 134,000 = P (1.052)⁶

⇒ P = 134,000 / 1.35

⇒ P = $99,259

Thus, The value of money Brianna need to invest is,

⇒ P = $99,259

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Hi!

Given:

[tex]2xy*xy^2[/tex] if [tex]x=2[/tex] and [tex]y=4[/tex]

Plug in the numbers for [tex]x[/tex] and [tex]y[/tex]

[tex]2(2)(4)*(2)(4)^2[/tex]

Using PEMDAS (Order of Operations - see below), simplify exponents first:

[tex]2(2)(4)*(2)(16)[/tex]

Multiply from left to right:

[tex](4)(4)*(2)(16)[/tex]

[tex]16*32[/tex]

[tex]512[/tex]

Your answer is 512.

-------------------------------------------------------------------------------------------------------------

ORDER OF OPERATIONS:

P - Parentheses

E - Exponents

M/D - Multiplication/Division

A/S - Addition/Subtraction

-------------------------------------------------------------------------------------------------------------

For another question using PEMDAS, see:

https://brainly.com/question/1015001

Hello!

58, 65, 72, 79, 86

86+7 = 93

93+7 =100

100+7 =107

The sample of the speeds of 20 cars and at a 0.05 confidence level, we

have;

(a) There is not enough convincing evidence to suggest that the true mean speed of all cars travelling on Elm Street is more than 25 mph

(b) Type II error

(a) Based on the given data, using MS Excel, we have;

The sample size, n = 20

The mean, [tex]\overline x[/tex] = 25.86

The standard deviation of the sample, s = 2.284

The null hypothesis, H₀; [tex]\overline x[/tex] = 25 mph

Alternative hypothesis, Hₐ; [tex]\overline x[/tex] > 25 mph

Given that the sample size is less than 30, the t-test is used, and the t-score is found as follows;

[tex]t= \mathbf{\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}}[/tex]

Which gives;

[tex]t=\dfrac{25.86-25 }{\dfrac{2.284}{\sqrt{20}}} \approx \mathbf{1.684}[/tex]

Using a graphing calculator, we have;

The probability ≈  0.054

The critical-t ≈ 1.729

Given that the probability is larger than the significance level, we fail to

reject the null hypothesis.

There is not enough convincing statistical evidence to conclude that the

true mean of all cars travelling on Elm Street is more than 25 mph.

(b) The type of error is Type II error, given that there is a possibility that

the null hypothesis is failed to be rejected when it is actually false.

Given that the sample size is less than 30, it may be insufficient for the

Central Limit Theorem to be in effect.

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Answer:

The answer is the CD was for 3 years.

Step-by-step explanation:

First, write the equation.

I=Prt

Next, substitute the given values.

$198=$1,200×5.5%×t

Next, write the percent as a decimal.

$198=$1,200×0.055×t

Next, simplify.

$198=$66×t

Then, solve for t.

3=t

Ivy will receive $300 in interest at the end of one year.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To calculate the interest Ivy will receive at the end of one year, we need to multiply the amount she invested by the interest rate:

Interest = Principal x Rate

Here, the principal is $150,000 and the rate is 0.2% or 0.002 (as a decimal):

Interest = $150,000 x 0.002

Interest = $300

Thus,

Ivy will receive $300 in interest at the end of one year.

Learn more about expressions here:

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Hey there!

1/2(8 - 6y) + 1/5(10y - 25)

DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES

= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)

= 4 - 3y + 2y - 5

COMBINE the LIKE TERMS

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

= -3y + 2y + 4 - 5

= -1y - 1

≈ -y - 1

Therefore, your answer is: -y - 1

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

x = 2.25

Step-by-step explanation:

X equals to 2.25. This is because the scale factor between 8 and 6 is 1 1/3.

Next, we take 3 and divide it with 1 1/3, ending up with 2.25.

Answer:

4

Step-by-step explanation:

a²+b²=c²

|BD|²+|AC|²=|AB|²

|BD|²+3²=5²

|BD|²+9=25

|BD|²=25-9

|BD|²=16

then you root both sides

therefore |BD|=4

Answer:

27.) the candy bar sells for $5.90 with tax

28.) the candy bars sell for $4.80 with tax

Step-by-step explanation:

For amounts between $1.00 and $2.00, the tax is $0.10

For amounts greater than $2.00 and less than or equal to $4.00, the tax is $0.20.

For amounts greater than $4.00 and less than or equal to $6.00, the tax is $0.30.

For amounts greater than $6.00 and less than or equal to $8.00, the tax is $0.40.

For amounts greater than $8.00 and less than or equal to $10.00, the tax is $0.50

Answer:

The answer is 71.67

Step-by-step explanation:

I=PRT

P=2500

r=4.3%

t=8months which is two thirds of a year

2500×4.3%×2/3

I=71.67

Answer:

S = 3770.25 in^2

Step-by-step explanation:

20/15 = 4/3

5027/ 4/3 = 3770.25

Answer:

<2=10

Step-by-step explanation:

because if they are supplementary, they are on the same line, and a line is 180-degrees so 180-170=10-degrees which is angle 2.

Let the total number of apples in the basket be m

12% of the apples are rotten, and apples in good condition are 66

Therefore, according to the question,

[tex]88\% \: of \: m= 66[/tex]

[tex]→ \frac{88}{100}× m = 66[/tex]

[tex]→ m = \frac{(66 \times 100)}{88} [/tex]

[tex]→ m = 3 \times 25[/tex]

[tex]→ m = 75[/tex]

Therefore, total number of apples in the basket is 75.

[tex]\red\bigstar \huge \color{blue}{ \tt{answer}}[/tex]

Let the total number of apples in the basket be x

• The apples are rotten = 12%

• The apples in good condition = 66

So ,

[tex]\bold{88\% \: of \: x = 66 }[/tex]

[tex] \bold{↪\frac{88}{100} × x = 66 }[/tex]

[tex]\bold{↪x = \frac{(66×100)}{88} }[/tex]

[tex]\bold{↪x = 3 × 25}[/tex]

[tex] \bold{↪x = 75}[/tex]

[tex]\bold{∴}[/tex]Total number of apples in the basket is 75

Answer:

The amount increased by 102 units. The amount has increased by 120%

Step-by-step explanation:

187-85=102

85x=187

(187/85)-1=1.2

1.2*100=120

Answer:

Step-by-step explanation:

187 - 85 = 102

( 102 ÷ 85 ) × 100 = 120

Answer:

The answer is D

Step-by-step explanation:

First, find a and b from the given points.

y = abx

5 = ab3

10 = ab4

b = 10/5 = 2

5 = a(23)

a = 5/8

y = (5/8) 2x

Test the choices:

x = 2 ⇒ y = 5/2

This rules out (a) and (b).

x = 5 ⇒ y = 20

Answer:

Step-by-step explanation:

Equilateral triangle

Solve for area

A≈62.35in²

P Perimeter

36

in

a

a

a

a

a

a

a

P

A

Using the formulas

A=3

4a2

P=3a

Solving forA

A=3P2

36=3·362

36≈62.35383in²

Answer:

3 +7> 9-^2 = 47

Step-by-step explanation: i did this

Given that triangles OPQ and RST are similar triangles, the measure of side ST is: 75.3.

The ratio of the corresponding sides of two similar triangles are always equal, meaning the sides are proportional to each other.

Given:

Since Triangle OPQ is similar to triangle RST, therefore:

RS/OP = ST/PQ

Substitute

RS/17 = 31/7

Cross multiply

RS = (31 × 17)/7

RS = 75.3

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Answer:

56kmp

Step-by-step explanation:

That is all I know.

Answer:

1.6 kpm

Step-by-step explanation:

(32km)/(20min) = 1.6 km/min or kpm

Answer:

L = 2.25 feet.

Step-by-step explanation:

My work is shown in the attached image! Let me know if there are any errors or if you have any questions. Best wishes.

Answer:

(2*10)-(7+3)

Parentheses are used to avoid unwanted results.

Answer:

The minimum value is -7 because of the negative sign on the number

Answer: Its -6

Step-by-step explanation:

its -6 because the functions lowest points are -6

Based on the coupon rate on this corporate bond and the face value, the yield on the bond is 15.2%.

The number of periods is missing so we shall assume a maturity period of one year.

The rate can be found using an Excel worksheet or a financial calculator.

Using an Excel worksheet, the relevant function is the RATE function and the following details will be needed:

Nper = 1 year

Pmt = 6% x 5,000

= $300

Pv = (5,000 * 0.92)

= $4,600

Pv = -4600 because it should be negative.

Fv = $5,000

The yield you will get is 15.2% as shown in the attached image.

Find out more on bond yields at https://brainly.com/question/7967102.

Answer:

the needed amount of what? community service?If so about 6 days of work on saturday and 3 school days. :)

Answer: 168.7 degrees

Step-by-step explanation:

Supplementary angles have measures that add to 180 deg, so 180-11.3=168.7

We have two flower beds in this example, the first has a perimeter of 100 feet, and the second has a perimeter of 180 feet

The total is 280 feet

Given Data

Dimension of the first flower bed

Length = 17 feet

Width = 33 feet

Perimeter = 2L + 2W

Perimeter = 2*17 + 2*33

Perimeter =  34 + 66

Perimeter = 100 feet

Dimension of the second flower bed

Length = 40 feet

Width = 50 feet

Perimeter = 2L + 2W

Perimeter = 2*40 + 2*50

Perimeter = 80 + 100

Perimeter = 180 feet

The total length will be 100+180 = 280 feet

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Answer:

It's 50

Step-by-step explanation:

D on edge

Answer:

p=-60

Step-by-step explanation:

When you add a negative, you are just subtracting.

p/-2-27=3

p/-2-27+27=3+27

2(-p/2)=2(30)

-p=60

-p/-1=60/-1

p=-60

Hope this helps! Pls give brainliest!