The graph of the function y = x2 + 2 is shown. Which equation will shift the graph of the function down 4 units?
A) y = x2 + 6
B) y = x2 - 2
C) y = (x + 4)2 + 2
D) y = (x - 4)2 + 2

Answer:

[tex]\frac{61}{90}[/tex]

Step-by-step explanation:

We require to create 2 equations with the repeated value 7 after the decimal point

Let x = 0.6777777... ← multiply both sides by 10 and 100

10x = 6.777...... → (1)

100x = 67.777..... → (2)

Subtract (1) from (2) thus eliminating the repeating value

90x = 61 ( divide both sides by 60 )

x = [tex]\frac{61}{90}[/tex]

The decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.

To rewrite the decimal 0.67 with the repeating 7 as a simplified fraction, we can use the concept of infinite geometric series.

Let x = 0.677777...

Multiply both sides of the equation by 10 to shift the decimal point:

10x = 6.777777...

Now, subtract the original equation from the shifted equation to eliminate the repeating 7s:

10x - x = 6.777777... - 0.677777...

Simplifying, we get:

9x = 6

Divide both sides of the equation by 9 to solve for x:

x = 6/9

The fraction 6/9 can be further simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

x = (6/3) / (9/3)

x = 2/3

Therefore, the decimal 0.67 with the repeating 7 can be written as the simplified fraction 2/3.

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3 x 1/10 is 0.3 because it represents one tenth of 3, while 3 x 10 is 30 as it increases the value of 3 tenfold. Powers of ten and negative exponents demonstrate that each step in exponent changes the scale of the number by a factor of ten.

The reason why 3 x 1/10 is less than 3 x 10 is due to the values being multiplied by 3. When multiplying 3 by 1/10, you are essentially taking one tenth of 3, which gives you 0.3. However, when multiplying 3 by 10, you are increasing 3 tenfold, which results in 30.

To understand the scale, considering that each positive power of 10 is ten times bigger than the previous one, for instance from 3.2 to 3.2 x 10, and each negative power is ten times smaller, like from 3.2 to 3.2 x 1/10 . Powers of ten and their associated exponents allow us to easily compare and calculate with vastly different magnitudes, and this concept underlies the multiplication comparisons posed in the initial question.

Answer:

x = 90.

Step-by-step explanation:

< 1 and < 4 are corresponding angles and are congruent if line  a is parallel to line b. So:

3x - 160 = x + 20

2x = 180

x = 90.

Answer:

18

Step-by-step explanation:

Finding the remainder of 28254 divided by 52.

1. Use calculator to divide 28254 by 52:

2. Take whole part of the quotient and multiply by divisor:

3. Subtract this number from the initial dividend:

This is the remainder: 18

Final answer:

The remainder when 28,254 is divided by 52 is 9. This is found by dividing the number step by step until no more digits can be brought down, leaving the remainder.

Explanation:

The student is asking for the remainder when 28,254 is divided by 52. To solve this, we perform the division process until we reach a point where we cannot divide any further without going into decimals. The number that is left over at this point is the remainder. Below is a step-by-step explanation of the process.

The remainder when 28,254 is divided by 52 is 9.

Answer:

Probability of getting blue both times = [tex]\frac{16}{81}[/tex]

Step-by-step explanation:

A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green.  

It is spun twice.  

We have to find the probability of getting blue both times?.

For both times , the probability of getting blue is the same.

Probability = [tex]\frac{number of favorable cases}{total number of cases}[/tex]

The number of favorable cases for blue = 4

Total number of cases = 9

Hence the probability = [tex]\frac{4}{9}[/tex]

We have to get it two times so final probability = [tex]\frac{4}{9}\times \frac{4}{9} = \frac{16}{81}[/tex]

Answer:

[tex]y=-4x+8[/tex]

Step-by-step explanation:

step 1

Find the slope

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

take two points from the data

(0,8), and (8,-24).

substitute

[tex]m=\frac{-24-8}{8-0}[/tex]

[tex]m=\frac{-32}{8}[/tex]

[tex]m=-4[/tex]

step 2

Find the equation of he line in slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]m=-4[/tex]

[tex]b=8[/tex] ----> the y-intercept is given

substitute

[tex]y=-4x+8[/tex]

Answer:

Here's what I get  

Step-by-step explanation:

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent.

If ΔRST ≅ ΔXYZ then

∠R = ∠X

∠S = ∠Y

∠T = ∠Z

RS  = XY

ST  = YZ

RT  = XZ

To prove ΔRST ≅ ΔXYZ, perform a sequence of transformations and apply CPCTC to identify congruent parts.

To prove that ΔRST ≅ ΔXYZ, we need to perform a sequence of transformations that move ΔRST onto ΔXYZ. Once the triangles are superimposed, we can use the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) to identify congruent parts.

CPCTC states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent. In this case, the parts of ΔRST that are congruent to the corresponding parts of ΔXYZ are:

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Question is not proper, Proper question is given below.

Denzel is comparing websites for downloading music. One charges a $5 membership fee plus $0.50 per song. Another charges $1.00 per song, but has no membership fee. Write and solve an equation to find how many songs Denzel would have to buy to spend the same amount at both websites.

Answer:

Denzel would have to buy 10 songs to spend the same amount at both websites.

Step-by-step explanation:

Let the number of songs be 'x'.

Given:

One charges a $5 membership fee plus $0.50 per song.

So the total cost at one site will be membership cost plus charges per song multiplied by number of songs.

framing in equation form we get;

Total Cost at one site = [tex]5+0.5x[/tex]

Another website charges $1.00 per song, but has no membership fee.

So the total cost at Another site will be charges per song multiplied by number of songs.

framing in equation form we get;

Total Cost at Another site = [tex]1\times x=1x[/tex]

To find the number of songs that results in same cost we should equate the two expression and solve.

[tex]5+0.5x=x[/tex]

Combining like terms we get;

[tex]5 = x-0.5x\\\\5=0.5x[/tex]

Now Dividing both side by 0.5 we get;

[tex]\frac{0.5x}{0.5} = \frac{5}{0.5} \\\\x=10\ songs[/tex]

Hence Denzel would have to buy 10 songs to spend the same amount at both websites.

Step-by-step explanation:

making x subject in eq 1

x= (-1-9y)/-14

substituting the value of x in eq 2

17(-1-9y/-14)=7+9y

(-17-153y)/-14=7+9y

-17-153y=-98-126y

-17+98=153y-126y

81=27y

y=3

substituting this value of y in eq 1

-14x=-1-9(3)

-14x=-28

x=2

(x,y) = (2,3)

Answer:

x-intercept: (18/5,0)

y-intercept: (0,-2)

Step-by-step explanation:

btw .. you put the equation twice it's supposed to be " -5x+9y=-18 "

Answer:

I think its like $6.67

Step-by-step explanation:

divide 1000 by 375 then multiply the answer to that by 2.50 u should get 6.666666666666667 round it to 6.67

Final answer:

The perimeter of the square playground can be found by adding the lengths of all four sides. Two equivalent expressions for the perimeter are 8n + 8 and 4(2n + 2).

Explanation:

To find the perimeter of the playground, we need to add up the lengths of all four sides. Since the playground is a square, all four sides are equal in length.

The length of each side of the playground can be found by subtracting twice the width of the sidewalk from the overall length of the sidewalk. This is because the sidewalk wraps around the playground on all sides.

So, the length of each side of the playground is (2n+3) - 2(0.5) = 2n + 2.

The perimeter of the playground is then 4 times the length of each side, which is 4(2n + 2) = 8n + 8 yards.

Two equivalent expressions for the perimeter of the playground are 8n + 8 and 4(2n + 2).

Answer:

26 years of age.

Step-by-step explanation:

The average annual income, I, in dollars, of a lawyer with an age of x years is modeled with with the following function:

I = - 425x² + 45500x - 650000 .......... (1)

If the average annual income of the lawyer at the age of x years is $250000, then from the equation (1) we can write

- 425x² + 45500x - 650000 = 250000

⇒ - 425x² + 45500x - 900000 = 0

⇒ - 17x² + 1820x - 36000 = 0

Now, using the quadratic formula,

[tex]x = \frac{- 1820 \pm \sqrt{(1820)^{2} - 4(-17)(- 36000) } }{2(- 17)} = \frac{-1820 + 929.73}{- 34} = 26[/tex] years (Approximate)

{We have neglected the other root as we need the youngest age}(Answer)

Answer: 27

Step-by-step explanation:

Other answer is wrong

Answer:

The Width of the garden will be 9 feet.

Step-by-step explanation:

Given:

Manny has wood =48 feet

Length of the garden = 15 feet

The equation which can be used  [tex](2l+2w) = 48[/tex].

We need to find the width of the garden.

Solution :

Now Length of the garden is given we will substitute in the given equation to find the width.

[tex]2l+2w=48\\\\2\times15+2w=48\\\\30+2w=48[/tex]

Now Using Subtraction property we will subtract both side by 30 we get;

[tex]30+2w-30=48-30\\\\2w =18[/tex]

Now Using Division Property we will divide both side by 2 we get;

[tex]\frac{2w}{2}=\frac{18}{2}\\\\w= 9\ ft[/tex]

Hence the Width of the garden will be 9 feet.

Answer:

its A 9 ft

Step-by-step explanation:

i know things...

Answer:

They will cost $80.

Step-by-step explanation:

First, find the out how much 1 pen cost(unit rate).

To do that, divide 100 by 10.

100÷10= 10

So, each pen cost $10.

Now, multiply the cost of 1 pen times 8.

10×8= 80

This concludes that 8 of the same pens cost $80.

Answer:

(-9, 3)

Step-by-step explanation:

To rotate a point 270°:

R₂₇₀ (x, y) = (y, -x)

So the answer would be (-9, 3).

Answer:

140 degrees

Step-by-step explanation:

Due to ∠3 and ∠4 being vertical angles (they are across from one another) their measures are the same, therefore:

⇒ m∠3=m∠4

and since their measures are given in terms of x to find x just substitute:

⇒ x+30=2x-80 ⇒ x=110

We substitute x in m∠3=x+30 and find that m∠3=140 degrees

Answer:

The answer is 140 i just did the lesson

Step-by-step explanation:

Step-by-step explanation:

[tex]\text{The distributive property:}\\\\a(b-c)=ab-ac\\\\8(y-7)=(8)(y)-(8)(7)=8y-56\\\\\text{If you want whole solution:}\\\\8(y-7)=-16\\8y-56=-16\qquad\text{add 56 to both sides}\\8y-56+56=-16+56\\8y=40\qquad\text{divide both sides by 8}\\\dfrac{8y}{8}=\dfrac{40}{8}\\\boxed{y=5}[/tex]

Answer:

y=5

Step-by-step explanation:

8(y-7)= -16

(8)y-(8)7= -16

8y-56= -16

-16+56= 40

40/8= 5

y=5

(when you get y by itself)

hoped this helped a little bit.

Answer:

all the constants

Step-by-step explanation:

Answer:

Step-by-step explanation:

94 beats per minute during one workout.

If the rate was maintained for 25 minutes, the heart beats = 94×25

= 2350 beats

Answer:[tex]\frac{15}{28}[/tex]

Step-by-step explanation:

Number of strawberry = 2

Number of cherry = 3

Number of  = 3

Total number = 8

Brent randomly takes 2 yogurt containers from the bag

without replacement ,we are to find the probability that hat neither will be strawberry yogurt.

Let r represent  raspberry and c represents  Cherry ,then Bent selection could be :

{ rr , cc , rc , cr}

Calculating this , we have

([tex]\frac{3}{8}[/tex] x  [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x  [tex]\frac{2}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x  [tex]\frac{3}{7}[/tex] ) + ([tex]\frac{3}{8}[/tex] x  [tex]\frac{3}{7}[/tex] )

= [tex]\frac{30}{56}[/tex]

= 15/28

Therefore , the probability that neither will be strawberry yogurt= 15/28

Answer:

10.

Divide b into thirds, and then add together 2 of those thirds.

15/3 = 5

5x2 is 10.

Sorry if that doesn't make sense but it's how I do it in my head lol.

Answer:

45,2316

Step-by-step explanation:

You have to move the numbers to their new respective places as told by the description of the new place

The answer: d. < 1 and < 8

Answer:

Graph is attached below.

The graph illustrates the music that Jada may have downloaded with the $15 (s)he spent. The x-axis represents the number songs and the y-axis represents the number of albums. The data shows what combination of music she may have downloaded. The number of songs and albums have a negative correlation because if more money is spent on one variable, there is less money available to spend on the other.

Step-by-step explanation:

How to create a graph:

Using the data from part 1, plot the points (6, 3) (22, 1) and (30, 0) onto the graph. Label the x and y axis as the question asks. The axis should have arrows at the end. Include a title for the graph.

Do not connect the points because this indicates that all the space between the points are possible. Connecting the points includes decimal numbers and you can't buy part of a song or album, only a whole song or album.

Answer:

[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]

Step-by-step explanation:

Domain of Functions

Given a function h(x), we call the domain of h, all the values x can take so h exists. It's commonly easier to find the values of x for which h does NOT exist and then exclude them from the general domain of the real numbers.

The question provides us with the following functions

[tex]\displaystyle f(x)=x^2-3x-18[/tex]

[tex]\displaystyle g(x)=x^2-36[/tex]

[tex]\displaystyle h(x)=\frac{x^2-3x-18}{x^2-36}[/tex]

We called h(x) to the newly created function f/g(x)

To investigate the possible points of nonexistence for h, we factor h(x)

[tex]\displaystyle h(x)=\frac{(x-6)(x+3)}{(x-6)(x+6)}[/tex]

We can clearly see the denominator has two zeros at

[tex]\displaystyle x=6,\ x=-6[/tex]

A rational function cannot exist where the denominator is zero, regardless of the possible simplification with the numerator, as in this case. For example, for x=6 the function gets the value 0/0 and it's not defined there. We cannot simplify the common factor because they are part of the original function.

So, the domain of h is

[tex]\displaystyle (-\infty,\ -6 )\bigcup (-6,\ 6)\bigcup (6,+\infty )[/tex]

Or equivalently

[tex]\displaystyle \mathbb{R}-\left \{ -6,\ 6 \right \}[/tex]

The domain of the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, is all real numbers except x = 6 and x = -6. This is because we can't have g(x) equals to zero in (f/g)(x). Hence the domain is (-∞, -6) U (-6, 6) U (6, ∞).

In Mathematics, when dealing with the domain of the function (f/g)(x) it is important to understand that the domain is the set of all possible x values that we can input into the function. For the function (f/g)(x), given f(x)=x^2-3x-18 and g(x)=x^2-36, the denominator g(x) cannot be zero as this would mean dividing by zero, which is undefined in Mathematics. So we need to find the values of x for which g(x) ≠ 0. To do this, we set g(x) equal to zero and solve for x. So, x^2-36=0. Simplifying this, we get (x+6)(x-6) = 0. Hence the roots of the equation are  x = 6, x = -6.

These are the values for which g(x) will become zero. Since we can't have g(x)=0 in (f/g)(x), the domain of the function (f/g)(x) is all real numbers except x = 6, x = -6. So, the domain of (f/g)(x) is (-∞, -6) U (-6, 6) U (6, ∞).

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It takes 10.155 years until you have $3,000 ⇒ 3rd

Step-by-step explanation:

The formula for compound interest, including principal sum is:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where

∵ You decide to put $2,000 in a savings account

∴ P = 2000

∵ You want to save for $3,000

∴ A = 3000

∵ The account has an interest rate of 4% per year and is

   compounded monthly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 12 ⇒ compounded monthly

- Substitute all of these values in the formula above to find t

∵ [tex]3000=2000(1+\frac{0.04}{12})^{12t}[/tex]

- Divide both sides by 2000

∴ [tex]1.5=(1+\frac{1}{300})^{12t}[/tex]

∴ [tex]1.5=(1\frac{1}{300})^{12t}[/tex]

- Change the mixed number to an improper fraction

∴ [tex](1.5)=(\frac{301}{300})^{12t}[/tex]

- Insert ㏒ for both sides

∴ [tex]log(1.5)=log(\frac{301}{300})^{12t}[/tex]

- Remember [tex]log(a)^{n}=nlog(a)[/tex]

∴ [tex]log(1.5)=(12t)log(\frac{301}{300})[/tex]

- Divide both sides by [tex]log(\frac{301}{300})[/tex]

∴ 121.84 = 12 t

- Divide both sides by 12

∴ 10.155 = t

It takes 10.155 years until you have $3,000

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Answer:

The converse of the Pythagorean theorem states that if the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Answer:

its C basically

Step-by-step explanation: