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Answer:

  x = 18

Step-by-step explanation:

Congruent angles have equal measures.

  74° = (4x +2)°

  72 = 4x . . . . . . divide by °, subtract 2

  18 = x . . . . . . .  divide by 4

The give quadratic function is dilated by the given coefficient, and shifted

horizontally to the left.

(a) The transformation of the common function f(x) are;

Please find attached the required graph created with MS Excel

(b) Where t = 0, represent the year 2,000 we have;

(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion

Reasons:

The given function is f(t) = 0.0037·(t + 14.979)²

Year 1990 is t = 0

(a) The given common function is; f(x) = x²

The transformation of the quadratic function are;

The coefficient 0.0037 widens the common function such that f(t) is wider

than f(x).

The constant, 14.979 added to the variable, t, shifts the graph of the

common function horizontally to the left.

Therefore;

Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.

(b) The amount of mortgage debt in 2,000 is given as follows;

With t' = 0 represent the year 2,000, we have;

At year 1990, t' = -10

Which gives, t' = t + 10

From which we have;

f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)²  = 0.0037·(t' + 24.979)²

Therefore;

The function with t = 0 representing the year 2,000 is presented as follows;

f(t) = 0.0037·(t + 24.979)²

(c) In the year 2014, we have;

t = 2014 - 2000 = 14

Which gives;

f(14) = 0.0037·(14 + 24.979)² ≈ 5.622

The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars

Learn more about transformation of quadratic functions here:

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Answer:

x ft is the answer since X = 10

so it means 10 ft

Answer:

what is that answer plss

Answer:

Angles are [tex]67^0,53^0[/tex]

Step-by-step explanation:

Let the angles be [tex]x,y[/tex]

One fifth of sum of two angles is 24

[tex]\frac{x+y}{5} =24\\\\x+y=120[/tex]

The  difference is [tex]14[/tex]

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

[tex]2x=134\\\\x=67^0[/tex]

[tex]y=120-67\\\\=53^0[/tex]

Answer:

x < - 1

Step-by-step explanation:

You have to treat it is a linear equation.

First, - 5 from both sides, resulting in -2x < 2.

Lastly, you need to find x on it's own so you have to divide by - 2.

Therefore, the answer would be x < -1.

Hope this helps :)

Answer:

See explanation

Step-by-step explanation:

Dilation of 1.5 about the origin. (Each new point is 1.5 times as far from the origin.)

G (-1, 3)  G' (-1.5, 4.5)

F (-2, -2)  F' (-3, -3)

G'x / Gx = -1.5/-1 = 1.5

G'y / Gy = 4.5 / 3 = 1.5

F'x / Fx = -3 / -2 = 1.5

F'y / Fy = -3 / -2 = 1.5

Answer: call 911

Step-by-step explanation: call 911

Answer:

C .......

Step-by-step explanation:

Answer:

D. x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction

Step-by-step explanation:

Evaluate 0 and 1 (xe+ex)Dx

Check the picture below.

it will be c

as

negative with negative erased together

Answer: 6 divided by 5 is 1.2

Step-by-step explanation: I used Siri lol

Answer:

1.2 in decimal form. equivalent form-12/10. i really dont know what your asking. so i hope this is what you wanted.

Step-by-step explanation:

Answer:

85*65=5525

85*43=3655

5525-3655=1870

Hope This Helps!!!

The resulting coordinate will be D'(2, 6), E'(4, -6), and F'(0, 10),

Let the coordinate of the triangle DF be given as D(1, 3), E(2, -3) and F(0, 5).

For the coordinates D(1, 3), E(2, -3), and F(0, 5), assuming the coordinate point is dilated by a factor of 2, the resulting coordinate will be D'(2, 6), E'(4, -6), and F'(0, 10),

Learn more on dilation here: https://brainly.com/question/10253650

Note that the question is answered on a general term.

Answer:

√5

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 star and a thanks :)

its d becuase i used math-way

Step-by-step explanation:

b

=

4

Answer:

Step-by-step explanation:

Given equation:

Add 12 to both sides:

Correct graph is D, where point 4 is marked

Answer:

2,983,562 if you mean hundredth

if to the nearest hundred then 2,983,600

Step-by-step explanation:

Answer:

Ascending order = 7,7,7,8,10,11,12,12

a) n = 8

= median = (n/2+(n/2+1)/2

= (4th term + 5th term)/2

= 8+10/2

= 9

b) range = 12-7 = 5

c) the mode = 7 (highest occuring value)

The median of the given list of numbers is 9.

The range of the given list of numbers is 5.

The mode of the given list of numbers is 7.

We have,

a) To find the median of a set of numbers, we arrange them in ascending order and determine the middle value.

If there is an odd number of values, the median is the middle number.

If there is an even number of values, the median is the average of the two middle numbers.

Arranging the numbers in ascending order: 7 7 7 8 10 11 12 12

There are eight numbers in this set, so the middle two numbers are 8 and 10.

Taking their average, the median is (8 + 10) / 2 = 9.

b) The range is the difference between the highest and lowest values in the set.

The lowest value is 7, and the highest value is 12.

So the range is 12 - 7 = 5.

c) The mode is the value that appears most frequently in the set.

In the given list, the number 7 appears three times.

Therefore,

The median of the given list of numbers is 9.

The range of the given list of numbers is 5.

The mode of the given list of numbers is 7.

Learn more about the median here:

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[tex]\text{Given that,}\\\\f(x) = x^3 -7x^2 +2x -8\\\\\\\text{(x+2) will be a factor of f(x) if } f(-2) = 0 \\\\\\f(-2) = (-2)^3 -7(-2)^2 +2(-2) -8 = -48 \\\\\\\text{Since}~ f(-2) \neq 0, ~ (x +2) \text{is not a factor of f(x).}[/tex]

Amount Lucy will be paying in interest will be $38,596.2  

Using the compound amount formula to get the amount after she will pay back after 20 years expressed as:

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

Substitute the parameters into the formula;

[tex]A=73,250(1+\frac{0.0315}{12} )^{20(12)}\\A= $73,250 (1.8761)\\A= \$137,421.49[/tex]

If Excel calculates the monthly payment to be $411.77, the amount paid for 20 years will be $411.77 * 240months = $98,824.8

Amount Lucy will be paying interest will be $137,421- $98,824.8 = $38,596.2  

Learn more on compound interest here: https://brainly.com/question/24924853

Factorization involves breaking down an expression.

The sum of cubes is given as:

[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]

(a) Verify the formula

Expand the expression on the right-hand side

[tex](a^3 + b^3) = a^3 -a^2b + ab^2 +a^2b - ab^2 + b^3[/tex]

Collect like terms

[tex](a^3 + b^3) = a^3 -a^2b +a^2b+ ab^2 - ab^2 + b^3[/tex]

[tex](a^3 + b^3) = a^3 + b^3[/tex]

The formula has been verified

(b) Factorized 8x^3+ 27

We have:

[tex]8x^3 + 27[/tex]

Express 27 as 3^3

[tex]8x^3 + 27 =8x^3 + 3^2[/tex]

Express 8 as 2^3

[tex]8x^3 + 27 =2^3x^3 + 3^3[/tex]

Rewrite as:

[tex]8x^3 + 27 =(2x)^3 + 3^3[/tex]

Given that:

[tex](a^3 + b^3) = (a + b)(a^2 -ab + b^2)[/tex]

The expression becomes

[tex]8x^3 + 27 =(2x + 3)((2x)^2 - (2x)3 +3^2)[/tex]

[tex]8x^3 + 27 =(2x + 3)(4x^2 -8x3 +9)[/tex]

(c)The other factor of 2^3 - b^3

By difference of cubes, we have:

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]

So, the equation becomes

[tex]2^3 - b^3=(2-b)(2^2+2b+b^2)[/tex]

This gives

[tex]2^3 - b^3=(2-b)(4+2b+b^2)[/tex]

Hence, the other factor of [tex]2^3 - b^3[/tex] is [tex]4+2b+b^2[/tex]

(c) Factor x^3 - 1

We have:

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex]

Express 1 as 1^3 in x^3 - 1

[tex]x^3 - 1 =x^3 - 1^3[/tex]

[tex]x^3 - y^3=(x-y)(x^2+xy+y^2)[/tex] becomes

[tex]x^3 - 1^3=(x-1)(x^2+x+1^2)[/tex]

[tex]x^3 - 1^3=(x-1)(x^2+x+1)[/tex]

Read more about factorization at:

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Answer:

Yes

Step-by-step explanation:

[tex]f[/tex](x) = 0.20x + 35 : 29.5

Answer:

Step-by-step explanation:

C