Sophie has $4.20 worth of dimes and quarters. She has twice as many quarters as dimes. Write a system of equations that could be used to determine the number of dimes and the number of quarters that Sophie has.

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

Answer:

what is that answer plss

Answer:

A = 12√3

Step-by-step explanation:

first find the limits by finding the zeros

0 = 9 − 3x²

3x² = 9

x² = 3

x = ±[tex]\sqrt{3}[/tex]

[tex]A = \int\limits^a_b ({9 - 3x^2\\}) - 0\, dx[/tex]

where b = [tex]-\sqrt{3}[/tex] and a = [tex]\sqrt{3\\}[/tex]

A = 9x - x³ [tex]\left \{ {{\sqrt{3} } \atop {-\sqrt{3} }} \right.[/tex]

[tex]A = 9\sqrt{3} - \sqrt{3} ^3 - (9(-\sqrt{3)} - (-\sqrt{3} )^3)[/tex]

[tex]A = 9\sqrt{3} -3\sqrt{3} +9\sqrt{3} - 3\sqrt{3}[/tex]

[tex]A = 12\sqrt{3}[/tex]

Answer:

B

Step-by-step explanation:

==========================================================

Explanation:

The ratio 3:2 scales up to 3x:2x for some positive whole number x.

We have 3x white pieces, 2x black pieces, and 3x+2x = 5x pieces total. Set this equal to the 15 mentioned and solve for x.

5x = 15

5x/5 = 15/5

x = 3

Therefore, there are 3x = 3*3 = 9 white pieces and 2x = 2*3 = 6 black pieces, which gives 9+6 = 15 total. The ratio 9:6 reduces to 3:2 after dividing both parts by the GCF 3.

Answer:

6c+2(5-7c)=6c+10-14c

A. -8c+10 is correct option.

Answer:

unfortunately i cannot tell you the exact answers; however, i can suggest something instead. my suggestion is that if there's any math notes that are available, maybe you could look over them-then apply that to the problems.

Step-by-step explanation:

I hope this helps you!

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]

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 :)

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:

https://brainly.com/question/15105480

Answer:

You get more points by answering people's questions. You use points to get help from other people.

Answer: Answer people's questions to get points and use those points to get an answer to your question.

Answer:

723 -> 01011010011

Step-by-step explanation:

Answer:

Well your Hypotenuse is 10 and your other angle is 8 so it is most likely 6 because you see a change in 2 each time and it is about 2 units smaller because all right triangles follow a pattern

Step-by-step explanation:

if it was too go even higher it would go to 12,14,16 etcetera

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

Using the combination formula and the probability concept, it is found that there is a 0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

Hence:

[tex]D = C_{3,2}C_{3,1}{C_{10,1}} = \frac{3!}{2!1!} \times \frac{3!}{1!2!} \times \frac{10!}{1!9!} = 90[/tex]

Total outcomes:

Four marbles are taken from a set of 13, hence:

[tex]T = C_{13,4} = \frac{13!}{4!9!} = 715[/tex]

Then, the probability is:

[tex]p = \frac{D}{T} = \frac{90}{715} = 0.1259[/tex]

0.1259 = 12.59% probability that she gets at least two red ones, given that she gets at least one green one.

To learn more about the use of the combination formula and the probability concept, you can check combination formula and the probability concept,

Check the picture below.

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

Mathematical processes are the steps used to determine the result of operations

The dimension of the rectangle is given as:

[tex]Length = 5x^2 - 8x + 9[/tex]

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

(1) The perimeter of the triangle

This is the sum of the side lengths of the rectangle.

So, we have:

[tex]Perimeter = 2 \times (Length + Width)[/tex]

This gives

[tex]Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)[/tex]

Collect like terms

[tex]Perimeter = 2 \times (5x^2 - 7x + 14)[/tex]

Open brackets

[tex]Perimeter = 10x^2 - 14x + 28[/tex]

Hence, the perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]

(2) The area of the triangle

This is the product of the dimensions of the rectangle.

So, we have:

[tex]Area = Length \times Width[/tex]

This gives

[tex]Area = (5x^2 - 8x + 9) \times (x + 5)[/tex]

Open brackets

[tex]Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45[/tex]

Collect like terms

[tex]Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45[/tex]

[tex]Area = 5x^3 +17x^2 -31x + 45[/tex]

Hence, the area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]

Read more about areas and perimeters at:

https://brainly.com/question/15656646

Answer:

c

Step-by-step explanation:

it just is that's the right book

Answer:

the answer would be 12 I say this because 72 divied by 6 would equal 12

Answer:

12 dollars

Set up a proportion.

6/72=1/x

Solve by cross-multiplying (my preferred method) and then you will end up with the final answer of x=12.

12 is the answer :)

PLEASE MARK BRAINLIEST!

THANK YOU & HAVE A WONDERFUL DAY :))

Answer:

0.7 is 7/10 Example out of ten cookies 7 are chocolate chip

0.07 is 7/100 Example out of 100 cookies 7 are chocolate chip

Hope This Helps!!!

Answer:

linear = 3x+y = 12, y = x/2 -3, y=x

nonlinear y = 6/x -2, y=3x³+5

Answer:

85*65=5525

85*43=3655

5525-3655=1870

Hope This Helps!!!

[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]

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

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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