Suppose you have 18 more quarters than dimes. You have a total of $8.00. How many of each coin do you have? Use the substitution method to answer the question.

Answer:

See below for answers and explanations (with attached graph)

Step-by-step explanation:

It helps to transform the equation into vertex form by completing the square because it tells us a lot about the characteristics of the parabola:

[tex]\displaystyle y=-6x^2+12x-8\\\\y=-6\biggr(x^2-2x+\frac{4}{3}\biggr)\\\\y-6\biggr(-\frac{1}{3}\biggr) =-6\biggr(x^2-2x+\frac{4}{3}-\frac{1}{3}\biggr)\\\\y+2=-6(x^2-2x+1)\\\\y+2=-6(x-1)^2\\\\y=-6(x-1)^2-2[/tex]

Since vertex form is [tex]y=a(x-h)^2+k[/tex], we identify the vertex to be [tex](h,k)\rightarrow(1,-2)[/tex] and the axis of symmetry to be [tex]x=h\rightarrow x=1[/tex]. The y-intercept can be found by setting [tex]x=0[/tex] and evaluating:

[tex]y=-6(x-1)^2-2\\\\y=-6(0-1)^2-2\\\\y=-6(-1)^2-2\\\\y=-6(1)-2\\\\y=-6-2\\\\y=-8[/tex]

Hence, the y-intercept of the parabola is [tex]y=-8[/tex], or [tex](0,-8)[/tex] as an ordered pair.

Answer:

I dont think 2 50 doallr bills is gonna work

Step-by-step explanation:

all of this added togather is 122.66 and 2 50 is a 100 so yah

Answer:

In 15 years the final balance will be $632.15

Step-by-step explanation:

The final balance would be $632.15 and the total compound interest would be $332.15. If you have trouble with these kind of questions in the future I suggest using a compound interest calculator that can be found online :)

The area of the Area  of the polygon is known to be 9 units². Find more about polygon below

The area of a polygon is one that is defined as the measurement of the given area that is known to be covered by it.

Note that to calculate the area, it will be

Area = 1/2 (5 + 1) x 3 = 9 units²

Thus the answer of 9 units is correct.

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Answer:

volume = 216cm

Step-by-step explanation:

V = (1/2) × b × h × l

V = 1/2 × 6 × 8 × 9

v=216

Answer:

216 cubic centimeters

Step-by-step explanation:

To calculate the volume of a triangular prism, we can use the formula:

V = (length x width x height) / 2

To solve this problem, in particular, all we have to do is substitute the values:

V = (8 x 6 x 9) / 2

V = 216 cubic centimeters

Hope this helps!!

Answer: 400

Step-by-step explanation: cube root 8000 then that times itself

Answer:

250 $3 tickets and 100 $2 tickets were sold.

Step-by-step explanation:

easy :)

The ratio of the length of candle A to the length of candle B at first will be 3 / 5.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

Candle A and candle B were lit at the same time. candle a could last 3 hours and candle b could last 5 hours. after 1 hour, both candles were equal in length.

Then the ratio of the length of the candle A to the length of candle B at first will be

Let the length of candle A is x and the length of candle B be y.

The common speed will be S.

Then we have

Time = length / speed

For candle A, we have

Candle A = x / S = 3 ...1

For candle B, we have

Candle B = y / S = 5 ...2

From equations 1 and 2, we have

x / 3 = y / 5

x / y = 3 / 5

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Answer:x=61

Step-by-step explanation​

856−5x3{131}=2

8(x−9)+5(5−18)+1(15−6x)=2

8x−72−65+15−6x=2

2x=122

x=61

sorry if i'm wrong

Answer:

students in the drama club: 57

students in the yearbook club: 44

Step-by-step explanation:

101 - 13 = 88

88 / 2 = 44

101 - 44 = 57

44 in the drama club and 57 in the yearbook club

Answer:

531,441

Step-by-step explanation:

3^2=9

9^6=531,441

Answer:

[tex] \sqrt{ {2}^{6 } } = 27 if thats what you meant here is another answer{ {2}^{6} = 64[/tex]

Answer:

Down payment

Step-by-step explanation:

Down payment is the amount you pay for the purchase of a house that decreases the amount of the loan. It decreases the amount of interest paid over the lifetime of the loan

Answer:

Step-by-step explanation:

Answer:

M = 61

nm = 31

kn = 45

L = 119

Step-by-step explanation:

its a parallelogram so everything is obvious

Wrong answer sorry. Hope you find it!

Step-by-step explanation:

where is the figure and question

A right rectangular pyramid when sliced vertically, the  shape of the cross-section is known as Triangle.

This is known to be a kind of shape that is said to be in  a closed form and it is also known to be a 2-dimensional shape that has 3 sides, 3 angles, and also 3 vertices.

Note that when the when the right rectangular pyramid is sliced vertically (down) by a plane passing through the  of the pyramid, the new shape of the cross-section is a triangle.

See full question below

A right rectangular pyramid is sliced vertically (down) by a plane passing through the  of the pyramid. What is the shape of the cross-section?

A. Rectangle

B. Pyramid

C. Triangle

D. Trapezoid

See full question below

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Expression: 5z² - 2z + 1 = 0

Discriminant formula: b²- 4ac

Identify: a = 5, b = -2, c = 1

Solve for discriminant: (-2)²- 4(5)(1) = 4 - 20 = -16

p = 1 also can be rewritten as 2nd equation: 0m + 1p = 1

Build Augment Matrices by taking coefficient's:

[tex]\left[\begin{array}{ccc}1&-1&|| \ \ 2\\0&1&|| \ \ 1\end{array}\right][/tex]

Solve:

Add row 2 to row 1 : R₁ = R₁ + R₂ and restore it back

[tex]\rightarrow \ \left[\begin{array}{ccc}1+0&-1+1& \ \ \ \ || \ 2+1\\0&1&|| \ \ 1\end{array}\right][/tex]

[tex]\rightarrow \ \left[\begin{array}{ccc}1&0& || \ \ 3\\0&1&|| \ \ 1\end{array}\right] \ \ \ = The \quad reduced \quad matrix[/tex]

Solution = (m, p) = (3, 1)

Answer:

14.  -16

15.  m = 3  and  p = 1

Step-by-step explanation:

Discriminant

[tex]b^2-4ac\quad\textsf{when}\quad ax^2+bx+c=0[/tex]

Given equation:   [tex]5z^2-2z+1=0[/tex]

Therefore:

Substituting the values into the discriminant:

[tex]\begin{aligned}\implies b^2-4ac & = (-2)^2-4(5)(1)\\& = 4-20\\& = -16\end{aligned}[/tex]

As the discriminant is negative, this implies there are no real roots.

Augmented Matrices

[tex]\begin{array}{c}ax+by=p \\cx+dy=q\end{array} \implies \left[\begin{array}{r r | r}a & b & p \\ c & d & q\end{array}\right][/tex]    

Use elementary row operations to convert into:

[tex]\left[\begin{array}{r r | r}1 & 0 & h \\ 0 & 1 & k\end{array}\right] \implies \begin{array}{r}x=h\\y=k\end{array}[/tex]

Given:

[tex]\begin{aligned}m-p & =2\\ p & = 1\end{aligned} \implies \left[\begin{array}{r r | r}1 & -1 & 2 \\ 0 & 1 & 1\end{array}\right][/tex]

[tex]\left[\begin{array}{r r | r}1 & -1 & 2 \\ 0 & 1 & 1\end{array}\right] \begin{array}{c}R_1 + R_2 \rightarrow R_1 \\\rightarrow\end{array} \left[\begin{array}{r r | r}1 & 0 & 3 \\ 0 & 1 & 1\end{array}\right][/tex]

Therefore:  

[tex]m=3[/tex]

[tex]p=1[/tex]

The number of whole revolutions for 1000 meters is 265, while the time taken to move 1000 meters with a speed of 40rev/min is 7minutes.

This is the number of times a body moves round  a circular path.

A revolution is equal to the circumference of a circle.

Analysis:

r  = 120/2 = 60cm

1 revolution of a circle = 2πr

Let n be the number of revolutions

so that 2πr x n = 1000 x 100 since 100 cm = 1 m

n = 100000/2πr = 265 revolutions

If the Fan turns 40 rev / minute

Then it 265 revolutions = 1000 meters, 265/40 = 7 minutes

In conclusion, the number of revolutions for 1000 meters is 265 and the time taken for 265 revolutions is 7 minutes.

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Answer: Please see the analysis

The polygon abcdef in the coordinate plane shown with area of 18 square units.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

We have vertices for the polygon:

a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)

After marking the coordinates on the coordinate plane and connecting the lines, we will get a polygon.

We can find the area of the shape:

Area of the shape = 18 square units

Thus, the polygon abcdef in the coordinate plane shown with area of 18 square units.

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Amount earned per week=400-380=$20

Price of one shoe=70$

Total weeks

Minimum 4 weeks

Answer:

4 weeks

Step-by-step explanation:

Given:

Therefore,

Weekly surplus = weekly net income - weekly expenses

                          = $400 - $380

                          = $20

Given:

Number of weeks = cost of new shoes ÷ weekly surplus

                              = $70 ÷ $20

                              = 3.5

                              = 4 weeks (rounded to nearest week)

Therefore, it will take 4 weeks to save enough to buy the shoes.

Answer:

sin

Step-by-step explanation:

sin=O opposite/hypotenuse

Answer:

The answer is c because of how the equation is set and made

The radical equation is √x+3=13. Therefore, option C is the correct answer.

A radical equation is an equation in which a variable is under a radical. To solve a radical equation: Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

In option C, x is under radical, so it is radical equation.

Here, √x+3=13

√x=13-3

√x=10

Therefore, option C is the correct answer.

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The equation of the circle represented by the pizza is x^2 + y^2 = 4

The given parameters are:

Radius, r = 2

Center, (a,b)= (0,0) i.e. origin

The equation of the circle is calculated as:

(x - a)^2 + (y - b)^2 = r^2

This gives

(x - 0)^2 + (y - 0)^2 = 2^2

Evaluate the exponents

x^2 + y^2 = 4

Hence, the equation of the circle is x^2 + y^2 = 4

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Answer:

Part A: The x-intercepts represent the prices of the erasers at which the profit will be $0. The function is increasing from [-∞, 4] and decreasing from [4,+∞]. This means that when the price of the eraser is less than 4, the profit will increase until it gets to 4 and decrease for any value greater than 4, where $4 is the price at which the company has the maximum profit.

Part B: From the interval [1,4], the average rate of change is 50.625, which means that for every $1 increase in the price of erasers, the profit goes up by $50.625.

Part C:

The domain of this function is [0,+∞] because this is the only part of the function that is positive. The function cannot have -x-values because it does not make sense to make the price of an eraser 'negative'.

Step-by-step explanation:

The equation of this parabola is [tex]f(x) = -16.875(x-4)^2 + 270[/tex].

Part A:

The x-intercepts represent the prices of the erasers at which the profit will be $0. The function is increasing from [-∞, 4] and decreasing from [4,+∞]. This means that when the price of the eraser is less than 4, the profit will increase until it gets to 4 and decrease for any value greater than 4, where $4 is the price at which the company has the maximum profit.

Part B:

To find the average rate, we can use the slope formula, but first, we must find the y-values at each given x-value. We can plug in 1 and 4. [tex]f(1) = -16.875(1-4)^2 + 270 = 118.125[/tex]. We know that at x = 4, the y-value is 270 because the vertex is at (4,270). Now we can apply the slope formula [tex]\frac{270 - 118.125}{4 - 1} = 50.625[/tex]. This means that from the interval [1,4], the average rate of change is 50.625, which represents that for every $1 increase in the price of erasers, the profit goes up by $50.625.

Part C:

The domain of this function is [0,+∞] because this is the only part of the function that is positive. The function cannot have -x-values because it does not make sense to make the price of an eraser 'negative'.

hope this helped! :)