You have a cup with 17 coins inside. The total inside the cup is $5. 50. Determine how many half dollars and quarters are inside the cup. Use a system of equations. Be sure to define the variables and show all work

I think that the answer would be 14

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

Now, According to the question:

Finding Slope From Two Points Formula

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,

m = slope of the line

x₁ = the x-coordinate of the first point

y₁ = the y-coordinate of the first point

x₂ = the x-coordinate of the second point

y₂ = the x-coordinate of the second point

Then rise from A to B = y₂ - y₁

Run from A to B = x₂ - x₁

Then the slope, m = rise/run = (y₂ - y₁) / (x₂ - x₁)

Hence, we derived the slope formula.

Here are the steps to find the slope of a line given two points on it.

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Multiplying the  second equation by -4 eliminates the x terms when adding the first equation.The second equation is 4x + 5y = -8

In order to eliminate the x terms when adding the first equation, you need to multiply the second equation by -4. The formula and calculation steps are as follows:

Formula:

Equation 1 + (-4 x Equation 2)

4x + 5y = -8

-4(4x + 5y) = -4(-8)

-16x -20y = 32

Adding the two equations together gives:

0x + 25y = 24

Therefore, multiplying the second equation by -4 eliminates the x terms when adding the first equation.

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If the sum of 21 and a difference of 6 then the numbers are 27/2 and 15/2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The two numbers be a and b.

Therefore, (a + b) = 21 and (a - b) = 6.

Adding these two equations, The variable 'b' will cancel out and we'll have

2a = 27.

a = 27/2.

And, 27/2 + b = 21.

b = 21 - 27/2.

b = (42 - 27)/2.

b = 15/2.

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Answer:

1,520 pounds

Step-by-step explanation:

40x 38 = 1520

The value of x is 8 and  the measure of the two marked angles is  60°.

When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.

we know that ,

10x-20=7x+4   (it is corresponding opposite angle)

3x=24

x=8

the value of x is 8.

the measure of the two marked angles is 10*8-20= 80°-20°= 60°.

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The equation the line is, y-3x=1

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

Here, we have to points (-1,-2) and, (3,10)

So, by using the formula of equation of straight line of two-point form, we get,

(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )

=>(y+2)/(x+1)=(10+2)/(3+1)

=>y+2=3x+3

=>y-3x=1

Hence, the required equation is,  y-3x=1

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In one min Charlie can read is [tex]2\frac{1}{7}[/tex] pages at a constant rate.

A single unit's value may be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary technique. We typically utilize this technique for math computations.

In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or less quantities are subsequently determined. This approach is known as the unitary method for this reason. Due to the fact that they generate two distinct sorts of variations, there are two different types of unitary approaches.

In [tex]\frac{2}{3}[/tex] min Charlie can read [tex]1\frac{3}{7} = \frac{10}{7}[/tex] pages

In one min Charlie can read is: [tex]\frac{10}{7}*\frac{3}{2} = \frac{30}{14} = 2\frac{2}{14} =2\frac{1}{7}[/tex]

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The actual length of the car based on the model will be 350 inches.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the ratio of the model car was 2:35. If the model is 20 inches long, the actual length of the car will be:

= 20 ÷ 2/35

= 20 × 35/2

= 350 inches.

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Complete question

The ratio of the model car was 2:35. If the model is 20 inches long. then what would be the actual length of the car??

In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.

First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).

[tex]3/4 cups * 1 = 3/4 cups\\[/tex]

Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:

[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]

Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:

[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]

Mario can make 2.25 batches of cookies using all of his chocolate chips.

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Answer:

I'm pretty sure the answer for this is 28 :))

There is no single answer to this question. It depends on what values are chosen for x and y , equation has an infinite

The equation 5x + 2y = -7 is an indeterminate equation with two unknowns, x and y. This means that the equation has an infinite number of solutions, depending on the values of x and y. For example, if x = 3 and y = -2, then the equation would be satisfied. If x = 2 and y = -3, then the equation would also be satisfied. Therefore, the number of solutions for this equation is infinite.There is no single answer to this question. It depends on what values are chosen for x and y.

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Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Area = length x breadth.

Here,

Given : A triangle land which has

height = 2miles

and base = 1.5+ 1.5 = 3 miles

Thus,

To find the area of triangle :

=> Area = 1/2*b*h

=>Area = 3*2/2

=> Area = 3 miles square

Therefore , the solution of the given problem of area comes out to be the land acquired by university is of 3 miles square area.

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Answer: 2.4

Step-by-step explanation:

we start from the right most digit, that is 8. Since 8 is greater than 5, we add 1 in the number before 8, that is 3. When we add 3 and 1 we get 4. This way, we get our answer 2.4 , which is correct to 2 significant figures.

hope that helps...

Answer:

it looks like a reflection or translation but my gut is saying translation

Answer: 8 3/4 because first find your common denominator, then solve the math and you will get 8 3/4

Answer: 60

Step-by-step explanation:

If you subtract how much money you already had(54.75) from what you spent(79.99) you get 25.24. You then add 25.24 to the koney you had left(34.76) to get you answer of 60

The equation of line in slope intercept form is,

⇒ y = x - 2

When the graph is shift down 9 units.

Then, Equation of line become,

⇒ y = x - 11

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (2, 0) and (0, -2).

Now,

Since, The equation of line passes through the points (2, 0) and (0, -2).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 2 - 0) / (0 - 2)

m = - 2 / -2

m = 1

Thus, The equation of line with slope 1 is,

⇒ y - 0 = 1 (x - 2)

⇒ y = x - 2

And, When the graph is shift down 9 units.

Then, Equation of line become,

⇒ y = x - 2 - 9

⇒ y = x - 11

Therefore, The equation of line in slope intercept form is,

⇒ y = x - 2

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The number of vegetable plates can be made = 120

We know that a combination is nothing but a way of selecting items from a collection. In combination the order of selection does not matter.

We know that a formula for a combination is,

^nC_r = n! / r!(n - r)!

where,  ^nC_r = number of combinations

n = total number of items in the collection

r = number of choosing items from the collection

and n! = n × (n - 1) × (n - 2) × . . . × 1

Here, we have n = 10 and r = 3

Using combination formula,  the total number of plates made:

^10_C_3

= 10! / (3! × (10 - 3)!)

= 10! / (3! × 7!)

= (10 × 9 × 8 × 7!) /( 3! ×7!)

= (10 × 9 × 8) / (3 × 2 × 1)

= (90 × 8) / 6

= 720/6

= 120

Therefore, 120 vegetable plates maybe made

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If you double the amount of fluid ounces, the amount of cups also double

There is a proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.

The donation is proportional to the dinner bill

The donation for a dinner bill of $50 is $9

If there are 8 fluid ounces in one cup

8 : 1 = 16 : x

8/1 = 16/x

8 × x = 16 × 1

8x = 16

x = 16/8

x = 2

The difference between weight = 1

The difference between cost = $0.68 - $0.47

= $0.21

$0.89 - $0.68

= $0.21

$1.10 - $0.89

= $0.21

Cost of mailing 6-ounce letter

1 : 0.47 = 6 : x

1/0.47 = 6/x

1 × x = 6 × 0.47

x = $2.82

The donation for a dinner bill $50 is

Dinner bill : donation

25 : 4.50 = 50 : x

25/4.50 = 50/x

25 × x = 50 × 4.50

25x = 225

x = 225/25

x =$ 9

Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.

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The total amount of solid sphere chocolate in the box is 1695.6 cubic centimeters.

The space occupied within an object's borders in three dimensions is referred to as its volume.

The volume or the space inside the borders of the sphere is given by the formula:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Given that the diameter is 6cm, the radius r = 3cm.

Substituting the value of radius in volume we have:

[tex]V = \frac{4 (3.14)(3)^3}{3}[/tex]

[tex]V= 113.04[/tex]

The box contains 15 candies hence the total volume will be:

V = 15 * 113.04

V = 1695.6 cubic centimeters.

Hence the total amount of chocolate in the box is 1695.6 [tex]cm^3[/tex].

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The value of polynomial p(x) when x=0 is 35.

What is a polynomial?

An expression made up of indeterminates and coefficients and utilising solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables is referred to as a polynomial.

The complete question is as follows:

Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).

Given,

p(x) is a polynomial of smallest degree where

    p(-3) = p(√7) = p( 1-√6) = 0

     p(-1) = 8

 So the factors of p are (x+3),(x-√7) and (x - 1+√6)

Given p has rational coeffecients. So we should remove √7 and √6. This can be done by multiplying with conjugates.

(x-√7)*(x+√7) = x²-7

(x-1+√6) * (x-1-√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5  

Now the polynomial can be written as

p(x) = c (x+3)(x²-7) (x²-2x-5 )

Here c is a constant and can be determined using p(-1) = 8

p(-1) = c ( -1+3)(-1² - 7 )(-1²-2*(-1) -5)

8 = c(2)(-6)(-2)

c = 1/3

Now the polynomial p(x) = 1/3(x+3)(x²-7) (x²-2x-5 )

Therefore p(0) = 1/3 (3) (-7)(-5) = 35

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The coefficient of x⁸y⁹ is 81662929920.

A binomial is a two-term algebraic expression. Examples of binomials include a + b, x - y, and more.

The binomial expansion formulae are used to find the powers of the binomials that cannot be extended using the algebraic identities. 

Given expansion (3x + 2y)¹⁷

to find the coefficient of x⁸y⁹

this is found by binomial expansion,

(x + y)ⁿ = ∑ₙˣ⁻⁰ ⁿCₓxⁿ⁻ˣyˣ

here n = 17 and x = 9

(3x + 2y)¹⁷ = ¹⁷C₉ (3x)¹⁷⁻⁹ (2y)⁹

¹⁷C₉ = 24310

(3x + 2y)¹⁷ = 24310 (6561) (x)⁸ (512) (y⁹)

(3x + 2y)¹⁷ = 81662929920x⁸y⁹

Hence the coefficient is 81662929920.

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Answer:  A

Step-by-step explanation:  They both go up but they have diffrent patterns

hopes this helps any

Answer:

A.

Step-by-step explanation:

the 'x' slot is going up two and the 'y' slot is going up one every change.

The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.

The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.

So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

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The robot is moving in the direction indicated by the formula ((i)²¹*(-i)²²)d, or in the beginning direction.

What is complex plain?

When a line is rotated in the complex plane either clockwise or anticlockwise, it is multiplied by -i or I depending on which direction the line is rotated. The direction vector is rotated 90 degrees in the clockwise direction to make a right turn. It is the same as increasing the complex number by -i.

A left turn is represented as a 90° anticlockwise rotation of the direction vector. It is comparable to increasing the complex number by i.

There are 21 left turns of the robot. The direction vector will now be di21. Once it has been rotated 22 times to the right, the direction vector will now be  (di²¹)*(-i)²²=d((i)²¹*(-i)²²).

Consequently, the robot's current direction is:

d((i)²¹*(-i)²²)= di²¹⁺²²=di⁴³= d(-i)= -di

No matter what, the direction will always be the same, hence the sequence is irrelevant.

Hence, the equation that will indicate where the robot is moving is  ((i)²¹*(-i)²²)d, or in the starting direction. Furthermore, the final direction it faces does not depend on the order.

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Answer:

A. The car spends 2.05 hours going 55 miles per hour

B. The car spends 1 hour going 35 miles per hour

C. The trip takes 3.6 hour

Step-by-step explanation:

The equation is

55x+35y=200

Let's solve A

We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x

55x+35(2.5) = 200

55x + 87.5 = 200

55x = 112.8

x = 2.05 hours going 55 miles per hour

So, the car spends 2.05 hours going 55 miles per hour

Let's solve B

55(3)+35y=200

165 + 35y = 200

35y = 35

y = 1 hour

So, the car spends 1 hour going 35 miles per hour

Let's solve C

We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x

55x+35(0)=200

55x = 200

x = 3.6  hours

So, the trip takes 3.6 hour

The difference in ages of Marcelle and Megan is 95/12 as an improper fraction and as a mixed number is 7 whole number and the fraction 11/12.

We shall convert the fractions to have similar denominators and simply apply subtraction for the numerators as follows:

Marcelle's age = 15 whole number, 1/2

Marcelle's age = 31/2

Megan's age = 7 whole number, 7/12

Megan's age = 91/12

LCM of 2 and 12 is 12 so;

Marcelle's age = 31/2 × 12/12

Marcelle's age = 186/12

difference in their age (186 - 91)/12

difference in their age = 95/12

Therefore, the difference in the ages of Marcelle and Megan is the fraction 95/12 or as a mixed number is 7 whole number and the fraction 11/12

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Answer:

Step-by-step explanation:

In 12 hours, the train will travel 487.5 miles

8/325=40.625

40.625 x 12 = 487.5