find the coordinates of the intersection of the diagonals of parallelogram PQRS with vertical P(-5,5) Q(2,5) , R(4,-3) and S(-3,-3)

He answered 16 questions correctly, and got 3 wrong answers.

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Explanation:

Let

x,y,z are nonnegative whole numbers.

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Since there are 20 questions total, this means the first equation to set up is:

x+y+z = 20

Solving for y leads to

x+y+z = 20

y+z = 20-x

y = 20-x-z

We'll use this later.

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Another equation to set up is 7x-4y = 100 because Eric earns 7 points per correct answer and loses 4 points for each incorrect answer, and all that leads to 100 points total which was his quiz score. We'll ignore the questions he left blank since they add 0 points.

Let's plug the equation in which we isolated y

7x-4y = 100  

7x-4(20-x-z) = 100

7x-80+4x+4z = 100

7x+4x+4z = 100+80

11x+4z = 180

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Now we can guess and check to see which pair of x and z values will make that last equation above true. I suggest starting with the smallest possible value of x and using that x value to solve for z.

If x = 0, then,

11x+4z = 180

11(0)+4z = 180

4z = 180

z = 180/4

z = 45

So if Eric got 0 correct answers, then he left 45 questions blank. But that isn't possible because there are only 20 questions total. So we'll ignore the case that x = 0.

If we increase x by 4, and decrease z by 11, then we get another ordered pair solution to this equation

So another solution is (x,z) = (4,34)

Note that

11x+4y = 180

11(4) + 4(34) = 180

But like before, z = 34 isn't possible since 20 is the max.

Increase x by 4 again, and drop z by 11 to get (x,z) = (8,23). Again we run into the same issue as before.

Increase x by 4 again, and decrease z by 11 to get (x,z) = (12, 12). Now we have both x and z smaller than 20, but note how x+z = 12+12 = 24 which exceeds the total number of questions. So we rule this case out as well.

Do another round of "increase x by 4, decrease z by 11" to get to (x,z) = (16, 1). This is the only case left because anything beyond this, z will be negative.

Luckily, this final case does work. If Eric answers x = 16 questions correctly, then he left z = 1 of them blank. That must mean y = 20-x-z = 20-16-1 = 3 questions were incorrect.

We can see that:

7x-4y = 7(16)-4(3) = 112-12= 100

meaning that (x,y) = (16,3) is a solution to 7x-4y = 100.

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To summarize, we found that the only possible solution is (x,y,z) = (16, 3, 1)

Meaning x = 16 questions were correct, y = 3 were wrong, and z = 1 question was left blank.

Answer:

1. x = 67.5

2. x = 2.5

3. x = 35.2

4. x = 2.0

5. x = 17.0

Step-by-step explanation:

Question 1

The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:

2x/9 = 15

2x = 9(15)

Next solve for x:

2x = 135

x = 67.5

Question 2

The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:

20x/8.7 = 5.8

20x = 8.7(5.8)

Next, solve for x:

20x = 50.46

x = 2.523

Round to the nearest tenth:

x = 2.5

Question 3

The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:

5x/16 = 11

5x = 11(16)

Next, solve for x:

5x = 176

x = 35.2

Question 4

The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:

0.5x/0.06 = 17

0.5x = 17(0.06)

Next, solve for x:

0.5x = 1.02

x = 2.04

Round to the nearest tenth:

x = 2.0

Question 5

The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:

29(44)/x = 75

29(44) = 75x

Next, solve for x:

1276 = 75x

x = 17.0133

Round to the nearest tenth:

x = 17.0

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

[tex]r = \sqrt[3]{\frac{3*36\pi}{4\pi}} = \sqrt[3]{3*9} = \sqrt[3]{27} = 3[/tex] m

Answer: B (3 m).

Answer:

21 ounces of juice.

63 ounces of water

Step-by-step explanation:

let :

x = ounces of strawberry juice to make the strawberry infused water.

3x = ounces of water needed to make the strawberry infused water.

3x + x = 84

4x = 84

divide both sides of the equation by 4

x = 21 ounces

3x = 3 x 21 = 63 ounces

Answer:

12 y

Step-by-step explanation:

π. x².y = ⅓. π (½x) ².h

=> eliminate π,

x²y = ⅓. ¼x².h

=> eliminate x²,

y = 1/12 h

h = 12 y

so, height of the cone = 12 y

Answer:

Step-by-step explanation:

website for info:

https://www.symbolab.com/solver/pre-calculus-distance-calculator

Answer:

so the answer is about 8.40

Steps

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find the number in the tenth place and look one place to the right for the rounding digit. Round up if the number is greater than or equal to 5 but since 2 is less than 5, stays the same

16.820⇒16.82

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8.264⇒8.364

Remember round up if the number is greater than or equal to 5 and round down if the number is less than 5.

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now that we have rounded everything. It is time to estimate 16.82-8.364.

16.82 is close to 16.80 and 8.364 is close to 8.40.

16.80-8.40=8.40

Answer:

50 percent

1/2 of 6 is 3

Answer:

50 percent

Step-by-step explanation:

Answer: 1331

Step-by-step explanation: v=lwh

The volume would be 1,331 cm cubed. I hope this helps, have a good day!

Answer:

1.6lb

30oz

800g

Step-by-step explanation:

That's the order.

Answer:

You can use symbolab for problems such as these, they'll provide step-by-step guides on how to do it. Symbolab is a math calculator that shows you how to solve each problem.

Answer:

2x+10+3x-10=90

5x=90

x=18

the answer is 18 because the figure is a rectangle and recatngle angles equal 90

Answer:

Where is I on the square?

Answer:

118

Step-by-step explanation:

4x² + 3y

= 4(5)² + 3(6)

=4(25) + 18

= 100 + 18

= 118

Answer:

You are right. It's 56

Step-by-step explanation:

You do half of the solid (4*7) with is 28. Then because it is only half you would double your answer to get 56.

V = L * W

V = 4 * 7

V = 28

Then double it.  28 * 2 = 56

Answer:

12 + 4x = 4(3 + x)

Step-by-step explanation:

Think about what you need to multiply (3 + x) by to get 12 + 4x.

Answer:

(2.6, 4.8)

Step-by-step explanation:

The midpoint segment formula is expressed as;

M(X, Y) = [(ax2+bx1)/a+b, (ay2+by1)/a+b]

X = ax1+bx2)/a+b

Y = ay1+by2)/a+b

Given X(-1,3) to Z(5,6) and a = 2, b = 3

X = 2(-1)+3(5)/2+3

X =(-2+15)/5

X =13/5

X = 2.6

Similarly;

Y = 2(3)+3(6)/2+3

Y =(6+18)/5

Y =24/5

Y = 4.8

hence the required coordinate of Y is (2.6, 4.8)

Answer:

B

Step-by-step explanation:

It's kind of ahrd to see but you can see that the x coordinate is for sure 4

b is the only possible answer

Answer:

can you show the table?

Step-by-step explanation:

to help with figuring the answer cause there no context

Answer:

101.

Step-by-step explanation:

3^4 equals 81.

4 times 5 is 20.

81 plus 20 equals 101.

Your answer is 101.

Answer:

I don't know how you wanted to round it

1)

SA = 8(7) + 12(7) + 10(7) + [tex]\frac{1}{2}[/tex] [tex]\sqrt{-8^4+2(8x12)^2+2(8x10)2-12^4+2(12x10)^2-10^4}[/tex]

SA = 289.3725

V = [tex]\frac{1}{4}[/tex] (7) [tex]\sqrt{-8^4+2(8x12)^2+2(8x10)2-12^4+2(12x10)^2-10^4}[/tex]

V = 277.80389

2)

SA = 8.1(13) + 8(13) + 8.1(13) +  [tex]\frac{1}{2}[/tex] [tex]\sqrt{-8.1^4+2(8.1x8)^2+2(8.1x8.1)^2-8^4+2(8x8.1)^2-8.1^4}[/tex]

SA = 370.94749

V = [tex]\frac{1}{4}[/tex] (13) [tex]\sqrt{-8.1^4+2(8.1x8)^2+2(8.1x8.1)^2-8^4+2(8x8.1)^2-8.1^4}[/tex]

V = 366.2587

Answer:

The estimated number of children who attended the parade is 6,336.

Step-by-step explanation:

Since the route for Millburn's Fourth of July parade stretches 2 miles (10,560 feet), and spectators are usually evenly distributed along both sides of the route, and along one side of 50 feet of the route, you count 15 children, to estimate the number of children who attended the parade, the following calculation must be performed:

(10,560 / 50) = 211.2

211.2 x 15 x 2 = X

211.2 x 30 = X

6.336 = X

Therefore, the estimated number of children who attended the parade is 6,336.

Answer:

6x³(2x - x² + 3)

Step-by-step explanation:

Given

12[tex]x^{4}[/tex] - 6[tex]x^{5}[/tex] + 18x³ ← factor out 6x³ from each term

= 6x³(2x - x² + 3)

Answer:

Hello! Mizuki here to help. The correct option you choose should be the second one(hoping you meet it)

Just hoping and not trying to achieve the goal won't help. The others are important step(s) to achieve a goal.

Step-by-step explanation:

Answer:

is that letter c

Step-by-step explanation:

follow me

$775 at 6% simple interest for 3 years.

Substituting the given values in the formula, We get,

[tex] \sf: \implies \dfrac{775 \times 6 \times 3}{100} [/tex]

Calculating further, We get,

[tex] \sf: \implies \dfrac{13950}{100} [/tex]

Dividing, We get,

[tex] \sf: \implies \$ 139.50[/tex]

∴ The Simple Interest is $139.50

Answer:

x= -1 y= -5

There for: (x, y). (-1,-5).

Step-by-step explanation:

Step one:

y=y

5x=9x+4

5x-9x=4

-4x=4

x= -1

Step two:

y=5x

y= 5(-1)

y= -5

Hope u find this helpful

Step-by-step explanation:

y=5x

y=9x+4

Substituting value of x in equation 2

y=9x+4

5x=9x+4

5x-9x=4

-4x=4

so x = -1

again

y=5x

y=5 * (-1)

so y = -5.

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

A matched subject design makes use of different sets of  experimental groups for a treatment. then, each test subject in one group is matched with another equivalent subject in another group.

the advantage of this is that it reduces the error of variance

Respuesta:

A = 51,167

b = 28,5 pies

c = 45,4 pies

Explicación paso a paso:

C = 90 °

B = 38 ° 50 '

Convertir B a grado

1 ° = 60 '

x ° = 50 '

Multiplicar en cruz:

60x = 50

x = 50/60

x = 0,83333 °

Por lo tanto, 38 ° 50 '= 38 ° + 0.833 ° = 38.833 °

Recordar :

A + B + C = 180 ° (Suma de ángulos en un triángulo)

A + 38.833 + 90 = 180

A + 128.833 = 180

A = 180 - 128,833

A = 51,167 °

Usando identidades trigonométricas, podríamos encontrar byc

Para obtener b:

Tan B = opuesto / adyacente = b / 35.4

Tan 38,833 = b / 35,4

b = Tan 38,833 * 35,4

b = 28,5 pies

Para obtener c:

Podríamos usar:

Sin A = opuesto / hipoteno = 35,4 / c

Sin 51,167 = 35,4 / c

c * sin 51,167 = 35,4

c = 35,4 / sen 51,167

c = 45,4 pies

(5^-2)^2 and 5^2•5^-6