Suppose you have 20 coins that total $4.00. Some coins are nickels and some are quarters. Which of the following pairs of equations would you use to find out how many of each coin you have?

Answer:

The side lengths are 5, 12, 13

Step-by-step explanation:

These are the side lengths we know before we have solved the problem.

a= x   b= x+7   c= 13

If we put this into the Pythagorean theorem, we get

[tex]13^{2} = x^{2} +(x+7)^{2}[/tex]

Expand

[tex]169 = 2x^2+14x+49\\[/tex]

Subtract 169 from both sides

[tex]0 =2x^2+14x-120[/tex]

Solve using the quadratic formula

a= 2   b= 14   c= -120

[tex]\frac{-14\pm \sqrt{14^2-4\cdot \:2\left(-120\right)}}{2\cdot \:2}[/tex]

[tex]x= \frac{-14\pm \:34}{2\cdot \:2}[/tex]  

If we separate the solutions we get

[tex]x= \frac{20}{4} = 5[/tex]

and

[tex]x= \frac{-48}{4} = -12[/tex]

Since this is a question about length, we can ignore the negative.

So the longer leg is 12ft and the shorter leg is 5ft

The shorter length is 5feet and the longer length is 12 feet

Let the shorter leg = x

Let the longer leg = x+7

Therefore,

x² + (x+7)² = 13²

x² + x² + 14x + 49 = 169

Collect like terms

2x² + 14x + 49 - 169 = 0

2x² + 14x - 120 = 0.

Divide by 2

x² + 7x - 60

By using quadratic equation

x² + 12x - 5x - 60

x(x + 12) - 5(x + 12)

Therefore, x - 5 = 0

x = 0 + 5.

x = 5

The shorter length is 5ft

Longer length = 5+7 = 12 feet

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Answer: A

Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours

Answer:

So if you take the 12 and add it to the 7 you get 19 then do 19 mines 7 and you get 12 so always add the sum to the number given to get the missing number

Step-by-step explanation:

Have a great day

Answer:

-7

Step-by-step explanation:

the full coordinate would be  3,-7. just line up the number directly above it and to the left/right and write it down x,y

Answer: 2/1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Line is passing through the points (2, 3) & (5, 9)

Slope = (9 - 3)/ (5 - 2) = 6/3 = 2

Slope of the line is 2.

Answer:

8 Batches

Step-by-step explanation:

Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.

Answer:

I got 4x=5y sorry if i'm wrong

Answer:

-3.5

Step-by-step explanation:

Rise over run

Answer:

9 cm

Step-by-step explanation:

2.5x4=10

Answer:

$2675

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Texas was not around during George Washington so that cant be correct

Texas was not around during the constitution of 1824

Texas did not want more restaurants lol

So Texans considered themselves  independent from Mexico is correct

Answer:

Step-by-step explanation:Texas was not around during George Washington so that cant be correct Texas was not around during the constitution of 1824 Texas did not want more restaurants So Texans considered themselves  independent from Mexico is correct

took it on edge 2020 and got it write with this

Answer:

wooowooowowowowowowowowow

Step-by-step explanation:

Answer:

epic ninja

Step-by-step explanation:

ninja

Answer:

2.25

Step-by-step explanation:

1.5 / 0.666 (repeating) = 2.25

Answer:

There are 2 one-quarter cup servings in 1 half cup

In 5.25 cups there are 21 one-quarter cup servings

Step-by-step explanation:

So 21 quarter cup servings divided by 2 quarter cup servings per half cup serving will yield the number of half cup servings.

21/2 is 10.5, so there are ten and half, half cup servings in 5.25 cups

Answer:

D. 78°

Step-by-step explanation:

ABCD is a parallelogram.

Measures of the opposite angles of a parallelogram are equal.

Therefore,

[tex]3x = x + 52 \\ \\ 3x - x = 52 \\ \\ 2x = 52 \\ \\ x = \frac{52}{2} \\ \\ x = 26 \\ \\ m\angle B = (3x) \degree \\ \\ m\angle B = (3 \times 26) \degree \\ \\ m\angle B = 78\degree[/tex]

Answer:

im guessing it says they give $5 to the father

if that is the case then the answer is c

Step-by-step explanation:

Answer: The expected number of spades that you will draw is 0.751 spades

Step-by-step explanation:

The expected value can be calculated as:

∑xₙ*pₙ

Where xₙ is the n-th event, and pₙ is the probability of that event.

First, let's count the possible events and calculate the probability for each one.

x₀ = drawing 0 spades.

Out of 52 cards, we have only 13 spades, then 52 - 13 = 39 are not spades.

Then the probability of not drawing a spade in the first draw is:

p1 = 39/52

In the second draw we will have a card less than before in the deck (so we have 38 cards that are not spades, and 51 cards in total), then the probability of not drawing a spade is:

p2 = 38/51

And with the same reasoning, in the third draw the probability is:

p3 = 37/50

The joint probability for this event will be:

p₀ = p1*p2*p3 = (39/52)*(38/51)*(37/50) = 0.413

Second event:

x₁ = drawing one spade.

Let's suppose that in the first draw we get the spade, the probability will be:

p1 = 13/52

In the second draw, we get no spade, then the probability is:

p2 = 39/51

in the third draw we also get no spade, the probability is:

p3 = 38/50

And we also have the case where the spade is drawn in the second draw, and in the third draw, then we have 3 permutations, this means that the probability of drawing only one spade is:

p₁ = 3*p1*p2*p3 = 3*(13/52)(39/51)*(38/50) = 0.436

third event:

x₂ = drawing two spades:

Let's assume that in the first draw we do not get a spade, then the probabilities are:

p1 = 39/52

p2 = 13/51

p3 = 12/50

And same as before, we will have 3 permutations, because we could not draw a spade in the second draw, or in the third, then the probability for this case is:

p₂ = 3*p1*p2*p3 = 3*( 39/52)*(13/51)*(12/50) = 0.138

And the last event:

x₃ = drawing 3 spades.

The probabilities will be:

p1 = 13/52

p2 = 12/51

p3 = 11/50

And there are no permutations here, so the joint probability is:

p₃ = p1*p2*p3 = (13/52)*(12/51)*(11/50) = 0.013

Now we can calculate the expected value:

EV = 0*0.413 + 1*0.436 + 2*0.138 + 3*0.013 = 0.751

The expected number of spades that you will draw is 0.751 spades

Answer:

Step-by-step explanation:

x=2

X+4= 6

Move + 4 to the other side to get X by itself

Sign changes from +4 to -4

X+4-4=6-4

X=6-4

X= 2

Answer: X= 2

Answer:

21

Step-by-step explanation:

solved it

Answer:?????

Step-by-step explanation:

what do u need help with/?//???/???

Answer:

[tex]3.10* 10^0[/tex]

Step-by-step explanation:

Given

[tex]3.091403[/tex]

Required

Express in standard form

A number in standard form can be expressed as:

[tex]a * 10^b[/tex]

Where

[tex]1 \leq a \leq 10[/tex]

i.e.

a is between 1 and 10 (inclusive) and preferable, a should be in 2 decimal places

We have that:

[tex]3.091403[/tex] is between 1 and 10.

So, in standard form it is:

[tex]3.091403 * 10^0[/tex]

Approximate to 2 decimal places

[tex]3.10* 10^0[/tex]

Hence, the standard form of [tex]3.091403[/tex] is [tex]3.10* 10^0[/tex]

Answer:

about 7.0710678cm

Step-by-step explanation:

it's a square so the sides are equal.

the diagonal is 100cm

This makes a right triangle with two sides

since the sides are equal, they both are equal to the square root of 50, which is half of 100

the square root of 50 is about 7.0710678cm

Answer:

Step 3.

Step-by-step explanation:

When 10.2b - 5 = 18.92, you cannot combine the unlike terms together on the left side to get 5.2b. Instead, add 5 to both sides:

10.2b = 18.92 + 5 = 23.92.

Answer: step 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

B is the answer

Answer:

sorry i had too

Step-by-step explanation:

someone passed this to me) 90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Answer: a = 5

Step-by-step explanation:

5(a + 3) = 40

5a + 15 = 40

5a -15 = -15

5a = 25

5a/5a = 25/5a

a = 5

Hope this helps :)