Sam has a total of 43 quarters and nickels in her purse. If her change is worth $7.75, how many nickels and how many quarters does Sam have?
Warning: This is Algebra 1

Answers

Answer 1

Answer:

i need help with this too\

Step-by-step explanation:

Answer 2
Let q= the number of quarters
Let n=the number of nickels

q+n=43 This equations represents the total number of coins.
0.25q+0.05n=7.75 This equations represents her change totaling to $7.75.

Multiply the second equation by 100 to simplify the arithmetic.

q+n=43
25q+5n=775 Multiply the first equation by -5.

-5q-5n=-215
25q+5n=775 Add the two equation in which the n variable gets eliminated.
20q=560 Divide both sides by 20.

q=28 Substitute q=28 into the first equation and solve for n.
28+n=43
-28 -28
n=15 Therefore, she has 28 quarters and 15 nickels in her purse.

Hope this helps.

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9514 1404 393

Answer:

  (x, y, z) = (8√7/105, 2√7/21, 4√7/35)

Step-by-step explanation:

The algebra is straightforward, if tedious.

We'll define X = x^2, Y = y^2, Z = z^2, -1/16 = a, -1/25 = b, -1/36 = c. Then the equations become ...

  √X = √(Y +a) +√(Z +a) . . . . [eq1]

  √Y = √(Z +b) +√(X +b) . . . . [eq2]

  √Z = √(X +c) +√(Y +c) . . . . [eq3]

__

As with any radical equation, you square both sides, isolate the remaining radical, then square both sides again. Each squaring introduces extraneous solutions.

The equations are symmetrical, so we can do the tedious stuff on the first one, then make the appropriate substitutions to see the other two equations.

  X = Y +a + 2√((Y+a)(Z+a)) +Z +a

  X - Y - Z -2a = 2√((Y+a)(Z+a)) . . . . isolate the remaining radical

  (X -Y -Z -2a)^2 = 4(Y+a)(Z+a) . . . . square both sides again

  X^2 +Y^2 +Z^2 +4a^2 -2XY -2XZ +2YZ -4aX +4aY +4aZ = 4YZ +4aY +4aZ +4a^2

Subtracting the right side gives ...

  X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4aX = 0 . . . . [eq4]

Then the remaining equations are ...

  X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4bY = 0 . . . . [eq5]

  X^2 +Y^2 +Z^2 -2XY -2XZ -2YZ -4cZ = 0 . . . . [eq6]

Subtracting [eq6] from [eq5] gives a relation between Y and Z:

  -4bY +4cZ = 0

  Z = bY/c . . . . [eq7]

Substituting this into [eq4], we have ...

  X^2 +Y^2 +(bY/c)^2 -2XY -2X(bY/c) -2Y(bY/c) -4aX = 0

  X^2 +Y^2(1 -2b/c +(b/c)^2) -2XY(1 +b/c) -4aX = 0 . . . . [eq8]

Subtracting [eq5] from [eq4] gives a relation between X and Y:

  -4aX +4bY = 0

  Y = aX/b . . . . [eq9]

Substituting this into [eq8], we have ...

  X^2 +(aX/b(1 -b/c))^2 -2X(aX/b)(1 +b/c) -4aX = 0

Dividing by X* gives a linear equation in X:

  X(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c)) -4a = 0

  X = 4a/(1 +(a/b(1 -b/c))^2 -2a/b(1+b/c))

Substituting the above values for a, b, c, we have ...

  X = 64/1575

  x = √X = √(64/1575) = 8/(15√7)

  Y = X(25/16)

  y = x(5/4) = 2/(3√7)

  Z = Y(36/25)

  z = y(6/5) = 4/(5√7)

The solution is ...

x = 8√7/105 ≈ 0.201581y = 2√7/21 ≈ 0.251976z = 4√7/35 ≈ 0.302372

_____

* At this point the equation is of the form pX^2 +qX = 0 or X(pX +q) = 0. One solution is X=0, which is extraneous. The solution of interest is X = -q/p.

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Answers

Answer:

The Symmetric Property states that for all real numbers x and y , if x=y , then y=x . Transitive Property. The Transitive Property states that for all real numbers x ,y, and z, if x=y and y=z , then x=z .

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What is the domain of Graph 1

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The domain of a fraction is this set of all possible inputs for the function

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Answer:

Step-by-step explanation:

b = bouquet c = centerpieces

13b + 4c = 487

6b + 2c = 232


Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of
change of money in his savings account per week?
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Answers

Answer:

$12.5

Step-by-step explanation:

all you do is divide the 4 weeks to the $50 he earns and get $12.5 every week.

An ice chest contains 7 cans of apple​ juice, 6 cans of grape​ juice, 6 cans of orange​ juice, and 4 cans of mango juice. Suppose that you reach into the container and randomly select three cans in succession. Find the probability of selecting three cans of mango juice.

Answers

Answer:

4/1771

Step-by-step explanation:

Step one:

given

sample space

7 cans of apple​ juice,

6 cans of grape​ juice,

6 cans of orange​ juice, and

4 cans of mango juice

Sample size= (7+6+6+4)

                       = 23

Step two:

Required

The probability of randomly selecting three cans of mango juice in succession

Note: we are selecting without replacement

let the probability of selecting three cans of mango juice be

the first selection is= 4/23

The second = 3/22

the third= 2/21

[tex]P(x)= 4/23*3/22*2/21[/tex]

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

I took the test. Hope this helps! :)

Mr. Stokes bought 6 1/2 pounds of meat for a party. He used 2 1/4 pounds of meat to make tacos. The rest he used to make 1/4 pound burgers. How many burgers did Mr. Stokes make?

Answers

9514 1404 393

Answer:

  17

Step-by-step explanation:

The remaining amount of meat is ...

  6 1/2 - 2 1/4 = 4 1/4 = 17/4 . . . pounds

The number of 1/4 pound burgers that can be made with that amount of meat is ...

  (17/4)/(1/4) = 17/1 = 17

Mr. Stokes made 17 burgers.

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Answers

Answer:

9x-12

Step-by-step explanation:

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Answer:  x = -4/3

Step-by-step explanation:

3(x−4)=12x

Step 1: Simplify both sides of the equation.

3(x−4)=12x

(3)(x)+(3)(−4)=12x  (Distribute)

3x+−12=12x

3x−12=12x

Step 2: Subtract 12x from both sides.

3x−12−12x=12x−12x

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Answers

Answer:

you have to get rid of the numbers and then get rid of the letters until only s is left

Step-by-step explanation:

4s - 13= 51

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s= 16

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b =

Answers

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Answer:

a=132

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Step-by-step explanation:

,

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Answer:

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Step-by-step explanation:

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Answer:

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Answers

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I also have felt like this recently. Try talking to someone about it. :)

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answer:

x = 15

Step-by-step explanation:

AEB is a right angle, a right angle is 90 degrees

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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