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Systems of Equations Word Problems Practice
1. Luis made a $150 bank deposit using $5 bills and $10 bills. He gave the teller a total of 24
bills. How many $10 bills were in the deposit?
1st equation:
2nd equation:
What did you have to multiply the first equation by, if anything?
What did you have to multiply the second equation by, if anything?
Answer:
cils Gabby bought a nens and Spencils

The given pyramid's volume is 40 cubic units.

Step-by-step explanation:

Step 1:

It is given that base areas of the pyramid and the prism are the same. The height is also equal.

The rectangular prism's height is 15 units so as per the given question, the height of the pyramid is also 15 units.

Step 2:

The volume of this pyramid is obtained by multiplying [tex]\frac{1}{3}[/tex] with the product of the pyramid's length, width, and height.

For the given pyramid, length = 2 units, width = 4 units and the height = 15 units.

The pyramid's volume [tex]= \frac{1}{3} (length)(width)(height)[/tex] = [tex]\frac{1}{3} (2)(4)(15) = \frac{1}{3} (120)[/tex] = 40 cubic units.

So the volume of the given pyramid is 40 cubic units.

Answer:

12

Step-by-step explanation:

x/6 = 2

x = 6×2 = 12

Answer:

X=12 (sorry for the handwriting)

Answer:

B.Dining out

Step-by-step explanation:

A, C, and D are very important and without those she would be in big trouble. She does not need to dine out. Instead of dining out she can go to a normal grocery store and buy cheap food there.

Answer:

It would be DINNING OUT.

Step-by-step explanation:

Because it is something you can stop paying for and save money on. It is a variable expense.

Answer: 2/5 pizza

Step-by-step explanation:

Answer: × = 8

Step-by-step explanation:

-2 (3 x - 9 ) + 5x = 10

Step 1: Open the bracket

-6× + 18 + 5x = 10

Step 2: Combine like terms

-6× + 5× = 10 -18

-1× = -8

×= -8/-1

×=8

Answer:

x=8

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Given

(x - 5)(-3) = 18

Expand the bracket

x X -3 -5 x -3 = 18

-3x + 15 = 18

Subtract 15 from both sides

-3x + 15 - 15 = 18 - 15

-3x = 3

Divide both sides by -3

-3x/-3 = 3/-3

x = -1

Answer:

45pi yards

Step-by-step explanation:

C = Pi x D

D = 45 yards

C = Pi x 45 yards

C = 45Pi yards, or 141.3716694 yards

Answer:

x=10

y=2

Step-by-step explanation:

1)add the equations and find what x is.

x-y=8

+x+y=12

—————

2x=20

— —

2 2

x=10

3)fill in x for the second equation.

x+y=12

since x=10,replace x with 10.

10+y=12.

subtract 19 from both sides.

10+y=12

-10 -10

—————-

y=2

Answer: OPTION B

Step-by-step explanation:

You can observe that the exercise provides you two Linear functions.

The first Linear function is the function f(x). This is:

[tex]f(x) = 2x+1[/tex]

And the other Linear function is the function g(x):

[tex]g(x) = x+14[/tex]

In order to find [tex](gof)(x)[/tex], you need to follow these steps shown below:

Step 1:

You must substitute the function f(x) into the function g(x); this means that the function f(x) will be in the place of the variable "x" of the function g(x); as you can observe below:

[tex](gof)(x) = (2x+1)+14[/tex]

Step 2:

Finally you must combine the like terms (You can notice that the like terms are 1 and 14; then you must add them). Therefore, you get that  [tex](gof)(x)[/tex] is:

[tex](gof)(x) = 2x+1+14\\\\(gof)(x) = 2x+15[/tex]

Answer:

1. The quadratic equation is 3x² +17.5x - 58.5 = 0

2. The values of x are 2.38 and -8.21, but we only take 2.38 for our problem.

3. The dimensions of the combined area are approximately 6.38 inches and 12.64 inches.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Photograph dimensions = 4 inches * 6 inches

Frame dimensions = x inches * 3x - 0.5 inches

Area of the combined area of the photograph and the frame = 80.5 inches²

2. Write a quadratic equation for the combined area. Then use the quadratic equation formula to find x.

One side of the combined area of the photograph and the frame = 4 + x inches

Second side of the combined area of the photograph and the frame = 6 + 3x - 0.5 inches

Now, we can write the quadratic equation this way:

Combined area of the photograph and the frame = One side * Second side, replacing with the values we know:

80.5 = (4 + x) * (6 + 3x - 0.5)

80.5 =  (4 + x) * (5.5 + 3x)

80.5 = 22 + 5.5x + 12x + 3x²

3x² +17.5x - 58.5 = 0

Using the quadratic formula, where, a = 3, b = 17.5 and c = - 58.5, we have:

x = (-b +/- √b² - 4ac)/2a

x = (-17.5 +/- √17.5² - 4 * 3 * -58.5) 2 * 3

x = (-17.5 +/- √306.25 + 702)/6

x = (-17.5 +/- √1,008.25)/6

x = (-17.5 +/- 31.75)/6

x₁ = 14.25/6 = 2.38

x₂ = -49.25/6 = -8.21

We took the value of x₁ because x₂ is negative and we can't have a negative value for the length or the width, therefore:

80.5 = (4 + x) * (5.5 + 3x)

Replacing x, we have:

80.5 = (4 + 2.38) * (5.5 + 3 * 2.38)

80.5 = 6.38 * 12.64

80.5 ≅ 6.38 * 12.64

Decimal point moved 5 places to the right, since 10⁵ has 5 zeros in it.

Step-by-step explanation:

52.48 is multiplied by 10 to the power of 5, that is 100, 000, we will get ,

[tex]52.48 \times 10^{5}=5248000.00[/tex]

When 52.48 is multiplied by 100,000, we will get 5248 followed by 5 zeros, 524800000.

Now we have to count the decimal point from left to right, so we will get 5248000.00, zeros after the decimal point has no value.

The decimal point should be moved _5__ places to the right because there are _5__ zeros in 10 to the power of 5.

Answer:

67 [tex]\frac{1}{2}[/tex]  [tex]cm^3[/tex]

Step-by-step explanation:

the volume of a rectangular prism is the three sides multiplied together, [tex]h*w*l[/tex]

converting the mixed number to improper fraction to make multiplying easier.

[tex]\frac{9}{2} *6*\frac{5}{2}[/tex] = [tex]\frac{135}{2}[/tex]

converting back to mixed number in simplest form

[tex]\frac{135}{2}[/tex]= 67 R 1

[tex]\frac{135}{2}[/tex]= 67 [tex]\frac{1}{2}[/tex]

Answer: A and B are true

Step-by-step explanation:

Interest is 0.022, that is 2.2% = 2.2/ 100= 0.022

Principal is %100 as stated in the question

Mark as brainliest

Answer:

The answer is C

Step-by-step explanation:

Because 1 is 90 because it shaped like a L 2 is 45 because its narow, and 3 is the smallest of them all. I also did it before

Answer:

multiply by -2

Answer:

Bend down

Step-by-step explanation:

Bebebe

Answer:

V=62.8

Step-by-step explanation:

3.14(2)^2(5)

3.14(4)(5)

12.56(5)

62.8

Answer: 0.6

Step-by-step explanation:

Total population of class = 50

There are 27 athletes, and 9 musicians However, 6 of the musicians are also athletes.

Therefore, totals for athletes and musicians are:

27 + 9 -6 = 30

Thus, the probability of choosing an athlete or a musician is 30/50= 0.6

We could also use the formula:

P(A or M) = P(A) + P(M) - P(A and M)

P(A or M)=27/50+9/50-6/50

P(A or M)=30/50=0.6

I hope this helps!

Answer:

f(-2) = 3/8

Step-by-step explanation:

f(x)=6•4^x

Let  x=-2

f(-2) = 6 * 4^-2

The negative in the exponent means it goes to the denominator

f(-2) = 6 * 1/ 4^2

       = 6/4^2

        =6/16

Simplifying

        =3/8

Answer:

Option B, -4 and 4

Step-by-step explanation:

Step 1:  Subtract 15 from both sides

y^2 - 1 - 15 = 15 - 15

y^2 - 16 = 0

Step 2:  Factor

y^2 - 16

(y + 4)(y - 4)

Step 3:  Find the solutions

y + 4 - 4 = 0 - 4 and y - 4 + 4 = 0 + 4

y = -4 and y = 4

Answer:  Option B, -4 and 4

Answer:

-4 and 4

Step-by-step explanation:

All you need to do is solve for y

[tex]y^{2} - 1 = 15\\[/tex] (plus 1 to both sides)

[tex]y^{2} = 16[/tex] (take square root of 16)

[tex]y = \sqrt{16}[/tex]

[tex]y = +-4[/tex] (whenever you to the root of a perfect square you want the positive and negative root)

To double check if your answer is right: plug in -4 and +4 in as y and see if it equals 15

1. [tex](4)^{2} - 1 =15[/tex]

[tex]16-1 = 15\\15= 15[/tex]

(positive 4 checks out)

2. [tex](-4)^{2} - 1 = 15[/tex]

[tex]16 - 1 = 15\\15 = 15[/tex]

( negative 4 checks out)

Answer:

d

Step-by-step explanation:

8/root3

Answer:

75% are so 15%

Step-by-step explanation:

To determine the percentage of the jury not over 35 years old, divide the number of jurors not over 35 by the total number of jurors (3/12) and then multiply by 100, resulting in 25 percent.

If nine out of twelve jurors are over 35, then three out of twelve jurors are not over 35. To find out what percentage of the jury is not over 35, we use the following calculation:

Therefore, 25 percent of the jury is not over 35 years old.

Answer:

B. 5 × 5 × 8

Step-by-step explanation:

Each of the boards have an area of 25. You have 8 of them.

Answer:

b. 5 × 5 × 8

Step-by-step explanation:

"...the total area is five feet × five feet times eight"

Equation:

(5 × 5) × 8

Simply remove brackets:

5 × 5 × 8

Answer:

86'

Step-by-step explanation:

Answer:

The right answer is, 4.

Step-by-step explanation:

Why:

164x5 = 820

So:

824-820 = 4

Step-by-step explanation:

Yes, it is a parallelogram because the opposite angles are congruent

Option C

Answer:

yes opposite angles are congruent.

Step-by-step explanation:

On both sides 36 and 144 are congruent or equal

Answer: Angle x equals 19 degrees

Step-by-step explanation: We have two polygons, one with five sides and the other with eight sides. The question states that the pentagon has exactly one line of symmetry which means the line that runs down from point D to line AB divides the shape into exactly two equal sides. Hence angle A measures the same size as angle B (in the pentagon).

First step is to calculate the angles in the pentagon. The sum of angles in a polygon is given as

(n - 2) x 180 {where n is the number of sides}

= 3 x 180

= 540

This means the total angles in the pentagon can be expressed as

A + B + 84 + 112 + 112 = 540

A + B + 308 = 540

Subtract 308 from both sides of the equation

A + B = 232

Since we have earlier determined that angle A measures the same size as angle B, we simply divide 232 into two equal sides, so 232/2 = 116

Having determined angle A as 116 degrees, we can now compute the value of angle A in the octagon ABFGHIJK. Since the figure is a regular octagon, that means all the angles are of equal measurement. So, the sum of interior angles is given as

(n - 2) x 180 {where n is the number of sides}

= 6 x 180

= 1080

If the total sum of the interior angles equals 1080, then each angle becomes

1080/8

= 135 degrees.

That means angle A in the octagon measures 135, while in the pentagon it measures 116. The size of angle x is simply the difference between both values which is

x = 135 - 116

x = 19 degrees

Answer:

24

Step-by-step explanation:

The equations just need to be equal so you multiply 3 by 6 to get 8 and then 4 by 6 to get 24

3 / 4 = 18 / 24

Answer:

Where is the question

Step-by-step explanation: