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A piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels. Which expression correctly shows the amount remaining in the piggy bank?

Answer:

(1) [tex](x,y) = (-2,-4)[/tex]

(2) [tex]y = 4x -26[/tex]

(3) [tex]x = 1[/tex]

Step-by-step explanation:

(1):

[tex]2x - y = 0[/tex]

[tex]x + 3y = -14[/tex]

Required: Solve for x and y

Make x the subject in [tex]x + 3y = -14[/tex]

[tex]x = -3y - 14[/tex]

Substitute -3y - 14 for x in the first equation

[tex]2x - y = 0[/tex]

[tex]2(-3y-14) - y = 0[/tex]

Open bracket

[tex]-6y - 28 - y = 0[/tex]

Collect Like Terms

[tex]- y-6y = 28[/tex]

[tex]-7y = 28[/tex]

Divide both sides by -7

[tex]y = -4[/tex]

Substitute -4 for y in [tex]2x - y = 0[/tex]

[tex]2x - (-4) = 0[/tex]

[tex]2x + 4 = 0[/tex]

Collect Like Terms

[tex]2x = -4[/tex]

Divide by 2

[tex]x = -2[/tex]

Hence, the solution is:

[tex](x,y) = (-2,-4)[/tex]

(2):

[tex](x_1,y_1) = (7,2)[/tex] -- points

[tex]m = 4[/tex] --- slope

Required: Determine the line equation

This is calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives:

[tex]y = 4(x - 7) + 2[/tex]

Open bracket

[tex]y = 4x - 28 + 2[/tex]

[tex]y = 4x -26[/tex]

(3)

[tex]4 - 5x + 3 = 4x - 2[/tex]

Required: Solve for x

Collect Like Terms

[tex]- 5x -4x = - 2-3-4[/tex]

[tex]-9x = -9[/tex]

Divide both sides by -9

[tex]x = 1[/tex]

Answer:

r

Step-by-step explanation:

Answer: 63

Step-by-step explanation:

3(-3)^2 + 2(6)^2 (multiply 3 times -3) & (multiply 2 times 6)

-9^2+12^2 (-9 to the 2nd power and 12 to the 2nd power)

-81+144 (add them up)

=63

The value of the expression is 3a² + 2b² is 69.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

Expression: 3a² + 2b²

Not, put the value of a= -3 and b=6 we get

= 3a² + 2b²

= 3(-3)² + 2(4)²

= 3 x 9 + 2 x 16

= 37 + 32

= 69

Hence, the value of expression is 69.

Learn more about Expression here:

https://brainly.com/question/14083225

#SPJ2

Answer:

w = 2.63157894736

Step-by-step explanation:

8w+3-2w=11(-4w+2) | Given

6w + 3 = -44w + 22 | Combine like terms & distribute

50w + 3 = 22 | Add 44w to both sides

50w = 19 | Subtract 3 from both sides (simplified)

w = 2.63157894736 | Divide both sides by 50 (value of w)

The total price for the gallons of paint will be 35.75p

The total price for the rollers will be 6r

So the equation if the customer have 190 will be

price for gallons of paint + price for rollers = 190

35.75p + 6r = 190

(This is the equation)

Answer:

x = 2.4/20= 0.12

Step-by-step explanation:

Multiply both sides by 4 to eliminate the fraction 1/4:

1      20

--- = ------

x      2.4

Next, we cross-multiply.  This eliminates the fractions:

20x = 2.4

Dividing both sides by 20 results in an equation for x:  x = 2.4/20= 0.12

Answer:

x = 10

Step-by-step explanation:

To isolate the variable (x) you would first write out x - 3 = 7. Now to make x on its own we have to get rid of the -3 so to do that we would add the reciprocal of -3 (or the opposite) which is +3. x - 3 + 3 = 7 + 3 or x = 10.

Answer:

It will be 16pie =50 andpie4^2

Step-by-step explanation:

Hope this Helped

Answer:

45 mph

Step-by-step explanation:

Using the equation d = rt, we can rearrange the equation to be t = d/r

Since the amount of time was the same, we can set d/r equal to each other for both speeds.

Let x represent the average speed.

[tex]\frac{d}{r}[/tex] = [tex]\frac{d}{r}[/tex]

[tex]\frac{180}{x}[/tex] = [tex]\frac{200}{x+5}[/tex]

Cross multiply and solve for x:

200x = 180x + 900

20x = 900

x = 45

So, the average speed was 45 mph

Answer:

The height is 16

Step-by-step explanation:

Given

Shape:  Cube

[tex]Volume = 4096cm^3[/tex]

Required:

Determine the height of the house.

Volume is represented as:

[tex]Volume = L^3[/tex]

Make L the subject

[tex]L = \sqrt[3]{Volume}[/tex]

This gives:

[tex]L = \sqrt[3]{4096}[/tex]

[tex]L= 16[/tex]

The height is 16

Answer:

56888

Step-by-step explanation:

guy is unavailable right now because this video is not available

Answer:

X=x−4

Step-by-step explanation:

2(x−3)+X=5x−2(x+5)

Use the distributive property to multiply 2 by x−3.

2x−6+X=5x−2(x+5)

Use the distributive property to multiply −2 by x+5.

2x−6+X=5x−2x−10

Combine 5x and −2x to get 3x.

2x−6+X=3x−10

Subtract 2x from both sides.

−6+X=3x−10−2x

Combine 3x and −2x to get x.

−6+X=x−10

Add 6 to both sides.

X=x−10+6

Add −10 and 6 to get −4.

X=x−4

Answer:

1.4

Step-by-step explanation:

Given the expression 2.1/1.5.

This can also be expresses as;

2.1/1.5

= 21/10 ÷ 15/10

= 21/10 × 10/15

= 21/15

= 7/5

= 1.4

Hence the result is 1.4

Answer: $3.50

Step-by-step explanation:

Let the cost of domestic shipping be x.

Since the cost of international shipping is $2.50 greater than the cost of domestic shipping. This will be:

= x + 2.50

Since we are further told that three of the cards will be shipped domestically, and two will be shipped internationally and that $22.50 will be spent on shipping, this will be express in an equation as:

3x + 2(x + 2.50) = 22.50

3x + 2x + 5.00 = 22.50

5x = 22.50 - 5.00

5x = 17.50

x = 17.50/5

x = $3.50

The cost if domestic shipping is $3.50

Answer:

35

Step-by-step explanation:

100 / 50 = 2

70 / 2 = 35

Answer:

14.28%

Step-by-step explanation:

Given that,

You can get a pair of shoes that normally cost $84 for only $72.

We need to find the discount percentage. So, it can be calculated as follows :

[tex]\%=\dfrac{84-72}{84}\times 100\\\\\%=14.28\%[/tex]

So, the required percentage is 14.28%.

Answer and Step-by-step explanation:

       |\

       |   \

       |     \

       |        \

       |           \

       |              \   9 + x

x - 9 |                 \

       |                    \

       |                      \

       |                        \

       |                          \

       |_____________\

                    x

That is your triangle.

Now, since its a right triangle, we can use the Pythagorean theorem to solve for x.

The equation for the Pythagorean theorem is this: [tex]A^{2} + B^{2} = C^{2}[/tex]

So we plug in the values.

[tex](x^{2} ) + (x-9)^{2} = (x + 9)^{2}[/tex]

We solve for x.

[tex]x^{2} + x^{2} -18x + 81 = x^{2} + 18x + 81[/tex]

Get everything to the left side of the equation. (x^2 + x^2 = 2x^2, - x^2 = x^2;

-18x - 18x = -36x;    81 - 81 = 0)

[tex]x^{2} -36x = 0[/tex]

Add 36x to both sides, then divide by x.

[tex]x^{2} = 36x\\\\x = 36[/tex]

Shortest Leg = 36 - 9 = 27

Longest Leg = 36

Hypotenuse = 45

#teamtrees #WAP (Water And Plant)

Answer:pretty sure it’s both 35°

Step-by-step explanation:

Slope = change in Y / change in x:

Slope = (5- 5) / (-1 - -9)

Slope = 0/8

Because the change in Y = 0, the slope = 0

Slope = 0

Answer:

0

Step-by-step explanation:

(-9,5) and (-1,5)

To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(5 - 5) / (-1 - 9)

Simplify the parentheses.

= (0 ) / (-10)

Simplify the fraction.

0/-10

= 0

This is your slope.

This is also a horizontal line, which will have a slope of 0.

Answer:

its b

Step-by-step explanation:

Answer:

y = 32

Step-by-step explanation:

[tex]\frac{1}{2} y + 22 = 38[/tex]

Subtract 22 from both sides to isolate the y variable.

[tex]\frac{1}{2} y = 16[/tex]

Divide both sides by [tex]\frac{1}{2}[/tex], which is the same as multiplying by 2.

y = 32

1/2y + 22 = 38

         -22    -22

1/2y = 16

x2      x2   ---> This is because if 1/2y = 26, that means y times 1/2 is 26, but we                  want to know what y times 1 is because y times 1 is equal to y so we multiply by 2 because 1/2 times 2 equals 1.

y = 32

Given:

The equation is

[tex]25+x=31[/tex]

25 is subtracted from both sides.

To find:

The missing values for the given blanks.

Solution:

We have,

[tex]25+x=31[/tex]

If 25 is subtracted from both sides, we get

[tex]25+x-25=31-25[/tex]

[tex](25-25)+x=6[/tex]

[tex]0+x=6[/tex]

So, the missing values for the blanks are 0 and 6 respectively.

It is also written as

25   +   x    =   31

-25                 -25

-----------------------------

 0   +   x    =   6

------------------------------

Therefore, the missing values for the blanks are 0 and 6 respectively.

Answer:

I believe the answer would be [tex]\sqrt{6}+\sqrt{2}[/tex] or 3.8637

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

create a function where x is the money you insert in cents and y is the amount of gumballs you get.

y = x - 5 (meaning you get five less gumballs than the amount of cents you insert)

Therefore, when x = 35:

y = 35 - 5 = 30.

You will get 30 gumballs.

Answer:

Step-by-step explanation:

Step 1: Convert into improper fractions

Step 2: Find  least common denominator and find equivalent fractions

Step 3 : Do the required operation

[tex]3\frac{1}{2}+2\frac{1}{4}-1\frac{1}{2}=\frac{7}{2}+\frac{9}{4}-\frac{3}{2}\\[/tex]

Least common denominator of 2 , 4 = 4

   [tex]=\frac{7*2}{2*2}+\frac{9}{4}-\frac{3*2}{2*2}\\\\=\frac{14}{4}+\frac{9}{4}-\frac{6}{4}\\\\=\frac{14+9-6}{4}\\\\=\frac{17}{4}\\\\=4\frac{1}{4}[/tex]

Answer:

126

Step-by-step explanation:

Answer:

(4x-5)(x+2)

Step-by-step explanation: