Lina packs 3-inch cups into boxes
measuring 12 inches by 15 inches.
How many cups fit in one box?

Answer:

1st Place:  Mei

2nd Place:  Mary

3rd Place:  Brooke

1. Simplifying

9x + 2y = 30

Solving

9x + 2y = 30

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.

9x + 2y + -2y = 30 + -2y

Combine like terms: 2y + -2y = 0

9x + 0 = 30 + -2y

9x = 30 + -2y

Divide each side by '9'.

x = 3.333333333 + -0.2222222222y

Simplifying

x = 3.333333333 + -0.2222222222y

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2. Simplifying

6x + 4y = 12

Solving

6x + 4y = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4y' to each side of the equation.

6x + 4y + -4y = 12 + -4y

Combine like terms: 4y + -4y = 0

6x + 0 = 12 + -4y

6x = 12 + -4y

Divide each side by '6'.

x = 2 + -0.6666666667y

Simplifying

x = 2 + -0.6666666667y

Answer:

For graphing, your answer is...(4,-3)

Step-by-step explanation:

1.Subtract 9x on both sides...

2y=30-9x

6x+4y=12

2. Divide each term by 2, then simplify...

-Divide... 2y=30-9x by 2.

2y/2=30/2+-9x/2

6x+4y=12

3. Reduce expression by...cancelling your common factors...

Cancel...2 from 2y/2

6x+4y=12

Divide y by 1...

y=30/2+-9x/2

6x+4y=12

4.Simplify each term...

-Divide thirty by two.

y=15+-9x/2

6x+4y=12

-Move your negative in the front of your fraction.

y=15 - 9x/2

6x+4y=12

5.  Subtract 6x from both sides of your equation...

y=15 - 9x/2

4y=12-6x

6. Divide each term by four...divide terms in 4y=12-6x by four...

y=15 - 9x/2

4y/4=12/4+-6x/4

-Reduce expression by cancelling common factors in 4y/4...

Divide y by one...

y=15 - 9x/2

y=12/4+-6x/2

7. Simplify each term...Divide twelve by four...

y=15 - 9x/2

y=3+-6x/4

-Reduce expression by cancelling all common factors...

Your factor is 2 our of -6x...

y=15 - 9x/2

y=3+2(-3x)/4

-Cancel the common factors.. two out of four...

y=15 - 9x/2

y=3+2(-3x)/2(2)

-Cancel common factors again...

y=15 - 9x/2

y=3+-3x/2

8. Move your negative over to the front of your fraction...

y= 15 - 9x/2

y=3 - 3x/2

You get... (4,-3)

I hope this helps you and I also do hope that this is what you are looking for! If not, then my bad! Good luck, mate!

Hey!

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

Solution:

20% = 0.2 (percentage as decimal)

190 x 0.2 = 38 (discount)

190 - 38 = 152 (sale price)

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

Answer:

The sale price of the printer is $152.

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

Hope This Helped! Good Luck!

Answer:

The answer is B. 54 cm

Step-by-step explanation:

When you find the volume of a rectangle you have to multiply the length, width, and height. The length is 9, width 3, and height 2. When you multiply them together you'll get 54

Answer:

Answer to D: 3/5

Step-by-step explanation:

There are 5 songs.

And 3 of them have the word "Mama" in the title.

Make 5 the total amount of songs and 3 songs are how many times the word "Mama" appears once in each song.

Answer:

-3.2x=-16

Step-by-step explanation:

The coefficient of determination for this data set​ would be 0.91

A correlation coefficient is a number between -1 and 1 that tells you the strength and direction of a relationship between variables. In other words, it reflects how similar the measurements of two or more variables are across a dataset.

The correlation coefficient for this data set will be positive, since the dependent variable increases as the independent variable decreases.

Since the data appears to be fairly linear, the correlation coefficient will be close to 1 which means 0.91 is our best choice.

Hence, The coefficient of determination for this data set​ would be 0.91

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Answer:

[tex]y=0.25x[/tex]

Step-by-step explanation:

We are given that a graph which shows the relationship between the late fines the library charges and the number of days late.

From given graph we can see that

The graph passes through the points (2,0.5)  and (10,2.5).

We have to find the equation for the relationship.

Slope formula:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

By using the formula

Slope of graph=[tex]m=\frac{2.5-0.5}{10-2}[/tex]

Slope of graph=m=[tex]\frac{2}{8}=\frac{1}{4}[/tex]

Point slope- form:[tex]y-y_1=m(x-x_1)[/tex]

We have [tex]y_1=2.5,x_1=10[/tex]

Substitute the values then we get

The equation of for the relationship

[tex]y-2.5=\frac{1}{4}(x-10)[/tex]

[tex]y-2.5=0.25x-2.5[/tex]

[tex]y=0.25x-2.5+2.5=0.25x[/tex]

Hence, the equation for the relationship is given by

[tex]y=0.25x[/tex]

Hey!

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To Solve We Need:

By looking at the picture we can see that the measure of N is 48 degrees.

A triangle needs a total of 180 degrees to be a complete triangle.

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

Solution:

180 - 48 = 132 degrees

132 / 2 = 66 degrees

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Answer:

L and M measure 66 degrees!

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

Hope This Helped! Good Luck!

Answer:

La and M 66 degrees !

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

15= 100%

3/15 = 1/5

100% divided by 5 is 20%

proportion: 1/5

Mimi has 15 cousins, and after subtracting the 3 who do not live in Texas, 12 of her cousins live there. By setting up a proportion, we calculate that 80% of Mimi's cousins live in Texas.

Mimi has 15 cousins, and all but 3 live in Texas. To find the percentage of her cousins that live in Texas, we first need to calculate the number of cousins who live in Texas. We do this by subtracting the 3 that do not live in Texas from the total number of cousins, which is 15.

Number of cousins living in Texas = Total cousins - Cousins not living in Texas
Number of cousins living in Texas = 15 - 3 = 12

Next, we set up a proportion to find the percentage. The proportion is based on the number of cousins in Texas over the total number of cousins:

Proportion = (Number of cousins in Texas / Total number of cousins) ×100%
Percentage = (12 / 15)× 100%
Percentage = 0.80 × 100%
Percentage = 80%

Therefore, 80% of Mimi's cousins live in Texas.

Answer:

  B) 116.88 inches

Step-by-step explanation:

we know that

To find out the length of 12 basketballs lined up next to each other, multiply the diameter of one basketball by 12

[tex]12(9.47)=113.64\ in[/tex]

therefore

The logical answer between the options is 116.88 inches, because the length cannot be less than 113.64 in

Answer:

90 Years = 47,304,000 Minutes = 47304000 Minutes.

Step-by-step explanation:

Answer: C. 966

Step-by-step explanation: First find the ft. of the entire area, the deck, and pool. Then get the area of the pool

Entire area: (35+7+7) * (20+7+7)= 1666

Pool: 35*20=700

Then subtract the ft. of the entire area by the pool

1666-700= 966

Answer:

120 mins

or

2hrs

Step-by-step explanation:60 min=1 hr

60 min/5=12 min

12(4)=48 min

24 min=1/5 of room

24(5)=120 min

120 min=2 hrs

It would take 2 hours to paint one room.

Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Time taken to paint 2/5 of the room = 4/5 hour

To find the time taken to paint one room,

Use ratio property,

2/5 room takes = 4/5 hour

1 room takes = 4/5 x 5/2 hours

                      = 4 / 2 hours

                      = 2 hours.

The one room takes 2 hours to paint.

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Answer:

Step-by-step explanation:

[tex]\dfrac{4x+6}{2}=\dfrac{3x-15}{3}\qquad\text{cross multiply}\\\\3(4x+6)=2(3x-15)\qquad\text{use the distributive property}\\\\(3)(4x)+(3)(6)=(2)(3x)+(2)(-15)\\\\12x+18=6x-30\qquad\text{subtract 18 from both isdes}\\\\12x=6x-48\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\6x=-48\qquad\text{divide both sides by 6}\\\\x=-8[/tex]

x=-8

Given equation is (4x+6)/2=(3x-15)/3, we need to find x

Multiply the numerator of one fraction to the denominator of other and denominator of the first term to the numerator of another term is called Cross Multiplication Method.

Given, (4x+6)/2=(3x-15)/3

Apply cross multiplication method

3(4x+6)=2(3x-15)

12x+18=6x-30

12x-6x=-30-18

6x=-48

Divide both sides by 6

x=-8

Therefore value of x in  (4x+6)/2=(3x-15)/3 is '-8'.

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Answer:

Slope:

[tex]m = -\displaystyle\frac{1}{2}[/tex]

Step-by-step explanation:

We are given the equation:

[tex]y = -\displaystyle\frac{1}{2}x + \displaystyle\frac{1}{4}[/tex]

Comparing this equation to the slope-intercept form:

[tex]y = mx + c[/tex]

where m is the slope of line and c is the y-intercept that is the value of y when x is zero.

on comparing, we get:

[tex]m = -\displaystyle\frac{1}{2}\\c = \displaystyle\frac{1}{4}[/tex]

The slope of the given line is

[tex]m = -\displaystyle\frac{1}{2}[/tex]

The slope of the given line is -1/2

The standard equation of a line is expressed as y = mx +b

where

m is the slope

b is the y-intercept

Given the equation y = -1/2x + 1/4

Compare the equations

mx = -1/2 x

m = -1/2

Hence the slope of the given line is -1/2

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Answer:

$98

Step-by-step explanation:

x+6(120-x)=230

x+720-6x=230

-5x=-490

x-98

x represented how much money Hannah had.

Answer:

6^6

Step-by-step explanation:

6^4 x 6^3 / 6^-1

exponent rule add exponents 4+3=7 so 6^7

exponent rule subtract exponents 7-(-1) so

Answer= 6^8

Answer:

1644624

At least that's what i got on my calculator

Final answer:

To simplify an algebraic equation, combine like terms, reduce fractions, and cancel factors; multiply or divide both sides by the same number if needed, and check your work by substituting values back into the original equation.

Explanation:

Simplifying Algebraic Equations

To simplify an algebraic equation, you need to eliminate terms wherever possible. This process may involve combining like terms, reducing fractions, and canceling out factors. Multiplication or division by the same number on both sides of the equation does not change the equation's equality, so apply these operations carefully to all terms. Often, you'll want to collect constants inside the parentheses to consolidate them into a single value, making the equation simpler. After simplifying, it's important to check your answer to ensure that it is reasonable, which may involve plugging the solution back into the original equation or assessing the steps you've taken to make sure no errors were made.

Let's consider an example:

Simplify the equation by dividing both sides by a common factor, if applicable.

Collect like terms together and simplify further.

Check the simplified equation by substituting numbers to see if both sides remain equal or by ensuring logical algebraic steps were taken.

Remember, solving for an unknown variable requires doing the same operation on both sides of the equation, thereby maintaining balance. Systematic simplification and attentive checking are your keys to mastering algebraic equations.

Answer:

if this question was a volume question, then the answer would be 215.784ft^3

why: length times width times height

if this is not what you needed ignore it. I am basing this off of the given number.s

Step-by-step explanation:

Answer:8

Step-by-step explanation: trust me

The relationship between y and x, given that g is the midpoint of FH is y = (1/3)x + (1/3).

If g is the midpoint of FH, it means that FH is divided into two equal segments, FG and GH, such that FG = GH.

Given that FH = 6y - 2, set up an equation to represent this:

FH = FG + GH

Substituting the values we know:

6y - 2 = FG + GH

Since FG = GH then

6y - 2 = x + x

Now, combine like terms:

6y - 2 = 2x

To find the value of y, isolate it on one side of the equation:

6y = 2x + 2

Now, divide both sides by 6 to solve for y:

y = (2x + 2) / 6

y = (2/6)x + (2/6)

y = (1/3)x + (1/3)

So, y is equal to (1/3)x + (1/3).

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Answer:

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x ------> the amount of money that should be invested at the rate of 5.25%

25,000-x -----> the amount money that should be invested at the rate of 4%

in this problem we have

[tex]t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150[/tex]

substitute in the formula above

[tex]I=P_1(r_1t)+P_2(r_2t)[/tex]

[tex]1,150=x(0.0525*1)+(25,000-x)(0.04*1)[/tex]

Solve for x

[tex]1,150=0.0525x+1,000-0.04x[/tex]

[tex]0.0525x-0.04x=1,150-1,000[/tex]

[tex]0.0125x=150[/tex]

[tex]x=\$12,000[/tex]

[tex]|$25,000-x=\$13,000[/tex]

therefore

The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

Answer:

Step-by-step explanation:

Let x be the investment at 5.25% and y at 4%

Then we have

[tex]x+y =25000\\5.25x+4y = 115000[/tex]

We have to solve this system to get x and y

Multiply I equation by 4

[tex]100000=4x+4y\\115000=5.25x+4y\\-----------------------------\\15000 = 1.25x\\x = 12000\\y =25000-12000 = 13000[/tex]

12000 should be invested in 5.25% and 13000 in 4% interest.

Answer:

Yes, you are correct :)

Answer:

1/4

Step-by-step explanation:

Answer:

10^6 aka D

Step-by-step explanation:

We know this because we start off with 1. we take the decimal and swipe it 6 places to the right filling the gaps with zero. As shown in the problem itself.

Answer:

10^6

Step-by-step explanation:

10^6 is 10 × 10 × 10 × 10 × 10 × 10, and that is 1,000,000.

Answer:

- 9

Step-by-step explanation:

Given

A² - B² ← substitute A = 4 and B = - 5 into the expression

= 4² - (- 5)²

= 16 - 25

= - 9

4x^2 - 36 = 0

4x^2 = 36

x^2 = 36/4

x^2 = 9

sqrt{x^2} = sqrt{9}

x = - 3 and x = 3