Adding and subtracting fractions with different denominators

We know that:

[tex]1. \space\ V_{Rectangular \space\ prism} = 10 \text\] units^{3}\\\\2. \space\ L_{Small \space\ cube} = \frac{1}{2} \space\ units\\\\ 3. \space\ V_{Small \space\ cube} = L ^{3}[/tex]

Step-1: Find the volume of the small cube.

[tex]V_{Small \space\ cube} = L ^{3}[/tex]

[tex]V_{Small \space\ cube} = (\frac{1}{2}) ^{3}[/tex]

[tex]V_{Small \space\ cube} = (\frac{1}{2}) (\frac{1}{2}) (\frac{1}{2})[/tex]

[tex]V_{Small \space\ cube} = \frac{1}{8} \space\ units^{3}[/tex]

Step-2: Divide.

[tex]\frac{10}{\frac{1}{8} }\\\\ \Rrightarrow(10)(8)\\ \\ \Rrightarrow 80[/tex]

Hence, 80 cubes can be fit in the rectangular prism.

volume of rectangular prism = 10 units³

volume of each cube = [tex]\frac{1}{2} \times\frac{1}{2} \times\frac{1}{2} = \frac{1}{8} units^3[/tex]

required cubes = [tex]\frac{10}{ \frac{1}{8} }= 80[/tex]

Answer:

a = 5

Step-by-step explanation:

a = 5

all you have to do is divide both sides by 3

Answer:

A=5

Step-by-step explanation:

Divide each term by 3 and simplify :)

Hope I helped!

Hilary trip is an illustration of a scalene triangle

The triangle that represents Hilary's trip can be classified by the side lengths.

From the figure, the side lengths of the triangles are:

919 miles, 586 miles and 1212 miles

The lengths are not equal.

Triangles that do not have equal side lengths are scalene triangles

Hence, the triangle that represents Hilary's trip is a scalene triangle

To do this, we simply calculate the perimeter of the triangle.

So, we have:

P = 919 miles + 586 miles + 1212 miles

P = 2717 miles

Hence, Hilary completed 2717 miles

Read more about scalene triangles at:

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Answer:

32%

Step-by-step explanation:

1224 + 576 = 1800

100% = 1800

1% = 18 (divide by 100)

576 / 18 = 32

32% = 576

Answer:

32%

Step-by-step explanation:

576+1224=1800

576/1800=32/100

32%

Answer:

28%

Step-by-step explanation:

Let number of children be 2x, then number of adults be 3x

Total number is 5x

Let number of children under 10 be 7y, number of children be 3y,

then total number of children is 10y

so 2x = 10y, x = 5y, y/x = 1/5

younger children = children under 10, number is 7y

so the % is 7y/5x = 7/5 * y/x = 7/5 * 1/5 = 7/25 = 28/100 = 28%

Answer:

x = 6

Both the angles are equal

7x + 4 = 9x - 8

9x - 7x = 4 + 8

2x = 12

x = 6

Solution:

We know that:

This means that:

Step-by step calculations:

Open the parenthesis:

Subtract 7x both sides:

Add 8 both sides:

Divide 2 both sides:

Answer:

The equation has two answers

X = 0

X = 2

Step-by-step explanation:

The answer is absolute value or positive or negative, So it is

[tex] |x - 1| = 1[/tex]

[tex] |x - 1| = - 1[/tex]

We solve the equations and the answer is obtained

Hey there!

|x - 1| = 1 

TRANSLATE:

x - 1 = 1 or x - 1 = -1

SOLVING for: x - 1 = 1

x - 1 = 1

ADD 1 to BOTH SIDES

x - 1 + 1 = 1 + 1

CANCEL out: -1 + 1 because it give you 0

KEEP: 1 + 1 because it help solve for the current x-value

NEW EQUATION: x = 1 + 1

SIMPLIFY IT!
x = 2

Thus, your answer is: x = 2

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
SOLVING for: x - 1 = -1

x - 1 = -1

ADD 1 to BOTH SIDES

x - 1 + 1 = -1 + 1

CANCEL out: -1 + 1 (the LEFT SIDE) because it give you 0

KEEP: -1 + 1 (the RIGHT SIDE) because it give you the current x-value

NEW EQUATION: x = -1 + 1

SIMPLIFY IT!
x = 0

Thus, your answer is: x = 0

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
Therefore, your overall answer is:

x = 2 or x = 0

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

yes i am

Step-by-step explanation:

thank you for noticing my style

Answer:

The answer should be A. [tex]x \in (-\infty,\, 2)[/tex].

Step-by-step explanation:

Start with the second inequality, which is more straightforward than the first. Add [tex]3[/tex] to both sides of this equation to separate [tex]x[/tex] from the numbers:

[tex]x - 3 + 3 \le -1 + 3[/tex]. The direction of the inequality sign shall stay the same.

[tex]x \le 2[/tex].

On the other hand, simplifying the first inequality takes a bit more work. Start by dividing both sides by [tex](-3)[/tex]. However, keep in mind that dividing or multiplying both sides of an inequality with a negative number will invert the direction of the inequality sign. For example, the left-hand side of an inequality might have been greater than the right-hand side. When both sides are multiplied with a number less than zero, the new left-hand side would become smaller than the new right-hand side.

Because [tex](-3)\![/tex] is a negative number, dividing both sides of the first inequality inequality by [tex](-3)[/tex] will turn the "greater-than" sign into a "less-than" sign.

The inequality used to be:

[tex]-3\, (x + 2) > 15[/tex].

After dividing both sides by the negative number [tex](-3)[/tex], it becomes:

[tex]\displaystyle \frac{(-3)\, (x + 2 )}{(-3)} < \frac{15}{(-3)}[/tex].

[tex]\displaystyle (x + 2) < -5[/tex].

[tex]x < -7[/tex].

The question connected the two original inequalities with "or". Therefore, the conditions will be satisfied as long as either of at least one of the two inequalities is true. Note, that [tex]x < 2[/tex] is true whenever [tex]x <-7[/tex] is true. Therefore, any real number that is smaller than [tex]2[/tex] will meet the requirements- not just those that are smaller than [tex](-7)[/tex].

The corresponding interval will be [tex](-\infty,\, 2)[/tex].

Answer:

1. 48x+6

2.36+48x

3.48x+32

4.36+48x

I think it will help you.

Answer:

Step-by-step explanation:

Salamat po ikaw na pong bahala kung Tama po

Answer:

x = 12

Step-by-step explanation:

ΔABC is a right triangle, therefore we can use Pythagoras' Theorem to find the value of x.

Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Therefore,

Substitute these values into the equation and solve for x:

⇒ x² + 16² = 20²

⇒ x² + 256 = 400

⇒ x² = 400 - 256

⇒ x² = 144

⇒ x = √(144)

⇒ x = ±12

As length is positive, x = 12 units (only)

Answer:

MPG is miles per gallon so we just need to divide the miles by the gallons

345/16=21.56

so i guess a?

i mean thats rounded wrong but its the closes one

a

Hope This Helps!!!

Answer:

Step-by-step explanation:

Area=bh/2=64, b=2h --->h2=64 --> h=8 (positive root) and b=16.

Answer:

[tex] \\ [/tex]

Step-by-step explanation:

Using formula:

[tex] \: \: \: \: \: \: \: \: \: \: {\underline{\boxed {\pmb{ \sf{Volume \: of \: cylinder = \pi r^2h}}}}} \: \pink\star [/tex]

[tex] \\ [/tex]

Where,

[tex] \\ [/tex]

Substituting the required values in the above formula :

[tex] \\ [/tex]

[tex] \dashrightarrow \sf \: \: Volume = 3.14 \times {(15)}^{2} \times 17 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: Volume = 3.14 \times 225 \times 17 \\ \\ [/tex]

[tex]\dashrightarrow \sf \: \: Volume = 706.5 \times 17 \\ \\ [/tex]

[tex]\dashrightarrow~~{\boxed {\pink{\pmb{\sf {Volume = 12016.5 \: {cm}^{3}}}}}} \\ \\ [/tex]

Hence,

Answer :

⠀

Explanation :

We know,

[tex]{ \longrightarrow \qquad{\boldsymbol {\pmb{ Volume_{(cylinder)} = \pi {r}^{2} h \: }}}}[/tex]

Where,

⠀

Substituting the values in the formula :

[tex]{ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times ({15})^{2} \times 17 \: }}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \: \times 225 \times 17}}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ { \sf{ Volume_{(cylinder)} = 3.14 \times 3825 }}}}[/tex]

⠀

[tex]{ \longrightarrow \qquad{ \pmb{ \sf{ Volume_{(cylinder)} = 12010.5 }}}}[/tex]

⠀

Therefore,

Answer:

where where is it

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

Never gonna give you up, never gonna let you down, never gonna run around and dessert you.

Answer:

270 mL of pure alcohol is needed.

Step-by-step explanation:

In 540 mL of the mixture, you have 540*10% = 54 mL of pure alcohol.

If you add x mL pure alcohol, then you have (540 + x) mL solution, in it there is (54 + x) mL of pure alcohol

so (54 + x)/(540 + x) = 40%

Then

54 + x = 0.4(540 + x)

54 + x = 216 + 0.4 x

0.6x = 216 - 54 = 162

x = 162/0.6 = 270 mL

The probability that the participant was a nonsmoker is 25%.

Given that at the beginning of a certain study of a group of persons, 15% were classified as heavy smokers, 30% as light smokers, and 55% as nonsmokers, and in the five-year study, it was determined that the death rates of the heavy and light smokers were five and three times that of the nonsmokers, respectively, to calculate, if a randomly selected participant died over the five-year period, the probability that the participant was a nonsmoker, the following calculation must be performed:

Therefore, the probability that the participant was a nonsmoker is 25%.

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Answer:

3cm

Step-by-step explanation:

uhh i drew it but i cant show picture hope this is right tho!!!

Answer:

The correct answer is 2:1 :)

Answer:

4:2

Step-by-step explanation:

Answer:

perimeter= a+b+c

Step-by-step explanation:

perimeter= 4+8+4= 16cm

Answer:

-6 -4

Step-by-step explanation:

Answer:

4 mL

Step-by-step explanation:

Multiply .25 by 2 because you are dispensing it twice a day.

.25 x 2 = .5, so you dispense .5 mL a day.

Now, multiply .5 mL a day x 8 days.

.5 x 8 = 4

Therefore, you should dispense 4 mL.

Answer:

3.55

Step-by-step explanation:

This is simply combining like terms.

First, lets evaluate the terms separately.

x = 8 - (-2.25)

x = 8 + 2.25 (Negative signs cancel out)

x = 10.25 (Combine like terms)

y = 6 - 4.2 - (-4.9)

y = 6 - 4.2 + 4.9 (Negative signs cancel out)

y = 6.7 (Combine like terms)

Now, lets plug in these values to x - y.

(10.25)  - (6.7)

3.55

The value of x - y is equal to 3.55.

"bc is twice half of angle D"

Answer:

The correct answer is, F-1(x) = 5(x-3)/3

Step-by-step explanation:

The inverse of given function f(x) = 3-x/5 would be equal to 3(x - 5)/5

Suppose that the given function is [tex]f:X\rightarrow Y[/tex]Then if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is ;

[tex]f^{-1}: Y \rightarrow X[/tex]

We have been given a function of x as ; 3-x/5.

To find the inverse we will just switch x and function of x with each other.

That means we have;

x = 5/3  f(x) + 5

5/3 f(x) = x - 5

f(x) = 3(x - 5)/5

Learn more about inverse functions here:

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Answer:

4.6

Step-by-step explanation:

to find mean you add up all the numbers then divide by how many numbers there are. 5+4+1+8+5= 23   Since there are 5 numbers you divide 23 by 5 which equals 4.6

✏️VOLUME

Solution:

Figure #1.

Since the given is a rectangular prism, use the formula:

Where:

Given:

» Substitute the givens on the formula.

Therefore, the volume of the rectangular prism is 1 620 in.³

Figure #2

Since the given a cube, use the formula:

Where:

Given:

» Substitute the given on the formula.

Therefore, the volume of the cube is 729 in.³

Figure #3

Since the given is a cylinder, use the formula:

Where:

Given:

» Substitute the givens on the formula.

Therefore, the volume of the cylinder is 351.68 in.³

Answer:

Number #1

Number #2

Number #3

•••••••••••••••••••••••••••••••••••••••••••••••••

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The equation that shows the number of minutes, x, it will take for the tank and the container to have the same amount of water will be 340 - 6x = 6x.

Based on the information given, the equation that shows the number of minutes, x, it will take for the tank and the container to have the same amount of water will be 340 - 6x = 6x. Therefore, the number of minutes will be:

340 - 6x = 6x

Collect like terms

340 = 6x + 6x

340 = 12x

x = 340/12

x = 28.33 minutes.

In 28.33 minutes, they'll have the same content.

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