Consider the following piece-wise function. Which of the below correctly describes the graph shown?

[tex]2\frac{3}{4}+3 \frac{5}{8}=6\frac{3}{8}[/tex]

Solution:

Given expression is [tex]2\frac{3}{4}+3 \frac{5}{8}[/tex].

To simplify the expression [tex]2\frac{3}{4}+3 \frac{5}{8}.[/tex]

Let us first convert the mixed fraction into improper fraction.

[tex]2\frac{3}{4}+3 \frac{5}{8}=\frac{(2\times 4) + 3}{4}+ \frac{(3 \times 8)+5}{8}[/tex]

            [tex]=\frac{8+ 3}{4}+ \frac{24+5}{8}[/tex]

            [tex]=\frac{11}{4}+ \frac{29}{8}[/tex]

Take LCM for the denominators (LCM of 4, 8 = 8) and make the same.

            [tex]=\frac{11\times2}{4\times 2}+ \frac{29\times1}{8\times1}[/tex]

            [tex]=\frac{22}{8}+ \frac{29}{8}[/tex]

            [tex]=\frac{51}{8}[/tex]

Now, divide 51 by 8 and again write it in the mixed fraction.

             [tex]=6\frac{3}{8}[/tex]

[tex]2\frac{3}{4}+3 \frac{5}{8}=6\frac{3}{8}[/tex]

Hence, the simplified answer is [tex]6\frac{3}{8}[/tex].

Answer: x = -9

Step-by-step explanation: 6x + 4(3) = 8( x + 4) -2

0pen brackets and collect like terms,

6x + 12 = 8x + 32 -2

collect the like term

6x + 12 = 8x + 32  -2

6x -8x = 32 -2 - 12

-2x = 18, divide through by  -2

Therefore x = -9

Answer:

Step-by-step explanation:

x

Use a table of values to graph the equation.

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V = Abxh/3 = (12cmx12cm)x8cm/3 = 144cm²x8cm/3 = 384 cm³

Answer:

384 cm³

Step-by-step explanation:

Volume = a^2(h/3)

a = base edge = 12 cm

h = height of pyramid = 8 cm

Volume = 12^2*(8/3)

Volume = 144*(8/3)

Volume = 48*8

Volume = 384 cm³

the answer is 350.50, the 4th answer

Answer:

D) 8

Step-by-step explanation:

You multiply 10 by 12 to get 120 so you multiply x by 12 to get 96.

96 = 12x

/12     /12

8   =   x

Answer:

The correct option is last one  77 degrees.

Therefore the measure angle W is 77 degrees.

Step-by-step explanation:

Given:

Exterior angle = 122°

∠W = (2x-13)°

∠Y= x°

To Find:

∠W = (2x-13)° = ?

Solution:

Exterior Angle Property:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Angle W and Angle Y are the interior angles of Exterior angle 122°.

∴ [tex]Exterior\ angle=m\angle W+m\angle Y[/tex]

Substituting the values we get

[tex]122=2x-13+x\\3x=135\\\\x=\dfrac{135}{3}=45\\\\x=45[/tex]

Now Substitute 'x' in angle W we get

[tex]m\angle W=2\times 45 -13=77\°[/tex]

Therefore the measure angle W is 77 degrees.

Answer:

77 is the answer

Step-by-step explanation:

Answer:

x² - 5x + 4

Step-by-step explanation:

Note that (p - q)(x) = p(x) - q(x)

p(x) - q(x)

= x² - 1 - 5(x - 1) ← distribute

= x² - 1 - 5x + 5 ← collect like terms

= x² - 5x + 4

Answer: $28.80

Step-by-step explanation:

Answer: $30.00

Step-by-step explanation:

Because of he wants to buy 12 and they cost 2.40 then you multiply both of the 12 ans 2.40 and you get 28.8. Round it up to 30.00.

Answer:

Step-by-step explanation:

y = x - 6

to find the inverse, switch x and y and solve for y

x = y - 6

x + 6 = y...rearrange

y = x + 6 <== ur inverse

The inverse of the equation y = x - 6 is achieved by swapping x and y and then solving for y. This results in the equation y = x + 6, which is the inverse function.

The function that is the inverse of y = x - 6 can be found by switching the x and y in the equation, then solving for y. By performing this operation:

1. Switch x and y: x = y - 6

2. Solve for y: y = x + 6

Therefore, the inverse function of y = x - 6 is y = x + 6.

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Answer:

Step-by-step explanation:

Rent cost 7.50

For x days the rent to pay = 7.50×n

= 7.50n

There are 175 pages in the book.

Step-by-step explanation:

Given,

Pages read by Elena = 55 pages

Let,

x be the number of pages of book.

Pages read by Andre = [tex]\frac{1}{5}\ of\ total\ pages = \frac{1}{5}x[/tex]

As Elena has read 20 more pages than Andre, therefore,

[tex]\frac{1}{5}x+20=55\\\\\frac{1}{5}x=55-20\\\\\frac{1}{5}x=35[/tex]

Multiplying both sides by 5

[tex]5*\frac{1}{5}x=35*5\\\\x=175[/tex]

There are 175 pages in the book.

Keywords: fraction, variable

Learn more about functions at:

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Answer:

3 teaspoons of salt is needed to cook the recipe for 8 people.

The correct option is d. 3 teaspoons.

Step-by-step explanation:

Given:

Mike has a recipe that feeds one person that calls for 3/8 teaspoon of salt.

Now, to find the quantity of salt is needed to cook the recipe for 8 people.

As, given the unit rate is:

[tex]\frac{3}{8}[/tex]  teaspoon salt per person.

So, to get the salt needed to cook for 8 people we multiply 8 by [tex]\frac{3}{8}[/tex]  :

[tex]8\times \frac{3}{8}[/tex]

[tex]=\frac{24}{8}[/tex]

[tex]=3\ teaspoons.[/tex]

Therefore, 3 teaspoons of salt is needed to cook the recipe for 8 people.

The correct option is d. 3 teaspoons.

Answer:

D

Step-by-step explanation:

Given the equation y = 3x - 9

Check each of the given equations

A

y = 3(x - 9) ← distribute

   = 3x - 27 ≠ 3x - 9 ← False

B

y = [tex]\frac{1}{3}[/tex](x - 3) ← distribute

   = [tex]\frac{1}{3}[/tex] x - 1 ≠ 3x - 9 ← False

C

y = [tex]\frac{1}{3}[/tex](x - 27) ← distribute

  = [tex]\frac{1}{3}[/tex] x - 9 ≠ 3x - 9 ← False

D

y = 3(x - 3) ← distribute

  = 3x - 9 ← True

Answer:

255

Step-by-step explanation:

234+(564-543)

234+(21)

234+21

255

Answer:

56cm^2

Step-by-step explanation:

The area of triangle is found by multiplying height to the base and that divided by two

(h × b)÷2 ➡ (8×14)÷2 = 56

Answer:

72 feet is the answer. The shadow of the 63 ft tower.

To find the shadow length of a 63-foot building given a 7-foot stop sign's 8-foot shadow, a proportion is used, resulting in a shadow length of 72 feet.

A student asked how to find the length of the shadow cast by a 63-foot tall building given that a 7-foot tall stop sign casts an 8-foot long shadow. This problem can be solved using simple proportions since the ratio of the height of an object to the length of its shadow is constant when the sun's angle is constant. The proportion is as follows: height of stop sign / length of stop sign's shadow = height of building / length of building's shadow. Plugging in the numbers: 7 / 8 = 63 / x, where x is the length of the building's shadow. Solving for x, we find that x = 8 * 63 / 7 = 72. Therefore, the length of the shadow cast by the 63-foot tall building is 72 feet.

Answer:

b = -8

Step-by-step explanation:

crossmultiply

The value of W is 0.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations that are formed according to rules which is dependent on the context.

for example, a+23 = 105, a²+b²+10a =100, etc.

12×1= 12+W​

W = ?

[tex]12\times 1= 12+W\\12 = 12+W\\12-12 = W\\W =0[/tex]

Hence, the value of W is 0.

Learn more about expressions:

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Answer:

A

Step-by-step explanation:

By leaf plot...

==============================================================

Explanation:

The first row has a stem of 1 and a leaf of 6. The stem and leaf combines to 16. For this problem, the stem will always be the tens digit while the leaf values will be the units digit. If there are multiple leaves for a given row, then we use the same stem value.

In row 2, we have "2" as the stem and multiple leaves. The first three leaves for this row are {2, 2, 5}. They pair up with the stem to form the values 22, 22, 25.

So far the data set is 16, 22, 22, 25. Only choice C has this sequence of values at the start of it. Choice B comes close, but it does not have a second copy of 22. So we cross choice B off the list. Choice D is off the list because the first value '5' is not represented on the stem and leaf plot (the stem would be 0 to represent the value 05 which is just 5). Choice A is false for similar reasons.

Answer:

1. 192 books.

2. 96 books.

3. 24 books.

Step-by-step explanation:

1. Let's find the volume of each book and the volume of the box, this way:

Volume of a book = 4 * 6 * 1 = 24 inches ³

Volume of the box = 24 * 24 * 8 = 4,608 inches ³

2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?

Greatest number of books = Volume of the box/Volume of a book

Greatest number of books = 4,608/24

Greatest number of books = 192

3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.

The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.

Greatest number of layers = Height of the box/Width of a book

Greatest number of layers = 8/1 = 8

Minimum number of layers = Height of the box/Height of a book

Minimum number of layers = 8/4 = 2

Upon saying that, we have:

Number of books per layer = Greatest number of books/Minimum number of layers

Number of books per layer = 192/2 = 96

4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.

Number of books per layer = Greatest number of books/Number of layers

Number of books per layer = 192/8

Number of books per layer = 24

Answer: 5/6

Step-by-step explanation:

All we need do is to try to change 50 minutes to hour.

Remember that 60 minutes make 1 hour , so we need to find 50 minutes out of 1 hour , that is 50 minutes out of 60 minutes. Which is 50/60. Therefore:

50 minutes is 50/60 fraction of an hour

50/ 60 is the same as 5/6 in reduced form

Answer:

Step-by-step explanation:

1hour is 60minutes

= 50/60

= 5/6

Answer:

y = 4x + 6

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 4, thus

y = 4x + c ← is the partial equation

To find c substitute (- 1, 2) into the partial equation

2 = - 4 + c ⇒ c = 2 + 4 = 6

y = 4x + 6 ← equation of line

Answer:

N(number of songs) times 0.99 equals to 7.92. N×0.99=7.92

n= number of songs

product=*

n*0.99=7.92

if you need the answer it would be 6.93

Answer:

  $1343

Step-by-step explanation:

After subtracting 15% from 100% of the original price, the price Mr. Quick paid is 85% of the original price.

  0.85 × 1580 = 1343

Mr. Quick paid 1343 for his computer.

Answer:

7x-7

Step-by-step explanation:

6x-(-x) double negative --> add

7x

-2-5= -7

Answer:

7x-7

Step-by-step explanation:

Let's simplify step-by-step.

6x−2−(−x+5)

Distribute the Negative Sign:

=6x−2+−1(−x+5)

=6x+−2+−1(−x)+(−1)(5)

=6x+−2+x+−5

Combine Like Terms:

=6x+−2+x+−5

=(6x+x)+(−2+−5)

=7x+−7

Answer:

40 pounds

Step-by-step explanation:

I see no ratios shown above so I guessed

Explanation:

For reasons unknown, Brainly gets bent by the use of "f(x)". So, an appropriate answer cannot be posted as text. I have posted it as attached pictures.

The expression f(f^-1(x)) represents the composition of a function and its inverse, which always returns the original input x.

The expression f(f^-1(x)) involves the composition of a function and its inverse. A function composed with its inverse will always yield the original input, this property is fundamental in the concept of inverse functions. So f(f^-1(x)) will equal x in all and every case.

The reason why this is the case can be visualized by the definition of an inverse function. Given a function f(x), the inverse function f^-1(x), by definition, undoes the operation of f(x). This means that, if we apply f(x) and then apply f^-1(x), we will come back to our starting point.

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Answer:

73.12 yd²

Step-by-step explanation:

Find the triangle first

A=½bh

a=½×12×8

a=6×8

a=48->triangle

semicircle=

a=½×pi×r²

a=½×3.14×4²

a=½×3.14×16

a=8×3.14

a=25.12

add these two

48+25.12=73.12 yd²

Answer: He needs 3 stripes.

Final answer:

To cover the perimeter of a 14 feet by 10 feet room, Jim will need 3 strips of wallpaper border as the total perimeter is 48 feet and each wallpaper strip is 20 feet long.

Explanation:

To determine how many strips of wallpaper border Jim will need for his rectangular room, we need to calculate the total perimeter of the room. The formula for the perimeter of a rectangle is:

Perimeter = 2 × (Length + Width)

For Jim's room:

Perimeter = 2 × (14 feet + 10 feet)

Perimeter = 2 × 24 feet

Perimeter = 48 feet

Now, we know each strip of wallpaper is 20 feet long, so we divide the total perimeter by the length of one strip:

Number of strips needed = Total Perimeter ÷ Length of one strip

Number of strips needed = 48 feet ÷ 20 feet

Number of strips needed = 2.4

Since Jim cannot purchase a fraction of a strip, he will need to buy 3 strips of wallpaper border to cover the entire perimeter of his room.

Note: It's assumed that there's no significant wastage when the wallpaper strips are applied, and the strips are used efficiently.