Explain how to simplify this complex fraction. Interpret the meaning of the result.

Answer:

12

Step-by-step explanation:

28/2=14

16+14=30

30-6=24

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

4*2=8

10-8=2

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

24/2=12

Complete Question:

4 friends evenly divided up a n-slice pizza. One of the friends,Harris, ate 1 fewer slice than he received. How many slices of pizza did Harrison eat?

Answer:

Harrison ate [tex]\frac{n}{4}-1[/tex] slices of pizza.

Step-by-step explanation:

Given data, 4 friends evenly divided up a ‘n’ slice pizza.

Thereby, the number of slices that each friend get =  [tex]\frac{n}{4}[/tex]

Now, given Harrison ate 1 fewer slice than he received. As he received  [tex]\frac{n}{4}[/tex] slices, so 1 fewer than [tex]\frac{n}{4}[/tex] means [tex]\frac{n}{4}-1[/tex]

Thus, Harrison ate [tex]\frac{n}{4}-1[/tex] slices of pizza.

Answer:

n/4 - 1

Step-by-step explanation:

Hope this helps!

Answer: z = 70

Explanation: To solve this proportion for z, we can use cross products.

*Image provided.*

When we get the equation 5z = 350, we can get z by itself on the left side of the equation by dividing both sides of the equation by 5. On the left, the 5's cancel each other out and we have z. On the right, 350 divided by 5 simplifies to 70 so we have z = 70.

Answer:

z = 75

Step-by-step explanation:

Answer:

(12-7x)

Step-by-step explanation:

144 − 49x²

by observation, we can see that 144 = 12² and 49 = 7²

hence we can rewrite the equation

144 − 49x²

= 12² - 7²x²

= 12² - (7x)²

recall that the expression x² - y² = (x+y)(x-y)

hence,

12² - (7x)²

= (12 + 7x)(12-7x)

(12-7x) appears in the expression above, hence 12 -7x is a factor

Answer:

Answer is C

Step-by-step explanation:

Answer:

24 hours in first week and 29 hours in second week.

Step-by-step explanation:

Given: Orlando work at $6/h in first week and at $7/h in second week.

           Total earning is $347 in both weeks.

Let the number of hours Orlando work in first week be`x` hours

∴ working hours in second week is (x+5) hours

Now, solving to find the number of working hours.

⇒ Total earning= earning in first week+earning in second week.

⇒ [tex]\$ 347= x\times 6+(x+5)\times 7[/tex]

Opening the parenthesis and solving it.

⇒ [tex]\$ 347= 6x+7x+35[/tex]

Subtracting both side by 35

⇒ [tex]312= 13x[/tex]

∴ x= [tex]\frac{312}{13} = 24\ h[/tex]

∴ Working hours in first week is 24 hours

   Working hours in second week is [tex]24+5= 29\ h[/tex]

Answer:

e) Shamika= 224 balloon, Crystal= 112 balloon, Aliya= 114 Balloon.

f)  We know,Crystal sold "b" balloon

           Aliya sold (b+2) balloon

          Shamika sold 2b balloon.

As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.

Now, solving to find how much each student sold balloon at school´s winter dance.

As we know total cost is $900 and each balloon cost is $2.

∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]

Total quantity= [tex]{b+(2+b)+2b}[/tex]

∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]

Once we solve, we will get the value of b as 112 balloon, which is the number of balloon sold by Crystal.

Substituting the value of b in the equation of Aliya and Shamika, we will get the number of balloon sold by them.

Which is 114 and 224 respectively.

Step-by-step explanation:

Given: Crystal sold "b" balloon

           Aliya sold (b+2) balloon

          Shamika sold 2b balloon.

As per data given in question part c that each balloon cost $2 and Total cost of balloon is $900.

Now, solving to find how much each student sold balloon at school´s winter dance.

As we know total cost is $900 and each balloon cost is $2.

∴ Total cost= [tex]Total\ quantity \times cost\ of\ each\ unit[/tex]

Total quantity= [tex]{b+(2+b)+2b}[/tex]

∴ [tex]\$ 900= {b+(2+b)+2b}\times \$ 2[/tex]

Opening the parenthesis.

⇒[tex]\$ 900= (b+2+b+2b)\times \$ 2[/tex]

⇒[tex]\$ 900= 2+4b \times 2[/tex]

Dividing both side by 2

⇒ [tex]\$ 450= 2+4b[/tex]

Subtracting both side by 2

⇒ [tex]\$ 448= 4b[/tex]

Cross multiplying

∴[tex]b= \frac{448}{4} = 112[/tex]

∴ b= 112.

Hence, we can say Crystal have sold 112 balloons.

Next subtituting the  value of "b" in the equation for Aliya and Shamika to get number of balloon they have sold.

We know, Aliya sold b+2 balloons

∴ Aliya sold= [tex]112+2= 114\ balloon[/tex]

Aliya sold 114 balloon.

We know, Shamika sold 2b balloons

∴[tex]2\times 112= 224 balloon.[/tex]

Shamika sold 224 balloon.

Answer:

y = 5x + 4

Step-by-step explanation:

y - 4 = 5(x - 0)

That is point-slope form. I'm not sure if you want it in slope intercept form, but slope intercept form of the equation is -

y = 5x + 4

Answer:

Step-by-step explanation:

thx i needed this

Answer:

[tex]sin \theta =\frac{-8}{10} =-\frac{4}{5}[/tex]

Step-by-step explanation:

For this case we have a point given (-6,-8) and we know that this point is terminal side of 0​

We can assume that the length of th opposite side is given by:

b=-8 and the length for the adjacent side would be a=-6

And we can find the hypothenuse on this way:

[tex] c= \sqrt{a^2 +b^2}=\sqrt{(-6)^2 +(-8)^2}=10[/tex]

From the definition of sin we know this:

[tex]sin O =\frac{opposite}{hypothenuse}[/tex]

And if we replace we got this:

[tex]sin \theta =\frac{-8}{10} =-\frac{4}{5}[/tex]

We can aslo find the cos with the following identity:

[tex]cos^2 \theta + sin^2 \theta = 1[/tex]

And then:

[tex]cos \theta = \pm \sqrt{1-sin^2 \theta}=\pm \sqrt{1- (-4/5)^2}=\pm \frac{3}{5}[/tex]

But since both corrdinates are negative we are on the 3 quadrant and then [tex]cos \theta= -\frac{3}{5}[/tex]

Answer:

The volume of the shipping box is [tex]V=27\ in^3[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

The volume of the triangular prism is equal to

[tex]V=BH[/tex]

where

B is the area of the triangular base

H is the height of the prism

In this problem we have

[tex]H=9\ in[/tex]

Find the area of the triangular base B

[tex]B=\frac{1}{2}bh[/tex]

we have

[tex]b=3\ in\\h=2\ in[/tex]

substitute

[tex]B=\frac{1}{2}(3)(2)=3\ in^2[/tex]

Find the volume of the triangular prism

[tex]V=BH[/tex]

we have

[tex]B=3\ in^2[/tex]

[tex]H=9\ in[/tex]

substitute

[tex]V=(3)(9)=27\ in^3[/tex]

(a) m=6h+15 can be used to find the total amount of money for h hours of babysitting.

(b) After 6 hours of babysitting, Scott will have $51.00

Step-by-step explanation:

Given,

Amount Scott has = $15.00

Per hour amount of babysitting = $6.00

a) Write an equation for the amount of money (m) Scott has after a number of hours babysitting (h).

Total amount of money = m

Number of hours babysitting = h

Total amount of money = Per hour earning from babysitting*Number of hours + Amount Scott has

[tex]m=6h+15[/tex]

m=6h+15 can be used to find the total amount of money for h hours of babysitting.

b) After how many hours of babysitting will Scott have $51.00?

Putting m = 51

[tex]51=6h+15\\51-15=6h\\36=6h\\6h=36[/tex]

Dividing both sides by 6

[tex]\frac{6h}{6}=\frac{36}{6}\\h=6[/tex]

After 6 hours of babysitting, Scott will have $51.00

Keywords: linear equation, division

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Answer:

Italy Time is in the Central European Time Zone . Central European Standard Time ( CET ) is 1 hours ahead of Greenwich Mean Time ( GMT+1 ).

Step-by-step explanation:

Central European Time Zone

Italy's time zone is one hour ahead of GMT (Greenwich Mean Time), so if it is 1 PM GMT, it would be 2 PM in Italy. This reflects the Time Zone Difference concept.

If Italy's time zone is GMT + 1, and it is currently 1 PM GMT, then the time in Italy would be 2 PM. This is due to the fact that Italy is one hour ahead of GMT (Greenwich Mean Time). Therefore, to convert from GMT to Italy's time zone, one simply needs to add one hour. For example, if it was 5 PM in GMT, it would be 6 PM in Italy, and so on. This concept is referred to as Time Zone Difference.

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Answer:

Volume of the rectangular prism is [tex]11\frac{1}{4}[/tex] cubic feet.

The number of small cubes required is 90.

Step-by-step explanation:

The rectangular prism has a length of [tex]2\frac{1}{2}[/tex] feet, a width of 3 feet, and a height of  [tex]1\frac{1}{2}[/tex] feet.

Now, the volume of the rectangular prism will be [tex](2\frac{1}{2} \times 3 \times 1\frac{1}{2}) = (\frac{5}{2} \times 3 \times \frac{3}{2}) = \frac{45}{4}[/tex] cubic feet i.e. [tex]11\frac{1}{4}[/tex] cubic feet. (Answer)

Now, the volume of the small unit cubes of side lengths of [tex]\frac{1}{2}[/tex] feet will be [tex](\frac{1}{2})^{3} = \frac{1}{8}[/tex] cubic feet.

So, the number of small cubes required to fill the large cube will be [tex](\frac{45}{4} \div \frac{1}{8}) = 90[/tex]. (Answer)

Answer:

yes

what grade

Step-by-step explanation:

Answer:

it's -1/2

Step-by-step explanation:

you need to go half way between 0 and -1 and that's -1/2

Answer:

-0.5 or -1/2

Step-by-step explanation:

You can solve using operations or with a number line.

To find the value halfway between two numbers, add the two numbers and divide the sum by 2.

Q = (0 + -1)/2

Q  = (0 - 1)/2

Q = -1/2

Q = -0.5

Number line:

<- (-1) --------- (-0.5) ---------- 0 ----------- (0.5) --------- (1) ->

Find halfway between 0 and 1.

Q = -0.5

He could have scored 7, 14, 21, 28, 35, or 42 points (all multiples of 7 less than 45).

answer: B

Answer:

11

Step-by-step explanation:

- 7 + 8 = 11 and the absolute value of 11 is 11

To prove congruence by SSS, two statements are needed about equal sides: AC―――― ≅ ED―――― and DE―――― ≅ BC――――. A third unlisted statement equating the other sides is also required.

To prove two triangles are congruent using the Side-Side-Side (SSS) Postulate, we need to establish that all three corresponding sides of the triangles are equal in length. Statement B indicates that AC―――― ≅ ED――――, which provides one pair of corresponding sides. Statement C suggests that DE―――― ≅ BC――――, providing a second pair of corresponding sides. Lastly, if we had information that AB―――― = DF――――, not provided in the options but necessary to complete the SSS congruence, then we could establish the congruence of the two triangles. Therefore, the statements needed for SSS congruence proof are options B and C, along with an unlisted statement that equates the third pair of corresponding sides.

Answer:-18

Step-by-step explanation: if f(x)= -9x

And x =2

-9(2)

= -18

Answer:

f(-2)=-18

Step-by-step explanation:

given f(x)=9x...........(1)

put x=-2 in equation (1)

f(-2)=[tex]9\times(-2)[/tex]

f(-2)=-18 answer

Answer:

1915 miles more to drive to complete their trip.

Step-by-step explanation:

Given:-

Total distance to travel (D) = 2598 miles.

Distance travelled (d) = 683 miles.

To calculate = remaining distance (r) to complete trip.

Remaining distance = Total distance minus Distance travelled

i.e.  [tex]r=D-d[/tex]

[tex]r=2598-683[/tex]

[tex]r=1915\ miles[/tex]

Therefore kalsbeeks have to travel 1915 miles more to complete their trip.

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

The total length of this line is 15 units. FG is 6 units long.

This means that the probability of p being on FG would be [tex]\frac{6}{15}[/tex] which can be simplified to [tex]\frac{2}{5}[/tex]

Answer:

2/5

Step-by-step explanation:

Line EH has three line segments:

EF which measure 4

FG which measures 6

GH which measures 5

The total measure of the line (EH) = 4 + 6 + 5 = 15

So if we are calculating the probability of landing on FG,

6 / 15

Reduce the fraction to make,

2 / 5

with an expression like 3x6 you can separate parts of the expression using parentheses like: 3(2+4)

you can find ways to separate a variable (like 6) into a sum of two addends

ex 1+5

0+6

3+3

so a distributive version of 3x6 is 3(2+4) = (3x2) + (3x4)

Answer:

see explanation

Step-by-step explanation:

(1)

Given the perimeter then the third side is the perimeter subtract the sum of the 2 given sides, that is

third side

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

= 4x + 3y - 2x ← collect like terms

= 2x + 3y

(2)

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 2x + 6 and h = x - 2, thus

A = [tex]\frac{1}{2}[/tex](2x + 6)(x - 2) ← expand factors using FOIL

   = [tex]\frac{1}{2}[/tex](2x² + 2x - 12) ← distribute

   = x² + x - 6 ← in standard form

Answer:

option 3 ⇒ f⁻¹(x) =  [tex]\frac{x^{2} -2 }{3} [/tex]

Step-by-step explanation:

Given F(x) = [tex]\sqrt{3x+2}[/tex]

let y = f(x)

y = [tex]\sqrt{3x+2}[/tex]   ⇒ squaring the both sides

y² = 3x + 2  ⇒ subtract 2 from both sides

y² - 2 = 3x ⇒ divide both sides by 3

[tex]\frac{y^{2} -2 }{3} = x[/tex]

replace the location of x and y

∴ y = [tex]\frac{x^{2} -2 }{3} [/tex]

So, y will be f⁻¹(x)

∴ f⁻¹(x) =  [tex]\frac{x^{2} -2 }{3} [/tex]

Answer:

x = 31°

Step-by-step explanation:

Since, CB ║ FG and AB is a transverse, so ∠ BAG = ∠ ABC = 28° {Alternate angles}

Now, ∠ CAG = 90° = ∠ CAD + ∠ BAG

⇒ ∠ CAD = 90° - 28° = 62°

From, Δ ADE, ∠ ADE + ∠ DEA + ∠ EAD = 180°

⇒ ∠ ADE = 180° - 62° - 3x = 118° - 3x.

Now, ADB being a straight line, so ∠ ADE + ∠ EDC + ∠ CDB = 180°

⇒ 118 - 3x + x + 4x = 180

⇒ 2x = 62

⇒ x = 31° (Answer)

Answer:

x=11

Step-by-step explanation:

7(x)-7(3)=56

7x-21=56

7x-21+21=56+21

7x=77

7x/7=77/7

x=11

The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree

Step-by-step explanation:

The formula to find the angle between the positive part of x-axis and a line y = m x + b is tan(Ф) = m, where

∵ The equation of the line is [tex]y=\frac{5}{4}x[/tex]

∵ The form of the equation of a line is y = m x + b

∴ m = [tex]\frac{5}{4}[/tex] and b = 0

∵ Ф is the angle between the line and the positive part of x-axis

∵ tan(Ф) = m

∴ tan(Ф) = [tex]\frac{5}{4}[/tex]

- To find Ф use the inverse function of tan ( [tex]tan^{-1}[/tex]

∵ Ф = [tex]tan^{-1}(\frac{5}{4})[/tex]

∴ Ф = 51.34°

- Round it to the nearest degree

∴ Ф = 51°

The measure of the angle formed with the positive x-axis and the equation of the given line is 51° to the nearest degree

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Answer:

[tex]3a^4[/tex]

Step-by-step explanation:

What is the cube root of  [tex]27a^{12}[/tex]? This is the question.

We can write:

[tex]\sqrt[3]{27a^{12}}[/tex]

We will use the below property to simplify:

[tex]\sqrt[n]{a*b}=\sqrt[n]{a}  \sqrt[n]{b}[/tex]

So, we have:

[tex]\sqrt[3]{27a^{12}} =\sqrt[3]{27} \sqrt[3]{a^{12}}[/tex]

We will now use below property to further simplify:

[tex]\sqrt[n]{x} =x^{\frac{1}{n}}[/tex]

Thus, we have:

[tex]\sqrt[3]{27} \sqrt[3]{a^{12}} =3*(a^{12})^{\frac{1}{3}}[/tex]

We know power to the power rule:  [tex](a^z)^b=a^{zb}[/tex]

Now, we have:

[tex]3*(a^{12})^{\frac{1}{3}}\\=3*a^{\frac{12}{3}}\\=3a^4[/tex]

This is the correct answer:  [tex]3a^4[/tex]

Answer:

T=50+86.49N

Step-by-step explanation:

you just have to combine A and B.

Total (T)=A(50+30.65N)+B(55.85N) thank just open the prentices and add 30.65N and 55.85N=86.49N. so total is initial savings+ weekly savings by both.

Answer:

I thinks its r = 11

Step-by-step explanation:

So you just need to take the number to the r and multipliy it by r So,

9x2=18

then minus it by the other number which would Be 7 so.

18-7=11

Answer:

11

Step-by-step explanation:

(-9 times 2) - 7

18 - 7

11