Translate into a variable expression. Then simplify.



1. a number n minus the difference between the number and seven



2. a number n increased by two-thirds of the number



3.twelve more than the square of a number n added to the difference between the number and fifteen



4.the sum of two times a number n and fourteen added to the product of fourteen and the number



5.The sum of two numbers is twenty-six. Using x to represent the smaller of the two numbers, translate "the difference between two more than the larger number and twice the smaller number" into a variable expression. Then simplify.



6.A financial advisor has invested $14,000 in two accounts. If one account contains x dollars, express the amount in the second account in terms of x.



7. A 9-foot board is cut into two pieces of different lengths. Express the length of the longer piece in terms of the length L of the shorter piece.

Step-by-step explanation:

this is practically a cylinder.

the volume of a cylinder is

ground area × height = pi×r² × height.

r being the radius (half of the diameter).

so, we have here

V = pi×10² × 13 = pi × 100 × 13 = 1300pi =

= 4,084.07045... cm³

1 liter = the content of a cube with 10 cm side length.

10×10×10 cm³ = 1000 cm³ = 1 liter.

the pan has a volume of 4,084.07045... cm³, so, yes, it has the capacity of 4 liters as 4×1000 cm³ (and a little bit extra).

Answer:

108

Step-by-step explanation:

9(8 plus 4)

Simply do 8 plus 4 = 12 then 12x9=108

Step-by-step explanation:

2x-10x+6=4x-6

2x-10x-4x=-6-6

-12x=-12

x=1

Check the picture below.

The solution is, the combined volume of the boxes is 180 unit cube.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

from the given diagram, we get,

there is two boxes in the diagram.

now, we have to find the combined volume.

here, we get,

the boxes are cuboids.

we know that,

Volume of  cuboid = length * width * height

V = l*w*h

here, we get, from the figure,

for 1st box, l = 3, w = 5 , h = 8

so, V  = 3 * 5 * 8 = 120

and, for 2nd box, l = 4, w = 5, h = 3

so, V = 4*5*3 = 60

we get, the combined volume 120 + 60 = 180

Hence, The solution is, the combined volume of the boxes is 180 unit cube.

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Answer:

$22.00

A tip in sales is an added monetary contribution to the worker responsible for your bill. Tips are usually in percentage form and represent a portion of the total before you add a tip.

To find a tip in sales, convert the percentage to a decimal and then add 1 to that decimal. Finally, multiply the total by this sum.

To solve, first convert the percentage into a decimal by dividing by 100.

[tex]\displaystyle \frac{10}{100}[/tex]

[tex]0.1[/tex]

Then, add 1 to this quotient.

[tex]1+0.1 =1.1[/tex]

Finally, multiply the total ($20) by this sum.

[tex]20\times 1.1[/tex]

[tex]22[/tex]

Therefore, the total cost is $22.00.

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The total cost to the nearest cent is $22.00 when haircut is $20 and tip is 10%.

To find the total cost, we need to add the cost of the haircut and the tip amount.

Given:

Haircut cost = $20

Tip percentage = 10%

First, calculate the tip amount:

Tip = (10/100) × Haircut cost

Tip = (10/100) × $20

Tip = $2

Add the haircut cost and the tip amount to find the total cost:

Total cost = Haircut cost + Tip

Total cost = $20 + $2

Total cost = $22

Therefore, the total cost to the nearest cent is $22.00.

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The greatest common factor of 9ab², 108ab³ is 9ab².

The factor of a number is the number that divides a number evenly; without any remainders. The factors of a number can either be positive or negative. For example, a factor of 10 is 2. This is because 10 divided by 2 is 5. 2 divides 10 evenly.

The greatest common factor is the highest factor that is common to two or more numbers. The highest common factor of 10 and 20 is 10. This is because it is the greatest common factor that is common to both numbers.

Factors of  9ab², 108ab³ = 3ab², 9ab²

The greatest common factor = 9ab²

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a. The stand form is f(x) = x^3 - 13x - 12

degree = 3

constant term = - 12

b. The stand form is g(x) = 3 x^3 - 39x - 36

degree = 3

constant term = - 36

Given data

f(x) = (x + 1)(x+3)(x-4)

g(x) = 3(x + 1)(x+3)(x-4)

for f(x) = (x + 1)(x+3)(x-4) we have

f(x) = (x + 1)(x+3)(x-4)

f(x) = ( x + 1 ) ( x^2 - 4x + 3x - 12 )

f(x) = (x + 1) ( x^2 - x - 12 )

f(x) =  x^3 - x^2  - 12x +  x^2 - x - 12

f(x) = x^3 - 13x - 12

degree = 3

constant term = -12

g(x) = 3(x + 1)(x+3)(x-4)

g(x) = 3(x + 1) ( x^2 - 4x + 3x - 12 )

g(x) = 3(x + 1) ( x^2 - x - 12 )

g(x) = 3 (  x^3 - x^2  - 12x +  x^2 - x - 12 )

g(x) = 3 ( x^3 - 13x - 12 )

g(x) = 3 x^3 - 39x - 36

degree = 3

constant term = - 36

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Answer: The reason that you would use addition to check subtraction is because it is the easiest, fastest, and most reliable way to check your subtraction problem.

Step-by-step explanation:

for example. you do something like: 42 - 19 = 23

you just add 19 and 23. if you get 42 then that means your answer if correct.

hope it helps

Answer:

8 gallons

Step-by-step explanation:

Answer:

4³

Step-by-step explanation:

using the rules of exponents

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]

then

4² × [tex]4^{4}[/tex] / 4³

= [tex]4^{(2+4)}[/tex] / 4³

= [tex]4^{6}[/tex] / 4³

= [tex]4^{(6-3)}[/tex]

= 4³

60 percent of the original price is saved if the futon bed is purchased.

The original price of the futon bed is $500

The new price is $200

The first step is to calculate the price change

Price change= 500-200

= 300

The amount saved can be calculated as follows

300/500 × 100

= 0.6 × 100

= 60

Hence 60 percent of the original price which is $500 will be saved

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Probability is the measure of the likelihood that an event will occur in a Random Experiment.  The probability of selecting a senior from non geography is 0.1132

Probability is the measure of the likelihood that an event will occur in a Random Experiment

Given

                      Geography Majors           Non Geography Majors

Freshmen               15                                          14

Sophomores             11                                          16

Juniors                     13                                         11

Seniors                      14                                         12

The  total number of students are 106

The number of seniors in non geography is 12

So probability of selecting one senior from 106 is 12/106

Probability(senior of non geography)=12/106=0.1132

Therefore required probability is 0.1132.

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Answer:
The two shapes are similar, therefore, [tex]\frac{\text{KJ}}{\text{WZ}} = \frac{\text{JM}}{\text{YZ}}[/tex]

[tex]\frac{12}4 = \frac6n\\\to 3n = 6\\\to n =2[/tex]

The side length YZof a trapezoid WXYZ will be 2 cm.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.

The side lengths are given as:

JK = 12 cm

MJ = 6 cm

WX = 4 cm

WZ = n cm

From the diagram, the trapezoid JKLM is similar to the trapezoid WXYZ.

If the two polygons are similar then the ratio of the corresponding sides of the polygon is constant. The ratios are written as,

JK/WX = KL/XY = LM/YZ = MJ/ZW

JK/WX = MJ/ZW

12/4 = 6/n

3 = 6/n

n = 6/3

n = 2

The side length YZof a trapezoid WXYZ will be 2 cm.

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The P-intercept of the function P(x) is 0.

The n -intercepts of the function are n = 0, -3 and -7

We are given the function;

P(n) = 3n⁴ + 30n³ + 63n²

Now, the P intercept of the function P(n) will occur when n = 0. Thus;

P(0) =  3(0)⁴ + 30(0)³ + 63(0)²

P(0) = 0

Thus, the P intercept of the function P(x) is 0.

Now, the n-intercept will be the roots of the given function P(x). Thus;

3n⁴ + 30n³ + 63n² = 0

n²(3n² + 30n + 63) = 0

Thus;

n² = 0 or 3n² + 30n + 63 = 0

Using quadratic equation calculator we have;

n = 0, -3 and -7

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The rug will have dimension of 8ft. wide and 22ft. long.

Dimensions of room :

Wide (w) = 18 ft.

Long (l) =  32 ft.

Area of the room = l × w

                            = 32 × 18 = 576 ft²

Cynthia wants to leave a uniform strip of floor around the rug.

Let the width of the rug = x ft.

Then the dimensions of the rug will be = (18- 2x)ft. × (32- 2x)ft.

Area of the rug = (18 - 2x) × (32 - 2x) ft²

176 = (18 - 2x) × (32 - 2x)

176 = 576 - 36x - 64x + 4x²

  4x² - 100x + 400 = 0    ( Divide the equation by 4 )

      x² - 25x + 100 = 0  

x² - 20x - 5x + 100 = 0

x(x - 20)  -5(x - 20) = 0

       (x - 20) (x - 5) = 0

            x = 20, 5

If we take 20 as x then it will become a negative number when we will substract it from dimensions of the rug.

Therefore, The width of the rug  will be 5 ft.

Thus, The Dimension of the rug = (18- 2x)ft. × (32- 2x)ft.

                                                   = (18 - 10) × (32 - 10)

                                                   = 8ft. × 22ft.

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Answer:

4:25 I think

Step-by-step explanation:

just added them all up I don't know if that's what you needed yho

Answer:

15:85 or 4:25

Step-by-step explanation:

jfhfjfjfjfjfndndndndndjdjfjfnnfjfjdjfjfjf

Answer:

.49 if you're dividing them.

Step-by-step explanation:

Answer:yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to see two other ways to write the ratio 3:8.

A ratio is a way of saying that some number of one thing is always associated with some (often different) number of another thing. The two things may or may not be measured with the same units, and may or may not refer to parts of the same object.

Here, we're concerned with how we write a ratio. One way is shown in the problem statement:

  3 : 8 . . . . . . . . using a colon

Two other ways to write the same ratio are ...

  3 to 8 . . . . . . using the word "to"

  3/8 . . . . . . . . using a fraction bar

__

Additional comment

A ratio is in "simplest form" if the numbers involved are mutually prime (have no common factors).

Sometimes an extended ratio is useful for specifying the relationship between more than two measures, for example, 3 : 8 : 5.

Answer:

[tex]3^{16/5}[/tex]

Step-by-step explanation:

[tex]3^3 \times \sqrt[5]{3} \\ \\ =3^3 \times 3^{1/5} \\ \\ =3^{16/5}[/tex]

When you subtract a constant from y = x², the following happens to the graph: C. graph moves DOWN.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive.

In conclusion, when a constant is subtracted from y = x², we can reasonably infer and logically deduce that the graph moves down as shown in the image attached below.

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Complete Question:

When you subtract a constant from y = x²  what happens to the graph? Eg  y = x² - 2

answer choices

Graph moves UP

Graph moves to the RIGHT

Graph moves DOWN

Graph moves to the LEFT

a) The rate % at the beginning of 2008 rounded off to four decimal places will be 25.1682 % per year.

b) The rate % at the beginning of 2017 rounded off to four decimal places will be 28.2573 % per year .

c) The rate % at the beginning of 2017 rounded off to two decimal places will be 28.26% per year.

What is a function ?

A function is a relationship between inputs and outputs where each input has precisely one output and the output can be linked to its input.

It is given that , a function which represents rate % is f(t) = 10.72 × [tex](0.9t + 10)^{0.3}[/tex]. Also , t = 0 corresponding to the year 2000.

The rate % of Americans age 55 and older changing at the beginning of 2008 i.e., t = 8 , rounded off to four decimal places will be :

So : f(t) = 10.72 × [tex](0.9* 8 + 10)^{0.3}[/tex]

f(t) = 10.72 × [tex](7.2+ 10)^{0.3}[/tex]

f(t) = 10.72 × [tex](17.2)^{0.3}[/tex]

f(t) = 10.72 × 2.347

f(t) = 25.1682 % per year

The rate % of Americans age 55 and older changing at the beginning of 2017 i.e., t = 17 , rounded off to four decimal places will be :

f(t) = 10.72 × [tex](0.9* 17 + 10)^{0.3}[/tex]

f(t) = 10.72 × [tex](15.3 + 10)^{0.3}[/tex]

f(t) = 10.72 × [tex](25.3)^{0.3}[/tex]

f(t) = 10.72 × 2.6359

f(t) = 28.2573 % per year  

The rate % of Americans age 55 and older changing at the beginning of 2017 rounded off to two decimal places will be :

f(t) = 28.26% per year  

Therefore , the answers are  :

a) The rate % at the beginning of 2008 rounded off to four decimal places will be 25.1682 % per year.

b) The rate % at the beginning of 2017 rounded off to four decimal places will be 28.2573 % per year .

c) The rate % at the beginning of 2017 rounded off to two decimal places will be 28.26% per year.

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The property which equality 2 demonstrate is: d. Associative property of multiplication.

The associative property of multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged (grouped).

This ultimately implies that, the associative property of multiplication suggest that the way in which factors are arranged (grouped) when multiplying three (3) numbers does not change the product.

Mathematically, the associative property of multiplication can be represented by this expression:

(a × b) × c = a × (b × c)  ≡ (8 × 5) × 6.75 = 8 × (5 × 6.75)

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