Mathematics College

## Answers

**Answer 1**

**Answer:**

x=18

**Explanation: **

Given the equation:

[tex]\frac{x}{6}-7=-4[/tex]

To solve for x, follow the steps below.

**Step 1:** Add 7 to both sides of the equation.

[tex]\begin{gathered} \frac{x}{6}-7+7=-4+7 \\ \implies\frac{x}{6}=3 \end{gathered}[/tex]

**Step 2:** Multiply both sides of the equation by 6.

[tex]\begin{gathered} \frac{x}{6}\times6=3\times6 \\ x=18 \end{gathered}[/tex]

**The value of x that makes the equation true is 18.**

## Related Questions

Sheridan Company purchased a truck for $79,000. The company expected

the truck to last four years or 120,000 miles, with an estimated residual

value of $12,000 at the end of that time. During the second year the truck

was driven 45,000 miles. Compute the depreciation for the second year

under each of the methods below and place your answers in the blanks

provided.

Units-of-activity

Double-declining-balance

### Answers

The **depreciation **in year 2 using the **units of activity **method is $23,125.

The **depreciation **in year 2 using the **double declining balance **is $19,750.

**What is the depreciation in year 2?**

**Depreciation **is when the value of an asset declines as a result of wear and tear.

**Deprecation **in year 2 using the **units of activity **method = (miles driven in year 2 / total miles) x (cost of the asset - salvage value)

**Deprecation **= (45,000 / 120,000) x ($79,000 - $12,000)

**Deprecation ** = $23,125

**Deprecation **using the **double declining method **= (2/ useful life) x cost of the asset

**Depreciation in **year 1 = (2/4) x 79,000 = $39,500

Book value in year 2 = 79,000 - $39,500 = $39,500

**Depreciation in **year 2 = (2/4) x $39,500 = $19,750

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Write a compound inequality for the graph shown below.Use x for your variable.++-10-9-8-7 -6 -5 4-3-2-1002 3 4 5 6 7 8 9 10 xDand口口>DorOSONO?X

### Answers

The question said we should write a compound inequality of the given graph.

We are also asked to use x as the variable.

From the graph, we can see that both end values are shaded dots, which means x is inclusive of those two values.

Since:

x ≥ -5

and

x ≤ 6

Therefore, the compound inequality of the given graph is:

**-5 ≤ x ≤ 6**.

of the 800 participants in a marathon, 120 are running to raise money for a cause. How many participants out of 100 are running for a cause?a.8 b. 20c. 15d. 12OMG i hate iready please heeeelp

### Answers

To find how many participants out of 100 are running for a cause we can use the next proportion:

[tex]\frac{800\text{ total participants}}{100\text{ total participants}}=\frac{120\text{ running for a cause}}{x\text{ running for a cause}}[/tex]

Solving for x:

[tex]undefined[/tex]

Find the value of r in the equation below.11 = = 12

### Answers

[tex]\begin{gathered} 11=x-12 \\ 11+12=x-12+12 \\ x=23 \end{gathered}[/tex][tex]undefined[/tex]

what digit is in the thousands place 506,234

### Answers

The thousands place is corresponding to the digit that if fourth from the unit.

So the digit in the thousands place of 506,234 is 6.

what are the bounds of integration for the first integral ?

### Answers

We are going to use the properties of definite integrals. Note that if c belongs to the interval [a,b] and is integrable in [a,c] and [c,b], then f is integrable in [a,b]. Moreover,

[tex]\int_a^cf(x)dx+\int_c^bf(x)dx=\int_a^bf(x)dx[/tex]

Applying this property to the presented case, we obtain that

[tex]\begin{gathered} \int_a^bf(x)dx=\int_{-5}^9f(x)dx+\int_9^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_{-5}^{13}f(x)dx-\int_{-5}^2f(x)dx \\ \int_a^bf(x)dx=\int_2^{13}f(x)dx \end{gathered}[/tex]

**Note:** Another way to interpret the exercise is to interpret the integral as the area under the curve.

**Thus, the answer to the exercise is a= 2 and b = 13.**

Given that sino =V48and cotê is negative, determine 0 and coté. Enter the angle O in degrees from the interval [0°, 360). Write the exact answer. Do not round.

### Answers

In this problem

we have that

sin(theta) is positive and cos(theta) is negative

That means

the angle theta lies on the II quadrant

Remember that

[tex]\cot (\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]

Find out the value of cos(theta)

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

substitute the given value

[tex](\frac{\sqrt[]{48}}{8})^2+\cos ^2(\theta)=1[/tex][tex]\cos ^2(\theta)=1-\frac{48}{64}[/tex][tex]\begin{gathered} \cos ^2(\theta)=\frac{16}{64} \\ \cos ^{}(\theta)=-\frac{4}{8} \end{gathered}[/tex]

Find out the value of cot(theta)

substitute given values

[tex]\cot (\theta)=-\frac{4}{\sqrt[\square]{48}}[/tex]

simplify

[tex]\cot (\theta)=-\frac{4}{\sqrt[\square]{48}}\cdot\frac{\sqrt[]{48}}{\sqrt[]{48}}=-\frac{4\sqrt[]{48}}{48}=-\frac{\sqrt[]{48}}{12}=-\frac{4\sqrt[]{3}}{12}=-\frac{\sqrt[]{3}}{3}[/tex]

Find out the angle theta

using a calculator

angle in II quadrant

theta=120 degreesConvert to radians ---->

1. Patty is arranging the chairs for an awards ceremony. She wants to put the 36 chairs into a rectangular array. Choose the ways that Patty can arrange the chalrs. 1. Select all the expressions that have a product of 640. 16 x 40 (4 x 4) * (4 x 10) 40 = 16 (4 x 4) * (8 x 6) (2 x 5) * (8 x 2) x (2 x 2)

### Answers

The pieces of construction paper ordered can be determined as,

[tex]\begin{gathered} N=22\times64 \\ =1408 \end{gathered}[/tex]

**Thus, the required pieces of construction paper is 1408.**

Show work and/or describe how the expression for the completing the square method and the expression associated with the quadratic formula are equivalent.

### Answers

Given a general quadratic expression:

[tex]ax^2+bx+c=0[/tex]

firs, lets divide both sides of the equation by 'a' :

[tex]\begin{gathered} (\frac{1}{a})(ax^2+bx+c=0)^{} \\ \Rightarrow\frac{a}{a}x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ \Rightarrow x^2+\frac{b}{a}x+\frac{c}{a}=0 \end{gathered}[/tex]

next, we can move the term c/a to the right side of the equation:

[tex]\begin{gathered} x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ \Rightarrow x^2+\frac{b}{a}x=-\frac{c}{a} \end{gathered}[/tex]

now we are ready to complete the square on the left side. What we have to do, is to take the constant that is multiplying x (in this case,b/a), and first, we divide it by 2, and then elevate to the square the result:

[tex]\begin{gathered} \frac{b}{a}\frac{\cdot}{\cdot}2=\frac{b}{2a} \\ \Rightarrow(\frac{b}{2a})^2=\frac{b^2}{4a^2} \end{gathered}[/tex]

then, adding this number on both sides of the equation, we get:

[tex]x^2+\frac{b}{a}x+\frac{b^2}{4a}=-\frac{c}{a}+\frac{b^2}{4a^2}[/tex]

which we can write like this:

[tex](x+\frac{b}{2a})^2=\frac{-4ac+b^2}{4a^2}_{}[/tex]

applying the square root on both sides,we get the following:

[tex]\begin{gathered} \sqrt[]{(x+\frac{b}{2a})^2}=\sqrt[]{\frac{b^2-4ac}{4a^2}}=\pm\frac{\sqrt[]{b^2_{}-4ac}}{2a} \\ \Rightarrow x+\frac{b}{2a}=\pm\frac{\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]

finally, we can solve for x:

[tex]\begin{gathered} x+\frac{b}{2a}=\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]

as we can see, if we have a general quadratic equation, we can us the completing the square method to deduce the quadratic formula

I need to write and simplify an algebraic expression for the perimeter of each shape.please help!

### Answers

For the square, we have that each side's length is 2p, since the perimeter is the sum of the length of all sides of a geometric figure, this means that we have to add all the lengths of the square like this:

[tex]\begin{gathered} P=2p+2p+2p+2p_{} \\ \Rightarrow P=8p \end{gathered}[/tex]

And we can do the same with the 3 sides of the triangle:

[tex]\begin{gathered} P=2x+2x+3x+1 \\ \Rightarrow P=7x+1 \end{gathered}[/tex]

Find the area of a regular heptagon with an apothem of 5 cm. Round to the nearest tenth.

### Answers

**Answer:**

[tex]84.3\text{ cm}^2[/tex]

**Explanation:**

Here, we want to calculate the area of the regular heptagon

Mathematically, we use the formula below:

[tex]A\text{ = a}^2n\text{ tan\lparen}\frac{180}{n})[/tex]

where:

a is the length of the apothem which is 5 cm

n is the number of sides of the polygon which is 7 (heptagon is a 7-sides polygon)

Substituting the values, we have it that:

[tex]\begin{gathered} A\text{ = 5}^2\times7\text{ }\times\text{ tan }\frac{180}{7} \\ \\ A\text{ = 84.3 cm}^2 \end{gathered}[/tex]

hentIf TR = 11 ft, find the length of PS.IfР P.TentR16d ArcsSnd ArcsRound to 2 decimal places.and Arcs

### Answers

**SOLUTION**

This is a length of arc problem.

The formula for finding the length of an arc is:

[tex]\frac{\theta}{360}\times2\pi r[/tex]

r=TR=PT=11ft

[tex]\begin{gathered} \frac{\theta}{360}\times2\pi r \\ r=11ft \\ \theta=164^o \end{gathered}[/tex][tex]\begin{gathered} \frac{164}{360}\times2\pi(11) \\ =\frac{164}{360}\times2\times3.14\times11 \\ =31.4698ft \\ =31.47ft(to\text{ 2 decimal places)} \end{gathered}[/tex]

**The final answer is 31.47ft.**

What makes 3 + 7 + 2 = 0 + 2 true?

### Answers

Assuming that the question for this case is:

[tex]3+7+2=x+0+2[/tex]

We can subtract in both sides of the equation 2 and we got:

[tex]x=3+7+2-2=10[/tex]

And the solution for this case would be 10

. Find the value of each expression. Show your work. (a) 1.42 (b) 300 = 2(0.5 +4.5) ? 3 ) te) -23

### Answers

For the first expression, we have 1.4², this can be expressed as 1.4×1.4 and then we get:

[tex]1.4^2=1.4\times1.4=1.96[/tex]

For the second expression, 300 ÷ 2(0.5 + 4.5)² we must start by solving the sum inside the parenthesis, then we get:

300 ÷ 2(0.5 + 4.5)² = 300 ÷ 2(5)²

Then, solve the exponent on the right of the division symbol:

300 ÷ 2(5)² = 300 ÷ 2×25

Now, solve the multiplication

300 ÷ 2×25 = 300 ÷ 50

Now, we can solve the division

300 ÷ 50 = 6

Then, **300 ÷ 2(0.5 + 4.5)² = 6**

For the last expression, we must start with the exponent:

[tex]\begin{gathered} \frac{1}{3}\div2(\frac{1}{2})^3 \\ \frac{1}{3}\div2\times\frac{1}{2^3} \\ \frac{1}{3}\div2\times\frac{1}{8}^{} \end{gathered}[/tex]

Now we can solve the multiplication:

[tex]\frac{1}{3}\div2\times\frac{1}{8}^{}=\frac{1}{3}\div\frac{2}{8}^{}[/tex]

In order to divide one fraction by another one we just have to keep the first fraction unchanged, change the ÷ for a × and flip the second fraction, like this:

[tex]\frac{1}{3}\div\frac{2}{8}^{}=\frac{1}{3}\times\frac{8}{2}=\frac{1\times8}{3\times2}=\frac{8}{6}=\frac{4}{3}[/tex]

Then,** the value of the last expression is 4/3**

hello can you help me with this trigonometry question read carefully of how it has to be answered

### Answers

Area of a circle = πr²

Replacing with radius = 8.4 in:

Area of a circle = π(8.4)²

Area of a circle = 221.6708 in²

This area corresponds to 2π radians. To find the area corresponding to 2.37 radians, we can use the next proportion:

[tex]\frac{2\pi\text{ rad}}{2.37\text{ rad}}=\frac{221.6708^{}}{x^{}}\text{ }[/tex]

Solving for x:

[tex]\begin{gathered} 2\pi\cdot x=221.6708\cdot2.37 \\ x=\frac{525.359796}{2\pi} \\ x=83.6136\text{ sq. in} \end{gathered}[/tex]

write a polynomial function of least degree with integral coefficients that had the given zeros. -3,3,-2

### Answers

x³ + 2x² - 9x - 18 is the **polynomial** function of **least degree** with integral coefficients that had the **zeros** -3 , 3 , -2.

Given, the **zeros** of a **polynomial** be,

-3 , 3 and -2

As, the polynomial has 3 **zeros** then the **degree** of the polynomial is also be , 3.

Let the **polynomial** be,

p(x) = (x - (-3))(x - 3)(x - (-2))

p(x) = (x + 3)(x - 3)(x + 2)

On **multiplying** the factors, we get

p(x) = (x² - 3²)(x + 2)

p(x) = (x² - 9)(x + 2)

p(x) = (x³ - 9x + 2x² - 18)

p(x) = x³ + 2x² - 9x - 18

So, x³ + 2x² - 9x - 18 is the **polynomial** function of **least degree** with integral coefficients that had the **zeros** -3 , 3 , -2.

Hence, x³ + 2x² - 9x - 18 is the **polynomial** function of **least degree** with integral coefficients that had the **zeros** -3 , 3 , -2.

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Find the shaded area (round answer to 3 sig figs).

### Answers

1. Let us find the area of the sector:

[tex]\begin{gathered} \frac{\theta}{360}\cdot\pi\cdot r^2\text{ (Area of a sector formula)} \\ \frac{85}{360}\cdot\pi\cdot(12\operatorname{cm})^2\text{ (Replacing)} \\ \frac{85}{360}\cdot\pi\cdot144cm^2\text{ (Raising 12 to the power of 2)} \\ 0.236\cdot\pi\cdot144cm^2\text{ (Dividing)} \\ 106.814cm^2\text{ (Multiplying)} \end{gathered}[/tex]

2. The area of the triangle would be:

[tex]\begin{gathered} At=\frac{1}{2}\cdot ab\cdot\sin (\theta)\text{ (Area of a non right-angled triangle)} \\ At=\frac{1}{2}\cdot(12)\cdot(12)\cdot\sin (85)\text{ (Replacing)} \\ At=71.726cm^2 \end{gathered}[/tex]

3. Subtracting the area of the triangle from the area of the sector, we have:

106.814 cm^2 - 71.726 cm^2 = 35.088 cm^2

The answer is 35.088 cm^2

I will make seafood salad using strawberries and blueberries he uses 5 cups of strawberries for every 3 cups of blueberries which measure represents the amount of strawberries Alan uses for every bowl of fruit salad

### Answers

His salad calls for 8 cups of salad to maintain the given ratio. (5 cups of strawberries for every 3 cups of blueberries) So the ratio is 5/8 for the strawberries.

Let x be what he needs for 1 cup of fruit

5/8 = x

That's because there are 5 cups of strawberries for every 8 ( 5 strawberries + 3 blueberries ) items he needs.

A farmer gets 24.5 L of milk from each of his cows per day.He milks all five cows and pours the milk equally into 0.5-L bottles. How many 0.5-L bottles can he fill?

### Answers

There are 245 **bottles **to fill the **milk**.

**What is Division method?**

**Division **method is used to distributing a group of things into equal parts. Division is just **opposite **of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A **farmer **gets 24.5 L of **milk **from each of his cows per day.

And, He milks all five cows and **pours **the milk equally into 0.5-L bottles.

Now,

Since, A **farmer **gets 24.5 L of milk from each of his cows per day.

And, He milks all five cows.

So, The total **amount **of milk = 24.5 x 5 L

= 122.5 L

Since, He **pours **the milk equally into 0.5-L bottles.

So, The **number **of bottles = 122.5 L ÷ 0.5 L

= 245

Thus, There are 245 **bottles **to fill the **milk**.

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5/6 year = how many months

### Answers

We will solve as follows:

We multiply the value we want to know (5/6) times the number of months that are in a year(12 months) and divide it by the number of years 12 months represent:

[tex]m=\frac{(\frac{5}{6})\cdot(12)}{1}\Rightarrow m=10[/tex]

So, **5/6 of a year are 10 months**.

If a triangle ABC is at: A = (10, 7) B = (4, -4) C= (- 11, -9) and if it is translated right 2 and down 7, find the new point B'

### Answers

Answer;

**B'** **(6, -11)**

Explanations:

Translations is a** transformation technique** used to change the position of an object in an **xy-plane.**

Given the coordinate of a triangle ABC given as A (10, 7) B (4, -4) C (- 11, -9). If it is translated right 2 and down 7, the** translation rule** will be;

(x, y) -> (x+2, y-7)

Determine the new point B'

B' = (4+2, -4-7)

B' = (6, -11)

Therefore the c**oordinat**e of the new point B' is **(6, -11)**

The equation y = kx represents a proportional relationship between x and y, where k is the constant of proportionality. For a moving object, the equation d = st represents a proportional relationship between distance (d) and speed (s) or between distance (d) and time (t). Explain the different ways that you can define the constant of proportionality for this equation. Then describe some other equations that represent proportional relationships in the real world and explain why they're useful. Research on the Internet, if needed.

### Answers

d = st

if speed is constant, there is a proportional relation between distance (d) and time (t). The constant (s) can be defined as:

s = d/t

and you can compute it knowing the distance travelled in some time

if time is constant, there is a proportional relation between distance (d) and speed (s). The constant (t) can be defined as:

t = d/s

and you can compute it knowing the distance travelled at some speed.

Acceleration (a) is defined as:

a = s/t

this equation can be rewritten as:

s = at

where *a *is the constant of proportionality.

Another example is Hook's law, which states:

F = ke

where *F* is the force applied to a spring*, k* is the spring constant, and* e* is the extension of the spring.

Leila bought a sofa on sale for $268. This price was 33% less than the original price.What was the original price?

### Answers

Let *P* be the original price.

Since $268 is 33% less than the original price, then $268 is equal to 67% of the original price:

[tex]268=\frac{67}{100}\times P[/tex]

Then:

[tex]\begin{gathered} P=\frac{100}{67}\times268 \\ =400 \end{gathered}[/tex]

**Therefore, the original price was $400.**

**Answer: $356.44**

**Step-by-step Explanation: **To find the original price of the sofa you need to multiply 33% by $268, but you need to turn the percent into a decimal, to do so you need to divide 33 by 100 & that is 0.33. So 0.33 x $268 is 88.44. After, you add both $268 and $88.44 to get the original price & that is $356.44.

can you help me is it < > or =

### Answers

The correct answer is

[tex]\frac{1}{4}\times4\frac{1}{2}<4\frac{1}{2}[/tex]

can you tell me if I did the equation right

### Answers

**Answer:**** The equation is correct**

Peter, a cyclist, rides 5.673 kilometers, takes a break, and then rides an additional 4321 meters.a. How many hectometers total did he ride?How many decimeters did he ride?

### Answers

Explanation:

a) First Distance = 5.673 kilometers

2nd distance = 4321 meters

Total distance = 1st distance + 2nd distance

Total distance = 5.673 kilometers + 4321 meters

Conversion from kilometers to meters:

1 kilometer = 1000meters

5.673 kilometers = 5673 meters

Total distance in meters = 5673 meters + 4321 meters

Total distance in meters = 9994 meters

Conversion of meters to hectometers:

100 meters = 1 hectometers

9994 meters = x

cross multiply:

100(x) = 9994(1)

100x = 1994

x = 1994/100

x = 19.94 hectometers

Hence, he rode 19.94 in hectometers

b) converting to decimeters:

It is easier to convert from meters to decimeters

0.1 meters = 1 decimeter

9994 meters = y

y(0.1) = 1(9994)

0.1y = 9994

y = 9994/

Which of the following shows that f(x) grows at the same rate as g(x)? (5 points)the limit as x goes to infinity of the quotient of f of x and g of x equals 1000the limit as x goes to infinity of the quotient of f of x and g of x equals 0the limit as x goes to infinity of the quotient of f of x and g of x equals infinityNone of these

### Answers

The **function** f(x) grows at the same **rate** as the function g(x) according to the condition :** **[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} =1000[/tex].

We are given two functions. The functions are f(x) and g(x). The definitions of the functions are not given explicitly, but we need to find the relationship between the functions. Both functions grow at a certain rate. We need to find the condition that shows that the function f(x) grows at the same rate as the function g(x). The ratio of the limiting values of the two functions must be a **finite** and **non-zero constant** for the functions to have the same rate of growth.

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PLEASE HELP!!!!! I really really really really really need help with this math problem can someome help me please its has to be done in 20 mins!!!!!!!! PLEASE HELP!!!

### Answers

A) To do that we will draw a line inside the triangle that is perpendicular to the base as I have don above.

B) We will also do the same for B

7 in. 6in. 9 in. it's the formula of a triangle

### Answers

**Area of a Triangle**

Given a triangle of base length B and height length H, the area can be calculated by the formula:

[tex]A=\frac{B\cdot H}{2}[/tex]

The base and the height must be perpendicular.

The height of the given triangle is H=7 in. We need to calculate the length of the base.

We are providing a new image where a variable x is introduced to help us calculate the base length:

The triangle formed by the sides 9-7-x is right, so we can calculate the value of x by applying the Pythagora's Theorem:

[tex]7^2+x^2=9^2[/tex][tex]49+x^2=81[/tex]

Solving for x:

[tex]\begin{gathered} x^2=81-49=32 \\ x=\sqrt[]{32} \end{gathered}[/tex]

The length of the base is:

[tex]B=9+\sqrt[]{32}[/tex]

Thus, the area of the triangle is:

[tex]A=\frac{7\cdot(9+\sqrt[]{32})}{2}[/tex]

Calculating:

**A = 51.3 square inches**

what is the lcm of 6 and 8

### Answers

to determine the lcm of 6 and 8, express these numbers as the product of prime numbers:

**6 = 2x3**

**8 = 2x2x2**

the same factors determine the lcm. In this case, the factors