For income tax purposes, a man uses a method called
straight-line depreciation to show the loss in value of a copy
machine he recently purchased. A man assumes that he can
use the machine for 5 years. The following graph shows the
value of the machine over the years. What loss in value
occurred during the first year?

Part A

1 hour = 60 minutes

0.5 hours = 30 minutes (multiply both sides by 0.5)

11.5 hours = 11 hours + 0.5 hours

11.5 hours = 11 hours + 30 minutes

11.5 hours = 11 hours, 30 minutes is the answer

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

Part B

20% = 20/100 = 0.20

The lion sleeps 20% more than the cat, which means the lion sleeps 0.20*11.5 = 2.3 hours more

This leads to 11.5 + 2.3 = 13.8 hours being the total time the lion sleeps

1 hour = 60 minutes

0.8 hours = 48 minutes (multiply both sides by 0.8)

13.8 hours = 13 hours + 0.8 hours

13.8 hours = 13 hours + 48 minutes

13.8 hours = 13 hours, 48 minutes is the amount of time the lion sleeps

Answer: 0.68

Step-by-step explanation:

given data:

ABC market share = 30%

number of customers surveyed = 800

probability that more than 32% prefers ABC

Solution:

32% of 800

= 256 persons

p ( x ≥ 256 )

= 1 - ( 256/800 )

= 1 - 0.32

= 0.68

the probabiliy that more than 32% of those who carried out the survey would prefer ABC brand is 0.68.

Answer:

[tex]\frac{7}{2}[/tex]in

Step-by-step explanation:

First you must set up an equation. [tex]\frac{1}{2}x=\frac{7}{4}[/tex]

Then, you must solve for x.          [tex]x=\frac{7}{2}[/tex]

Answer:

I am not totally sure but the answer might be 0.0655.

Answer:

Step-by-step explanation:

19 - 3i - 5 + 4i

14 + i

Answer:

10.67% increase

Step-by-step explanation:

We can find percent increase with (difference/original) x 100

7.47 - 6.75

= 0.72 (difference)

(0.72/6.75) x 100

= 10.67% increase

Answer:

2/5 is greater

Step-by-step explanation:

to compare you need to make them common denominator, and that could be10. to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2. this will turn it into 4/10. 4/10 is greater than 3/10

The solution is : 2/5> 3/10

2/5 is greater than 3/10

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

Here, we have,

the given fractions are,

2/5 and 3/10

now, we have,

to compare you need to make them common denominator,

and that could be10.

to make both denominators equal to ten just multiply the top and bottom of 2/5 by 2.

i.e. 2*2/5*2

=4/10

this will turn it into 4/10.

now, we get,

4/10 is greater than 3/10

Hence, 2/5> 3/10 , 2/5 is greater than 3/10.

To learn more on fraction click:

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Answer:

x² - 2

Step-by-step explanation:

To obtain (g ￮ f)(x), substitute x = f(x) into g(x), that is

g(x² - 3)

= x² - 3 + 1

= x² - 2

Answer:

✔ x² - 2

Step-by-step explanation:

EDG 2020

Answer:

a=-1

b=10

Step-by-step explanation:

Answer:

a: -1

b: 10

edge 2020

Answer:

[tex]x=\frac{55}{3},\:y=\frac{22}{3}[/tex]

Step-by-step explanation:

Solve by Substitution ;

[tex]\begin{bmatrix}x+2y=33\\ x-y=11\end{bmatrix}\\\\\mathrm{Isolate}\:x\:\mathrm{for}\:x+2y=33:\quad x=33-2y\\\\\mathrm{Subsititute\:}x=33-2y\\\\\begin{bmatrix}33-2y-y=11\end{bmatrix}\\\\Simplify\\\begin{bmatrix}33-3y=11\end{bmatrix}\\\\\mathrm{Isolate}\:y\:\mathrm{for}\:33-3y=11:\quad y=\frac{22}{3}\\\mathrm{For\:}x=33-2y\\\\\mathrm{Subsititute\:}y=\frac{22}{3}\\x=33-2\times\frac{22}{3}\\\\x=\frac{55}{3}\\\\x=\frac{55}{3},\:y=\frac{22}{3}[/tex]

Answer:

x=(k+3)/y

Step-by-step explanation

First, we simplify by adding 3 to both sides of the equation

xy-3+3=k+3

Now it's xy=k+3

To get x we divide both sides by y

So x=(k+3)/y

Answer:

[tex]x = \frac{k + 3}{y} [/tex]

Step-by-step explanation:

Do all u can to make x stand alone.

Just obey the rules of fhe operations when they cross the equal sign.

Answer:

r≈4.775

Step-by-step explanation:

the formula for this is: r=(3V /4π)^⅓

Answer:

4 you dumba**. Jesus christ

Step-by-step explanation:

Answer:

Hey there!

The big square has an area of 6x6 or 36 units.

However, we subtract 8 to get 28 because the 8 white squares do not count.

Let me know if this helps :)

Answer:

28units²

Step-by-step explanation:

6² = 36

36 - 8 = 28

Answer:

14.48 ft

Step-by-step explanation:

The relation between the location of the focus (c), the vertex on the major axis (a) and the vertex on the minor axis (b) with respect the center is:

b² = a² - c²

From the question:

c = 4 ft

a= 30/2 = 15 ft

Replacing into the equation:

b² = 15² - 4²

b = √209

b = 14.48 ft

So, he should build the whisper chamber at 14.48 ft out from the center along the minor axis

Answer: The answer to this questiojn is 14.48 feet, but if rounded to the nearest tenth, then it should be 14.5 (As it was on my question)

Answer:Answer:

81 miles

Step-by-step explanation:

From the question 7/10 of the trip has been said to be downhill. It therefore means that 3/10 is not downhill.

Miles = 270

Downhill = 7/10

Not downhill = 3/10

Now we have To calculate Miles that are not downhill (uphill)

But first I calculated for the number of downhill miles

270x7/10

Downhill = 189 miles

To get the number of not downhill miles

I subtracted 189 from the total number of miles on the question.

270 - 189

= 81 Miles.

Therefore 81 Miles of the trip are not downhill.

If you have anymore questions or need clarity please let me know on the comment section. Thank you and Good luck!

Step-by-step explanation:

third

hope it helps you

Answer: (6^-8/7^-12)

Step-by-step explanation:

In this type of problems, you apply the laws of indices which stated that

( a²/b²)³ =( a²×³/b²×³)

= ( a6/b6)

From this question now, applying the above principle

(6²/7³)-4

= (6²×-⁴/7³×-⁴)

= (6^-8/7^-12)

So the answer is C

Answer:

answer is -3

Step-by-step explanation:

-6x+4+3x+3=34

-3x+7=34

-3x=34-7

-3x=27

x=27/-3

x=-3

Answer:    2a - 10

Step-by-step explanation:

a represents the number of students in the art club.

The number of students in a school's math club is ten less than twice the number of students in the art club.

ten less = - 10

twice the number of students in the art club = 2*a

2a - 10 = the number of students in the math club

Answer:

36 fliers

Step-by-step explanation:

1/3*72 = 24 fliers posted last week (.333*72)

72-24 = 48 fliers left

1/4*48 = 12 fliers posted this week (.25*48)

48-12= 36 fliers not posted  

Linda has 36 fliers left to post.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given: Linda had 72 fliers to post around town. Last week, she posted 1/3

of them. This week, she posted 1/4 of the remaining fliers.  

1st-week Linda posted 72/3=24 and remaining fliers72-24=48

2nd the week Linda posted 48/4=12 and remaining fliers 48-12=36

∴The remaining fliers left to be posted are 36

Hence, Linda has 36 fliers left to post.

Learn more about the unitary method here:

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Answer:

A reduce the fraction is

5\1

Answer:

C. 4i-2

Step-by-step explanation:

EDGE 2020

Answer:

The solution of the inequation [tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex] is [tex]\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)[/tex].

Step-by-step explanation:

First of all, let simplify and factorize the resulting polynomial:

[tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex]

[tex]6\cdot x^{2}-11\cdot x -10 \geq 0[/tex]

[tex]6\cdot \left(x^{2}-\frac{11}{6}\cdot x -\frac{10}{6} \right)\geq 0[/tex]

Roots are found by Quadratic Formula:

[tex]r_{1,2} = \frac{\left[-\left(-\frac{11}{6}\right)\pm \sqrt{\left(-\frac{11}{6} \right)^{2}-4\cdot (1)\cdot \left(-\frac{10}{6} \right)} \right]}{2\cdot (1)}[/tex]

[tex]r_{1} = \frac{5}{2}[/tex] and [tex]r_{2} = -\frac{2}{3}[/tex]

Then, the factorized form of the inequation is:

[tex]6\cdot \left(x-\frac{5}{2}\right)\cdot \left(x+\frac{2}{3} \right)\geq 0[/tex]

By Real Algebra, there are two condition that fulfill the inequation:

a) [tex]x-\frac{5}{2} \geq 0 \,\wedge\,x+\frac{2}{3}\geq 0[/tex]

[tex]x \geq \frac{5}{2}\,\wedge\,x \geq-\frac{2}{3}[/tex]

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

b) [tex]x-\frac{5}{2} \leq 0 \,\wedge\,x+\frac{2}{3}\leq 0[/tex]

[tex]x \leq \frac{5}{2}\,\wedge\,x\leq-\frac{2}{3}[/tex]

[tex]x\leq -\frac{2}{3}[/tex]

The solution of the inequation [tex]6\cdot x^{2} \geq 10 + 11\cdot x[/tex] is [tex]\left(-\infty,-\frac{2}{3}\right]\cup\left[\frac{5}{2},+\infty\right)[/tex].

Answer:

Approximately 201 squared inches.

Step-by-step explanation:

So, the composite figure is made up of a square and a semi-circle. The square has side lengths of 12 and the semi-circle has a radius of 6.

The total area of the figure would be the area of the square plus the area of the semi-circle. Thus, find the area of each individual figure.

Square:

The area of a square is given by:

[tex]A=l^2[/tex]

Where l is the side length.

Substitute 12 for l:

[tex]A=(12)^2\\A=144\text{ in}^2[/tex]

So the square is 144 square inches.

Semi-circle:

The area of a semi-circle is given by:

[tex]A=\frac{1}{2}\pi r^2[/tex]

Substitute 6 for r and 3.14 for π:

[tex]A=\frac{1}{2}(3.14)(6)^2\\ A=56.52[/tex]

Therefore, the total area is:

[tex]TA=144+56.52\\TA=200.52\text{ in}^2\approx201\text{ in}^2[/tex]

Answer:

it will be one out six to roll a four

Step-by-step explanation:

there is one being rolled to be a 4 out of six

Step-by-step explanation:

"Determine the number and type of roots for the equation using one of the given roots. Then find each root. (inclusive of imaginary roots.)"

Given one of the roots, we can use either long division or grouping to factor each cubic equation into a binomial and a quadratic.  I'll use grouping.

Then, we can either factor or use the quadratic equation to find the remaining two roots.

1. x³ − 7x + 6 = 0; 1

x³ − x − 6x + 6 = 0

x (x² − 1) − 6 (x − 1) = 0

x (x + 1) (x − 1) − 6 (x − 1) = 0

(x² + x − 6) (x − 1) = 0

(x + 3) (x − 2) (x − 1) = 0

The remaining two roots are both real: -3 and +2.

2. x³ − 3x² + 25x + 29 = 0; -1

x³ − 3x² + 25x + 29 = 0

x³ − 3x² − 4x + 29x + 29 = 0

x (x² − 3x − 4) + 29 (x + 1) = 0

x (x − 4) (x + 1) + 29 (x + 1) = 0

(x² − 4x + 29) (x + 1) = 0

x = [ 4 ± √(16 − 4(1)(29)) ] / 2

x = (4 ± 10i) / 2

x = 2 ± 5i

The remaining two roots are both imaginary: 2 − 5i and 2 + 5i.

3. x³ − 4x² − 3x + 18 = 0; 3

x³ − 4x² − 3x + 18 = 0

x³ − 4x² + 3x − 6x + 18 = 0

x (x² − 4x + 3) − 6 (x − 3) = 0

x (x − 1)(x − 3) − 6 (x − 3) = 0

(x² − x − 6) (x − 3) = 0

(x − 3) (x + 2) (x − 3) = 0

The remaining two roots are both real: -2 and +3.

"Find all the zeros of the function"

For quadratics, we can factor using either AC method or quadratic formula.  For cubics, we can use the rational root test to check for possible rational roots.

4. f(x) = x² + 4x − 12

0 = (x + 6) (x − 2)

x = -6 or +2

5. f(x) = x³ − 3x² + x + 5

Possible rational roots: ±1/1, ±5/1

f(-1) = 0

-1 is a root, so use grouping to factor.

f(x) = x³ − 3x² − 4x + 5x + 5

f(x) = x (x² − 3x − 4) + 5 (x + 1)

f(x) = x (x − 4) (x + 1) + 5 (x + 1)

f(x) = (x² − 4x + 5) (x + 1)

x = [ 4 ± √(16 − 4(1)(5)) ] / 2

x = (4 ± 2i) / 2

x = 2 ± i

The three roots are x = -1, x = 2 − i, x = 2 + i.

6. f(x) = x³ − 4x² − 7x + 10

Possible rational roots: ±1/1, ±2/1, ±5/1, ±10/1

f(-2) = 0, f(1) = 0, f(5) = 0

The three roots are x = -2, x = 1, and x = 5.

"Write the simplest polynomial function with integral coefficients that has the given zeros."

A polynomial with roots a, b, c, is f(x) = (x − a) (x − b) (x − c).  Remember that imaginary roots come in conjugate pairs.

7. -5, -1, 3, 7

f(x) = (x + 5) (x + 1) (x − 3) (x − 7)

f(x) = (x² + 6x + 5) (x² − 10x + 21)

f(x) = x² (x² − 10x + 21) + 6x (x² − 10x + 21) + 5 (x² − 10x + 21)

f(x) = x⁴ − 10x³ + 21x² + 6x³ − 60x² + 126x + 5x² − 50x + 105

f(x) = x⁴ − 4x³ − 34x² + 76x − 50x + 105

8. 4, 2+3i

If 2 + 3i is a root, then 2 − 3i is also a root.

f(x) = (x − 4) (x − (2+3i)) (x − (2−3i))

f(x) = (x − 4) (x² − (2+3i) x − (2−3i) x + (2+3i)(2−3i))

f(x) = (x − 4) (x² − (2+3i+2−3i) x + (4+9))

f(x) = (x − 4) (x² − 4x + 13)

f(x) = x (x² − 4x + 13) − 4 (x² − 4x + 13)

f(x) = x³ − 4x² + 13x − 4x² + 16x − 52

f(x) = x³ − 8x² + 29x − 52

Answer:

344.1 Ib/ft²

Step-by-step explanation:

This has to do with conversion

23.0Ib/gal × 2ft

Step 1

First we convert 23.0lb/gal to Ib/ft³

1 Ib/gal = 7.48051948 Ib/ft³

23.0lb/gal = X Ib/ft³

Cross Multiply

1 Ib/gal × X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³

X Ib/ft³ = 23.0lb/gal × 7.48051948 Ib/ft³/1 Ib/gal

X Ib/ft³ = 172.05194804 Ib/ft³ =

Step 2

Since 23.0lb/gal = 172.05194804 Ib/ft³

172.05194804 Ib/ft³ × 2 ft

= 344.10389608Ib/ft²

Approximately to 1 significant figure

= 344.1 Ib/ft²

Answer:

10 m

Step-by-step explanation:

15m - 5m = 10 m

both numbers have m which are alike

Answer: 10m

Step-by-step explanation: you subtract five from fifteen