Write a simplified expression for the length of AC.
A X + 2 B
7x - 3
AC =
Write a simplified expression for the length of QR.
HELP ME PLASE

Answer:

π − 12

Step-by-step explanation:

lim(x→2) (sin(πx) + 8 − x³) / (x − 2)

If we substitute x = u + 2:

lim(u→0) (sin(π(u + 2)) + 8 − (u + 2)³) / ((u + 2) − 2)

lim(u→0) (sin(πu + 2π) + 8 − (u + 2)³) / u

Distribute the cube:

lim(u→0) (sin(πu + 2π) + 8 − (u³ + 6u² + 12u + 8)) / u

lim(u→0) (sin(πu + 2π) + 8 − u³ − 6u² − 12u − 8) / u

lim(u→0) (sin(πu + 2π) − u³ − 6u² − 12u) / u

Using angle sum formula:

lim(u→0) (sin(πu) cos(2π) + sin(2π) cos(πu) − u³ − 6u² − 12u) / u

lim(u→0) (sin(πu) − u³ − 6u² − 12u) / u

Divide:

lim(u→0) [ (sin(πu) / u) − u² − 6u − 12 ]

lim(u→0) (sin(πu) / u) + lim(u→0) (-u² − 6u − 12)

lim(u→0) (sin(πu) / u) − 12

Multiply and divide by π.

lim(u→0) (π sin(πu) / (πu)) − 12

π lim(u→0) (sin(πu) / (πu)) − 12

Use special identity, lim(x→0) ((sin x) / x ) = 1.

π (1) − 12

π − 12

Answer:

26

Step-by-step explanation:

Answer:

g(x) = -3|x|.

Step-by-step explanation:

Multiplying by 3 stretches the graph vertically by a factor 3 and the negative reflects in the x-axis.

The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by

f ( x ) = -3 | x |

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs),

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:  y=f(x+c) (same output, but c units earlier)

Right shift by c units:  y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be g ( x ) = | x |

Now , let the transformed function be f ( x )

The value of the function f ( x ) is calculated by

Step 1 :

Vertical stretch by a factor of 3

The Vertical stretch by a factor is done by

k: y = k × f(x)

So , multiplying the parent function by 3 , we get

f ( x ) = 3 | x |

Step 2 :

Reflection in the x-axis ,

The value of f ( x ) is multiplied by -1

So ,

f ( x ) = -3 | x |

Therefore , the transformed function f ( x ) = -3 | x |

Hence , The equation that represents a vertical stretch by a factor of 3 and reflection in x-axis of the graph of function g ( x ) = | x | is given by

f ( x ) = -3 | x |

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Answer:

It will take him 15 hours, Good luck!!

Step-by-step explanation:

Answer:

there was no data available for those numbers

Step-by-step explanation:

if you want to graph at intervals of (for example) 15, but your numbers are ranging from 115 - 200, you don't want to a huge blank space from 0 - 115 on the y-axis.

if you create a break at the bottom (and only the bottom) you can start at 100 and have intervals of 15 from there. this eliminates dead space on a graph.

Answer & Step-by-step explanation:

[tex]8.5x-6.1=-7.1[/tex]

Add 6.1 to both sides:

[tex]8.5x-6.1+6.1=-7.1+6.1\\\\8.5x=-1[/tex]

Isolate the variable x. Divide both sides by 8.5:

[tex]\frac{8.5x}{8.5} =\frac{-1}{8.5}\\\\ x=-\frac{1}{8.5}[/tex]

Round to the nearest tenth. Simplify division:

[tex]-\frac{1}{8.5}=-0.11764705...=-0.1[/tex]

So, x≈-0.1

:Done

Step-by-step explanation:

1 / (sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the first fraction by ½ cos 10°.

½ cos 10° / (½ cos 10° sin 10°) − √3 / (cos 10°)

Multiply top and bottom of the second fraction by ½ sin 10°.

½ cos 10° / (½ cos 10° sin 10°) − ½√3 sin 10° / (½ sin 10° cos 10°)

Combine fractions.

(½ cos 10° − ½√3 sin 10°) / (½ sin 10° cos 10°)

Change ½ to sin 30°, and change ½√3 to cos 30°.

(sin 30° cos 10° − cos 30° sin 10°) / (½ sin 10° cos 10°)

Use angle sum formula.

sin(30° − 10°) / (½ sin 10° cos 10°)

sin 20° / (½ sin 10° cos 10°)

Multiply top and bottom by 4.

4 sin 20° / (2 sin 10° cos 10°)

Use double angle formula.

4 sin 20° / sin 20°

4

We are given the equation 1 / sin(10°) - √3 / cos(10°) = 4, and want to prove that 1 / sin(10°) - √3 / cos(10°) equals 4.

Let's start by combining the expressions '1 / sin(10°)' and '√3 / cos(10°)' in the expression '1 / sin(10°) - √3 / cos(10°).'

1 / sin(10°) - √3 / cos(10°)

= cos(10°) - √3sin(10°) / sin(10°) [tex]*[/tex] cos(10°)

Now let's multiply the numerator and denominator by a common value. In this case it's most suitable to multiply both by 2. We will receive the expression 2(cos(10°) - √3sin(10°)) / 2(sin(10°) [tex]*[/tex] cos(10°)). We can further simplify this expression knowing that 2(sin(10°) [tex]*[/tex] cos(10°)) = 2sin(20°).

2(cos(10°) - √3sin(10°)) / 2sin(20°)

We can now bring the two on the bottom to the numerator, becoming 1 / 2.  Remember that the ' 1 / 2 ' will be distributed now. After the distribution we receive the expression 4( 1 / 2(cos(10°) - √3 / 2sin(10°)) /  2sin(20°). We can now use the trivial functions 1 / 2 = sin(30°), and √3 / 2 = cos(30°).

4(sin(30°)(cos(10°) - cos(30°)(sin(10°) ) / sin(20°))

= 4((sin(30 - 10°)) / sin(20°) = 4

Answer:

C.

Step-by-step explanation:

The relationship is proportion if y/x is constant.

So it is C because 12/4 = 15/5 = 18/6 = 3.

Answer:

y = 5 + 0.9x

Step-by-step explanation:

If y is the total fee and x is the miles driven, we get following equation:

The total comprises of a constant initial rate ($5) and a charge for driven miles (0.9x)

Answer:

150 square feet every half hour.

Step-by-step explanation:

Answer:

150 square feet

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a - b)(a + b) = a² - b²

(8 - n⁷)(8 + n⁷) = 8² - (n⁷)² = 64 - n¹⁴      {(aˣ)ⁿ = aˣ*ⁿ }

Or

Use FOIL method

(8 - n⁷)(8 + n⁷) = 8*8 + 8*n⁷ + (-n⁷)*8 + (-n⁷)*n⁷

                       = 64 + 8n⁷ - 8n⁷ - n⁷⁺⁷

                       = 64 - n¹⁴

Answer:

it was 4.8 degrees higher

Step-by-step explanation:

all u have to do is subtract 103.4 from 98.6

Answer:

Wouldn't it be 4.8° F ?

Step-by-step explanation:

Since you can just subtract the two numbers and you get that.

103.4°F - 98.6°F = 4.8°F

Answer:

B. $200,000

Step-by-step explanation:

Let x be the amount placed at 5.5%

3x is the amount placed at 5%

This leaves the rest for the 4.5 %   500000- x - 3x = 500000-4x

Assuming simple interest

I = PRT where I is interest, P is principle, rate is rate and t  is time

Interest for the 5.5% for 1 year is

I = x * .055 * 1 = .055x

Interest for the 5.% for 1 year is

I = 3x * .05 * 1 = .15x

Interest for the 4.5% for 1 year is

I = 500000-4x * .045 * 1 = 22500 - 0.18 x

Add the interest together to get the income for 1 year

.055x+  .15x+22500 - 0.18 x=25,000

Combine like terms

0.025x+22500=25000

Subtract 22500

.025x =2500

Divide by .025

x =100000  

short term notes is 100000

3*x = 300000 = government bonds

The rest is utility bonds 500000- 100000-300000 = 100000

We want how much more in government bond than utility bond

300000 -100000 = 200000

Answer:

200000

Step-by-step explanation:

the short term =x

government bonds =3x

utility bonds: 500000-4x

0.055x+3(0.05(x)+0.045(500000-4x)=25000

0.055x+0.15x+22500-0.18x=25000-22500

0.055x+0.15x+22500-0.18x-22500=2500

0.025x=2500

x=2500/0.25

x=100000

government bonds=3x=3(100000)=300000

utility bond=(500000-400000)=100000

government bonds than in utility bonds:

300000-100000=200000

Answer:

22

Step-by-step explanation:

Simplify the following:

3 (2 + 7) - 5

Hint: | Evaluate 2 + 7.

2 + 7 = 9:

3×9 - 5

Hint: | Multiply 3 and 9 together.

3×9 = 27:

27 - 5

Hint: | Subtract 5 from 27.

| 2 | 7

- | | 5

| 2 | 2:

Answer: 22

Answer:22

Step-by-step explanation:

add the numbers in the  parathieses  so 2+7 and you get 9 so then your equation is 3(9)-5 or 3×9-5

then you multiply 3×9 and get 27 so then subtract 27 -5 and get 22 as your answer

Answer:

x=6

Step-by-step explanation:

127-83=9x-10

44=9x-10

+10.0 +10.0

54=9x

divide by 9 on both sides

x = 6

Answer:

The answer is 2

Step-by-step explanation:

4z+2y-x

4(4)+2(-6)-2

16+(-12)-2

16-12-2

4-2

2

Step-by-step explanation:

[tex]4z + 2y - x \\ = 4 \times 4 + 2 \times ( - 6) - 2 \\ = 16 + ( - 12) - 2 \\ = 16 + ( - 14) \\ = 2[/tex]

Answer:

The midpoint of CD is [tex](\frac{2+a}{2},\ \frac{7+b}{2})[/tex].

Step-by-step explanation:

Consider a line CD.

The point C is (2, 7).

Assume that the point D is, (a, b).

The formula to compute the midpoint is:

[tex](x,y)=(\frac{x_{1}+x_{2}}{2},\ \frac{y_{1}+y_{2}}{2})[/tex]

Compute the midpoint of CD as follows:

[tex](x,y)=(\frac{x_{1}+x_{2}}{2},\ \frac{y_{1}+y_{2}}{2})[/tex]

        [tex]=(\frac{2+a}{2},\ \frac{7+b}{2})[/tex]

Thus, the midpoint of CD is [tex](\frac{2+a}{2},\ \frac{7+b}{2})[/tex].

Answer:

Step-by-step explanation:

Given the expressions :

The list price of the item is 80 percent of the original price. The price of the item has been reduced by 80 percent.

Write a pair of linear equations using variables of your choice to prove that these two statements are not equivalent.

Let the original price = x

Expression 1 : The list price of the item is 80 percent of the original price

List price = 80% of x

List price = 0.8x

Expression 2: The price of the item has been reduced by 80 percent

Price = x - 80% of x

Price = x - 0.8x

Price = 0.2x

Multiply by percentages is different from an Incremental or decrement in percentage. The first expression above signifies a direct multiplication by the stated percentage while the second signifies a decrease in price based on a certain percentage of the original price.

Wording of percentages are so important for clarity in other to understand if the statement signifies a direct application of the percentage prescribed or a change in quantity, amount or size relative to the base unit.

Answer:-8, -6,-3, 4 is the correct answer

Step-by-step explanation:

Answer:

Answer A

Step-by-step explanation:

Answer:

the total she earns with "d" hours of dog walking and "b" hours of babysitting is given by:  8 d + 12 b

Step-by-step explanation:

If we use "d" to represent the number of hours that Susan walks the dog, and we define "b" as the number of hours she babysits, then the expression that represents the amount she earns by walking the dog is: $8 times d = 8 d

Similarly, the amount she earns by babysitting is $12 times b = 12 b

Then the total she earns with "d" hours of dog walking and "b" hours of babysitting is:  8 d + 12 b

Answer:

n=-1.5

Step-by-step explanation:

6-4n=12

Subtract 6 from 12

-4n=12-6

Simplify

-4n=6

Divide each side by -4

-4n/-4=6/-4

Simplify

n=-1.5

This question is not correctly written

Complete Question

A gaming console cost $299.99. Each game that comes with the console is an additional cost of $20.00. Mr. Yao decide to by x number of games Write a variable expression for cost of the number of games Mr. Yao bought

Answer:

Variable expression for the cost of the number of games that Mr Yao bought =

$20x

Where x = number of games that he bought.

Step-by-step explanation:

A variable expression can be defined as a mathematical expression where there is at least one (or more) unknown variable(s)that we have to look or solve for.

The unknown variable is always represented by letters of the alphabet, a, b, x, y e.t.c.

A variable expression can also be called an algebraic expression.

From the above question, we are told that:

Cost of a gaming console = $299.99

If you buy a game with the console = Additional $20.00

My Yao bought = x number of games

Variable expression for the cost of the x number of games that Mr Yao bought

$20 × x

= $20x

Where x = number of games that Mr Yao bought.

Answer:

6/49 or

StartFraction 6 over 49 EndFraction

Step-by-step explanation:

There are two negative fractions, the product of which results in positive.

(-2/7)* (-3/7) = 6/49

Answer:

6/7

Step-by-step explanation:

is correct

Answer:

[tex]3a \times x - y - x - y \\ 3a \times x - x - y - y \\ 3a \times - 2y - \\ - 6ay[/tex]

Answer:

8,3

Step-by-step explanation:

Answer:

[tex]\boxed{12}[/tex]

Step-by-step explanation:

[tex]6/\frac{1}{2} =6*2=12[/tex]

Answer:

82300000 in scientific notation = 8.23 × 107.

Step-by-step explanation:

Not sure if that's right.

Answer:

8.23×10^7

Step-by-step explanation:

to convert a number i to scientific form just drag the point to first non zero digit and write it with some multiple of 10

Answer:

-12-6x it's answer this question

Answer:

  no

Step-by-step explanation:

The only question here seems to be ...

  Have you ever been on or seen a ride like this at a fair or amusement park?

__

I have not seen such a ride.

I have not seen such a ride.

A large outdoor area with fairground rides, shows, refreshments, games of chance or skill, and other entertainments.

The only question here seems to be ...

 Have you ever been on or seen a ride like this at a fair or amusement park?

I have not seen such a ride.

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Answer:

                x = 1388.89

Step-by-step explanation:

x    - the sale price of new refrigerator

18%x = 0.18x   - the discount

0.18x = 250

x = 250÷0.18 = 1388.8888...

x = 1388.89