Identify the pair of angles shown in the figure. answers A. LINEAR PAIR B. COMPLEMENTARY C. CONGRUENT D. VERTICAL

Answer:

[tex]x+y+z \Rightarrow 2+2+6 = 10[/tex]

Step-by-step explanation:

First we have to factor the equation:

[tex]6xyz+30xy+21xz+2yz+105x+10y+7z=812[/tex]

The commom factor of first three terms and [tex]105x[/tex] is [tex]3x[/tex]. Note that [tex]105x=3x(35)[/tex]

[tex]3x(2yz+10y+7z+35)+2yz+10y+7z=812[/tex]

[tex]3x(2yz+10y+7z+35)+(2yz+10y+7z)=812[/tex]

In order to have two equal factors add 35 both sides:

[tex]3x(2yz+10y+7z+35)+(2yz+10y+7z+35)=847[/tex]

Let's factor [tex](2yz+10y+7z+35)[/tex]

[tex](2yz+10y+7z+35) \Rightarrow 2y\left(z+5\right)+7\left(z+5\right) \Rightarrow \left(z+5\right)\left(2y+7\right)[/tex]

Now we have:

[tex]3x(z+5)\left(2y+7\right)+\left(z+5\right)\left(2y+7\right)=847[/tex]

[tex](3x + 1) (2y + 7) (z + 5) = 847[/tex]

Now it is the interesting part: You have to figure out that 3 numbers multiplied by each other will result in 847.

We have [tex]847 = 7 \cdot 11 \cdot 11[/tex]

Let's try

[tex]2y+7=7\\2y=0[/tex]

I will stop right here. This is not true.

Let's try then

[tex]2y+7=11\\2y=4\\y=2[/tex]

Now let's try

[tex]z+5 = 11\\z=6[/tex]

Now let's try

[tex]3x+1=7\\3x=6\\x=2[/tex]

Note that in this case I didn't considered [tex]3x+1=11[/tex] because it would not be an integer.

Therefore,

[tex]x+y+z \Rightarrow 2+2+6 = 10[/tex]

Answer:

13.5

Step-by-step explanation:

In triangle ABC, DE || AC

Therefore by basic proportionality theorem:

[tex] \frac{BD}{DA} = \frac {BE}{EC} \\\\

\therefore \frac{4}{8} = \frac {BE}{9} \\\\

\therefore \frac{1}{2} = \frac {BE}{9} \\\\

\therefore BE = \frac{9}{2} \\\\

\therefore BE = 4.5\\

\because BC = BE + EC \\

\therefore BC = 4.5 + 9\\

\huge \red {\boxed {\therefore BC = 13.5}} \\[/tex]

Answer:

C

Step-by-step explanation:

SA=pi*r^2+pi*r*s

SA=3.14*3^2+3.14*3*8

SA=3.14*9+3.14*24

SA=103.62

SA= about 104 inches

Aubrey included the base (you can't put on a hat that has a bottom), the right work should be:

SAhat=pi*r*s

SAhat=3.14*3*8

SAhat=3.14*24

SAhat=75.36

SAhat= about 75

Thus, answer is C

Answer: x² + 5x = 3

Step-by-step explanation:Step-by-step explanation:

The rectangle has been divided into a square and three rectangles.

The area of

a square = (x)(x) = x²

a rectangle #1 = (2)(x) = 2x

a rectangle #2 = (3)(x) = 3x

a rectangle #3 = (2)(3) = 6

The area of a large rectangle is the sum of the square area and three rectangles, and is 9 cm². Therefore we have the equation:

x² + 2x + 3x + 6 = 9     subtract 6 from both sides

x² + 5x + 6 - 6 = 9 - 6

x² + 5x = 3

The equation is proven.

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The rectangle has been divided into a square and three rectangles.

The areas are;

square = (x)(x) = x²

rectangle 1 = (2)(x) = 2x

rectangle 2 = (3)(x) = 3x

rectangle 3 = (2)(3) = 6

The area of a large rectangle is the sum of the square area and three rectangles, and is 9 cm². Therefore, we have the equation:

x² + 2x + 3x + 6 = 9

x² + 5x + 6 - 6 = 9 - 6

x² + 5x = 3

Hence, proved.

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24nk

n=6

k=8

24 × (6) × (8)

24 × (48) = 1152

Answer:

24nk=1152

Step-by-step explanation:

24nk

Substituting the values in the equation

24*6*8

In order to evaluate these values we have to simply multiply the numbers

144*8

I hope it will help you

1152 is the answer

Answer:A D and E

Step-by-step explanation:

Answer:

Step-by-step explanation:

A, D, and E.

Answer: 1p/5

Step-by-step explanation:

Answer:

Gina will eat  pound cheese for lunch each day

Explanation

Amount of cheese bought = 1 pound and the amount of cheese used =  pound

So, the remaining amount of cheese

As this  pound cheese is splitting into 5 equal parts, so the amount of each part will be:  ÷ 5 =  ×  =  pound

So, Gina will eat  pound cheese for lunch each day.

Step-by-step explanation:

Answer:

142052 users in the U.S.

46558 users in Japan.

Step-by-step explanation:

[tex]x+y=188610\\x=3y+2378[/tex]

[tex](3y+2378)+y=188610[/tex]

[tex]4y+2378=188610[/tex]

[tex]4y=188610-2378[/tex]

[tex]\frac{4y}{4}=\frac{186232}{4}[/tex]

[tex]y=46558[/tex]

[tex]x=3y+2378[/tex]

[tex]x=3(46558)+2378[/tex]

[tex]x=139674+2378[/tex]

[tex]x=142052[/tex]

Answer:

C. 58 tables

Step-by-step explanation:

If there are 460 people, and each table seats 8 people, then we divide 460 by 8, giving us 57.5 tables. We cannot have a half of a table, so the answer is 58 tables.

Answer:

(x + 6 )(x + 6 )

2 numbers to add to 12 but also multiply to get 36

Answer:

(x+6)(x+6)

Step-by-step explanation:

x^2 + 12x + 36

What 2 numbers multiply to 36 and add to 12

6*6 =36

6+6 =12

(x+6)(x+6)

Answer:

144 p

Step-by-step explanation:

It was due to be returned on 26 November but she returned it on 12 December.

She was therefore with it for an extra 16 days.

The fine is 9p per day. Therefore, she will pay a fine of:

9 * 16 = 144 p

Answer:

Amelia rented a DVD and it was due to be returned on 26 November. She actually returned it to the shop on 12 December. The rental shop applies a fine of 9p for every day the DVD is overdue.

Work out the total fine paid by Amelia. Give your answer in £

Work Shown:

sec(80) = 1/cos(80) = 5.75877048314363 which rounds to 5.76

Make sure your calculator is in degree mode.

Answer:

f(x) = 86(1.04)x; grows approximately at a rate of 0.4% daily

Step-by-step explanation:

The base of the exponential function is 1.29 for 7 days, as in

f(x) = 86*(1.29)^x

The new rate for days can be calculated by dividing x by 7 (where x remains the number of weeks), namely

f(x) = 86*1.29^(x/7)

Using the law of exponents, b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

we simplify by putting b=1.29, a=7 to get

f(x) = 86*(1.29^(1/7))^x

f(x) = 86*(1.037)^x      since 1.29^(1/7) evaluates to 1.037

Rounding 1.037 to 1.04 we get a (VERY) approximate function

Answer:f(x) = 86(1.04)x

Step-by-step explanation:

Answer:

-4, -24

Step-by-step explanation:

The location of Z is either +10 or -10 units away from Y, since YZ = 10. Then Z could be located at either -4 or -24.

Answer:

-4, -24 are the two possible locations of Z

Step-by-step explanation:

Z's location could be ten to the left of -14 or ten to the right of -14.  -4 is ten to the right and -24 is ten to the left of Z.

Answer:

21

Step-by-step explanation:

You subtract 17 (x - 17) and multiply the answer by 8 (8(x - 17)).  This is equal to 32.  Solve for x

8(x - 17) = 32

8x - 136 = 32

8x = 168

x = 21

Answer:

If f and h are inverses, then:

f (h(x) ) = x   and also

h( f(x) ) = x

Step-by-step explanation:

Inverse function: The function f(x) goes from domain to range and the inverse function f^{-1} goes from Range to domain

Option C is correct

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The value of x must be equal to 1000

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as

For x > 0 , a > 0, and a ≠1,

y= logₐ x if and only if x = a^y

Then the function is given by

f(x) = logₐx

Given here  log x= 3 ⇒x=10³

                                 ⇒x=1000

Hence, The value of x must be equal to 1000

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Answer:

x=3.42

Step-by-step explanation:

Add 2.07 to each side

x=1.35+2.07=3.42

Answer:

x=3.42‬

Step-by-step explanation:

3.42- 2.07 = 1.35

Answer:

9.90 inches

Step-by-step explanation:

Area of a triangle is equal to base times height divided by 2.

[tex]bh/2[/tex]

Base and height is x.

[tex]xx/2=49[/tex]

Solve for x.

[tex]x^2=49 \times 2[/tex]

[tex]x^2=98[/tex]

[tex]x=\sqrt{98}[/tex]

[tex]x=9.899495[/tex]

Answer:

C

Step-by-step explanation:

2 units right and 3 units up

Answer:

[tex]\frac{4}{9}[/tex]

Step-by-step explanation:

The ratio of pencils to erasers is

[tex]9:4[/tex]

Convert the ratio to a fraction.

[tex]\frac{9}{4}[/tex]

The fraction is now pencils to erasers.

The fraction of the number of erasers to pencils is:

[tex]\frac{4}{9}[/tex]

Answer:

G(x)=-(x+3)+6

Step-by-step explanation:

f(x) means that whatevers in the parentheses is x. In g(x) x is equal to x+3

Answer:

15

Step-by-step explanation:

f(x)=5x+40

so f(5)=5(-5)+40

f(5)= -25+40

f(5)=15

Answer:

D) 5

Step-by-step explanation:

The smaller triangle is similar to the big triangle with the big triangle with a scale factor of 1.8.

5x × 1.8 = 45

Divide both sides by 1.8

5x = 25

Divide both sides by 5

x = 5

Answer:

4 + (-3) = 1

hope this helped :3

4 + (-3) = 1 this is the right answer

Answer:

3 divided by 10.

Step-by-step explanation:

I'm slightly confused as to what you're asking about, but I could only assume that you want me to represent that fraction as a division problem. In that case, I have listed the answer above. If you want it in decimal form, it is 0.3.

Answer:

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Answer:

31.

Step-by-step explanation:

1. Write out the problem.

6w-19 + k; w=8 and k=2

2. Figure out the first part of the problem.

So, if w=8 and 6 and w are next to each other, we should multiply 6*8, which is 48. Next, it says to subtract 19. 48-19=29.

3. Find out what the last part of the problem is.

Since the first part of the problem is 29 and k=2, we should add 29+2=31, which is the final answer.

Hope this helped :)