What is the measure of AC?

Answer:

w=6, x=7, t=7, n=90, w=15/2

Step-by-step explanation:

a) 5w = 30

30/5 = 6

w=6

b) 3x-5=16

Add 5 to each side.

3x+5=16+5

3x=21

21/3=7

x=7

c) 10-t=17

10-t=17

17-10-7

-t=-7

Negative and a negative is a positive.

t=7

d) n/5 = 18

n=18 * 5

n=90

e.) 4w-12=2w+3

4w=2w+3+12

4w=2w+15

4w−2w=15

2w=15

w= 15/2

Answer:

D

Step-by-step explanation:

The total number of students is 15+12= 27

The ratio of girls to total students is 12/27 = 4/9

Answer:

4 parrots

3 cages

Step-by-step explanation:

Bryan has one more parrot than cages and one more cage than half the number of parrots. The following system of equations can be modeled for the number of parrots (P) and cages (C):

[tex]P=C+1\\C-1=\frac{P}{2}[/tex]

Solving the linear system:

[tex]P-1-1=\frac{P}{2}\\0.5P = 2\\P=4\\C=P-1=4-1=3[/tex]

Bryan has 4 parrots and 3 cages.

Answer:

4. -2s^9

7. 8b^10

Step-by-step explanation:

First, focus on the number part of the expression. For 4), multiply -2 x -1 x -1 = -2. Then, look at the exponents. When you're multiplying exponents with the same base (in number 4, the base is s), you can add the exponents.

2+3+4 = 9; which makes it s^9. Multiply -2 x s^9, which gives you -2s^9.

Same thing for 7). Multiply all the numbers first. this gives you 8. (Remember two negatives equals a positive). Add all of the exponents of b together, which gives you 10. (when a variable has no exponent, it means that the exponent is 1.) Multiplying 8 and b^10 should give you 8b^10.

It may help to brush up on exponent rules and sign rules.

Answer:

C = 10 π cm

Step-by-step explanation:

Diameter is 2 x radius = 2*5.4 = 10.8 cm

radius r = 5 cm

diameter d = 10 cm

circumference C = 31.4 cm

area A = 78.5 cm2

In Terms of Pi π

circumference C = 10 π cm

area A = 25 π cm²

Formulas: Circle Formulas in terms of Pi π, radius r, and diameter d

Radius and Diameter:

r = d/2

d = 2r

Area of a circle:

A = πr2 = πd2/4

Circumference of a circle:

C = 2πr = πd

Answer:

c

Step-by-step explanation:

got it right on my test

Answer:

1/3 degreees/min

Step-by-step explanation:

In 15 min, temp. rises by 10 degrees

This means that 10 degrees / 15 min = 2 deg / 3 min

1/3 degree/min

The unit rate of change in °F per minute is 0.667°F/ min .

An equation is a statement formed when variables are equated by a constant or another variable by an equal sign.

It is given that

The rate of increase of temperature with increasing time is given

The unit rate of change in °F per minute has to be determined .

In 15 minutes , the temperature changes by  10°F

The rate of unit change is 10 / 15 = 0.667

20/30 = 0.667

40/60 = 0.667

Therefore the unit rate of change in °F per minute is 0.667°F/ min .

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Answer:

Center = (7, - 5)

Radius = 3

Step-by-step explanation:

[tex] {x}^{2} + {y}^{2} + 14x - 10y + 65 = 0 \\ {x}^{2} + 14x + {y}^{2} - 10 + 65 = 0 \\ ( {x}^{2} + 14x + {7}^{2}) - {7}^{2} + ({y}^{2} - 10y + {5}^{2}) \\- {5}^{2} + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 - 25 + 65 = 0 \\ (x + 7)^{2} + (y - 5)^{2} - 49 + 40= 0 \\ (x + 7)^{2} + (y - 5)^{2} - 9= 0 \\ (x + 7)^{2} + (y - 5)^{2} = 9 \\ (x + 7)^{2} + (y - 5)^{2} = {3}^{2} \\ equating \: it \: with \: \\ (x - h)^{2} + (y - k)^{2} = {r}^{2} \\ - h = 7 \implies \: h = - 7 \\ - k = - 5 \implies \: k = 5 \\ center = ( - h, \: - k) = (7, \: \: - 5) \\ \\ radius \: r = 3[/tex]

Answer:

They would fall in the same year every 10 years

Step-by-step explanation:

Here in this question, we are interrelated in calculating the number of years it will take the alumni reunion and the alumni soccer game to fall in the same year.

Now looking at the number of years, we can see we have every 2 and every 10 years

To get the year in which they happen at the same time, we can simply find the lowest common multiple of 2 and 10 and that would be 10

This can be visualized in a way that;

The reunion has happened now, and will happen in the next 10 years.

Now since the soccer game has happened now, in the next 10 years, we shall be having 5 episodes. This means that it will take up to the 10th year before we have the soccer game and the alumni reunion occurring at the same time and the mathematical reason for this is that , 10 is the lowest common multiple of 10 and 2

Answer:

1 times

Step-by-step explanation:

Hello,

The alumni have reunions every 10 years

But also have football games every 2 years

We have to find how often do the football and reunion fall the same year.

Working with a space of 10 years

In 10 years, reunions happen only once

In 10 years, soccer games happen five times

Assuming we're in the year 2020,

The next reunion would likely occur in year 2030.

But soccer games will happen in year 2022, 2024, 2026, 2028 and finally 2030.

Checking both soccer and reunion coincidence, we can only find one which is in year 2030.

So, soccer games and reunions happen once in 10 years

Answer:

32 servings

Step-by-step explanation:

Take the amount of honey and divide by the size of a serving

8 ÷ (1/4)

Copy dot flip

8 * 4/1

32

There are 32 servings

Answer:

32 servings

Step-by-step explanation:

Step-by-step explanation:

Ok, so the surface area is found by adding up all the areas of each individual shape of the entire solid.

I attached a picture of some of the missing values. That should help a little with visualizing.

Since the three rectangles are all the same values, you can substitute adding them by just multiplying lw (their individual areas) by 3.

The three triangles at the top are all the same as well, so you can multiply their areas ([tex]\frac{1}{2} bh[/tex] ) by 3, too.

Then there's the triangle at the bottom that is by itself, that will just have a 1 in front of it.

Now you can make your surface area equation:

[tex]SA=3lw+3(\frac{1}{2} b_1h_1)+\frac{1}{2} b_2h_2[/tex]

The b1h1 are the three triangles at the top and the b2h2 is the triangle at the bottom.

[tex]SA=3(10)(16)+3(\frac{1}{2})( 10)(6)+\frac{1}{2} (10)(8.7)\\SA=480+90+43.5\\SA=613.5[/tex]

If there's anything you need me to explain further, feel free to comment :)

Answer:

[tex]SA=613.5m^2[/tex]

Answer:

[tex]\Huge \boxed{\mathrm{613.5 \ m^2 }}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We can find the total surface area by adding the surface area of the triangular prism with the surface area of the triangular pyramid at the top.

Surface area of the triangular prism:

10 × 8.7 × 1/2 + 16 × 10 × 3

⇒ 523.5

Surface area of the triangular pyramid:

6 × 10 × 1/2 × 3

⇒ 90

Adding the surface areas:

523.5 + 90

⇒ 613.5

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

2^(3-5)

=2^-2

Answer:

[tex] \frac{ {2}^{4 + 3} }{2^{5 + 4} } [/tex]

[tex] \frac{ {2}^{7} }{2^{9} } [/tex]

= 2^7-9

= 2^-2

 Recursive formula of an arithmetic sequence is given by the expression,

                          [tex]T_n=a+(n-1)d[/tex]

                 Where, [tex]T_n=[/tex] nth term

                              [tex]a=[/tex] First term of the sequence

                              [tex]n=[/tex] Number of term

                              [tex]d=[/tex] Common difference

Therefore, number of sticks in the 6th pattern are 32.

                   And number of sticks in the nth pattern are [tex]T_n=5n+2[/tex]

From the picture attached,

Number of sticks in 1st pattern = 7

Number of sticks in 2nd pattern = 12

Number of sticks in 3rd pattern = 17

Sequence formed is 7, 12, 17..... nth term

This sequence has a common difference of 5 in each successive term so it will be an arithmetic sequence.

Therefore, nth term of the sequence will be,

       [tex]T_n=a+(n-1)d[/tex]

       [tex]T_n=7+(n-1)5[/tex]

       [tex]T_n=5n+2[/tex]

If [tex]n=6,[/tex]

       [tex]T_n=7+(6-1)5[/tex]

       [tex]T_n=7+25[/tex]

       [tex]T_n=32[/tex]

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Answer:

2

Step-by-step explanation:

2

-11/10

Step-by-step explanation:

so first get the x on one side of the equal sign and the numbers on the other.

x+2 4/5 = 3 1/6

- 2 4/5 - 2 4/5

x= -11/10

Step-by-step explanation:

b can be used to check her score

Answer:

C(n)=1.25n

Where n= number of cans

Step-by-step explanation:

C=cost

n=number of cans

Quantity Total cost

1 $1.25

2 $2.50

3 $3.75

4 $5.00

Total cost, c(n) =1.25n

Check

Total cost when n=4

Total cost c(4)=1.25×4

Total cost c(4)=5.00

Answer:

468

Step-by-step explanation:

Answer:

237

Step-by-step explanation:

This is written as 1+2+(3x78)

=3+234

=237

Answer: 2,695

Step-by-step explanation:

5-6+8*674/2

Multiply 8 and 674

5-6+5,392/2

Divide 5,392 by 2

5-6 + 2,696

Subtract 6 from 5

-1 + 2,696

Add

2,695

Step-by-step explanation:

5 - 6 = -1

-1 + 8 = 7

7 x 674 = 4,718

4,718 / 2 = 2,359

Answer:

3/4

Step-by-step explanation:

There is 2 Os and 8 in total.

So the probability of selecting O is 1/4

As the question asks everything but O, you subtract that answer from 1. 1-1/4=3/4

Answer:

3x + 9

Step-by-step explanation:

For value of (f+g)(x) add two functions up

x + 3 + 2x + 6 = 3x + 9

Answer: B. The test contains 10 three-point questions and 14 five-point questions

Step-by-step explanation:

14 * 5 = 70

10 * 3 = 30

70 + 30 = 100

14 + 10 = 24

Answer:

y=14

x=10

Step-by-step explanation:

x+y=24

3x+5y = 100

multiply the first equation by 3 and subtract from second one :

3x+3y=72

-

3x+5y=100

equal : -2y=-28

y=14

x=10

Answer:

x < 5

Step-by-step explanation:

7x + 5 < 3x + 25

Subtract 3x from each side

7x-3x + 5 < 3x-3x + 25

4x+5 < 25

Subtract 5 from each side

4x +5-5 < 25-5

4x < 20

Divide by 4

4x/4 < 20/4

x < 5

Answer

x<5

Step-by-step explanation:

7x + 5 < 3x + 25

you would subtract 3x from both sides

Leaving you with 4x+5< 25

next you would subtract 5 from both sides

leaving you with 4x<20

Then you would divide both sides by 4

leaving you with x <5

Hoped this helped

:)

Answer:  

1

Step-by-step explanation:

8-1,2,4.....

25-1,5...

Answer:

6.6 ounces left

Step-by-step explanation:

Take the amount she had and subtract the amount she used

8.3-1.7 =6.6

Answer:

She has 6.6 ounces left.

Answer:

the answer is show me your kitty cat

Step-by-step explanation:

Answer:

2 + an

Step-by-step explanation:

1 + 1 + na

2 + am

Answer:180.5

Step-by-step explanation:

9.5 x 19

361/2=180.5