MATHEMATICS
COLLEGE

Answer: (-10-6)=-16divided by 8=-2+9=7 hope it helps

MIDDLE SCHOOL

Hi I need help on this problem A.S.A.P 'thank you' Similarity In Right Triangles,

Find The Geometric Mean of 4 and 10

A)

B) 7

C)

D) 20

It would be c i do beleive

MIDDLE SCHOOL

A store has 40% off sale on headphones. With this discount, the price of one pair of headphones is $36.00

40 % off means we pay 60 % (must total 100%)

original price * 60 % = 36.00

change percent to decimal

original price * .6 = 36

divide each side by .6

orginal price = 60

HIGH SCHOOL

A forest ranger spots a fire on a 28 foot tower,the angle of depression from the tower to the fire is 11 degrees to the nearest foot how far is the fire from the base of the tower show the steps you use to find the solution.

The angle of depression is 11°.

The angle of elevation is also 11°.

d - distance from the base of the tower to the fire;

d = 28 ft / tan 11° = 28 ft / 0.19438 = 144 ft

Answer:

The fire is 144 ft from the base of the tower.

The angle of elevation is also 11°.

d - distance from the base of the tower to the fire;

d = 28 ft / tan 11° = 28 ft / 0.19438 = 144 ft

Answer:

The fire is 144 ft from the base of the tower.

COLLEGE

A catering service offers 4 appetizers, 10 main courses, and 9 desserts. A banquet chairperson is to select 3 appetizers, 8 main courses, and 3 desserts, for a banquet. In how many ways can this be done?

Answer: 15120

----------------------------------------

----------------------------------------

Work Shown:

There are 4 appetizers total. We want to select 3 of them. Order doesn't matter.

Use the nCr formula with n = 4 and r = 3

n C r = (n!)/(r!*(n-r)!)

4 C 3 = (4!)/(3!*(4-3)!)

4 C 3 = (4!)/(3!*1!)

4 C 3 = (4*3!)/(3!*1!)

4 C 3 = (4)/(1!)

4 C 3 = (4)/(1)

4 C 3 = 4/1

4 C 3 = 4

There are 4 ways to select just the appetizers

Call this value M = 4 (we'll use it later)

----------------------------

There are 10 main courses total. We want to select 8 of them. Order doesn't matter.

Use the nCr formula with n = 10 and r = 8

n C r = (n!)/(r!*(n-r)!)

10 C 8 = (10!)/(8!*(10-8)!)

10 C 8 = (10!)/(8!*2!)

10 C 8 = (10*9*8!)/(8!*2!)

10 C 8 = (10*9)/(2!)

10 C 8 = (10*9)/(2*1)

10 C 8 = 90/2

10 C 8 = 45

There are 45 ways to select just the main courses

Call this value N = 45 (we'll use it later)

----------------------------

There are 9 desserts total. We want to select 3 of them. Order doesn't matter.

Use the nCr formula with n =9 and r = 3

n C r = (n!)/(r!*(n-r)!)

9 C 3 = (9!)/(3!*(9-3)!)

9 C 3 = (9!)/(3!*6!)

9 C 3 = (9*8*7*6!)/(3!*6!)

9 C 3 = (9*8*7)/(3!)

9 C 3 = (9*8*7)/(3*2*1)

9 C 3 = 504/6

9 C 3 = 84

There are 84 ways to select just the desserts

Call this value P = 84 (we'll use it later)

----------------------------

Multiply the results from earlier:

M*N*P = 4*45*84 = 15120 which is the final result.

----------------------------------------

----------------------------------------

Work Shown:

There are 4 appetizers total. We want to select 3 of them. Order doesn't matter.

Use the nCr formula with n = 4 and r = 3

n C r = (n!)/(r!*(n-r)!)

4 C 3 = (4!)/(3!*(4-3)!)

4 C 3 = (4!)/(3!*1!)

4 C 3 = (4*3!)/(3!*1!)

4 C 3 = (4)/(1!)

4 C 3 = (4)/(1)

4 C 3 = 4/1

4 C 3 = 4

There are 4 ways to select just the appetizers

Call this value M = 4 (we'll use it later)

----------------------------

There are 10 main courses total. We want to select 8 of them. Order doesn't matter.

Use the nCr formula with n = 10 and r = 8

n C r = (n!)/(r!*(n-r)!)

10 C 8 = (10!)/(8!*(10-8)!)

10 C 8 = (10!)/(8!*2!)

10 C 8 = (10*9*8!)/(8!*2!)

10 C 8 = (10*9)/(2!)

10 C 8 = (10*9)/(2*1)

10 C 8 = 90/2

10 C 8 = 45

There are 45 ways to select just the main courses

Call this value N = 45 (we'll use it later)

----------------------------

There are 9 desserts total. We want to select 3 of them. Order doesn't matter.

Use the nCr formula with n =9 and r = 3

n C r = (n!)/(r!*(n-r)!)

9 C 3 = (9!)/(3!*(9-3)!)

9 C 3 = (9!)/(3!*6!)

9 C 3 = (9*8*7*6!)/(3!*6!)

9 C 3 = (9*8*7)/(3!)

9 C 3 = (9*8*7)/(3*2*1)

9 C 3 = 504/6

9 C 3 = 84

There are 84 ways to select just the desserts

Call this value P = 84 (we'll use it later)

----------------------------

Multiply the results from earlier:

M*N*P = 4*45*84 = 15120 which is the final result.

HIGH SCHOOL

Find the GCF of 6x^7 and 15x^3?

I believe the answer is 3x^3

since 3 is the greatest common factor for the whole number and both have at least x to the third

since 3 is the greatest common factor for the whole number and both have at least x to the third

MIDDLE SCHOOL

30 POINTS!!! A triangle is reduced. A triangle has a base of 16 inches, height of 12 inches, and side length of 20 inches. A smaller triangle has a base of 12 inches, height of 9 inches, and side length of blank. Not drawn to scale What is the perimeter of the reduced triangle, in inches? 15 21 36 48

Answer:

36 inches

Step-by-step explanation:

Perimeter of the larger triangle: P1

Perimeter of the smaller triangle: P2

It's probably a right angle triangle. Verifying through pythagoras theorem:

20² = 12² + 16²

400 = 144 + 256

P1 = 20+12+16 = 48

P1/P2 = side1/side2

48/P2 = 16/12

48/P2 = 4/3

P2 = 48 × 3/4

P2 = 36

Step-by-step explanation:

reduced triangle

use Pythagoras A²+b²=c2

so 12²+9²

144+81 is 225

√225 is 15 inches

MIDDLE SCHOOL

Mason is going to have a lemonade stand. His Aunt buys him 10 lbs. of Lemons. if he sells each cup for a quarter,how many cups does he need to sell to pay her back? The Price of 1 lb. of Lemons is $0.89.

I have already did 0.89 x 10 which gives me 8.90.

Please Help

8.90 divided by 0.25= 35.6 (round up to 36 because you cant sell .6 cups of lemonade)

he would have to sell 36 cups of lemonade to pay his aunt back

after he sells 36 cups and pays his aunt back the $8.90 he will have $0.10 left to keep for himself

Okay, so first we do:

10 lbs × $0.89 = 8.90 (Which you did already)

Then we see how many cups he needs to sell, in order to get to $8.90.

.25 × 36 = $9

So that would be the approximate answer.

The exact answer would be .25 × 35.6 = $8.9 or $8.90

Hope that helps!

10 lbs × $0.89 = 8.90 (Which you did already)

Then we see how many cups he needs to sell, in order to get to $8.90.

.25 × 36 = $9

So that would be the approximate answer.

The exact answer would be .25 × 35.6 = $8.9 or $8.90

Hope that helps!

MIDDLE SCHOOL

the sum of the areas of two circles is 80pie square meters. Find the length of a radius of each circle of one of them is twice as long as the other

That will be 5 because now you can tell

MIDDLE SCHOOL

Evaluate -tan²A + 1 + sec²A

Answer:

Step-by-step explanation: sec^2A-tan^2A+1

=1+1

=2

Answer:

Hello :

secA= 1/cosA

tanA = sinA / cosA

- tan²A + 1 + sec²A = - (sinA / cosA)² + 1 + ( 1/cosA)²

= - sin²A / cos²A + 1 + 1 /cos²A

= ( - sin²A + cos²A +1)/cos²A

= ( 1 - sin²A + cos²A ) / cos²A

but : 1 - sin²A = cos²A because : sin²A + cos²A = 1

so : - tan²A + 1 + sec²A = ( 2 cos²A) / (cos²A)

- tan²A + 1 + sec²A = 2