A right square pyramid is shown. The height of the pyramid is 40 units. The distance from the center of the base of the pyramid to vertex D is 30units, as shown.
Enter the length of segment AD, in units

Since you know the sequence is quadratic, we can find constants a, b, and c such that the n-th term of the sequence (denoted by f(n)) is

[tex]f(n) = an^2 + bn + c[/tex]

We're given f(1) = 3, f(2) = 11, and f(3) = 25. (We have three unknowns, so we only need three conditions.) Solve for the constants:

[tex]\begin{cases}f(1) = a + b + c = 3 \\ f(2) = 4a + 2b + c = 11 \\ f(3) = 9a + 3n + c = 25 \end{cases} \implies a=3, b=-1, c=1[/tex]

Then the n-th term of the sequence is

[tex]f(n) = \boxed{3n^2 - n + 1}[/tex]

the angle when a circle is divided into 12 angles.

angle at a point is:

=360°

so to find the angle you'll have to divide 360 by 12.

360 ÷ 12

= 30°

hence, the measure of each angle is 30°.

Answer:

30

Step-by-step explanation:

to find:

the angle when a circle is divided into 12 angles.

solution:

the angle at a point is:

=360°

so to find the angle you'll have to divide 360 by 12.

360 ÷ 12

= 30°

hence, the measure of each angle is 30°.

Answer:

see image

Step-by-step explanation:

You are subtracting fractions. To do this you must have a common denominator. Then subtract the numerators.

In your question, the denominators (expressions on the bottom) are ALREADY THE SAME, because (x+2)(x+1) is the same as x^2+3x+2.

So to subtract, keep the denominator and subtract the tops:

x - 1

The result can be written in either factored form or standard form. The answers are equivalent. See image.

Answer:

1.5 bananas to make each sundaes

Step-by-step explanation:

6 divided by 4

Answer:

8.

Step-by-step explanation:

1. In PEMDAS, parenthesis always comes first. In this equation, 14 divided by 2 is in parenthesis. this equals 7. Now the equation looks like the following: 10+45/9-(7).

3. In this equation, there are no exponents, nor is there multiplication, so we move on to division. The only division left in this equation is 45 divided by 9, which is equal to 5. Now the equation looks like the following:

10+5-(7)

4. Next in PEMDAS comes addition, which in this case is 10 plus 5, which is equal to 15. Equation presently: 15-(7)

5. Lastly, subtraction. 15 minus 7= 8, therefore the overall answer is 8.

Answer:

if it's m^2-16, than it's B, (m+4)(m-4)

Step-by-step explanation:

remember (a+b)(a-b)=a^2-b^2, or m^2-4^2=m^2-16

Answer:

D

Step-by-step explanation:

a local minimum is a low point in the graph, but it isn't the lowest. and If u look at the given interval choices, the only one that has a local minimum Is D.

Answer: 30

Step-by-step explanation: Before Joe had $45 in total, He then spent it on a movie which is $15. So $45-$15=30

Answer:

25+20-15=30

Step-by-step explanation:

Here You Go Bud

Answer:

[tex]h = 16.1[/tex]

Step-by-step explanation:

[tex]sin A /a = sin B / b = sin C/c[/tex]   where A is angle and a is side opposite of angle

[tex]sin (49) / h = sin(41)/ 14[/tex]       cross-multiply

[tex]h*sin(41) = 14 * sin(49)[/tex]

[tex]h = (14*sin(49))/ sin(41)[/tex]

[tex]h = 16.1[/tex]

Answer:

100.48

Step-by-step explanation:

2 x 16 x 3.14 = 100.48

Answer: x=20

Step-by-step explanation:

The two angles provided are vertical angles.

Vertical angles are equal in measurement.

This means we can set (3x+50) and (6x-10) equal to each other and solve for x

[tex]3x+50=6x-10[/tex]

Add 10 to both sides

[tex]3x+50=6x-10\\3x+50+10=6x-10+10\\3x+60=6x[/tex]

Subtract 3x from both sides

[tex]3x-3x+60=6x-3x\\60=3x[/tex]

Divide both sides by 3

[tex]\frac{60}{3} =\frac{3x}{3} \\20=x[/tex]

Answer:

Step-by-step explanation:

(3x + 50)° = (6x - 10)°

3x - 6x = -50 - 10

3x = -60

[tex]\frac{-3x}{-3}[/tex] = [tex]\frac{-60}{3}[/tex]

x=20°

Answer:

0.34

Step-by-step explanation:

Answer:

y=5

Step-by-step explanation:

Let me know if you need an explanation

Answer:

55. 16       56. 48       57.27

Step-by-step explanation:

You add all the sides that you are given together and then you subtract that from the perimeter given. EX. In question 55 you would do 20+12=32 so 48-32=16.

Answer:

The journal entries are shown below:

Treasury Stock A/c Dr $5,000 (50 shares × $100)

To Cash A/c $5,000

(Being treasure stock is purchased)

Cash A/c Dr $2,600 (50 shares × $52)

(Being treasury stock is sold at higher price and the remaining amount would be credited to the paid in capital account)

Cash A/c Dr $2,300       (50 shares × $46)

Paid in capital - Treasury stock $100

Retained Earnings A/c Dr $100

(Being treasury stock is sold at lower price and the remaining amount would be debited to the retained earning account)

Answer:

Step-by-step explanation:

The building and the person on it are illustrations of elevation and depression

The height of the building is 76.9 feet

To calculate the building height, we make use of the attached illustration

Considering the triangle DCB in the figure, we have:

tan(B) = DC/BD

Substitute known values

tan(28.3) = DC/(DA + 100)

Cross multiply

(DA + 100) * tan(28.3) = DC

Divide both sides by tan(28.3)

DA + 100 = DC/tan(28.3)

Subtract 100 from both sides

DA = -100 + DC/tan(28.3)

Considering the triangle DCA in the figure, we have:

tan(A) = DC/DA

Substitute known values

tan(33.5) = DC/DA

Make DA the subject

DA = DC/tan(33.5)

Substitute DA = DC/tan(33.5) in DA = -100 + DC/tan(28.3)

DC/tan(33.5) = -100 + DC/tan(28.3)

Evaluate the tangent ratios

0.56DC = -100 + 1.86DC

Collect like terms

-1.86DC + 0.56DC = -100

Evaluate

-1.3DC = -100

Divide both sides by -1.3

DC = 76.9 feet

Hence, the height of the building is 76.9 feet

Read more about elevation and depression at:

https://brainly.com/question/15580615

Answer:

B) (4, -1)

Step-by-step explanation:

A violates the rule of y <= x + 1, because 3 > 1 + 1

C violates the rule of y <= x + 1, because 5 > 0 + 1

D violates the rule of y > -x, because 0 < -(-4) = 4

B conforms to both rules: -1 > -4 and -1 <= 4 + 1.

Answer:

 B) (4,–1)

Step-by-step explanation:

A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.

Answer:

Making money

Step-by-step explanation:

selling motorcycle for 2,535

After 2 years the motorcycle is worth:

y = 4721(0.65)^2

= 1994.6

2535> 1994.6

Answer:

Joel is selling a motorcycle for $2,535. He bought the

motorcycle two years ago and paid $4,721 for it. It depreciated

35% during the two years. Is he losing money or making money

on this sale

Answer:

11340

Step-by-step explanation:

You would just multiple 27 by 420, since each room has a capacity:

27 x 420 = 11340

Answer:

8.6 mile

Explanation:

[tex]\sf equation \ follows : \ \ \ d = 1.2116\sqrt{h}[/tex]

what the captain sees:

[tex]\hookrightarrow \sf d_c = 1.2116\sqrt{15}[/tex]

what the sailor sees:

[tex]\hookrightarrow \sf d_s = 1.2116\sqrt{120}[/tex]

Difference between them:

[tex]\sf \rightarrow 1.2116\sqrt{120} \ - \ 1.2116\sqrt{15}[/tex]

[tex]\sf \rightarrow 8.58[/tex]

[tex]\sf \rightarrow 8.6[/tex]      (rounded to nearest tenth)

Answer:

8.6 miles (nearest tenth)

Step-by-step explanation:

[tex]d=1.2116\sqrt{h}[/tex]

where:

Captain

Given the Captain is 15 ft above the ocean:

[tex]\implies h = 15[/tex]

Substituting this into the equation:

[tex]\implies d_1=1.2116\sqrt{15}[/tex]

Lookout

Given the lookout is 120ft above the ocean:

[tex]\implies h = 120[/tex]

Substituting this into the equation:

[tex]\implies d_2=1.2116\sqrt{120}[/tex]

Solution

To find how much farther the lookout can see than the captain, subtract the distance the captain can see from the distance the lookout can see:

[tex]\implies d_2-d_1[/tex]

[tex]\implies 1.2116\sqrt{120}-1.2116\sqrt{15}[/tex]

[tex]\implies 1.2116(\sqrt{120}-\sqrt{15})[/tex]

[tex]\implies 8.579906391...[/tex]

[tex]\implies 8.6\: \sf miles\:(nearest\:tenth)[/tex]

Answer:

B. (2,8)

E. (4,4)

Explanation:

equation that can be created: y = 12 - 2(x)

where y is the remaining eggs and x is days

sequence:                  coordinates:

1st day: 12 - 2 = 10         (1,10)

2nd day: 10 - 2 = 8        (2,8)

3rd day: 8 - 2 = 6           (3,6)

4th day: 6 - 2 = 4           (4,4)

5th day: 4 - 2 = 2           (5,2)

6th day: 2 - 2 = 0           (6,0)

Answer:

"At most"  Means that you met largest possible number that you can use in a number set.

Step-by-step explanation:

Basically 6 is the highest number reached and cant go any higher but it can go lower.

Answer: $2053.51

Step-by-step explanation:

The formula for compound interest is [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Where

A = final amount

P = initial principal balance (1700 for this)

r = interest rate (0.065 for this)

n = number of times interest applied per time period (1 for this)

t = number of time periods elapsed (3 for this)

[tex]A=1700(1+\frac{0.065}{1})^{(3)(1)} \\A=1700(1.065})^{3} \\A=2053.51435[/tex]

Rounded that is 2053.51

The *graph of a function* (and not an equation) f(x) crosses the x-axis for any value of x such that f(x) = 0. We call x a root of f(x) in that case.

The simplest function with roots at both x = 3 and x = -8 is

f(x) = (x - 3) (x + 8)

since

f(3) = (3 - 3) (3 + 8) = 0 • 11 = 0

and

f(-8) = (-8 - 3) (-8 + 8) = -11 • 0 = 0

Answer:

[tex]\frac{25}{30}~and~\frac{28}{30}[/tex]

[tex]5 * 5 = 25[/tex]

[tex]5 * 6 = 30[/tex]

[tex]14 * 2 = 28[/tex]

[tex]15 * 2 = 30[/tex]

[tex]25~and~30 -- > \frac{25}{30}[/tex]

[tex]28~and~30-- > \frac{28}{30}[/tex]

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Finally, the problem is solved. Now that the problem is solved, we review what we just learned not through more problems, though.

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We learned how to efficiently make fractions' deominators match.

Questions related to this topic? Ask me in the comments box, please!