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iogann1982 [59]
3 years ago
5

Find the measure of angle B.

Mathematics
2 answers:
solniwko [45]3 years ago
4 0

The answer is C) 120

lutik1710 [3]3 years ago
3 0

Answer:

C) 120 degrees

Step-by-step explanation:

m<A + m<B + m<C = 180

45 + m<B + 15 = 180

m<B + 60 = 180

m<B = 120

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Expand (2x + 3)^5 using the Binomial Theorem and Pascal’s triangle. Show all steps.
kari74 [83]

Answer:

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

Step-by-step explanation:

(2x + 3)⁵

₅C₀ (2x)⁵ (3)⁰ + ₅C₁ (2x)⁴ (3)¹ + ₅C₂ (2x)³ (3)² + ₅C₃ (2x)² (3)³ + ₅C₄ (2x)¹ (3)⁴ + ₅C₅ (2x)⁰ (3)⁵

Use Pascal's triangle to find nCr.

\left\begin{array}{c}1\\1\ 1\\1\ 2\ 1\\1\ 3\ 3\ 1\\1\ 4\ 6\ 4\ 1\\1\ 5\ 10\ 10\ 5\ 1\end{array}\right

1 (2x)⁵ (3)⁰ + 5 (2x)⁴ (3)¹ + 10 (2x)³ (3)² + 10 (2x)² (3)³ + 5 (2x)¹ (3)⁴ + 1 (2x)⁰ (3)⁵

(2x)⁵ + 15 (2x)⁴ + 90 (2x)³ + 270 (2x)² + 405 (2x)¹ + 243

32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243

7 0
2 years ago
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)
Xelga [282]
Solution for part A is where the red line and the red line meet, (2,-1)
solution for part B: any point on the blue red line is a solution. (2, -1), (0, 3), (3, -3), (-2, 7)
solution for part C is where the green curve and the blue line meet, (0,3)
3 0
3 years ago
There is a spinner with 12 equal areas, numbered 1 through 12. If the spinner is spun one time, what is the probability that the
tresset_1 [31]

Answer:

1/12

Step-by-step explanation:

multiple of 3 and a multiple of 4 implies it can only be 12.

Since you only have the numbers from 1 to 12,

the prob(the 12) = 1/12

4 0
2 years ago
One-stray Problem Solving
anygoal [31]
A) 5000 m²
b) A(x) = x(200 -2x)
c) 0 < x < 100
Step-by-step explanation:
b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:
A(x) = x(200 -2x)
__
a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²
__
c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.
3 0
1 year ago
A tile factory earns money by charging a flat fee for delivery and a sales price of $0.25 per tile. One customer paid a
ddd [48]

Answer: R(x) = 0.25x + 500

Flat fee is computed by:

The sales price of each tile is 0.25 and the customer only bought 10,000 tiles.

So, $0.25 x 10,000 = $2500

So the total sales price per tile sold was $2,500.

The buyer paid $3,000, so the flat fee was included there.

So, $3,000 - $2,500 = $500

So the flat fee was $500.

~

The revenue function is the total income from producing the units. And it has a equation of: R(x) = price per unit x number of units sold plus any fee that is included

So the function describing the revenue of the tile from this sale is:

R(x) = 0.25x + 500

8 0
3 years ago
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