Assume ABC DEF. If DF = 12, EF = 7, and AB = 17, what is the length of DE? A. 32 B. 17 C. cannot be determined D. 7 E. 12 F. 15

The measure of five of of the interior angles of a hexagon are 150, 100, 80, 165, and 150. what is the measure of the sixth inte

givi [52]

Answer:

75°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

let x be the sixth angle, then sum and equate to 720°

150 + 100 + 80 + 165 + 150 + x = 720

645 + x = 720 ( subtract 645 from both sides )

x = 75

The sixth interior angle is 75°

7 0

3 years ago

Points M, N, and P are respectively the midpoints of sides AC , BC , and AB of △ABC. Prove that the area of △MNP is on fourth of

Hunter-Best [27]

Answer:

The area of △MNP is one fourth of the area of △ABC.

Step-by-step explanation:

It is given that the points M, N, and P are the midpoints of sides AC, BC and AB respectively. It means AC, BC and AB are median of the triangle ABC.

Median divides the area of a triangle in two equal parts.

Since the points M, N, and P are the midpoints of sides AC, BC and AB respectively, therefore MN, NP and MP are midsegments of the triangle.

Midsegments are the line segment which are connecting the midpoints of tro sides and parallel to third side. According to midpoint theorem the length of midsegment is half of length of third side.

Since MN, NP and MP are midsegments of the triangle, therefore the length of these sides are half of AB, AC and BC respectively. In triangle ABC and MNP corresponding side are proportional.

$\triangle ABC \sim \triangle NMP$

$MP\parallel BC$

$MP=\frac{BC}{2}$

By the property of similar triangles,

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{PM^2}{BC^2}$

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{(\frac{BC}{2})^2}{BC^2}$

$\frac{\text{Area of }\triangle MNP}{\text{Area of }\triangle ABC}=\frac{1}{4}$

Hence proved.

5 0

3 years ago

3. What is f(-3) if f(x) = |2x + 1] +5? (1 point) 0 10 12 or -10

kolbaska11 [484]

If $f(x) = |2x+1|+5$ , then $f(-3) = |2(-3)+1|+5$ . You replace all x's in the function with -3.

$\begin{aligned}f(-3) &= |2(-3)+1|+5\\[0.5em]&= |-6+1|+5\\[0.5em]&= |-5|+5\endaligned}$

Finish by evaluating the absolute value and then adding that to the 5 that's behind the absolute value.

Can you finish it from there?

8 0

3 years ago

Form a polynomial with zeros:−2 multiplicity 3; 1 multiplicity 2; 3 multiplicity 1;degree 6 You may leave your answer in factore

Darina [25.2K]

Answer:

f(x) = (x+2) (x+2)^3 (x-1) (x-6)

Step-by-step explanation:

The first zero, -2, corresponds to the factor x+2 of the polynomial.

Given that this zero, -2, has multiplicity 3, (x+2)^3 represent the first three factors of the polynomial.

The next factor stems from the zero 1: (x-1).

The next 6 factors stem from the zero 6: (x-6).

Writing the polynomial in factored form, we get:

f(x) = (x+2) (x+2)^3 (x-1) (x-6)

3 0

3 years ago

A rectangular prism has a height of 12 cm and a square base with sides measuring 5 cm. A pyramid with the same base and the heig

Ksju [112]

The answer is 200 cm³

The volume of the rectangular prism (V1) is:
V1 = l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
Thus: V1 = 12 · 5 · 5 = 300 cm³

The volume of pyramid (V2) is:
V2 = 1/3 · l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³

The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):
V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³

3 0

3 years ago