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skad [1K]
3 years ago
9

Ben uses a compass and a straightedge to construct ∠DEF ≅ ∠ABC, as shown below:

Mathematics
1 answer:
Len [333]3 years ago
5 0

Answer: Choice D

∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

======================================================

Explanation:

Effectively what Ben is doing is ensuring that

  • BH = EJ
  • BI = EK
  • HI = JK

are the three congruent corresponding sides. This is by construction. After those constructions, he would use SSS to prove the triangles congruent. Lastly, he can then say angle DEF is congruent to angle ABC due to CPCTC.

CPCTC = corresponding parts of congruent triangles are congruent.

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6. Lines C and D below are cut by transversal, t. Which of
ra1l [238]

Answer:

m∠8 = m∠2, option G

Step-by-step explanation:

Angles 8 and 2 are alternate interior angles, which means they are equal. Thus, the answer is option G, m∠8 = m∠2

8 0
3 years ago
The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =
vesna_86 [32]

Answer:

p(x) = (3x^{2} - 8x + 5)(x - 4)

Step-by-step explanation:

p(x) has degree 3

(x - 4) has degree 1

So p(x) can be rewritten as a polynomial of degree 2 multiplying (x-4)

So

p(x) = (ax^{2} + bx + c)(x - 4)

To find a, b and c, we have to divide p(x) by x - 4.

So

Finding a:

Dividing the first term of p(x) by x - 4.

\frac{3x^{3}}{x - 4} = 3x^{2}

So a = 3.

Now multiplying 3x² by, x - 4, we have:

3x^{2}(x - 4) = 3x^{3} - 12x^{2}

Subtracting p(x) from this:

3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20

Finding b:

Dividing the first term, after the subtraction, by x - 4.

\frac{-8x^{2}}{x - 4} = -8x

So b = -8.

Multiplying -8x by x - 4, we have:

-8x(x-4) = -8x^{2} + 32x

Then

-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20

Finding c:

\frac{5x}{x - 4} = 5

So c = 5.

Just to verify if the remainder is 0.

5(x - 4) = 5x - 20

5x - 20 - (5x - 20) = 0

Ok

Then:

p(x) = (ax^{2} + bx + c)(x - 4)

p(x) = (3x^{2} - 8x + 5)(x - 4)

7 0
3 years ago
Reduce to simplest form.<br> -5/8 - ( -4/3)<br><br> please help !!
lions [1.4K]

Answer: 17/24.

Step-by-step explanation: Consider marking this answer as brainliest if it helped you out.

6 0
3 years ago
Read 2 more answers
Question 4 (5 points)
klemol [59]

Answer: B (-2)

Step-by-step explanation:

[log base b of a = c] turns into [b^c = a]

You have log base 5 of 1/25 = ?, so it turns into 5^? = 1/25

This part is sort of guess and check, but we can look at it to find the answer pretty easily. First, it's 1/n, so we should use a negative power: 5^-1 = 1/5

In addition to being in the denominator, it's 25, which is 5^2.

So, if we want to put it in a reciprocal as well as square it, we can use -2:

5^(-2) = 1/(5^2) = 1/25

Since -2 (B) is the exponent we place on 5 to get 1/25, it is also the answer to log base 5 of 1/25.

8 0
3 years ago
Read 2 more answers
(b) Rewrite the percentage in the sentence below as a decimal.
Arturiano [62]
40% = 0.4
Explication:
40 / 100 = 0.4

5 0
3 years ago
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