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2 years ago

Factor the following trinomial, if possible 4x^2 + 4x - 3

1 answer:

6 0

<u> $4x^2+\underbrace{4x}_{6x-2x}-3=2x\cdot2x+\underbrace{2x\cdot3}_{6x}-1\cdot2x-1\cdot3\\\\=2x(2x+3)-1(2x+3)=\boxed{\boxed{(2x+3)(2x-1)}}$ </u>

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Find the length of YZ

emmainna [20.7K]

Larger triangle’s base length

a^2 + b^2 = c^2
a^2 + 3^2 = 8^2
a^2 = 8^2 - (3^2)
sqrt(a^2) = sqrt(55)
a = sqrt(55)
__________________

Smaller triangle’s base length:

The same formula applies.
a^2 + 3^2 = 5^2
a^2 = 5^2 - (3^2)
sqrt(a^2) = sqrt(16)
a = 4
____________

The finale!

Add the two side lengths of a, which is sqrt(55) + 4 (exact answer)
or... 11.416 (unrounded to thousandths place)

Good luck to you!

5 0

3 years ago

Which statement describes the lines whose equations are y=1/3x+12 and 6y=2x+6

ICE Princess25 [194]

First, you should solve both equations for the same variable. Since the first one is already solved for y, solve the second equation for y as well.

6y = 2x + 6 Divide both sides by 6
y = $\frac{1}{3}$ x + 1

You can see that both lines have a slope of $\frac{1}{3}$ .
Lines that have the same slope are parallel lines.

4 0

3 years ago

Which of the following theorems verifies that ABC~WXY?

Flura [38]

Answer:

ABC~WXY by AA

Step-by-step explanation:

In ΔABC

∠B = 90°

∠A = 27°

To Find ∠C

Angle sum property: The sum of all angles of triangle is 180°

∠A+∠B+∠C=180°

27°+90°+∠C=180°

∠C=180°-117°

∠C=63°

In ΔWXY

∠X = 90°

∠Y = 63°

We will use angle sum property

So, ∠W+∠Y+∠X=180°

90°+63°+∠W=180°

∠W=180°-(90°+63°)

∠W=27°

So, ∠A=∠W

∠B =∠X

∠C = ∠Y

So, ABC~WXY by Angle - Angle property.

Hence ABC~WXY by AA

3 0

3 years ago

Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and

mariarad [96]

9514 1404 393

Answer:

(a, b, c, d) = (1, -4, 1, -2)
(a, b, c, d) = (1, -4, 1, 2)
(a, b, c, d) = (1, -4, 2, 6)

Step-by-step explanation:

Once you remove the common factor from the terms, you are looking for factors of the remaining constant term that have a sum equal to the coefficient of the linear term. These factors are the constants in the binomial factors.

1. 8 = (-4)(-2) ⇒ x^2 -6x +8 = (x -4)(x -2)

(a, b, c, d) = (1, -4, 1, -2)

2. -8 = (-4)(+2) ⇒ 3x^3 -6x^2 -24x = 3x(x -4)(x +2)

(a, b, c, d) = (1, -4, 1, 2)

3. -12 = (-4)(3) ⇒ 2x^2 -2x -24 = 2(x -4)(x +3) = (x -4)(2x +6)

(a, b, c, d) = (1, -4, 2, 6) or (2, -8, 1, 3)

3 0

3 years ago

There are currently 18 pit bulls at the pound. Of the 18 pit bulls, four have attacked another dog in the last year. Joe, a memb

laila [671]

Answer: 0.7748

Step-by-step explanation:

Given : Number of bit bulls at the pound = 18

Number of pit bulls have attacked another dog in the last year =4

The proportion of pit bulls have attacked another dog in the last year: $p=\dfrac{4}{18}\approx0.22$

Number of the pit bulls selected = 6

The probability of that none of the pit bulls in Joe's group attacked another dog last year : $P(0)=(1-0.22)^6=0.225199600704\approx0.2252$

By using binomial , the probability that at least one of the pit bulls in Joe's group attacked another dog last year is given by :-

$P(x\geq 1)=1-P(x$

Hence, the required probability = 0.7748

3 0

3 years ago