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3 years ago

Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?

Mathematics

1 answer:

Inessa [10]3 years ago

3 0

6x⁴ + 7x² - 10
6x⁴ - 5x² + 12x² - 10
x²(6x²) - x²(5) + 2(6x²) - 2(5)
x²(6x² - 5) + 2(6x² - 5)
(x² + 2)(6x² - 5)

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Perimeter of an isosceles triangle is 90 m. If the length of the two equal sides is three fourth of the unequal side , find the

Sveta_85 [38]

Answer:

The length of the equal side is 27 meters each and that of the unequal side is 36 meters

Step-by-step explanation:

An isosceles triangle is a triangle with two sides being equal (also two equal base angles).

Let us assume the length of the two equal sides to be x meters each, and the length of the unequal side to be y meter. Since the perimeter of the triangle is 90 m, it can be expressed as:

x + x + y = 90

2x + y = 90

But the length of the equal side is three fourth of the unequal side, i.e x = 3/4y

Therefore:

2(3/4y) + y = 90

3/2y + y = 90

2.5y = 90

y = 90/2.5

y = 36 meters

Also x = 3/4 * 36 = 27 meters

The length of the equal side is 27 meters each and that of the unequal side is 36 meters

5 0

3 years ago

Quadrilateral ABCD has vertices A(1,0) B(5,0) C (7,2) D(3,2). Use slope to prove that ABCD is a parallelogram.

Galina-37 [17]

Answer:

$AD \parallel BC$

$AB \parallel CD$

Step-by-step explanation:

The vertices of quadrilateral ABCD are A(1,0) B(5,0) C (7,2) D(3,2).

The slope of side AB is

$M_{AB}=\frac{0-0}{5-1} =\frac{0}{4}=0$

The slope of side BC is

$M_{BC}=\frac{2-0}{7-5} =\frac{2}{2}=1$

The slope of side CD is

$M_{CD}=\frac{2-2}{3-7} =\frac{0}{-4}=0$

The slope of AD is

$M_{AD}=\frac{2-0}{3-1} =\frac{2}{2}=1$

$AD \parallel BC$

$AB \parallel CD$

We see that the opposite sides of the quadrilateral ABCD are equal.

Hence the quadrilateral is a parallelogram

4 0

3 years ago

Point B has coordinates (3,2). The x-coordinate of point A is −6. The distance between point A and point B is 15 units. What

xxTIMURxx [149]

Answer:

Distance between two points= √(x2-x1)²+(y2-y1)²

D= 15units

Let "k" be the y-coordinate of A

A(-6,k)

B(3,2)

15= √(3--6)²+(2-k)²

Taking square of both sides to eliminate the square root.

15²=(9)²+(2-k)²

225=81+4-4k+k²

k²-4k - 140=0

Using Quadratic Formula to evaluate

k= 14 or k=-10

The Possible coordinates of A are

(-6,14) or (-6,-10)

4 0

2 years ago

2.24 Exit poll: Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walke

iVinArrow [24]

Answer:

0.4929 = 49.29% probability that he voted in favor of Scott Walker

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Having a college degree.

Event B: Voting for Scott Walker.

They found that 57% of the respondents voted in favor of Scott Walker.

This means that $P(B) = 0.57$

Additionally, they estimated that of those who did vote in favor for Scott Walker, 33% had a college degree

This means that $P(A|B) = 0.33$

Probability of having a college degree.

33% of those who voted for Scott Walker(57%).

45% of those who voted against Scott Walker(100 - 57 = 43%). So

$P(A) = 0.33*0.57 + 0.45*0.43 = 0.3816$

What is the probability that he voted in favor of Scott Walker?

$P(B|A) = \frac{0.57*0.33}{0.3816} = 0.4929$

0.4929 = 49.29% probability that he voted in favor of Scott Walker

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3 years ago

W + (-2) = -18 for w. thinks for helping

Katen [24]

Answer:

w = -16

Step-by-step explanation:

w + (-2) = -18

-18 - (-2) = w = -16

w= -16

Check your work:

-16 + (-2) = -18

4 0

3 years ago

Read 2 more answers