Parallel lines are preserved in which of the following types of transformations?

Use synthetic division to show that the number given to the right of the equation is a solution of the equation. Then solve the

AysviL [449]

Answer:

$x = 2 \: or \: x = - 2 \: or \: x = - \frac{1}{2}$

Step-by-step explanation:

The given polynomial equation is

$2 {x}^{3} + {x}^{2} - 8x - 4 = 0$

We perform the synthetic division as shown in the attachment by dividing by x-2.

This gives a remainder of 0 and a quotient of

$2 {x}^{2} + 5x + 2$

This means the polynomial equation becomes:

$(x - 2)(2 {x}^{2} + 5x + 2) = 0$

We factor the quadratic term by splitting the middle term;

$(x - 2)(2 {x}^{2} + 4x +x + 2) = 0$

$(x - 2)(2 x(x+ 2) +1(x + 2) )= 0$

Collect common factors again:

$(x - 2)((x+ 2)(2x + 1) = 0$

The solution is:

$x = 2 \: or \: x = - 2 \: or \: x = - \frac{1}{2}$

8 0

3 years ago

8. What is the distance around the clock?

Elan Coil [88]

Answer:

The clock face is divided into sixty equal parts, each minute. The minute hand is located on the 20 minute mark at 6:20, the hour hand located between the 30 minute mark and the 35 minute mark. When the minute hand goes all sixty minutes, the hour hand only moves five, so to figure out the location of the hour hand, we look at how much the hour has progressed, in this case 20 minutes, or one third of the hour. So the minute hand has moved one third of the way through the hour, so has the hour hand moved one third of the way through the five minutes, or, five thirds of a minute, which is one and two thirds minute, one minute forty seconds. That puts the hour hand at thirty minutes plus one minute and forty seconds—at 31min 40sec—which is 11min 40sec farther than the minute hand.

Step-by-step explanation:

4 0

2 years ago

Simplify (6x2 + 11x − 3) + (2x2 − 17x − 4).

d1i1m1o1n [39]

Answer:

B. 8x^2-6x-7

Step-by-step explanation:

All you have to do is combine the like terms.

Like terms are the terms that have the same variable and same exponent.

The like terms in this equation are 6x^2 and 2x^2, 11x and -17x, and -3 and -4.

When you add 6x^2 and 2x^2, you get 8x^2

When you add 11x and -17x, you get -6x

When you add -3 and -4, you get -7.

Putting these all in order, your answer is

8x^2 - 6x - 7

8 0

3 years ago

Using triangle A B C as the pre-image and the origin as the center of dilation, which coordinate point is not a coordinate of a

Ostrovityanka [42]

Answer:

The correct option is:

begin ordered pair 4 comma 12 end ordered pair i.e. (4,12).

Step-by-step explanation:

We are given the coordinates of the point A,B and C of the triangle ΔABC as:

A(-1,3) , B(2,1) and C(-2,-1).

Now it is given that there is dilation of this triangle about the origin with a scale factor of 4.

This means that the change in the coordinates after the transformation is given by the rule:

(x,y) → (4x,4y)

As A → A' , B → B' and C → C'

Hence the coordinates A',B' and C' are given by:

A' are (4×-1,4×3)=(-4,12)

B' are (4×2,4×1)=(8,4)

and C' are (4×-2,4×-1)=(-8,-4).

<em>Hence the coordinate point which is not a coordinate of dilation is:</em>

<em>begin ordered pair 4 comma 12 end ordered pair i.e. (4,12)</em>

3 0

3 years ago

X A doghouse is to be built in the shape of a right trapezoid, as shown below. What is the area of the doghouse?

torisob [31]

Answer:

Area of of the doghouse which is in the shape of right trapezoid is 66.5 square feet.

Step-by-step explanation:

7 0

3 years ago

Parallel lines are preserved in which of the following types of transformations?​

Parallel lines are preserved in which of the following types of transformations?