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3 years ago

The multiplication property of equality could be used to solve which of the following equations?

Mathematics

2 answers:

MArishka [77]3 years ago

7 0

The third one; b÷(-2)=18

zysi [14]3 years ago

5 0

Answer:

b ÷ (-2) = 18

Step-by-step explanation:

find the equation that uses the multiplication property of equality

$(x + 2)(x - 3) = 0$

To solve for x we set each factor =0. Here we use zero factor property

$m + 7 = -12$

To solve for m , we subtract 7 from both sides. Here we use subtraction property of equality.

b ÷ (-2) = 18

$\frac{b}{-2} =18$

HEre the expression has division. To remove the denominator we multiply both sides by -2. So we use multiplication property of equality.

$-3 + y = 7$

To solve for y , we add 3 on both sides . WE use addition property of equality.

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A rocket is launched straight up from the ground with an initial velocity of 192 feet per second. The equation for the height of

Ivenika [448]

The equation for the height of the rocket at time t given

$h= -16t^2+192t$

We have to find the time t, when the rocket reaches 560 feet.

That means we have to find t when h = 560 ft. we will place 560 in the place of h to find t now.

$h= -16t^2+192t$

$560 = -16t^2+192t$

In the right side, we can check -16 is the common factor. So we will take out -16 from the rigbht side.

$560 = -16(t^2 - 12t)$

To get rid of -16 from the right side and move it to left side, we will divide both sides by -16.

$560/-16 = -16(t^2-12t)/-16$

$-35 = t^2 -12t$

Now we will move -35 to the righ side by adding 35 to both sides.

$-35+35 = t^2-12t+35$

$0 = t^2 -12t+35$

$t^2-12t+35 = 0$

We will factorize thee left side to find the values of t now. We need to find a pair of factors of 35 that by adding them we will get -12.

The pair of factors of 35 are -5 and -7 and by adding -5-7 we will get -12.

$t^2-12t+35 =0$

$(t-5)(t-7) =0$

So by using zero product property we will get

$t-5 =0$

$t-5+5 = 0+5$

$t=5$

Also $t-7 =0$

$t-7+7 = 0+7$

$t=7$

So we have got the rocket reaches at 560ft when t = 5 seconds and also when t = 7 seconds.

Now part b.

When the rocket completes its trajectory and hits the ground then the height or h = 0. So we will place h = 0 there in the equation.

$h= -16t^2+192t$

$0= -16t^2 + 192 t$

$0 = -16(t^2-12t)$

$-16(t^2-12t) = 0$

We will move -16 to the other side by dividing it to both sides.

$-16(t^2-12t)/-16 = 0/-16$

$t^2-12t = 0$

We will take out the common factor t from the left side. By taking out t we will get,

$t(t-12) = 0$

We will use zero product property now. By using that we will get,

$t = 0$

ans also $t-12 = 0$

$t-12+12 = 0+12$

$t = 12$

When the rocket completes its trajectory and hits the ground the time t can not be 0. When t =0, the rocket starts the trajectory.

So when the rocket completes its trajectory and hits the ground ,

then t = 12seconds.

So we have got the required answers.

6 0

3 years ago

Given: r || s and q is a transversal

shutvik [7]

Answer:

Given: $r || s$ and q is a transversal.

Alternative Interior Angle states that a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal are equal.

By alternative interior angle;

$\angle 3 \cong \angle 6$

Definition of Congruent angles are angles that have the same degree of measurement.

Therefore, $m\angle 3 = m\angle 6$ [By definition of Congruent] .....[1]

Linear Pair states that a pair of adjacent angles formed when two lines are intersect.

therefore, $\angle 4$ and $\angle 3$ are a linear pair. [by definition of linear pair]

Two angles of linear pairs are always supplementary , which means their measure are add up to 180 degree.

By the definition of supplementary angles, $m\angle 4 + m\angle 3 = 180^{\circ}$ .....[2]

Substitute equation [1] in [2] we get,

$m\angle 4 +m\angle 6 =180^{\circ}$

By the definition of supplementary angles,

$\angle 4$ is supplementary to $\angle 6$ Hence proved!

8 0

4 years ago

Read 2 more answers

A 12-ounce bottle of shampoo lasts Enrique 16 weeks . How long would you expect an 18-ounce bottle of the same brand to let him

Aleks04 [339]

Answer:

12 lasts 16

18 lasts x

x=16• 18/12

x= 24

4 0

3 years ago

Select the correct answer from each drop-down menu. Simplify. √63

harkovskaia [24]

Answer:

√63 can be written as

√ 9 × 7 = √ 9 × √7 = 3 × √ 7

= 3√7

Hope this helps you

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3 years ago

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When you payoff you car is it a asset or liability

yaroslaw [1]

It's technically an asset. But it can actually be both. You're liable and responsible for your car paid off or not.

4 0

4 years ago