Ask question

Ask question

All categories

3 years ago

5

Felicia is solving the expression -5(3x+2)+10x. Gregory is solving the expression -12-4x+?+?x. Both students simplified their an

swers to get the same expression. What are the values missing from Gregory's expression?

1 answer:

densk [106]3 years ago

7 0

Answer:

see the explanation

Step-by-step explanation:

we have

<em>Felicia</em>

$-5(3x+2)+10x$

Apply distributive property

$-5(3x)-5(2)+10x$

$-15x-10+10x$

Combine like terms

$-5x-10$

Let

a ----> the missing term with coefficient x in Gregory's expression

b ----> the missing constant term in Gregory's expression

so

$-12-4x+ax+b$

equate Gregory's expression to Felicia's expression

$-12-4x+ax+b=-5x-10$

so

$-12+b=-10$ -----> $b=2$

$-4x+ax=-5x$ ------> $a=-1$

so

Gregory's expression is

$-12-4x+2-x$

therefore

The missing terms are 2 and -x

You might be interested in

What is the missing number. Explain how you determined your answer. <br><br> 5–8–14–26–50–?—194

katrin2010 [14]

Answer:

5-8 is +3

8-14 is +3*2

14-26 is 3*4

26-50 is 3*8

which means 50 to the next number is 3*16, which is 48

48+50 is 98

Step-by-step explanation:

4 0

2 years ago

A tunnel is built in form of a parabola. The width at the base of tunnel is 7 m. On

uysha [10]

Given:

The width at the base of parabolic tunnel is 7 m.

The ceiling 3 m from each end of the base there are light fixtures.

The height to light fixtures is 4 m.

To find:

Whether it is possible a trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel.

Solution:

The width at the base of tunnel is 7 m.

Let the graph of the parabola intersect the x-axis at x=0 and x=7. It means x and (x-7) are the factors of the height function.

The function of height is:

$h(x)=ax(x-7)$ ...(i)

Where, a is a constant.

The ceiling 3 m from each end of the base there are light fixtures and the height to light fixtures is 4 m. It means the graph of height function passes through the point (3,4).

Putting x=3 and h(x)=4 in (i), we get

$4=a(3)((3)-7)$

$4=a(3)(-4)$

$\dfrac{4}{(3)(-4)}=a$

$-\dfrac{1}{3}=a$

Putting $a=-\dfrac{1}{3}$ , we get

$h(x)=-\dfrac{1}{3}x(x-7)$ ...(ii)

The center of the parabola is the midpoint of 0 and 7, i.e., 3.

The width of the truck is 4 m. If is passes through the center then the truck must m 2 m on the left side of the center and 2 m on the right side of the center.

2 m on the left side of the center is x=1.5.

A trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is possible if h(1.5) is greater than 2.8.

Putting x=1.5 in (ii), we get

$h(1.5)=-\dfrac{1}{3}(1.5)(1.5-7)$

$h(1.5)=-(0.5)(-5.5)$

$h(1.5)=2.75$

Since h(1.5)<2.8, therefore the trailer truck carrying cars is 4 m wide and 2.8 m high is going to drive through the tunnel is not possible.

6 0

3 years ago

Simplify each equation <br> (x^4)(x^2)

BartSMP [9]

Ok, so remember the exponentioal law that says
$( x^{m} )(x^{n})=x^{m+n}$ so

$( x^{4} )(x^{2})=x^{4+2}= x^{6}$

answe ris x^6

5 0

3 years ago

Read 2 more answers

Can anyone help me factor polynomials

Anarel [89]

C) x+3
first one factors to (x+3)(x-3)
second factors to (x+3)(x-2)

3 0

3 years ago

Find the rectangular coordinates of the point with the polar coordinates (3, 3 divided by 2 pi ). (1 point)

kifflom [539]

Answer:

The correct choice is (0,-3)

Step-by-step explanation:

To convert from polar coordinates to rectangular coordinates, we use the parametric equations:

$x=r\cos \theta$ and $y=r\sin \theta$

The point given to us in polar coordinates is $(3,\frac{3}{2}\pi)$ .

where $r=3,\theta=\frac{3\pi}{2}$

$x=3\cos (\frac{3\pi}{2})$ and $y=3\sin( \frac{3\pi}{2})$

$x=3(0)$ and $y=3(-1)$

$x=0$ and $y=-3$

The correct choice is (0,-3)

5 0

3 years ago