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3 years ago

Choose the correct description of the graph of the compound inequality:

1 answer:

8 0

First, let's solve the inequality:
x - 3 < -9
//add 3 to both sides:
x<-6

the second inequality:
x + 5 ≥ 10
//substract 5 from both sides:
x ≥ 5

So we need to map:

x<-6
x ≥ 5

Now, shading will be to the leftof -6 and to the right of 5 - this is compatible with answers A and B.

A closed circle means that the number is included, so the correct answer is A!

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Pencil cores are glued between slabs of cedar to make a pencil sand which. A total of 52,500 pencil sandwiches are made over 5 d

raketka [301]

Answer:

10,500

Step-by-step explanation:

You must divide 52,500 by 5.

5 goes into the 5 in 52,500 one time. 5-5 is 0. 5 doesn't go into 2 so put a 0. 5 goes into 25 five times. 25-25 is 0. 5 goes into 5 one time. subtract and add the zeros at end. And you get 10,500

8 0

3 years ago

A ball is projected in to the air. Its height at time t is given by the equation

Ksju [112]

The equation gives the height of the ball. That is, h is the height of the ball. t is the time. Since we are looking for the time at which the height is 8 (h=8), we need to set the equation equal to 8 and solve for t. We do this as follows:

$h=-16 t^{2} +60t+1$
$8=-16 t^{2} +60t+1$
$16 t^{2} -60t-1+8=0$
$16 t^{2} -60t+7=0$

This is a quadratic equation and as it is set equal to 0 we can solve it using the quadratic formula. That formula is:
$t= \frac{-bplus minus \sqrt{ b^{2}-4ac } }{2a}$
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."

In order to use the formula we need to identify a, b and c.
a = the coefficient (number in front of) $t^{2}$ = 16.
b = the coefficient of t = -60
c = the constant (the number that is by itself) = 7

Substituting these into the quadratic formula gives us:
$t= \frac{-(-60)plus minus \sqrt{ (-60)^{2}-4(16)(7) } }{2(16)}$
$t= \frac{60plus minus \sqrt{3600-448 } }{32}$
$t= \frac{60plus minus \sqrt{3152 } }{32}$

As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
$t= \frac{60+56.1426}{32} =3.63$
and
$t= \frac{60-56.1426}{32} =.12$

So the height is 8 feet at t = 3.63 and t=.12

It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.

3 0

3 years ago

a submarine descends 480 ft and 24 seconds the submarines elevation changes at a constant rate what is the elevation change of t

Vlad1618 [11]

Answer:

The submarine would be 900 below the ocean surface after 12 minutes assuming it started its descent at the surface of the ocean.

Step-by-step explanation:

The formula for distance traveled (in this case the distance a submarine descends) over a period of time is:

⋅

where

is the distance traveled (or descended),

is the rate of travel and

is the time.

In this problem we are told the rate,

is 75 feet per minute. And, we are told the time,

, to calculate for which is 12 minutes.

7 0

2 years ago

Evaluate the function at x = –2. y = 0 y = 3 y = –4 y = 2

dezoksy [38]

When x=-2, y is equal to 3

4 0

3 years ago

The graph shows the number of centimeters a particular plant grows over time. Given the points (0,0) and (4,6), how many centime

Studentka2010 [4]

Answer: 1.2 centimeters

Step-by-step explanation:

5 0

2 years ago