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4 years ago

Which expression is equivalent to -3 ( x + 10)

Mathematics

2 answers:

Aleksandr [31]4 years ago

5 0

Hey there!

$\bold{-3(x+10)}$

<em>Firstly, you have to distribute </em>
$\bold{-3(x) +(-3)(10)}$
$\bold{-3(x)=-3x}$
$\bold{-3(10)=-30}$
$\boxed{\boxed{\bold{Answer:-3x-30}}}$

Good luck on your assignment and enjoy your day!

~ $\bold{LoveYourselfFirst:)}$

maria [59]4 years ago

3 0

Answer:

-3x - 30

Step-by-step explanation:

Distribute (multiply) the -3 to everything in the parentheses.

-3 (x + 10)

-3 * x = -3x -3 * 10 = -30

Answer: -3x - 30

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Ball kicked into the air with an initial upward velocity of 60 ft/s. It’s height h in feet after t seconds is given by the funct

Free_Kalibri [48]

Answer:

Max height: 61.25 feet

Max height reached at 15/8 seconds, or 1.875 seconds

How long to hit the ground: (15 + 7√5)/8 or about 3.83 seconds

How high after 1 second: 49 feet

Step-by-step explanation:

Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.

The general form for a quadratic equation is ax² + bx + c,

here a is -16, and b is 60

To find the x coordinate of the vertex, use x = -b/(2a)

We have x = -60/[2(-16)]

x = -60/-32

x = 15/8

So at 15/8 seconds, the ball reaches is maximum height

Now plug that into the equation to find the y value, which will be the height...

y = -16(15/8)² + 60(15/8) + 5

y = -16(225/64) + 900/8 + 5

y = -225/4 + 450/4 + 20/4

y = 245/4

y = 61.25 feet

To find out how long the ball was in flight, solve the equation...

0 = -16t² + 60t + 5

Use quadratic equation...

x = -60/-32 ± √[60² - 4(-16)(5)]/-32

x = 15/8 ± (√3920)/-32

x = 15/8 ± (28√5)/-32

x = 15/8 ± (-7√5)/8

so x = (15 - 7√5)/8 and (15 + 7√5)/8

(15 - 7√5)/8 is negative, and we're talking about time, so this answer is ignored.

(15 + 7√5)/8 seconds is when the ball hits the ground

To find out out how high the ball was after 1 second, plug 1 in for x and simplify

h(1) = -16(1²) + 60(1) + 5

h(1) = -16 + 60 + 5

h(1) = 49

4 0

3 years ago

Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units

Lady_Fox [76]

Answer:

a. the motion is positive in the time intervals: $[0,2)U(6,\infty)$

The motion is negative in the time interval: (2,6)

b. S=7 m

c. distance=71m

Step-by-step explanation:

a. In order to solve part a. of this problem, we must start by determining when the velocity will be positive and when it will be negative. We can do so by setting the velocity equation equal to zero and then testing it for the possible intervals:

$3t^{2}-24t+36=0$

so let's solve this for t:

$3(t^{2}-8t+12)=0$

$t^{2}+8t+12=0$

and now we factor it again:

(t-6)(t-2)=0

so we get the following answers:

t=6 and t=2

so now we can build our possible intervals:

$[0,2) (2,6) (6,\infty)$

and now we test each of the intervals on the given velocity equation, we do this by finding test values we can use to see how the velocity behaves in the whole interval:

[0,2) test value t=1

so:

$v(1)=3(1)^{2}-24(1)+36$

v(1)=15 m/s

we got a positive value so the object moves in the positive direction.

(2,6) test value t=3

so:

$v(1)=3(3)^{2}-24(3)+36$

v(3)=-9 m/s

we got a negative value so the object moves in the negative direction.

$(6,\infty)$ test value t=7

so:

$v(1)=3(7)^{2}-24(7)+36$

v(1)=15 m/s

we got a positive value so the object moves in the positive direction.

the motion is positive in the time intervals: $[0,2)U(6,\infty)$

The motion is negative in the time interval: (2,6)

b) in order to solve part b, we need to take the integral of the velocity function in the given interval, so we get:

$s(t)=\int\limits^7_0 {(3t^{2}-24t+36)} \, dt$

so we get:

$s(t)=[\frac{3t^{3}}{3}-\frac{24t^{2}}{2}+36]^{7}_{0}$

which simplifies to:

$s(t)=[t^{3}-12t^{2}+36t]^{7}_{0}$

so now we evaluate the integral:

$s=7^{3}-12(7)^{2}+36(7)-(0^{3}-12(0)^{2}+36(0))$

s=7 m

for part c, we need to evaluate the integral for each of the given intervals and add their magnitudes:

[0,2)

s(t)=\int\limits^2_0 {(3t^{2}-24t+36)} \, dt

so we get:

$s(t)=[\frac{3t^{3}}{3}-\frac{24t^{2}}{2}+36]^{2}_{0}$

which simplifies to:

$s(t)=[t^{3}-12t^{2}+36t]^{2}_{0}$

so now we evaluate the integral:

$s=2^{3}-12(2)^{2}+36(2)-(0^{3}-12(0)^{2}+36(0))$

s=32 m

(2,6)

s(t)=\int\limits^6_2 {(3t^{2}-24t+36)} \, dt

so we get:

$s(t)=[\frac{3t^{3}}{3}-\frac{24t^{2}}{2}+36]^{6}_{2}$

which simplifies to:

$s(t)=[t^{3}-12t^{2}+36t]^{6}_{2}$

so now we evaluate the integral:

$s=6^{3}-12(6)^{2}+36(6)-(2^{3}-12(2)^{2}+36(2))$

s=-32 m

(6,7)

s(t)=\int\limits^7_6 {(3t^{2}-24t+36)} \, dt

so we get:

$s(t)=[\frac{3t^{3}}{3}-\frac{24t^{2}}{2}+36]^{7}_{6}$

which simplifies to:

$s(t)=[t^{3}-12t^{2}+36t]^{7}_{6}$

so now we evaluate the integral:

$s=7^{3}-12(7)^{2}+36(7)-(6^{3}-12(6)^{2}+36(6))$

s=7 m

and we now add all the magnitudes:

Distance=32+32+7=71m

7 0

3 years ago

Steak cost $3.85 per pound if you buy a 3 pound steak and pay for it with a $20 bill how much change will you get ?

Pie

Answer:

$ 8.45

Step-by-step explanation:

3.85 * 3 = 11.55

20 - 11.55 = 8.45

3 0

3 years ago

Read 2 more answers

Josefina is buying 10 pounds of salmon which costs $6.78 per pound. how much wil the salmon cost

Liono4ka [1.6K]

$6.78/pound*10pounds=$67.80

4 0

3 years ago

Read 2 more answers

-10x—16=14<br> -16x -6 = 14

Alla [95]

Answer: No solution

Step-by-step explanation:

-10x-16=14

-16x-6=14

-10x-16=-16x-6

-10x+16x-16=-16x+16x-6

6x-16=-6

6x-16+16=-6+16

6x=10

x=10/6

x=5/3

-16(5/3)-6=

-80/3-6*3/3=

-80/3-18/3=

(-80-18)/3=-98/3 $\neq$ 14

Hence, there is no solution

4 0

2 years ago