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3 years ago

Find the solution for this inequality -3x + 5 < 5

Mathematics

1 answer:

n200080 [17]3 years ago

6 0

Answer:

Step-by-step explanation:

-3x+5 = 2<5

two less than 5

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Simplify 5x(3x^2+2x-3)

Tcecarenko [31]

Answer:

$15x^3 +10x^2 - 15x$

Step-by-step explanation:

Hello!

Use the distributive property and multiply like terms.

<h3>Simplify</h3>

$5x(3x^2 + 3x - 3)$
$5x(3x^2) + 5x(2x) + 5x(-3)$
$15x^3 +10x^2 - 15x$

The simplified form is $15x^3 +10x^2 - 15x$ .

4 0

2 years ago

Read 2 more answers

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

Without using technology, describe the end behavior of f(x) = 3x32 + 8x2 − 22x + 43.

mr Goodwill [35]

F(x) = 3x^32 + 8x^2 -22x +43

The ends of all the polynomials with even degree behave like quadratic functions.

Given the the coefficient of x^32 is positive, the function opens upwards. Then the two ends go up.

8 0

3 years ago

Read 2 more answers

How old is Michael now?

anyanavicka [17]

Which Michael?? There are many many many Michaels in the world

3 0

3 years ago

solo savings bank received an initial deposit of $6000 it kept a percentage of this money in reserve based on the reserve rate a

iogann1982 [59]

Answer:

Reserve rate = 3%

Step-by-step explanation:

Reserve Ratio = Reserve Maintained with Central Bank / Deposit Liabilities × 100

Reserve maintained = $6,000

Deposit liabilities = $200,000

Reserve Rate = Reserve Maintained with Central Bank / Deposit Liabilities × 1000

=$6,000 / $200,000 × 100

=0.03 × 100

r=0.03 × 100

=3%

Therefore,

Reserve Rate =3%

8 0

3 years ago