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Amiraneli [1.4K]
3 years ago
13

Solve the inequality. 5c + 3 ≤ −2

Mathematics
1 answer:
givi [52]3 years ago
6 0

Answer:

c is greater than or equal to -1.

Step-by-step explanation:

Subtract 3 from both sides, divide by 5.

I have attached the work to your problem below.

I hope this helps.

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Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and passes through the point (2,
azamat

By "slope" I assume you mean slope of the tangent line to the parabola.

For any given value of <em>x</em>, the slope of the tangent to the parabola is equal to the derivative of <em>y</em> :

y=ax^2+bx+c\implies y'=2ax+b

The slope at <em>x</em> = 1 is 5:

2a+b=5

The slope at <em>x</em> = -1 is -11:

-2a+b=-11

We can already solve for <em>a</em> and <em>b</em> :

\begin{cases}2a+b=5\\-2a+b=-11\end{cases}\implies 2b=-6\implies b=-3

2a-3=5\implies 2a=8\implies a=4

Finally, the parabola passes through the point (2, 18); that is, the quadratic takes on a value of 18 when <em>x</em> = 2:

4a+2b+c=18\implies2(2a+b)+c=10+c=18\implies c=8

So the parabola has equation

\boxed{y=4x^2-3x+8}

6 0
3 years ago
What is the perimeter (please explain your answer)
Alex

Answer:

<em>Answer: B. 38 mm</em>

Step-by-step explanation:

<u>The Perimeter of a Shape</u>

The perimeter of a given shape is the sum of all exterior lengths surrounding the shape.

The figure shows a shape where all the external measures are given except the leftmost side.

This length is the sum of 3 mm + 10 mm = 13 mm.

Now calculate the perimeter:

P = 4 mm + 3 mm + 10 mm + 8 mm + 13 mm = 38 mm

Answer: B. 38 mm

4 0
3 years ago
Find the difference.
RoseWind [281]
The correct answer is C.
8 0
3 years ago
Read 2 more answers
Whats 2-2? I'm 8<br> Please help me
jolli1 [7]

Answer:

0

Step-by-step explanation:

2-2=0

6 0
3 years ago
For which conditions is p ∨ q false?
Gelneren [198K]

Answer:

D)p is false and q is false.

Step-by-step explanation:

This is the case of the disjunction operator. This operator creates a compound statement that:

1. It's true if either simple statement is true

2. It's false if both simple statements are false.

So p and q are statements and the only way the compound statement is false is when both simple statements are false. For instance:

For:

p: "Peter is home"

q: "Charles is home"

The disjunction would look like these two forms:

p v q

Other form to write this is as follows:

Peter is home OR Charles is home.

So the compound statement is false if both Peter and Charles aren't home.

7 0
4 years ago
Read 2 more answers
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