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horrorfan [7]
3 years ago
13

For the function f(x) = −2(x + 3)2 − 1, identify the vertex, domain, and range. The vertex is (3, −1), the domain is all real nu

mbers, and the range is y ≥ −1. The vertex is (3, −1), the domain is all real numbers, and the range is y ≤ −1. The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1. The vertex is (−3, −1), the domain is all real numbers, and the range is y ≥ −1.
Mathematics
2 answers:
monitta3 years ago
7 0

Answer:

The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1

Step-by-step explanation:

f(x) = −2(x + 3)^2 − 1

The vertex form is

f(x) = a ( x-h) ^2 + k  where ( h,k) is the vertex

f(x) = −2(x - -3)^2 − 1

The vertex is ( -3,-1) is the vertex

The domain is the values that x can take and x can take all real numbers

The vertex is the maximum since a is negative so the range is  all values less than -1

y ≤ −1

nalin [4]3 years ago
3 0

Answer:

The vertex is (−3, −1), the domain is all real numbers, and the range is y ≤ −1

Step-by-step explanation:

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3 years ago
Latoya has b decks of cards . Each deck has 52 cards in it , what is the expression for the total numbers of cards latoya has
Lerok [7]

Answer:

52b

Step-by-step explanation:

She has 52 cards per deck, and b decks.

This means she has 52b cards.

How this works:

For 1 deck, she has 52 cards, or 52×1 cards.

For 2 decks, she has 104 cards, or 52×1 cards.

For 5 decks, she has 260 cards, or 52×5 cards.

For 10 decks, she has 520 cards, or 52×10 cards.

Therefore, for b decks, she has 52×b, or 52b cards.

**This content involves writing algebraic expressions, which you may wish to revise. I'm always happy to help!

6 0
3 years ago
(4,-5) reflected over y = x
sweet-ann [11.9K]
Answer: (-5,4)

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x).
5 0
3 years ago
Lines AB and CD (if present in the picture) are straight lines. Find x. Give reasons to justify your solutions.
Olin [163]

Answer:

WORDS: The value of x is 15.

EQUATION: x = 15

Step-by-step explanation:

1. AB is a straight line therefore angles AOF, FOG, and GOB total 180º

2. If ∠FOG = 90º, AOF + GOB = 90º by subtraction & substitution property

3. 5x - 15 + 2x = 90 (now solve) --> by substitution

4. 7x - 15 = 90 --> by C.L.T. or <u>C</u>ombine <u>L</u>ike <u>T</u>erms

5. 7x = 105 --> by C.L.T. or <u>C</u>ombine <u>L</u>ike <u>T</u>erms

6. x = 15 --> by inverse operations (division)

Hope this helps!

8 0
3 years ago
The cost of 7 chairs and 2 tables is equal.If the cost of 6 chairs and 5 tables is 10575, find the cost of 12 chairs.​
Igoryamba

Answer:

5400

Step-by-step explanation:

Let x represent the cost of a chair and y represent the cost of a table. We can use this to set up a system of equations:

7x=2y

6x+5y=10575

We can solve this system using substitution.

Start by rewriting the first equation in terms of x.

7x=2y\\\text{Divide both sides by 7}\\x=\frac{2}{7}y

Substitute this into the second equation:

6(\frac{2}{7}y)+5y=10575\\\frac{12}{7}y+5y+10575\\\frac{12}{7}y+\frac{35}{7}y=10575\\\frac{47}{7}y=10575

Multiply both sides by 7

47y=74025

Divide both sides by 47

y=1575

This means...

7x=2(1575)\\7x=3150

Divide both sides by 7

x=450

One chair costs 450. Now, multiply this number by 12 to find the cost of 12 chairs.

450*12=5400

12 chairs cost 5400.

7 0
2 years ago
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