MATHEMATICS HIGH SCHOOL

For the function f(x) = –(x + 1)^2 + 4, identify the vertex, domain, and range. a. The vertex is (–1, 4), the domain is all real numbers, and the range is y ≥ 4.
b. The vertex is (–1, 4), the domain is all real numbers, and the range is y ≤ 4.
c. The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.
d. The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.

Answers

Answer 1

Answer: b; you can graph the function on a graphic calculator or use algebra find each of the desired aspects

Answer 2

Answer:

Answer:

the answer is B

Step-by-step explanation:

the domain equals to be (-1,4) and a equals more than 0 so it is y ≤ 4

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Describe the relationship between the two quantities.Amount of money earned; Number of hours worked
a. inverse
c. joint
b. direct
d. compound
Please select the best answer from the choices provided

Answers

Answer:

The answer is B.

Step-by-step explanation:

B is right because the amount of money you earn is based off of how many hours you have worked. If you work many hours your getting paid more.

X^2-5x-24=0

3x^2+x-4=0

Solve by factoring or using the quadratic formula

Answers

$x^2-5x-24=0\n\n-5x=3x-8x\n-24=3\cdot(-8)\n\nx^2-5x-24=0\n\n\Downarrow\n\n(x+3)(x-8)=0\iff x+3=0\ \vee\ x-8=0\n\nx=-3\ \vee\ x=8$

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$3x^2+x-4=0\n\na=3;\ b=1;\ c=-4\n\n\Delta=b^2-4ac\to\Delta=1^2-4\cdot3\cdot(-4)=1+48=49\n\nx_1=(-b-\sqrt\Delta)/(2a)\to x_1=(-1-√(49))/(2\cdot3)=(-1-7)/(6)=(-8)/(6)=-(4)/(3)\n\nx_2=(-b+\sqrt\Delta)/(2a)\to x_2=(-1+√(49))/(2\cdot3)=(-1+7)/(6)=(6)/(6)=1$

$x^2-5x-24=0\n x^2+3x-8x-24=0\n x(x+3)-8(x+3)=0\n (x-8)(x+3)=0\n x=8 \vee x=-3$

$3x^2+x-4=0\n 3x^2-3x+4x-4=0\n 3x(x-1)+4(x-1)=0\n (3x+4)(x-1)=0\n x=-(4)/(3) \vee x=1$

Alaina bought a square frame for her desk that has an area of 81 square inches. What is the perimeter of the frame? (answer should be a number only)

Answers

Given:

Area of a square frame = 81 square inches.

To find:

Perimeter of the frame.

Solution:

Let length of each side of the frame = a inches.

Area of square frame is

$Area=a^2$

$81=a^2$

Taking square root on both sides,

$\pm√(81)=a$

$\pm 9=a$

Side length cannot be negative. So, a=9 inches.

Perimeter of frame is

$Perimeter=4a$

$Perimeter=4(9)$

$Perimeter=36$

Therefore, the perimeter is 36 inches.

Final answer:

The perimeter of the frame is 36 inches.

Explanation:

To find the perimeter of a square, we need to know the length of its sides. Since the area of the frame is given as 81 square inches, we can find the length of one side by taking the square root of the area. The square root of 81 is 9, so each side of the frame measures 9 inches.

Since a square has four equal sides, we can find the perimeter by multiplying the length of one side by 4. Therefore, the perimeter of the frame is 9 inches x 4 = 36 inches.

Learn more about Perimeter here:

brainly.com/question/31695951

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The price of a silk scarf is $32. The sales tax is $1.92. What is the sales-tax rate?

Answers

Answer:

sales-tax rate = 6%

Step-by-step explanation:

The price of a silk scarf is $32. The sales tax is $1.92

Let the sale tax rate be s%

Price of silk scarf = $32

Sale tax = s% of 32

Sale tax = $1.92

Thus,

s% of 32 = 1.92

First we change s% to decimal

$(s)/(100)* 32=1.92$

$s=(1.92* 100)/(32)$

$s=6\%$

Hence, The sales-tax rate is 6%

The sales tax =1.92/32.00=0.06=6%

Roman has a certain amount of money. If he spends $15, then he has 1/4 of the original amount left. How much money did Roman have originally?Bly 13 x

Answers

Answer:

$60

Step-by-step explanation:

Method 1

We want to know how much money Roman originally has considering if he spends $15, then he has $(1)/(4)$ of the original amount left. So,

We know that $(1)/(4)$ = 15 so $(2)/(4)$ = 30 and double that will get 60 so 60 is the original amount

Method 2

Lets call the original amount 'x'

If he spends $15 he has $(1)/(4)$ of the original amount so,

$(1)/(4)$ x = 15

In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we divided 15 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.

$(1)/(4)$ x = 15

→ Multiply both sides by 4 to isolate x

x = 60

So $60 was the original amount

Solve 3(x-4)= -5 for x.

Answers

Answer:

x= 7/3 (fraction)

Step-by-step explanation:

If you plug it in it will work

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