The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.
The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).

Domain is the entire span left to right (on the x-axis) that the graph is on. Since the graph goes from x=-4 and ends at x=4, the domain would be from -4 to 4. The circle at -4 is open, so it does not include the point at -4, just everything leading up to it. So, the domain would be

[tex] - 4 < x \leqslant 4[/tex]

The range is similar, it is the entire span that the graph goes up and down (on the y-axis). The graph starts at the bottom at y=-2, and ends at y=5. The bottom point (4,-2) is closed, so the graph includes that point, and the top point (-4,5) is open and doesn't include the point. Therefore, the range would be

[tex] - 2 \leqslant x < 5[/tex]

Answer:

1) -4 2) -2

Step-by-step explanation:

i got it right

Answer:

5.40

Step-by-step explanation:

Cost of 70 gram vanilla beans is $42, so Jacques pay $42 for his vanilla beans.

What information do we have?

Cost of 1 kg vanilla beans = $600

Amount of vanilla beans bought by Jacque = 70 gram

Cost of 1 g vanilla beans = [600/1000]

Cost of 1 g vanilla beans = $0.6 per gram

Cost of 70 gram vanilla beans = 70 × Cost of 1 g vanilla beans

Cost of 70 gram vanilla beans = 70 × $0.6

Cost of 70 gram vanilla beans = $42

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Answer:

30 feet by 18 feet

Step-by-step explanation:

Area = length * width

A  = x*w

w = x - 12

A = 540 sq. ft

540 = x * (x -12)

x*x - 12x - 540 = 0

x*x - 12x  + 36  - 36 - 540 = 0

(x - 6)^2  -  576 = 0

x - 6 = 24

or x -6 = -24

x = 30  or x = -18

w = 30 - 12 = 18

30 ft by 18 ft

Answer:

Ashley's remaining available credit after her first purchase is $1025.00

Step-by-step explanation:

Here we are told that the borrower with the lower credit score will be charged $50.00 fee after the first purchase

Therefore, we have

Credit score Andrea = 895

Credit score for Ashley = 768

Therefore, Ashley has the lower credit score hence after her first purchase of a $425.00 Coach bag, we have

Available credit = Initial balance - Purchase - Charges

∴ Available credit = $1,500.00 - ($425.00 + $50.00) = $1025.00

Therefore, Ashley's remaining available credit after she purchases the $425.00 Coach bag = $1025.00.

Answer:

i think the answer is going to be 3

Step-by-step explanation:

Answer:

573.95 gallons/minute

Step-by-step explanation:

To find the amount of oil after 12 minutes you take the difference between the amount of oil that flows into the tank minus the the oil that flows aout the tanks. Then you have:

[tex]T(t)=F(t)-E(t)\\\\F(t)=t^2+\frac{1}{t+1}\\\\E(t)=\frac{ln(t+7)}{t+2}[/tex]

Being F(t) the flow that goes into the tank per minute, and E(t) the amount of oil that flows outside the tank per minute.

To know the total amount of F and E for t=12 you integrate these function:

[tex]\int_0^{12}F(t)dt=\frac{t^3}{3}+ln(t+1)|_{0}^{12}=578.56\frac{gallons}{minute}\\\\\int_{0}^{12}E(t)dt=\int_0^{12}[\frac{ln(t+7)}{t+2}]dt=4.61\frac{gallons}{minute}\\\\\int_0^{12}T(t)dt=578.56-4.61=573.95\frac{gallons}{minute}[/tex]

573.95 gallons/minute

Answer:

y = 4x-7

Step-by-step explanation:

We have a slope and a point

m = 4    (2,1)

Using the slope intercept form of the equation

y = mx+b

y = 4x+b

From the point x=2 and y =1

1 = 4(2)+b

1 = 8+b

Subtract 8 from each side

1-8 =8-8+b

-7 = b

We can write the equation by using m=4 and b = -7

y = 4x-7

Answer:

A

Step-by-step explanation:

Answer:

The HCF of 168 & 196 is 28

Step-by-step explanation:

The factors of 168 are: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

The factors of 196 are: 1, 2, 4, 7, 14, 28, 49, 98, 196

The highest factor that both 168 and 196 share is 28

Hope this helps :D

Answer:

28

Step-by-step explanation:

168 = 2³ × 3 × 7

196 = 2² × 7²

HCF(168 ; 196) = 2² × 7 = 4 × 7 = 28

Answer:

No,   2 is not 14

Step-by-step explanation:

Evaluate 2*7  you get  2*7 = 14

but 14 is not 2  so no.

Answer:

no

Step-by-step explanation:

No because, 2 times 7 is 14.

The solution to the equation -4x + 1 = x + (-4) using algebra tiles is x = 1

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

-4x + 1 = x + (-4)

Add 4 positive x-tiles to both sides and create zero pairs:

-4x + 1 + 4x = x + (-4) + 4x

1 = 5x - 4

Add 4 positive unit tiles to both sides and create zero pairs:

1 + 4 = 5x - 4 + 4

5x = 5

Divide the unit tiles evenly among the x-tiles:

5x/5 = 5/5

x = 1

The solution to the equation -4x + 1 = x + (-4) using algebra tiles is x = 1

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x = 1

Step-by-step explanation: did on edge

personally i would ask every one who orders a kids meal.

hope this helps

Answer:

the answer is c) Ask anyone who orders a kid's meals

Step-by-step explanation:

the answer is be like 20

Answer:

The answer is -1/2

Step-by-step explanation:

Answer:

y = -2x+2

Step-by-step explanation:

First we find the slope

m = (y2-y1)/(x2-x1)

   = (-2-4)/(2--1)

   = (-2-4)/(2+1)

   -6/3

  -2

We have the slope =-2

We can substitute it into the equation

y = mx+b where m is the slope and b is the y intercept

y =-2x+b

Use a point for x and y to solve for b

4 = -2(-1) +b

4 = 2+b

Subtract 2 from each side

4 -2 = -2+2+b

2 = b

We know m and b

y = -2x+2

Answer:

y = -2x + 2

Step-by-step explanation:

Slope: (-2-4)/(2--1) = -6/3 = -2

y - 4 = -2(x - -1)

y = -2x - 2 + 4

y = -2x + 2

Answer

4

3

Step-by-step explanation:

i did the test.

Question:

Which three-dimensional figures have lateral faces that are polygons? check all that apply.

- cones

- cylinders

- hemispheres

- prisms

- pyramids

- spheres

Answer:

The correct choices are;

- prisms and

- pyramids

Step-by-step explanation:

A polygon is a figure closed or bounded with several straight line segments and polygons are named based on how many sides, side size and sizes of angles that they have present.

A three sided polygon for example is called a triangle

A lateral face are the faces of a prism except the base

Based on the definitions, we note that out of the options, only prisms, and pyramids have lateral faces that are made up entirely of straight line segments, hence polygons. Therefore, the correct choices are prisms and pyramids.

Answer:

Actually the correct is Cylinders, Prisms, and Pyramids. I just did it

Step-by-step explanation:

Answer:

The factored from of the equation is (x+4)(x-6)=0.

Step-by-step explanation:

When solving this problem, we need to find the factored form of this problem. Remember that in factored form, the right-hand side of the equation must equal to 0.

We can simply convert the left-hand side to standard form first:

(x-4)(x+2)=16 --> x²-2x-8= 16.

Now, to set the right-hand side of the equation to 0, we must subtract -16 from both sides:

x²-2x-24=0.

Now, if we convert this to factored form, we will get:

(x+4)(x-6)= 0.

All of the other statements are false. This is the only true statement.

The parabola that opens downward when graphed is y = –3x^2, as the negative coefficient of the x^2 term determines the downward opening direction.

The student has asked which parabola opens downward when graphed. The general form of a parabola is y = ax2 + bx + c. The direction in which the parabola opens is determined by the coefficient a of the x2 term. If a is negative, the parabola opens downward, and if a is positive, the parabola opens upward. Looking at the provided equations, we can identify the equation with a negative a value:

Therefore, the equation of the parabola that opens downward when graphed is y = –3x2

Answer:

121 + 22i - 1

Step-by-step explanation:

Expand:

(11 + i)² = (11 + i)(11 + i)

Note that:

i² = -1

Use FOIL method. Multiply first terms, outside terms, inside terms, then the last two terms:

(11)(11) = 121

(11)(i) = 11i

(i)(11) = 11i

(i)(i) = -1

Combine like terms:

121 + 11i + 11i - 1

121 + (11i + 11i) - 1

121 + 22i - 1

121 + 22i - 1 is your answer.

~

Answer:

see below

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the diameter so we need the radius

r = d/2 =13/2 = 6.5

V = pi (6.5)^2 (19)

V = 802.75 pi mm^3  

We can approximate pi by 3.14

V =2520.635 mm^3

or by using the pi button

V =2521.913503  mm^3

Answer:

Two solutions:

Adding 7 to the left and 0 to the right: 7920

Adding 2 to the left and 5 to the right: 2925

Step-by-step explanation:

The multiples of 45 always have as last digit 0 or 5, so the digit to the right of 92 has to be 0 or 5.

If we use 0 as the last digit, our options of multiples will be just 7920 (7920 = 45 * 176)

If we use 5 as the last digit, our option of multiples will be just 2925 (2925 = 45 * 65)

So we have just two solutions for this problem:

Adding 7 to the left and 0 to the right: 7920

Adding 2 to the left and 5 to the right: 2925

6

Step-by-step explanation:

-2^3=-8

-10+(-8)=-10-8=-18

-18÷-3=6

Answer:

1

Step-by-step explanation:

Answer 1 is an impulse purchase. An impulse purchase is when someone does something just because they feel like it. She doesn't give herself time to think about the outcomes, how much it would cost, the type of dog, nada. She just buys it. Therefore, answer 1 is an example of impulse buying.

Answer:

13,300 divided by 19.7 % is 92893.4010152

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve for x by cross multiplying.

Exact Form:

x=6/5

Decimal Form:

x=1.2

Mixed Number Form:

x=1 1/5

i hope its correct plz tell me if im wrong

The polynomial function with a leading coefficient of 1 and the specified roots and multiplicities is f(x) = (x + 2)(x - 7)(x - 5)^27.

The polynomial function you are looking for, which has a leading coefficient of 1, roots at -2 and 7 each with a multiplicity of 1, and a root at 5 with multiplicity 27, is given by the expression:

f(x) = (x + 2)(x - 7)(x - 5)^27

The given roots indicate the factors of the polynomial, and the multiplicity of each root shows how many times that factor is repeated. Hence, the root -2 becomes (x + 2), the root 7 becomes (x - 7), and the root 5 with multiplicity 27 becomes (x - 5)^27. The leading coefficient is 1, which means these factors are not multiplied by any other constant.

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Answer:

£114

Let me know if it is incorrect so that I can review my answer and fix it! :)

Step-by-step explanation:

20% * £1200 = £240

£1200 + £240 = £1440

£1440 - £300 = £1140

£1140 / 10 = £114

Answer:

£114

Step-by-step explanation:

Total to be paid:

[1200 + (20% of 1200)] - 300

[1200 + (20/100 × 1200)] - 300

1200 + 240 - 300

1140

10 installments

Each:

1140/1

114