Part A: The x-intercepts of the graph are (-2, 0) and (2.5, 0). 2x² - x - 10 = 0 2x² - 5x + 4x - 10 = 0 x(2x - 5) + 2(2x - 5) = 0 (x + 2)(2x - 5) = 0 x = -2, 5/2 or 2.5 Part B: The vertex is going to be the minimum of the function. The coordinates are (0.25, -10.125). Vertex = (h,k) h = midpoint of the x-intercepts (because of symmetry) h = (-2 + 5/2) = 1/4 k = f(1/4) k = 2(1/4)² - 1/4 - 10 = -81/8 Vertex: (0.25, -10.125). y-intercept: when x = 0 2(0)² - 0 - 10 = -10 Part C: To graph f(x), I would draw a line connecting the x-intercepts, vertex and the y-intercept using the points (-2,0), (0,-10), (0.25, -10.125) and (2.5,0). These points are the answers from part A and B and that is why I can use them to draw the graph.

Answer:

A.17

Step-by-step explanation:

Answer:

x = 4

Well basically 20 divided by 5 is 4. which makes this clearly the answer because the slope is 20/x which is being divided. So when you times 5 x 4 you get 20. It all comes together in a way.

Answer:

kk

Step-by-step explanation:

kk

The length of RS is 55 unit.

The addition axiom states that when two equal quantities are added to two more equal quantities, their sums are equal. Thus, if a = b and y = z, then a + y = b + z.

We have, ST = 15 and RT = 40

Then RS can be get by adding the value ST + RT.

Apply Axiom of addition

then, RS

= RT + ST

= 40 + 15

= 55 unit.

thus, the length of RS is 55 unit.

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Answer:

Step-by-step explanation:

Last one

Answer:

175

Step-by-step explanation:

since 1 was 152 you have to add more to get number 8

Answer:

Inequality = 6 + x ≤ 10

x(Number of hours more of television Sarah can still watch this week) = 4 hours

Step-by-step explanation:

Define a variable, set up an inequality and solve that inequality to determine how many more hours of television Sarah can watch this week.

We are told in the question that:

Sarah is allowed to watch no more than 10 hours of television each week.

This means :

Sarah can watch tv for less than or equal to 10 hours in a week. Sarah has already watched 6 hours of television.

Hence:

The number of hours left that Sarah can watch television in a week is represented as x

Our Inequality Equation =

6hours + x hours ≤ 10 hours

6 + x ≤ 10

Solving the inequality

x ≤ 10 - 6

x ≤ 4 hours

This means Sarah still has no more than (less than or equal to) 4 hours or television left to watch in this week

Answer:

25

Step-by-step explanation:

90+x+2x+15=180

3x=75

x=25

Answer:

D. 24

Step-by-step explanation:

Plug in -14 to the equation:

f(x) = 2x - 4(x + 1)

f(-14) = 2(-14) - 4(-14 + 1)

Simplify:

f(-14) = -28 - 4(-13)

f(-14) = -28 + 52

f(-14) = 24

So, D is the correct answer.

Answer:

THE SMALLEST FORMS:

- smallest prism ---> the cube with all sides 2 ==> the volume is 2*2*2 = 8 cm^3

- smallest pyramid number one ---> the pyramid with base sides 2 and the height also 2 ==> the volume is (1/3)*2*2*2 = 8/3 cm^3

- smallest pyramid number two ---> the pyramid with base sides 2 and the lateral sides also 2 ==> the radius of the base is sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 2^2 - sqrt(2)^2 = 4 - 2 = 2 ==> pyramid_height = sqrt(2) ==> the volume is (1/3)*2*2*sqrt(2) = 4*sqrt(2)/3 cm^3

- smallest cylinder --> the cylinder of diameter 2 and height also 2 ==> the radius is diameter/2 = 2/2 = 1 ==> the volume is pi*(radius^2)*height = pi*(1^2)*2 = pi*1*2 = 2*pi cm^3

The lesser volume is the volume of the smallest pyramid number two. ==> it's wax cost is approximately 0.0075 * 4 * 1.42 / 3 $ per candle = 0.014 $ per candle ==> the total cost  per candle is approximately 0.014 + 1.6 = 1.614 $ per candle.

THE BIGGEST FORMS:

- biggest prism ---> the cube with all sides 10 ==> the volume is 10*10*10 = 1000 cm^3

- biggest pyramid number one ---> the pyramid with base sides 10 and the height also 10 ==> the volume is (1/3)*10*10*10 = 1000/3 cm^3

- biggest pyramid number two ---> the pyramid with base sides 10 and the lateral sides also 10 ==> the radius of the base is 5*sqrt(2) ==> [pyramid_height]^2 = [lateral_side]^2 - [base_radius]^2 = 10^2 - [5*sqrt(2)]^2 = 100 - 50 = 50 ==> pyramid_height = 5*sqrt(2) ==> the volume is (1/3)*10*10*5*sqrt(2) = 500*sqrt(2)/3 cm^3

- biggest cylinder --> the cylinder of diameter 10 and height also 10 ==> the radius is diameter/2 = 10/2 = 5 ==> the volume is pi*(radius^2)*height = pi*(5^2)*10 = pi*25*10 = 250*pi cm^3

The bigger volume is the volume of the biggest prism (the side-10 cube). ==> it's wax cost is  0.0075 * 1000 $ per candle = 7.5 $ per candle ==> the total cost per candle is 7.5 + 1.6 = 9.1 $ per candle

The range of the cost is the interval [1.614 ; 9.1]. Depending on other prices on the market,  you greed, and other factors you will put a profit margin: maybe 20% of the cost ; maybe a fixed margin like 5$. So the price per candle will be the cost per candle plus the profit margin per candle.

If I were to choose the base length I would have to say 6 because it is the arithmetic mean between 2 and 10: (2+10)/2 = 12/2 = 6. 2cm is too small, and 10cm is too big.

Also if you start with a rectangle of length 10 and width 2 and you have to find the rectangle with the largest area by being allowed to increase the width and decrease the width with the same quantity you get this:

Area of the new rectangle is (10-x)(2+x) = -x^2 + 8x + 20 = -x^2 + 8x -16 + 36 = -(x^2 - 2*x*4 + 4^2) + 36 = -(x-4)^2 + 36 = 36 - (x-4)^2 which has the maximum value of 36 because out of 36 you subtract a positive value. You get the maximum when (x-4)^2 = 0 ==> x-4=0 ==> x=4

The new length is 10-4=6 and the new width is 2+4=6.

Next I would choose the height of the prism (I like prisms :P) to be [the_golden_ratio]*[base_side] which is approximately 1.618 * 6 = 9.708 which I would round up to 10. ==> The volume would be 6*6*10 = 360 cm^3. ==> the cost would be 0.0075*360 + 1.6 = 2.7 + 1.6 = 4.3 $ per candle. And because my candle is so perfect I'd put the profit margin to be 5.69 $ per candle so I can proudly show it in the store with the price of 4.3 + 5.69 = 9.99 $ :)

Answer:

Guava has the most, Nelli juice has second most, Mango juice has third most Papaw juice has 4th most, Woodaple has the least

Step-by-step explanation:

Answer:

From smallest portion to biggest

Wood apple juice,

Papaw juice,

Mango juice,

Nelli Juice

Step-by-step explanation:

By looking at this graph we cam tell Guava juice has the most since it has the biggest section.

Now we can tell Wood apple juice isn't a popular option because it has the smallest section

Now to fill in the gaps, Papaw juice has the second least amount, then Nelli has third least amount, and and Guava Juice has the most.

Answer:

a^2 +3a-2

Step-by-step explanation:

Given the expression:

g(x) =  x^2 +3x-2

We are to find f(a). To get this, we will simply replace x with a in the expression as shown;

g(a) = a^2 +3a-2

hence the required domain is expressed as g(a) = a^2 +3a-2

Answer:

18ft2

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

sry if it wrong

Answer: D

Step-by-step explanation: Just solve for perimeter of a rectangle by just plugging the side length in with these equations.

Answer:

The chances of Yvonne to get a blue berry candy in the two cases are 1 and 1/2 in case 1 and 2/3 in the case 2.

Step-by-step explanation:

Maurice has a paper bag  with three hard candies

2 blueberries and 1 green apple

Yvonne and Kate want 1 candy each

It is not mentioned that ether Kate has taken a candy already before Yvonne or not so we will consider both the cases

Case 1

If Kate has picked a candy before Yvonne

Case 2

If Kate has not taken any candy from the bag before Yvonne

Probability that Yvonne will get a blueberry candy will be = 2/3

Therefore the chances of Yvonne to get a blue berry candy in the two cases are 1 and 1/2 in case 1 and 2/3 in the case 2.

Answer:

1,680

Step-by-step explanation:

n!/(n-r)!

in this case n= 8 and r= 4

so 8!/(8-4)! = 1,680

The possible permutation of 8 objects taken at 4 a time will be 1680.

The linear arrangement of the set of the orders or the linear arrangements of the numbers is called the permutation.

The number of possible permutations of 8 objects taken 4 at a time will be:-

[tex]^8C_4=\dfrac{8!}{(8-4)!}[/tex]

[tex]^8C_4=\dfrac{8!}{(4)!}[/tex]

[tex]^8C_4=\dfrac{8 \times 7\times 6\times 5\times 4\times 3\times 2}{4\times 3\times 2}=1680[/tex]

Therefore the possible permutation of 8 objects taken at 4 a time will be 1680.

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Answer: m = 6

Step-by-step explanation:

first, move the terms.

4m + 3m = 49 - 7

then, collect like terms and calculate.

7m = 42

then divide both sides.

m = 6

Answer:

m=42

Step-by-step explanation:

simplifying both sides of the equation then isolating the variable.

Answer:  No

Step-by-step explanation:

I took a test and this answer was correct.

Answer:

1i and -19i

Step-by-step explanation:

3-2=1, therefor: 1i

-11-8=-19, therefor: -19i

Answer:

b

the points make a sad face on the graph  and if you do the vertical line test you can see that its a function

Answer:

what's the question

................

Answer:5

Step-by-step explanation: the like moves at and angle bc u started going faster due to running

Answer:

B

Step-by-step explanation:)

Look at the graph it shows her walking the rest don't make sense

Answer:

x=3

Step-by-step explanation:

3^x+3=30

3^x=27

3^3=27

x=3

Answer:

Step-by-step explanation:

3 x 3 = 9 + 3 = 12

30 divided by 12

= 2.5

Answer:

I am confused on what you are asking but I think the answer is y=12345x

Step-by-step explanation:

its correct

Answer:

100

Step-by-step explanation:

1 hectometer = 100 meters

Answer:

70=A

Step-by-step explanation:

7=3+7=10x7=70=A

Answer:

Step-by-step explanation:

the 3rd one