Which of the binomials below is a factor of this trinomial?
4x2 + 21x + 5

Answer:

slope = - 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (1, - 1) ← 2 points on the line

m = [tex]\frac{-1-1}{1-0}[/tex] = - 2

Answer:

Slope = -2

Step-by-step explanation:

(0,1) and (1,-1)

Slope = (-1 -1)/(1-0)

Slope = -2

The minimum  happens at x = -b/2a

x = -30 / 2(3) = -30/6 = -5

Now replace x in the equation with -5 and solve:

3(-5)^2 + 30(-5) +27 = 75 - 150 + 27 = -48

The minimum is at (-5,-48)

The min is x= -b/2a

X=-30/2(3)

-30/6= -5

Answer:

The value of the expression would be 11.

Step-by-step explanation:

3 (4 - n) + 8

When n = 3:

3 (4 - 3) + 8

3 (1) + 8

3 + 8

11

Answer:

 11

Step-by-step explanation:

Let the number is n

Then as per statement of the question

"Eight more than three times the difference of four and a number"

Expression will be [3(4-n)+8]

Now for n = 3

Value of the expression will be [3(4 - 3 ) +8]

                    = [ 3 × 1 + 8 ]

                   = 11

A. We know that [tex]x[/tex] represents babysitting hours and [tex]y[/tex] represent tutoring hours.

Since she is allowed to work 20 hours per week, her babysitting hours plus her tutoring hours can't be more than 20 hours, in other words:

[tex]x+y\leq 20[/tex]

She babysits for $6 per hour and tutor for $10 per our. Since she wants to make at least $75, the sum of babysit hours and tutoring hours must be greater or equal $75, in other words:

[tex]6x+10y\geq 75[/tex]

Now we can put our inequalities together to create our system of inequalities:

[tex]x+y\leq 20[/tex]  (1)

[tex]6x+10y\geq 75[/tex]  (2)

B. To graph our system, we first need to find the equations of the lines bounding the inequalities. To do it we, are replacing the inequality sign with and equal and solving for [tex]y[/tex] in both inequalities.

For [tex]x+y\leq 20[/tex]

[tex]x+y=20[/tex]

[tex]y=20-x[/tex]

Now we can find the y and x intercepts to graph the line.

The y-intercept occurs when x = 0, so

[tex]y=20-0[/tex]

[tex]y=20[/tex]

The y-intercept has coordinates (0, 20)

The x-intercept occurs when y = 0, so

[tex]0=20-x[/tex]

[tex]-20=-x[/tex]

[tex]x=20[/tex]

The x-intercept has coordinates (20, 0)

For [tex]6x+10y\geq 70[/tex]

[tex]6x+10y=75[/tex]

[tex]10y=75-6x[/tex]

[tex]y=\frac{15}{2}-\frac{3}{5} x[/tex]

When x = 0,

[tex]y=\frac{15}{2}-\frac{3}{5} (0)[/tex]

[tex]y=\frac{15}{2}[/tex]

y-intercept = [tex](0,\frac{15}{2})[/tex]

When y = 0,

[tex]0=\frac{15}{2}-\frac{3}{5} x[/tex]

[tex]-\frac{15}{2}=-\frac{3}{5}x[/tex]

[tex]x=-\frac{15}{2}(-\frac{5}{3} )[/tex]

[tex]x=\frac{25}{2}[/tex]

x-intercept = [tex](\frac{25}{2} ,0)[/tex]

Now, since both inequalities have greater or equal/less or equal signs, the line bounding them are solid.

Now we can put it all together to create the graph of our system (check the attached picture).

The solution of the inequality is the shaded (purple) region where the two inequalities intercept.

C. As we can see in the graph the points (10, 5), (5, 8), and (2, 9) -as well as the x and y intercepts of both inequalities, are solutions of the system.

Let's choose the point (10, 5). To prove algebraically that the point is a valid solution of the system, we just need to replace the values in our system of inequalities and prove that both inequalities are true.

Since the point is (10, 5), x = 10 and y = 5

Replacing values in (1)

[tex]x+y\leq 20[/tex]

[tex]10+5\leq 20[/tex]

[tex]15\leq 20[/tex]

Since 15 is indeed less or equal to 20, the inequality is true.

Replacing values in (2)

[tex]6x+10y\geq 75[/tex]

[tex]6(10)+10(5)\geq 75[/tex]

[tex]60+50\geq 75[/tex]

[tex]110\geq 75[/tex]

Since 110 is greater or equal 75, the inequality is true.

Both inequalities are true, so (10, 5) represents a solution for the model.

Answer:

Weight of 4th graders, weight of 8th graders

Step-by-step explanation:

Got it right on IM

Plot 1 represents the weight of 4th grade students in pounds and plot 2 represents the weight of 8th grade students in pounds.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Given two dot plots in number line.

Both of the plots are using the same number line.

The values of numbers on the number line increases as we move towards right.

So the values market in the first plot is smaller values than that in the second plot.

If the weight of notebooks in kilogram is plotted in second plot, then the number of notebooks corresponding to each number in the number line should be same. But this is not the case, as in pot 1, there are 3 notebooks in the first value, but only 1 notebook in plot 2 as the first value.

Heights of skyscrapers can't be compared with ounces of water in bottle.

Weights of 3rd grade boys and girls will not be at this distance far.

So the option is c.

Hence the third option is the one representing the plots.

Learn more about Number Line here :

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Answer:

23.3 repeating

Step-by-step explanation:

23.333 or 23 1/3

Multiply (5/3)(2/3) = 10/9 now multiply that by 21 and you get 23.333 or 23 1/3 or 70/3

Answer:

73.4 units is the answer for the figure

Answer:

A. 73.4

Step-by-step explanation:

I jyst did the test lol

Answer:

the answer is C

Step-by-step explanation:

if there are 3 cups and he put seven in each then multiply 7 by 3 and you get 21 then take 3 away and you have 18

Carmen has 18 counters left.

To find out how many counters Carmen has left, we need to subtract the number of counters taken by Abe from the initial number of counters Carmen had.

Carmen initially had 7 counters in each of the 3 cups, so she had a total of 7 x 3 = 21 counters.

Abe took 3 counters, so we subtract 3 from 21 to find that Carmen has 18 counters left.

Therefore, option C, 18, is the correct answer.

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Answer:

B

Step-by-step explanation:

To find the height of a triangle given the area and the base, rearrange the area formula and plug in the known values. For an area of 36 square centimeters and a base of 6 centimeters, the height is calculated to be 12 centimeters.

The problem given states that a triangle has an area of 36 square centimeters and a base of 6 centimeters, and asks us to find the height. To solve this, we use the area formula for a triangle, which is Area = 1/2 × base × height. We have the area and the base, so we can solve for the height.

Step-by-step calculation:

Therefore, the height of the triangle is 12 centimeters (Answer b).

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here u go, see if u understand

Answer: There are two answers to this x=3 and x=11

Step-by-step explanation:

Answer:  The correct option is (A). x = 3.

Step-by-step explanation:  We are given to find the solution of the following quadratic equation :

[tex](x-2)(x+10)=13.[/tex]

We have

[tex](x-2)(x+10)=13\\\\\Rightarrow x^2-2x+10x-20=13\\\\\Rightarrow x^2+8x-20-13=0\\\\\Rightarrow x^2+8x-33=0\\\\\Rightarrow x^2+11x-3x-33=0\\\\\Rightarrow x(x+11)-3(x+11)=0\\\\\Rightarrow (x-3)(x+11)=0\\\\\Rightarrow x-3=0,~~~x+11=0\\\\\Rightarrow x=3, -11.[/tex]

So, the solution of the given equation is x = 3 and x = -11.

Thus, the correct option is (A). x = 3.

Answer:

True

Step-by-step explanation:

If the line is solid, it is part of the solution; if it is dotted or dashed, it is not.  Solid is ≥ ≤ while dashed is > <

Answer:

$21.25

Step-by-step explanation:

$500 * (1-.15)=$425 Sales Price

$425 * .05= $21.25 Commission

Answer:

d. Jessica can have up to 7 toppings on her pizza

Step-by-step explanation:

We know that the inequality that gives us the number of toppings Jessica can put on her pizza is [tex]0.75(t-1)+9.50\leq 14[/tex] where [tex]t\geq 1[/tex], so, to find the number of topics we just need to solve the inequality.

Let's do it step-by-step

Step 1. Subtract 9.50 from both sides of the inequality

[tex]0.75(t-1)+9.50-9.50\leq 14-9.50[/tex]

[tex]0.75(t-1)\leq 4.50[/tex]

Step 2. Distribute 0.75 to the two terms inside the parenthesis

[tex]0.75t-0.75\leq 4.50[/tex]

Step 3. Add 0.75 to both sides of the inequality

[tex]0.75t-0.75+0.75\leq 4.50+0.75[/tex]

[tex]0.75t\leq 5.25[/tex]

Step 4. Divide both sides of the inequality bu 0.75

[tex]\frac{0.75t}{0.75} \leq \frac{5.25}{0.75}[/tex]

[tex]t\leq 7[/tex]

Jessica can put up to 7 topping on her pizza.

We can conclude that the correct answer is d. Jessica can have up to 7 toppings on her pizza

Answer:

The central angle is [tex]40\°[/tex] or [tex]\frac{2}{9}\pi\ radians[/tex]

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=30\ cm[/tex]

substitute

[tex]A=\pi (30)^{2}[/tex]

[tex]A=900\pi\ cm^{2}[/tex]

step 2

Find the central angle in degrees for a sector with area [tex]100\pi\ cm^{2}[/tex]

Let

x----> the measure of the central angle in degrees

Remember that the area of the circle subtends a central angle of 360 degrees

so

using proportion

[tex]\frac{900\pi}{360}=\frac{100\pi}{x}\\ \\x=360*100\pi/900\pi \\ \\x=40\°[/tex]

step 3

Find the central angle in radians for a sector with area [tex]100\pi\ cm^{2}[/tex]

Let

x----> the measure of the central angle in radians

Remember that the area of the circle subtends a central angle of [tex]2\pi[/tex] radians

so

using proportion

[tex]\frac{900\pi}{2\pi}=\frac{100\pi}{x}\\ \\x=2\pi*100\pi/900\pi \\ \\x=\frac{2}{9}\pi\ radians[/tex]

Answer:

3/8 backyard in 1/4 hour

Step-by-step explanation:

Her rate is (1 backyard) / (2/3 hour), or 3/2 backyard per hour.

At this rate, after 1/4 hour, she will have mowed:

  3/2 backyard         1 hr

------------------------- * ---------  =  3/8 backyard in 1/4 hour

       1 hour                  4

Jesse will mow 0.375 or 37.5% of the yard after 1/4 hour given that she takes 2/3 of an hour to mow the entire yard.

To solve this problem, we first understand that to mow the entire yard, Jesse takes 2/3 of an hour. Thus, the proportion of the yard that Jesse mows in 1 hour is 1 / (2/3) = 1.5. So, in 1/4 of an hour, the proportion of the yard that Jesse mows is (1/4) * 1.5 = 0.375.

Therefore, Jesse will mow 0.375, or 37.5% of the yard after 1/4 hour.

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Answer:

177 balls

Step-by-step explanation:

Let's start with the space we need for each sphere. If we approximate the value of the area to that of a cube that has the same dimensions of the diameter

[tex]V=H*W*D=0.8*0.8*0.8= 0.51 inches3

I can calculate the volume of the box as

[tex]V=H*W*D=3*4*7.5= 90 inches3

Finally I divide the volume of the box between the volume I need for each sphere Vt/Vs= 90/0.51 ≅ 177 balls

To find the price per ounce of a 3-pound bag of sugar costing $9.12, multiply the pounds by 16 to get the total ounces (48), then divide the cost by the total ounces to get $0.19 per ounce.

To calculate the price per ounce of sugar for a 3-pound bag costing $9.12, first determine the total number of ounces, since there are 16 ounces in a pound. Multiplying 3 pounds by 16 ounces per pound gives us 48 ounces. Next, to find the price per ounce, you divide the total cost by the total number of ounces ($9.12 ÷ 48 ounces).

Performing the division gives us the cost per ounce of sugar: $9.12 divided by 48 ounces equals $0.19 per ounce.

Answer:

9π

Step-by-step explanation:

3²π = 9π

ANSWER

28.26 units square.

EXPLANATION

The area of a circle is given by

[tex]A = \pi \: {r}^{2} [/tex]

The radius of the circle is given as 3 units.

We substitute r=3 and π=3.14 into the formula to obtain:

[tex]A = 3.14 \: \times {3}^{2} [/tex]

[tex]A = 28.26sq. \: units[/tex]

Therefore the area of the circle 28.26 units square.

Hello there!

3: (12 + x) ÷ 3 or [tex]\frac{12 + x}{3}[/tex]

1: $6.30

To solve 3, look at the parts of the question.

"The quotient of.." means you are dividing.

"12 increased by a number" means you are adding a certain number to 12, which can be modeled by 12 + x.

"Divided by 3" Means the previous phrase, or 12 + x, is being divided by 3.

You can model the equation as: (12 + x) ÷ 3 or [tex]\frac{12 + x}{3}[/tex].

To solve 1, find the unit rate for the cost per bag of ice.

$3.60 / 4 bags = $0.90 a bag.

Now, multiply the unit rate by the number you are trying to find (7).

$0.90 x 7 = $6.30. This is your final answer.

I hope this was helpful, and have a great rest of your day! If you need more help with these specific questions let me know in the comments! ~ Saturns

Number Three: y=12+x/3

Number One: $0.90(7bags)= $6.30 ***See explanation below**

To solve number one, you'd have to find the unit rate.

Since you pay $3.60 for every 4 bags, you have to find the price per bag.

$3.60 / 4 bags = $0.90

Now, since unit price is proportional, you'd multiply .90 by 7 bags.

$0.90(7bags)= $6.30.

(I'm bored sooo....)

Hope this helps,

L@c3y

Answer:

Net Profit Margin: 38.89%

Net Profit: $70,000.00

Profit Percentage: 63.64%

Step-by-step explanation:

Answer:

"between 32 and 37"

Step-by-step explanation:

You can clearly look at the number line and see that each small line represents 1 unit.

Look at the box.

The left side of the box coincides with  2 units after 30, so 30 + 2 = 32

THe right side of the box coincides with  2 units after 35, so 35 + 2 = 37

Hence, the box part of the box plot contains all the values between 32 and 37

Answer:Quadratic because I think so and because it has fours in it so yeah good luck :p

Answer:

Linar

Step-by-step explanation:

it only has one variable

Answer:

y = [tex]\frac{1}{8}[/tex] x²

Step-by-step explanation:

For any point (x, y) on the parabola the focus and directrix are equidistant.

Using the distance formula

[tex]\sqrt{(x-0)^2+(y-2)^2}[/tex] = | y + 2 |

Square both sides

(x - 0)² + (y - 2)² = (y + 2)² ← expand parenthesis

x² + y² - 4y + 4 = y² + 4y + 4 ( subtract y² + 4y + 4 from both sides )

x² - 8y = 0 ( subtract x² from both sides )

- 8y = - x² ( divide both sides by - 8 )

y = [tex]\frac{1}{8}[/tex] x²

Answer:

0

Step-by-step explanation:

Solutions of systems are found where the graphs intersect one another.  These 2 functions will never intersect, therefore, there is no solution.  It is known as inconsistent.

1. True. You have to serve to earn points

2.false. You get one serve

3. True

4. True

5. Fair

Answer:

You must be serving to earn points

Question 1 options:

True  <---

False

Question 2 (1 point)

You are allowed 2 serves per side per point

Question 2 options:

True

False  <---

Question 3 (1 point)

A perfect play is Bump-Set-Spike

Question 3 options:

True  <---

False

Question 4 (1 point)

You must win by 2 points

Question 4 options:

True  <---

False

Question 5 (1 point)

If the ball hits the net it is considered:

Question 5 options:

Fair

Side-out  <---

Out

In

Step-by-step explanation:

I just did the quiz and I got %100. These were the answers. I hope it helps :)

Answer:

x = 25

Step-by-step explanation:

Step 1: Make a proportion

40/20 = 50/x

Step 2: Solve your proportion

2 = 50/x

2x = 50

x = 25

Answer:

try using a ruler

Step-by-step explanation:

Answer:

2 (2m+1) (m+2)

Step-by-step explanation:

4m² + 10m + 4

Factor out a 2

2(2m^2 +5m+2)

2 (2m+1) (m+2)

Answer:

The next three numbers are; 2,8, and 5.

Step-by-step explanation:

Answer:

fraction 2-7

0.285714285714

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

It would take Mauritania about 8 weeks to save up $16.