What are the roots of the graph below?

Answer:

C

Step-by-step explanation:

[tex]y^2+4y-32=0\\(y+8)(y-4)=0\\y=4,-8[/tex]

Therefore, the answer is C. Hope this helps!

Answer:

The z score of the 65-mph speed limit is -0.75

Step-by-step explanation:

The z score is given by the relation;

[tex]z = \frac{x- \mu}{\sigma}[/tex]

Where:

Z = Normal (Standard) or z score

x = Observed speed  score

μ = Mean, expected speed

σ = Standard deviation

Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;

[tex]z = \frac{65-71}{8}= \frac{-6}{8} = -\frac{3}{4}[/tex]

Hence the z score of the 65-mph speed limit =-3/4 or -0.75.

Answer:

no real solutions

Step-by-step explanation:

Answer:

Side AB has a length of 4, and side BC has a length of 11.7

Answer:

-8

Step-by-step explanation:

-8

Answer:

6.

Step-by-step explanation:

Difference between -1 and -7.

-1-(-7) = -1 + 7 = 6

two negative signs makes it a positive sign

Answer:

Therefore the largest number that these fractions can be divided by to give them a whole number is

a) 8/15 = The largest number is 8/15

b) 18/35 = The largest number is 18/35

Step-by-step explanation:

A quotient is the result obtained by dividing two numbers.

So that the quotient obtained is a whole number we have to find out, what number they can be divided by to give them that.

Let's assume the whole number is 1

a. 8/15

8/15 ÷ x = 1

8/15 × 1/x = 1

8/15x = 1

We would cross multiply

8 = 15x

We would divide both sides by 15

8/ 15 = x

Hence the largest number that would divide 8/15 and give it a whole number = 8/15

b) 18/35

18/35÷ x = 1

18/35 × 1/x = 1

18/35x = 1

We would cross multiply

18 = 35x

We would divide both sides by 35

18/ 315 = x

Hence the largest number that would divide 18/35 and give it a whole number = 18/35

Answer:

The answer is 2/105

Step-by-step explanation:

first we have to find the LCM of both denominators. IN this case, the LCM of 15 and 35 is 105. Then we have to find the GCF of these numerators. IN this case, the GCF of 8 and 18 is 2.

Now, put the GCF you found over the LCM.

ANSWER: 2/105

This fraction is the largest number you can divide both numbers by to get a whole number.

Hey there! I'm happy to help!

To find the volume of a cone, you multiply the base by the height and then divide by three.

The base of a cone is a circle. To find the area of a circle, we square the radius and then multiply it by pi (we will use 3.14). Let's find the base below.

6²=36

36×3.14=113.04

Now, we multiply by the height.

113.04×8=904.32

Finally, we divide by three.

904.32÷3=301.44

Therefore, the volume of this cone is about 301.44 units cubed.

Now you can find the area of cones! I hope that this helps! Have a wonderful day!

Answer:

301.44

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

7*4=28

2*4=8

Answer:

c=8

Step-by-step explanation:

Using cross. multiplication

multiply 2 by 28 2x28=56

Multiple c by 7 cx7=7c

divide both sides by 7

c=8

Answer:

14/50 or 28%

Step-by-step explanation:

THERE ARE 14 MALES WHO CHOSE INVISIBILITY AND 50 MALES IN TOTAL.

EZPZ

Answer:

There are a total of 2500 cups

Step-by-step explanation:

10% of the cups are green

you can set up a equation for this

x = total cups

.10x = 250

multiply both sides by 10 to make x a whole number

x = 2500

Answer:

Step-by-step explanation:

Tan θ = [tex]\sqrt{13} \div \sqrt{2}[/tex] = 2.5495

Therefore θ = [tex]Tan^{-1}[/tex] (2.5495) =68.5832°

Answer:

Tan θ =  2.5495097...

​

Answer:

7 is the most common roll with two six-s

( I hope this helped <3 )

Answer:

7/8

Step-by-step explanation:

I think the most common are 7/8.

Step-by-step explanation:

If the log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio.

Let a = log82x, b = log4x and c = log2x

If a = log8 2x; 8^a = 2x... (1)

If b = log4 x; 4^b = x ... (2)

If c = log2 x; 2^c = x...(3)

Since a, b c are in GP, then b/a = c/b

Cross multiplying:

b² = ac ...(4)  

From eqn 1, x = 8^a/2

x = 2^3a/2

x = 2^(3a-1)

From eqn 2; x = 4^b

x = 2^2b

From eqn 3: x = 2^c

Equating all the values of x, we have;

2^(3a-1) = 2^2b = 2^c

3a-1 = 2b = c

3a-1 = c and 2b = c

a = c+1/3 and b = c/2  

Substituting the value of a = c+1/3 and b = c/2 into equation 4 we have;

(c/2)² = c+1/3×c

c²/4 = c(c+1)/3

c/4 = c+1/3

Cross multiplying;

3c = 4(c+1)

3c = 4c+4

3c-4c = 4

-c = 4

c = -4  

Substituting c = -4 into equation 3 to get the value of x we have;

2^c = x

2^-4 = x

x = 1/2^4

x = 1/16    

Since the number x can be written as m/n, then x = 1/16 = m/n

This shows that m = 1, n = 16

m+n = 1+16

m+n = 17  

The required answer is 17.  

The value of m+n in which m and n are relatively prime positive integers is 17.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

There is a unique positive real number x such that the three numbers log82x, log4x and log2x, in that order, form a geometric progression with a positive common ratio. The progression is,

[tex]\log_82 x,\log_4x, \log_2x[/tex]

The above numbers are in geometric progression. Thus, the ratio of first two terms will be equal to the ratio of next two terms as,

[tex]\dfrac{\log_4x}{\log_82x}=\dfrac{\log_2x}{\log_4x}\\(\log_4x)^2={\log_2x}\times{\log_82x}\\[/tex]

Using the base rule of logarithmic function,

[tex]\left(\dfrac{\log x}{\log 4}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log8}\\\left(\dfrac{\log x}{\log 2^2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{\log2^3}[/tex]

Using the Power rule of logarithmic function,

[tex]\left(\dfrac{\log x}{2\log 2}\right)^2=\dfrac{\log x}{\log2}\times\dfrac{\log2x}{3\log2}\\\dfrac{\log x}{4}=\dfrac{\log 2+\log x}{3}\\3\log x=4(\log2x)\\\log x^3=\log(2x)^4\\x^3=16x^4\\x=\dfrac{1}{16}[/tex]

The number x can be written as

[tex]\dfrac{m}{n}[/tex]

Here, m and n are relatively prime positive integers. Thus, the value of m+n is,

[tex]m+n=1+16=17[/tex]

Hence, the value of m+n in which m and n are relatively prime positive integers is 17.

Learn more about the geometric sequence here;

https://brainly.com/question/1509142

Answer:

3 cones

Step-by-step explanation:

This is why the formula for the volume of a cone is 1/3 (π×r^2)× h, while the volume for a cylinder is (π× r^2)× h, respectively.

Answer:

C) 3 Cones.

Explanation:

Hope this helps! :)

Answer: x = 2

Step-by-step explanation:

[tex]10x - 15x + 5= -45 + 40[/tex]

subtract 5

[tex]10x - 15x= -45 + 40-5[/tex]

Combine like terms;

[tex]-5x=-10[/tex]

Divide by -5

[tex]x=\frac{-10}{-5}\\ x=2[/tex]

Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

[tex]10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2[/tex]

Answer: [tex]96ft^2[/tex]

Step-by-step explanation:

We have a composite figure. We have a rectangle and a triangle. Calculate each of these figures' areas individually and add them together.

Rectangle:

length=10ft

width=8ft

[tex]Formula:A=l*w\\A=(10ft)(8ft)\\A=80ft^2[/tex]

----------------------------------------------------------

Triangle:

base: 4ft

height: 8ft

[tex]A=\frac{hb}{2}[/tex]

[tex]A=\frac{(8ft)(4ft)}{2}[/tex]

[tex]A=\frac{32ft^2}{2}[/tex]

[tex]A=16ft^2[/tex]

-------------------------------------------------------------

Add them:

[tex]80ft^2+16ft^2=96ft^2[/tex]

Answer:

True

Step-by-step explanation:

Let A denotes the point (1,7)

Let B denotes the point (5,5)

We are supposed to find The length of the line segment containing the points

Formula : [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex](x_1,y_1)=(1,7)\\(x_2,y_2)=(5,5)\\ d = \sqrt{(5-1)^2+(5-7)^2}\\ d = \sqrt{4^2+(-2)^2}\\ d = \sqrt{4^2+(-2)^2}\\d=4.47[/tex]

So,The length of the line segment containing the points (1,7) and (5,5)  is 4.47 units is true.

Hence Option A is true

Answer:

Step-by-step explanation:

Area of a parallelogram = base × height

From the question

base = 14 cm

height = 5 cm

Substituting the values into the above formula we have

Area = 14 cm × 5 cm

Hope this helps you

Answer:

1,750

Step-by-step explanation:

Answer:

Step-by-step explanation:

In this problem, we have to find the area of an square adjacent to the third side of the right triangle.

To solve this problem, we need to use Pythagorean's Theorem, beacuse it's about a right triangle. Also, this theorem is about square areas, that's the geomtrical meaning of it.

[tex]h^{2} =32 \ u^{2} + 32 \ u^{2} = 64\ u^{2} \\h=\sqrt{64 \ u^{2} } =8u[/tex]

Therefore, the area of a square adjacent to the third side is 64 square units.

Answer:the answer is 8

Step-by-step explanation:

Answer:

12.9 [tex]in^{2}[/tex]

Step-by-step explanation:

So to find the area of this triangle, you will need to use the equation

Area = [tex]\frac{1}{2}[/tex]c*b*sin(A) = [tex]\frac{1}{2}[/tex]a*b*sin(C)

Here, we have ∠A, ∠C, and side c

We can use the fact that [tex]\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex] so solve for the other variables we do not have.

First we can find the other angle B. Since ∠A + ∠B + ∠C = 180°,

∠B = 180° - ∠A - ∠C, which is ∠B = 180° - 115° - 24° = 41°

Now that we have all three angles, we can solve for the sides

Since we only have side c, we will manipulate the equation with c and one of the others to solve for a or b. Let's solve for side b first.

Since [tex]\frac{b}{sin(B)} =\frac{c}{sin(C)}[/tex], solving for b would give us [tex]b=\frac{csin(B)}{sin(C)}[/tex]. Then plugging in our values we get [tex]\frac{4.2sin(41)}{sin(24)}[/tex]= 6.77 = b

Now we can solve for the remaining side, a, using the same method.

Since [tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}[/tex], solving for a would give us [tex]a=\frac{bsin(A)}{sin(B)}[/tex]. Then plugging on our values we get [tex]\frac{6.77sin(115)}{sin(41)}[/tex]= 9.36 = a

Now that we have all our angles and sides, we can plug in our numbers to either of our area equations ⇒

Area =[tex]\frac{1}{2}[/tex]c*b*sin(A)= [tex]\frac{1}{2}[/tex](4.2)(6.77)sin(115) = 12.9[tex]in^{2}[/tex] or [tex]\frac{1}{2}[/tex]a*b*sin(C) = [tex]\frac{1}{2}[/tex](9.36)(6.77)sin(24) = 12.9[tex]in^{2}[/tex]

Answer:

x = -9

Step-by-step explanation:

-4x = -1/2(10x + 18)

Distribute

-4x= - 5x -9

Add 5x to each side

-4x+5x = -5x+5x -9

x = -9

There's some unknown (but derivable) system of equations being modeled by the two lines in the given graph. (But we don't care what equations make up these lines.)

There's no solution to this particular system because the two lines are parallel.

How do we know they're parallel? Parallel lines have the same slope, and we can easily calculate the slope of these lines.

The line on the left passes through the points (-1, 0) and (0, -2), so it has slope

(-2 - 0)/(0 - (-1)) = -2/1 = -2

The line on the right passes through (0, 2) and (1, 0), so its slope is

(0 - 2)/(1 - 0) = -2/1 = -2

The slopes are equal, so the lines are parallel.

Why does this mean there is no solution? Graphically, a solution to the system is represented by an intersection of the lines. Parallel lines never intersect, so there is no solution.

Answer:

Exponential decay is the decrease in a quantity according to the law. (1) for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value.

Answer:

When a population or group of something is declining, and the amount that decreases is proportional to the size of the population, it's called exponential decay. In exponential decay, the total value decreases but the proportion that leaves remains constant over time.

Step-by-step explanation:

Answer:

C. Estimate the probability using your simulation.

Step-by-step explanation:

Answer:

equal to ab

Step-by-step explanation:

The area of a parallelogram is Area =  ab

therefore, the area is ab

Answer:

Less than ab

Step-by-step explanation:

Answer: C

Step-by-step explanation:

[tex]\frac{3a}{4}+\frac{2a}{3}-\frac{a}{12}[/tex]

Find the least common denominator of 4, 3, and 12.

4-3-12 | 3

4-1-4   | 4

1-1-1    |-------- 12

The first fractions needs to be multiplied by 3, and the second fraction, by 4

[tex](\frac{(3a)*3}{(4)*3})+(\frac{(2a)*4}{(3)*4})-\frac{a}{12}[/tex]

Solve;

[tex]\frac{9a}{12}+\frac{8a}{12}-\frac{a}{12}[/tex]

Add the fractions with positive signs and subtract the one with negative sign.

[tex]\frac{(9a+8a)-a}{12}[/tex]

Solve;

[tex]\frac{17a-a}{12}=\frac{16a}{12}[/tex]

Simplify by 4;

16/4=4

12/4=3

[tex]\frac{4a}{3}[/tex]

Answer:

(4a)/3

Step-by-step explanation:

3a/4+2a/3-a/12

find L.C.M

9a+8a-1a/12=16a/12

16a/12=(4a)/3

Answer:

the formulae for the volume of a cylinder= πr²h

so we then put the figures at their respective positions. and for the pie we put either 22/7 or 3.143 or 3.14