A line is perpendicular to y=3x-8 and intersects the point (6,1). How can we find the slope of this perpendicular line?

Answer:6

Step-by-step explanation:

Which graph represents the function f(x) = 5x + 3?

6

5

A++

4

34

2

1

o

-6 -5 -4 -3 -2 -14

1

2

3

4

5

х

2

3

The graph of the linear equation can be seen below.

Here we have the linear function:

y = 5x + 3

To graph this, we need to find two points on the equation and then connect them with a line.

By evaluating in 0 we get:

y = 5*0 + 3 = 3

So the point (0, 3) is on the line.

By evaluating on 1 we get:

y = 5*1 + 3 = 8

So we have the point (1, 8).

Now we just plot them and connect them with a line, the graph is the one below.

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Answer:

The bacteria population will change with a growth factor of 1/12 for every half an hour or 1/12 per 30 minutes. (I don't know what the options are, but anything related to the answer I gave should be right.)

Step-by-step explanation:

Simple mathematics should get you the right answer. Here we are dealing with a fraction in a fraction. The first scenario should look like this: 1/6 / 1. Basically, that looks like one-sixth over one. Obviously, if we divide 1/6 by 1, we would get 1/6 itself again and we want to know what growth factor the population changes by for every half an hour. There are 30 minutes in half an hour and 60 minutes in one hour. Let's use the simplified terms to our advantage. Now, our first scenario should look like this: 1/6 / 60. Looks better now doesn't it? (Check the linked image to see the full scenario and how I did it in this next part.) For me, I divided 60 by 30 to get the scale factor, which is 2, then I divide 2 by 1/6 to get 1/12. Finally, we have 1/12 per half an hour! If I am wrong, please let me know and I hope this helps! :D

Answer:

3015.9

Step-by-step explanation:

its 3015.9 to nearest 10th because formula of volume of cylinder is

v = pi x radius squared x height

so pi x 8 squared = 201.06192983...

REMEMBER - dont round until the end so scientific calculator is best for this

then you do (answer) x height = 3015.9

                                        (15)

hope this helped :D

Answer:

Step-by-step explanation:

A parallelogram is a shape that has two sets of parallel. There are a number of examples of parallelogram including but not limited to, square, rectangle, rhombus etc

From the question, the answer is, the shape is a rectangle. This is because the question says that the shape has its adjacent angles congruent, this means that they are supplementary(i.e they add up to 180). A rectangle is the one who fits the perfect description

Answer:

40°

Step-by-step explanation:

90°-50°=40°

Answer:

[tex] - 54[/tex]

Step-by-step explanation:

it is too easy use your calculator!(-_-メ)

Answer:

-54

Step-by-step explanation:

Answer:

12702

Step-by-step explanation:

Since there are 2 digits after the decimal in 14.60, add a decimal to the 870 and put two 0s after it (So it looks like this 870.00)

Then put the two numbers on top of each other, make sure to line up the decimals and multiply normally. When you're done, you should come out with the number 127020000. Since there is 2 digits behind the first number and 2 digits behind the second number, resulting in 4 digits, you're gonna count 4 numbers from the back of your answer and put a decimal there (so it is now 12702.0000) but you don't really need those 0s there so you can just remove them. (Answer 12702)

Hope this helped. If not, search up "Multiply a Whole Number by a Decimal | Math with Mr. J"  it might explain better

Answer:

Its A

Step-by-step explanation:

Answer:

D) 44

Step-by-step explanation:

The limit of the function k(x) as x approaches -15 from the right side is 44. Therefore, option D is correct.

Answer:27

Step-by-step explanation:

If you are adding 6$ taxthen it would be

21+6-27

Answer:

slope = -0.5

Step-by-step explanation:

There is a drop from 3 to 0. ∆y = -3

The run goes from  -2 to 4. ∆x = 6

slope = ∆y / ∆x

slope  = -3/6 = -1/2

slope = -0.5

Answer:

slope=-0.5

Step-by-step explanation:

(y2-y1)/(x2-x1)

(0-3)/(4-(-2))=-0.5

Algebra

Since the numbers are the same, you are allowed to add the exponents.

[tex] {7}^{7} \times {7}^{3} = {7}^{10} [/tex]

Answer:

[tex]7^{10}[/tex]

Step-by-step explanation:

The laws of exponents state that if two terms share a base they can be simplified. Specifically, the product exponent law says that if 2 like bases are being multiplied then the exponents can be added together. So, because the two bases are like and 7+3=10, the final answer is [tex]7^{10}[/tex].

Answer:

Option B

Step-by-step explanation:

Given the piecewise function, we see that there are two vertical asymptotes at lines x=-3 and x=3. Around the vertical asymptote x=-3, the limit of the function f(x) as x approaches -3 from the left side is ∞, and the limit of the function as x approaches -3 from the right side is -∞. The behavior of the function around the vertical asymptote x=3 is exactly the same. Therefore, option B is correct.

The statement which describes the behaviour of the function round the vertical asymptotes is b which is around x=-3+ limit of f(x)-=infinity and for limit f(x)+ is -x. Around x=3 the function behaves within the same manner as around x=-3.

Limit of a function describes the behaviour of a function as when the function behaves at a specific point.

We can see that there are two vertical asymptotes at lines x=-3 and x=3. round the vertical asymptote x=-3 the limit of the function as x approaches -3 from the left side is infinity and also the limit of the function as x approaches -3 from the proper side is -infinity.

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Answer:

4 and 5

Step-by-step explanation:

4+5=9

4*5=20

Answer:

5 an 4

Step-by-step explanation:

If you add 5+4 you get 9

And if you multiple 5×4 you get 20

Answer:

[tex]\cos(\theta)=\frac{4}{5}[/tex]

Step-by-step explanation:

Step 1:

Let us find the missing side. We know this is a right triangle, so we can use the pythagorean thereom to find the last side. Let us set 12 as variable a, 20 as variable c, and the unknown side as variable b.

[tex]a^2+b^2=c^2\\12^2_b^2=20^2\\b^2=400-144\\b^2=256\\b=\pm16[/tex]

We do know that a length can never be negative, so the side b would be 16.

Step 2:

According to SOHCAHTOA, cosine is utilizes the adjacent and hypotenuse of the given angle theta. Let us write the equation:

[tex]\cos(\theta)=\frac{adjacent}{hypotenuse} \\\\\cos(\theta)=\frac{16}{20} \\\\\cos(\theta)=\frac{4}{5}[/tex]

I hope this helps! Let me know if you have any questions :)

9514 1404 393

Answer:

  m∠RPQ = 20°

Step-by-step explanation:

Exterior angle QRS is equal to the sum of interior angles RPQ and PQR.

  7x +8 = (x +12) +(3x +20)

  3x = 24 . . . . . . . . . . . . . . . . . . subtract 4x+8

  x = 8

  m∠RPQ = (x+12)° = (8+12)°

  m∠RPQ = 20°

Answer:

6

Step-by-step explanation:

Let the first number be x

Let the second number be y

x + 2y= 4............equation 1

2x +y= 11............equation 2

From equation 1

x + 2y= 4

x = 4-2y

Substitute 4-2y for x in equation 2

2x + y= 11

2(4-2y) + y= 11

8-4y+y= 11

8-3y= 11

-3y= 11-8

-3y= 3

y= -1

Substitute -1 for y in equation 1

x + 2y= 4

x + 2(-1) = 4

x-2= 4

x = 4+2

x = 6

Hence the first number is 6

Step-by-step explanation:

everything can be found in the picture

Answer:

x = 50.8°

Step-by-step explanation:

We are given:

1.) Angle x

2.) Side opposite to angle x

3.) Hypotenuse

Therefore to find the angle x, we will use the sin inverse:

Sin(x) = Opposite / Hypotenuse

Sin(x) = 6.2/8

x = Sin⁻¹(6.2/8)

x = 50.8°

Hope this helps!

Answer:

A. y = [tex]\frac{1}{4}[/tex]x - 2

Step-by-step explanation:

10/3 = k/9

10 x 9 = 3 x k

90 = 3 k

k = 90/3

k = 30

Answer:

The 6th degree polynomial is [tex]p(x) = (x-1)^3(x-4)^2(x+3)[/tex]

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Zero 1 with multiplicity 3.

So

[tex]p(x) = (x-1)^3[/tex]

Zero 4 with multiplicity 2.

Considering also the zero 1 with multiplicity 3.

[tex]p(x) = (x-1)^3(x-4)^2[/tex]

Zero -3 with multiplicity 1:

Considering the previous zeros:

[tex]p(x) = (x-1)^3(x-4)^2(x-(-3)) = (x-1)^3(x-4)^2(x+3)[/tex]

Degree is the multiplication of the multiplicities of the zeros. So

3*2*1 = 6

The 6th degree polynomial is [tex]p(x) = (x-1)^3(x-4)^2(x+3)[/tex]

Step-by-step explanation:

[tex] {(3a - \frac{1}{6} b)}^{2} = 9 {a}^{2} - \frac{1}{2} ab - \frac{1}{2} ab + \frac{1}{36} {b}^{2} [/tex]

[tex]= 9 {a}^{2} - ab + \frac{1}{36} {b}^{2} [/tex]

Answer:

On a coordinate plane, an oval line crosses the y-axis 2 times and the x-axis two times.

Step-by-step explanation:

Vertical line test.

If you draw a vertical line, parallel to the y-axis and it crosses a line or shape twice, it is not a function.

On a coordinate plane, an oval line crosses the y-axis 2 times and the x-axis two times. The correct option is C.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

On taking the vertical line test it is observed that If you draw a vertical line, parallel to the y-axis and it crosses a line or shapes twice, it is not a function.

Therefore, on a coordinate plane, an oval line crosses the y-axis 2 times and the x-axis two times. The correct option is C.

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Answer:

22?

Step-by-step explanation: