What is the slope of the line that passes through the points (4, 10)(4,10) and (1, 10) ?(1,10)? Write your answer in simplest form.

A) The Slope is: 2

B) The interpretation of the slope is that there are two races for each number of track meet.

C) The y-intercept from the graph is at: y = 4

D) Equation of the line is: y = 2x + 4

The general form of equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the given graph, we can see that the slope is gotten from the formula:

A) Slope = (y₂ - y₁)/(x₂ - x₁)

Thus:

Slope = (10 - 4)/(3 - 0)

Slope = 6/3

Slope = 2

B) The interpretation of the slope is that there are two races for each number of track meet.

C) The y-intercept from the graph is at: y = 4

D) Equation of the line is:

y = 2x + 4

Read more about Slope at: https://brainly.com/question/3493733

#SPJ1

1. The algebraic expression for the word phrase  the quotient of r and 12 is r ÷ 12.

2. The word phrase for the algebraic expression is nine fewer than two times a number t.

Given,

1. The word phrase = the quotient of r and 12

We have to write an algebraic expression for the word phrase.

Here,

Quotient means the answer of a division.

That is, if a ÷ b = c. Then the quotient is c.

So, algebraic expression for the word phrase  the quotient of r and 12 is r ÷ 12.

2. The algebraic expression = 2t - 9

We have to write the word phrase for the algebraic expression.

2t - 9, that is,

nine fewer than two times a number t.

Learn more about algebraic expression and word phrase here:

https://brainly.com/question/10904792

#SPJ1

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

learn more on kite here: https://brainly.com/question/27975644

#SPJ9

Answer:

The answer is 1,2,3, and 5

Step-by-step explanation:

The person above me answered it correctly, I basically just copied and pasted it onto here :)

Options A and E are categorical.

Is your job as an IT administrator stressful?

Have you ever considered switching careers because of on-the-job stress?

Given,

- Is your job as an IT administrator stressful?

- What is your biggest source of stress?

- How has your job impacted your personal life?

- In the past week, how many hours of overtime did you work?

- Have you ever considered switching careers because of on-the-job stress?

We need to find which options are categorical.

The data that can be divided into groups are called categorical data.

Example:

People who know how to drive and who don't know how to drive.

We can have two groups here.

Yes and No.

Find which of the following are categorical.

- Is your job as an IT administrator stressful?

We can have two groups:

Yes and No.

It is categorical data.

- What is your biggest source of stress?

We can have different answers which can not be categorized into groups.

It is not categorical data.

- How has your job impacted your personal life?

Everyone will have different answers so it is not categorical data.

- In the past week, how many hours of overtime did you work?

Everyone will have a different answer so we can not make groups.

It is not categorical data.

- Have you ever considered switching careers because of on-the-job stress?

We can have answers as yes and no so we can make two groups

It is categorical data.

Thus Options A and E are categorical.

Is your job as an IT administrator stressful?

Have you ever considered switching careers because of on-the-job stress?

Learn more about categorical data here:

https://brainly.com/question/19587873

#SPJ2

Answer:

The answer is A, ST and WX

Step-by-step explanation:

The answer is A because ST and WX are the same size and shape, just mirrored.

Answer:

6

Step-by-step explanation:

Answer:

  f(x) = 3x² -x +4

Step-by-step explanation:

Use (x+1) for x and simplify.

  f((x+1) -1) = 3(x +1)² -7(x +1) +8

  f(x) = 3(x² +2x +1) -7x -7 +8

  f(x) = 3x² -x +4

Answer:

a)  $497.70

b)  392.4 square feet

c)  $1,200

Step-by-step explanation:

A regular octagon has 8 sides of equal length.

Given each side of the octagon measures 9 feet in length, and one side does not have a railing, the total length of the railing is 7 times the length of one side:

\(\textsf{Total length of railing}=\sf 7 \times 9\; ft=63\;ft\)

If the railing sells for $7.90 per foot, the total cost of the railing can be calculated by multiplying the total length by the cost per foot:

\(\textsf{Total cost of railing}=\sf 63\;ft \times \dfrac{\$7.90}{ft}=\$497.70\)

Therefore, the cost of the railing is $497.70.

\(\hrulefill\)

To find the area of the regular octagonal gazebo, given the side length and apothem, we can use the area of a regular polygon formula:

\(\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\;s\;a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}\)

Substitute n = 8, s = 9, and a = 10.9 into the formula and solve for A:

\(\begin{aligned}\textsf{Area of the gazebo}&=\sf \dfrac{8 \times 9\:ft \times10.9\:ft}{2}\\\\&=\sf \dfrac{784.8\;ft^2}{2}\\\\&=\sf 392.4\; \sf ft^2\end{aligned}\)

Therefore, the area of the gazebo is 392.4 square feet.

\(\hrulefill\)

To calculate the cost of the gazebo's flooring if it costs $3 square foot, multiply the area of the gazebo found in part (b) by the cost per square foot:

\(\begin{aligned}\textsf{Total cost of flooring}&=\sf 392.4\; ft^2 \times \dfrac{\$3}{ft^2}\\&=\sf \$1177.2\\&=\sf \$1200\; (nearest\;hundred\;dollars)\end{aligned}\)

Therefore, the cost of the gazebo's flooring to the nearest hundred dollars is $1,200.

a. To find the perimeter of the gazebo, we can use the formula P = 8s, where s is the length of one side. Substituting s = 9, we get:

P = 8s = 8(9) = 72 feet

Since one side is open, we only need to find the cost of railing for 7 sides. Multiplying the perimeter by 7, we get:

Cost = 7P($7.90/foot) = 7(72 feet)($7.90/foot) = $4,939.20

Therefore, the cost of the railing is $4,939.20.

b. To find the area of the gazebo, we can use the formula A = (1/2)ap, where a is the apothem and p is the perimeter. Substituting a = 10.9 and p = 72, we get:

A = (1/2)(10.9)(72) = 394.56 square feet

Therefore, the area of the gazebo is 394.56 square feet.

c. To find the cost of the flooring, we need to multiply the area by the cost per square foot. Substituting A = 394.56 and the cost per square foot as $3, we get:

Cost = A($3/square foot) = 394.56($3/square foot) = $1,183.68

Rounding to the nearest hundred dollars, the cost of the flooring is $1,184. Therefore, the cost of the gazebo's flooring is $1,184.

#SPJ1

Answer:

y° = 130°

Step-by-step explanation:

The angel adjacent to y° corresponds with the given measure of degree that the brace makes with the wire.

Thus, the measure of the angle adjacent to y° = 50° (Corresponding angles are congruent)

y° and the angle adjacent to y° form a linear pair on a straight line.

Therefore:

y° + 50° = 180° (linear pair)

subtract 50 from each side

y° + 50° - 50° = 180° - 50°

y° = 130°

Answer:

a. = 36km

b. Perimeter = 108km

c. Area = 486km^2

Step-by-step explanation:

Pythagoras theorem

a^2 + b^2 = c^2

27^2 + b^2 = 45^2

b^2 = 45^2 - 27^2

b^2 = 1296

b = \(\sqrt{1296}\)

b = 36km

Perimeter

a + b + c

27 + 36 + 45 = 108

Perimeter = 108km

Area = \(\frac{ab}{2}\)

Area = \(\frac{27 * 36}{2}\)

Area = \(\frac{972}{2}\)

Area = 486km^2

The factorization of equations 54 - 18 is 18(3 - 1). The value is 36.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

The number given is illustrated as:

54 - 18.

It should be noted that the common factor between the numbers is 18. This will be:

54 - 18 = 18(3 - 1)

The value will be:

= 18(3 - 1)

= 18(2)

= 36

Learn more about factor on:

brainly.com/question/25829061

#SPJ1

Answer:

x = 12

Step-by-step explanation:

It is a 90° angle which means that both of the angles need to add up to 90. 90-20 =70. 6×12 = 72.

6×9= 72

72-2 = 70

It adds up.

Hope this helps.

Answer:

\(\bold{x = \frac{-5 \± i\sqrt7}{2}}\)

Step-by-step explanation:

x^2 + 5x + 8=0

Comparing with ax^2+bx+c=0

we get a = 1, b = 5, and c = 8.

Using the quadratic formula, we have:

\(x = \frac{-b \± \sqrt{(b^2- 4ac)}}{ 2a}\)

Substituting these values, we get:

\(x =\frac{ -5 \± \sqrt{5^2 - 4*1*8}}{2*1}\)

\(x = \frac{-5 \± \sqrt{25 - 32}}{ 2}\)

\(x = \frac{-5 \± \sqrt{-7}}{ 2}\)

\(x = \frac{-5 \± i\sqrt7}{2}\)

Therefore, the solutions are:\(x = \frac{-5 \± i\sqrt7}{2}\)

The guests in the birthday party ate 33 cookies.

We know that Mrs. Smith made 6 1/4 dozen cookies and there were 3 1/2 dozen cookies left.

Let's first convert these fractions to a common denominator of 4, so we can easily subtract them.

6 1/4 dozen = 25/4 dozen

3 1/2 dozen = 14/4 dozen

Now we can subtract the number of cookies that were left from the number of cookies that were made:

25/4 - 14/4 = 11/4 dozen

To find out how many cookies this represents, we need to multiply by the number of cookies in one dozen.

There are 12 cookies in one dozen, so:

11/4 x 12 = 33

Therefore, the guests ate 33 cookies.

Read more about fractions at

https://brainly.com/question/1330447

#SPJ1

Answer:

\(P(t) = 100e^{0.0251t}\)

The doubling time is of 27.65 minutes.

Step-by-step explanation:

Exponential equation of growth:

The exponential equation for population growth is given by:

\(P(t) = P(0)e^{kt}\)

In which P(0) is the initial value and k is the growth rate.

A freshly inoculated bacterial culture of Streptococcus contains 100 cells.

This means that \(P(0) = 100\). So

\(P(t) = 100e^{kt}\)

When the culture is checked 60 minutes later, it is determined that there are 450 cells present.

This means that \(P(60) = 450\), and we use this to find k. So

\(450 = 100e^{60k}\)

\(e^{60k} = 4.5\)

\(\ln{e^{60k}} = \ln{4.5}\)

\(60k = \ln{4.5}\)

\(k = \frac{\ln{4.5}}{60}\)

\(k = 0.0251\)

So

\(P(t) = 100e^{0.0251t}\)

Doubling time:

This is t for which P(t) = 2P(0) = 200. So

\(200 = 100e^{0.0251t}\)

\(e^{0.0251t} = 2\)

\(\ln{e^{0.0251t}} = \ln{2}\)

\(0.0251t = \ln{2}\)

\(t = \frac{\ln{2}}{0.0251}\)

\(t = 27.65\)

The doubling time is of 27.65 minutes.

Answer:

im study about history it was my favourite subject!

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

for more such questions on volume

https://brainly.com/question/1972490

#SPJ8

Answer:

238 square feet

Step-by-step explanation:

Answer:

245 square feet.

Step-by-step explanation:

7 times 7 is 49

49 times 5 because there is 5 feet

= 245

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

Learn more about limits here:

https://brainly.com/question/12211820

#SPJ1

From the solution;

x = 62.62°

y = 8.9 cm

The sine rule (also known as the law of sines) is a mathematical formula that relates the sides and angles of a triangle. Specifically, it relates the ratios of the lengths of the sides of a triangle to the sine of the opposite angles.

By the use of the sine rule;

a/Sin A = c/Sin C

Sin C = cSin A/a

C = Sin-1(cSin A/a)

C = Sin-1(7.8 * sin 66.4/9.2)

C = 50.98°

B = 180 - (50.98° + 66.4)

B = 62.62°

Then;

a/Sin A = b/Sin B

9.2/Sin66.4 = b/Sin 62.62

b = 9.2 * Sin 62.62/Sin66.4

b = 9.2 * 0.89/0.92

b = 8.9 cm

Learn more about sine rule:https://brainly.com/question/30339234

#SPJ1

Answer:

Yes, it is a true statement

Step-by-step explanation:

Since two negatives cancel out the equation would be

4 + 10 and that equals 14.

So the statement is true!

Answer:

x = 8

Step-by-step explanation:

The goal is to make x by itself (isolate)

2x + 6 = 22

first, subtract 6 from each side

2x = 22 - 6

2x = 16

next, divide each side by 2

x = 16 / 2

x = 8

Where the daily growth factor is 1.15 and the starting height in inches is 7.

a. Given by, the function that calculates the height of the beanstalk in relation to the time since Gregory planted it.

\(f(t) = 7(1.15)^t\)

where the daily growth factor is 1.15 and the starting height in inches is 7.

B). The following ratios can be calculated using the formula from section (a):

f(1)/f(0) = (71.15¹)/(71.15⁰) = 1.15

f(2)/f(1) = (71.15²)/(71.15¹ = 1.15

f(1)/f(1) = (71.15¹)/(71.15¹) = 1

\(f(9.56)/f(8.56) = (71.15^{9.56})/(71.15^{8.56})\) ≈ 1.15

\(f(8.56)/f(8.55) = (71.15^{8.56})/(71.15^{8.55})\) ≈ 1.15

c. For the any value of z, we have:

\(f(z+1)/f(z) = (71.15^{(z+1)})/(71.15^z)\) = 1.15

and

\(f(z)/f(z-1) = (71.15^z)/(71.15^{(z-1)})\) = 1.15

For question 6:

a. As a increases throughout the function's domain, f(z) [Select an answer]

Since the base of the exponential function is less than 1 (0.69 < 1), as x increases, f(x) will approach 0.

b. The 1-unit growth factor of f is

The 1-unit growth factor for f is 0.69, since f(x+1)/f(x) = 0.69.

c. The -unit growth factor of f is

The 1/2-unit growth factor for f is (0.69)¹/₂, since f(x+1/2)/f(x) = (0.69)¹/₂.

d. The 6-unit growth factor of f is

The 6-unit growth factor for f is (0.69)⁶, since f(x+6)/f(x) = (0.69)⁶.

e. The 6-unit percent change of  f is

The 6-unit percent change for f is ((0.69)^6 - 1) * 100%, which is approximately -38.77%.

To know more about growth factor visit:

brainly.com/question/30859558

#SPJ1

Answer:

0/6 <--------------------------

\(500/30+200=16.\bar{6}+200=216.\bar{6}\)

Answer: one senior ticket is $8 and one student ticket is $14

Hope this helps a little

The sine equation for the object's height is given as follows:

d = -5sin(0.24t).

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The amplitude for this problem is of 5 inches, hence:

A = 5.

The period is of 1.5 seconds, hence the coefficient B is given as follows:

2π/B = 1.5

B = 1.5/2π

B = 0.24.

The function starts moving down, hence it is negative, so:

d = -5sin(0.24t).

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

Answer:

is dependent

Step-by-step explanation:

right on edge 2020

Answer:

answer to pt.1 and pt.2 of this question in the photo.

Step-by-step explanation: