What is the slope of the line that contains these points?

(5,-3),(6,-1),(7,1),(8,3)

Answer:

10 units

Step-by-step explanation:

Area of smaller ∆ ,

= 1/2 * 2 * 2 = 2 u

Area of larger ∆ ,

= 1/2 * 4 * 4 = 8u

Total area = 8u + 2u = 10 units

Answer:

29 Hope this helps

Step-by-step explanation:

"Given expression is :  

First we will simplify both numerator and denominator separately using order of operations. So....

Thus the expression.... "

-Sicista

Answer:

25 boys

Step-by-step explanation:

girls to boys

7:5

35:x

set up an equation

if

35/7 = 5

then

x/5 = 5

so, multiply both sides by 5 to isolate x.

x = 25

Using the Fundamental Counting Theorem, there are 240 ways to choose general education courses from these 4 areas.

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

Considering the number of options for each course, the parameters are given as follows:

\(n_1 = 5, n_2 = 4, n_3 = 4, n_4 = 3\).

Hence the number of ways is given by:

N = 5 x 4 x 4 x 3 = 240.

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Answer:

92

Step-by-step explanation:

2x49=98-6=92

Answer:

f(7) = 92

Step-by-step explanation:

To find f(7), substitute x = 7 into the given function.

\(\begin{aligned}f(7)&=2(7)^2-6\\&=2(49)-6\\&=98-6\\&=92\end{aligned}\)

A triangular prism is a three-dimensional geometric shape that consists of two triangular bases and three rectangular faces connecting them. It is a polyhedron with six faces, nine edges, and six vertices.

The two triangular bases of a triangular prism are congruent and parallel to each other. The rectangular faces are perpendicular to the triangular bases, and their lateral edges connect the corresponding vertices of the triangular bases.

The triangular bases are identical and parallel to each other. Each base has three vertices, three edges, and one face.There are three rectangular lateral faces connecting the corresponding vertices of the triangular bases. Each lateral face has two edges and one face.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Answer:

26 points

Step-by-step explanation:

Find the mean number of points by adding up all of the points and dividing it by 5

(21 + 25 + 36 + 16 + 32) / 5

130 / 5

= 26

So, the mean number of points is 26 points

Jody's team scored 21, 25, 36, 16 and 32 points at the last five football games. What is the mean number of points Jody's team scored ?

To find the mean, first of all we have to add up all the given points and then divide by how many number of points there are. So, there are total 5 points. Hence, we have to divide all the given points by 5.

So, Mean = \( \bf \frac{21 \: + \: 25 \: + \: 36 \: + \: 16 \: + \: 32}{5} \)

Mean = \( \bf \frac{130}{5} \)

Mean = \( \bf 26 \)

The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

To answer the question, we need to know what an equation is

An equation is a mathematical expression that show the relationship between two variables.

Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S

So, L.H.S = 9cos(sin¯¹(x))

= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])

9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]

= √[9² × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - x²}]   (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)

= √(81 – 81x²)

= R.H.S

So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

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Answer:

sec t = 1/(cos t) = 1/(-3/4) = -4/3

The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer:

he can buy 8 of lilies and 12 of rose and 48 of daisies

Ali can buy 3 flowers of lilies, 3 flowers of roses, and 18 flowers of daisies.

Suppose Ali buys x flowers of lilies, y flowers of roses, and z flowers of daisies.

According to the question

x+y+z = 24......(1)

3x+2y+0.5z = 24.......(2)

Here, we have three variables but only two equations.

2(2)-(1) gives, 5x+3y = 24......(3)

Since, x, y and z can take only integer values.

Numbers that are not fractions called integers.

So, from (3) only x=3 and y=3 is possible

So, z= 24-x-y

z=24-3-3 = 18

So, Ali can buy 3 flowers of lilies, 3 flowers of roses, and 18 flowers of daisies.

Therefore, Ali can buy 3 flowers of lilies, 3 flowers of roses, and 18 flowers of daisies.

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Answer: A. 6m

Step-by-step explanation: the graph shows at the x axis that it is time. so, go to two seconds and then go up to where the line is. it goes up to 6m so that is the answer.

Answer: D , p = n (800 - 450) - 3000

Step-by-step explanation: Firstly, you have to account for how much money Rafael is making off of each computer (800 - 450). That factor is then multiplied by the variable "n" which represents the amount of computers sold. Lastly, since this is an equation to calculate his monthly profits, you have to subtract the rent that he is paying ($3000) from the total profit that he made off of selling the computers. Therefore, giving you the equation

P (profit) = n (amount of computers sold) (800-450) - 3000 (rent).

The equation that represents Rafael's monthly profit selling 'n' numbers of computers is D. P = n(800 - 450) - 3000.

An equation represents equality for the terms that are on the both side of the equal sign.

Given Rafael buys computers for 450 dollars and sells them for 800 dollars each.

He also had to pay 3000 dollars for rent and utilities for the store and the number of computers sold in each month is given by 'n'.

∴ The equation that represents his profit(P) in a month is,

P = n(800 - 450) - 3000.

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Statistical inference is the process of using data from a sample to make generalizations or draw conclusions about a larger population.

Based on the sample data, assumptions are made about the fundamental traits of the population, and the uncertainty in those assumptions is quantified using statistical techniques.

Because it enables us to forecast the future and make judgements based on incomplete data, statistical inference is crucial. For instance, with a sample of data, it enables us to confidently estimate population parameters such as averages and proportions. This can be helpful in a variety of contexts, including marketing analysis, surveys of public opinion, clinical trials, and manufacturing quality control.

By comparing the results of several groups or treatments, statistical inference also enables us to assess the efficacy of interventions or treatments.This can inform decisions about which treatments are most effective or which interventions should be implemented.

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Answer: The percentage of people surveyed who liked blue cars is 50%.

Step-by-step explanation:

Total number of people partaking in survey= 36

number of people who like blue cars= 18

therefore, fraction of people who liked blue cars= \(\frac{18}{36}\)

hence, percentage of people who liked blue cars= (18/36)*100 %

                                                                                  = 50%  

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Answer:

Percentage of people who like blue-coloured cars is 50%

Number of people who were surveyed=36

Number of people who like blue-colored cars=18

Therefore, Percentage of people who like blue cars= (Number of people who like blue cars/ Number of people who were surveyed)*100

=(18/36)*100

=50%

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Answer:

The answer is

\( \huge - \frac{7}{4} \\ \)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\ \)

From the question we have

\(m = \frac{17 - 10}{ - 2 - 2} = \frac{7}{ - 4} = - \frac{7}{4} \\ \)

We have the final answer as

\( - \frac{7}{4} \\ \)

Hope this helps you

Answer:

19

Step-by-step explanation:

Answer:

19

because it has only two factors and prime has only two factors

Answer: y=-1/1-4

Step-by-step explanation: Slope-intercept is y=mx +b so start by finding the b aka the y-intercept which is (-4,0). Each point reached is a slope of -1/1.

Answer:

Step-by-step explanation:

a. 100005

1 x 1000000 + 0 x 100,000 +  0 x 10000 + 0 x 1000 + 0 x 100 +  0 x 10 + 5 x1

1 x 10^6  + 0  x 10^5  + 0 x 10^4  + 0 x 10^3 + 0 x 10^2 +  0 x 10^1  + 5 x 1

= 100,000 + 0 + 0 +0 +0 + 5

b.  84016

 8 x 10000 + 4 x 1000 + 0 x 100 + 1 x 10 + 6 x 1

80000 + 4000 + 0 + 10 + 6

c. 9078

9 x 1000 + 0 x 100 + 7 x 10  + 8 x 1

9000 + 0 +7 + 8

d. 113

1 x 100 + 1 x 10 + 3 x 1

100 + 10 + 3

e. 75

7 x 10 + 5 x 1

70 + 5

Answer:

LxWxH

Step-by-step explanation:

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

Answer:

\( \frac{29}{3} = 9 \frac{2}{3} \)

Answer:

(2,5) instead of rotating 270 degrees you could rotate 90 degrees clockwise the figure is going to end up in quadrant 1 and the numbers stay the same put become positive

Step-by-step explanation:

Answer:

option D)

Step-by-step explanation:

when a equilateral triangle  is rotated about x-axis

rotating equilateral triangle about x-axis will lead to the formation of cone in.

the height of the equilateral triangle  will represent height of the cone.

the base of the equilateral triangle will represent the circular base of the cone

and the slant height of the cone will represented by the sides.

hence, the correct answer will cone which is option D)

Answer:

\(a \sqrt[5]{b} \)

Step-by-step explanation:

solution Given:

\( \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } \)

since i indices rule if the power is same it can be multiplied or divided.

\( \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } \)

since power is added of like terms in multiplication

\( \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } \)

again simplifying

\( \sqrt[5]{ {a}^{5} b} \)

by using indices formula

\( \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } \)

we get

\(a \sqrt[5]{b} \)

Answer:

\(a \sqrt[5]{b}\)

Step-by-step explanation:

Given expression:

\(\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}\)

\(\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:\)

\((a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}\)

As the exponents are the same,

\(\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:\)

\((a^3b^2a^2b^{-1})^{\frac{1}{5}}\)

Collect like terms:

\((a^3a^2b^2b^{-1})^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\((a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}\)

Simplify the exponents:

\((a^5b^1)^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:\)

\((a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}\)

Simplify:

\(a^1 \cdot b^{\frac{1}{5}}\)

\(a \cdot b^{\frac{1}{5}}\)

\(\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:\)

\(a \sqrt[5]{b}\)

Using Proportion the table value is,

Cheese   Number of Pizzas

3 pounds          8

18 pounds        48

22.5 pounds    60

27 pounds        72

What is a proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

We have,

3 pounds bag of cheese makes 8 pizzas.

This means,

3 pounds = 8 pizzas

1 pound = 8/3 pizzas

Now,

1 pound = 8/3 pizzas

Multiply 18 on both sides.

18 pounds = 18 x 8/3

18 pounds = 48 pizzas

1 pound = 8/3 pizzas

Multiply 22.5 on both sides.

22.5 pounds = 22.5 x 8/3

22.5 pounds = 60 pizzas

1 pound = 8/3 pizzas

Multiply 27 on both sides.

27 pounds = 27 x 8/3

27 pounds = 72 pizzas

Thus,

The number of Pizzas for 3 pounds is 8.

The number of Pizzas for 18 pounds is 48.

The number of Pizzas for 22.5 pounds is 60.

The number of Pizzas for 27 pounds is 71.

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