Explain how to find the equation of a line given the point (5, 3) and it has a y-intercept of 13.

In a case whereby baseball game receives 3 raffle tickets and a $2 certificate for the team store. A group of people receives 39 raffle tickets the amount of money in certificates the group receive is  $26.

If one baseball game receives 3 raffle tickets and a $2 certificate for the team store, then we can say that each raffle ticket is worth 2/3 dollars ($2 divided by 3 tickets).

So, for 39 raffle tickets, the group would receive (39 x 2/3) = $26

Therefore, the amount of money in certificates the group receive is  $26

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Answer:

-16x+3y

Step-by-step explanation:

sum=add

(-6x + 9y)+(-10x – 6y)

Combine like terms

-6x+(-10x)

-16x

9y+(-6y)

3y

-16x+3y

Answer:

Area = 1808.64 cm

Step-by-step explanation:

Circumference of a circle = 2πr

Circumference = 150.72

π = 3.14

r = radius

150.72 = 2 x 3.14 x r

150.72 = 6.28 r

r = 150.72/6.28

r = 24cm

Radius = 24

Area of a circle = πr²

Area = 3.14 x 24²

Area = 3.14 x 576

Area =1808.64 cm

Answer:

1808.64 cm

Step-by-step explanation:

tried it on khan and it worked

Answer:

306 square meters.

Step-by-step explanation:

Divide the shape into 2 rectangles.

Lets do the one that is sticking to the top first.

The area is 6 * 15, which is 90.

Lets do the second rectangle. The area is:

27 * 8, which is 216.

Add them all up (90 + 216), which is 306.

Answer:

306m²

Step-by-step explanation:

Split the shape into two rectangles with the accureate lengths

The top-most of the two rectangles with length 6m and width 15m:

6 x 15 = 90 m² (area of rectangle A)

The bottom rectangle:

27(full length) x 8m(full width) = 216m²

Add the two areas together for the full shape

216 + 90 = 306m²

Answer:

-9/2

Step-by-step explanation:

Hope this helped!

y=\(\frac {-9}{2}\)

Answer:

solution given :

\(-\frac {1}{y+5}=-2 \)

here - and - will be cancelled and former

\(\frac {1}{y+5}=2 \)

now doing criss cross multiplication

we get

1=2 (y+5)

opening bracket

1=2y+10

1-10=2 y

y=\(\frac {-9}{2}\)

Answer:

graph D.

Step-by-step explanation:

The inequality that is being shown in the question means that the value of x is equal to or greater than 9. Greater values are represented as all of the values to the right of a certain number. On a number line "equal to" is represented by  a closed circle. Therefore, with this knowledge we can see that out of all of the provided options the only one that follows these set of rules would be graph D.

Answer:

y + 4 = -2(x + 1)

General Formulas and Concepts:

Algebra I

Coordinate Planes

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify variables

Point (-1, -4)

Slope m = -2

Step 2: Find Equation

Step 3: Graph

See Attachment

Use the point (-1, -4) as your starting point and use rise over run method to trace a line.

well, we know all three points are colinear, so the slope from the first two points is the same slope from either to the (c , -9) point, let's check the slope of the first two points given

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{(-5)}}} \implies \cfrac{1 +3}{10 +5}\implies \cfrac{4}{15}\)

so then, the slope from say hmmmm let's use (-5 , -3), the slope from (-5 , -3) and (c , -9) must also be the same 4/15

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{-9}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-9}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{c}-\underset{x_1}{(-5)}}} \implies \hspace{5em}\cfrac{-9 +3}{c +5}~~ = ~~\stackrel{slope}{\cfrac{4}{15}}\implies \cfrac{-6}{c+5}=\cfrac{4}{15} \\\\\\ -90=4c+20\implies -110=4c\implies \cfrac{-110}{4}=c\implies -\cfrac{55}{2}=c\)

first, we draw the triangle

To solve this we are to apply the Pythagorean theorem, which states

From the triangle;

hyp = 37 in, opp = 12 in, Adj = x in

hence,

Therefore,

The horizontal distance = 35 in

Answer:

c hope it helps

Step-by-step explanation:

So, the height of the pedestal is ((h1−h2)tanβ+h2tanα)/tanα−tanβ.

To find the height of the pedestal, we can use the concept of angles of elevation. The angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizontal.

From the given information, we know that the angles of elevation of the top and bottom of the statue from a point h2 metres above the ground level are α and β respectively.

We can use the tangent of the angle of elevation to find the height of the object. The tangent of the angle of elevation is equal to the height of the object divided by the distance from the base of the object to the point of observation.

Let's call the height of the pedestal as "h3"

So we can write the following equations:

h1/((h3+h1)-h2)= tan(α)

h1/((h3)-h2)= tan(β)

By solving the above equations we can get the value of h3 which is the height of the pedestal.

((h1−h2)tanβ+h2tanα)/tanα−tanβ

This is the final equation which gives the height of the pedestal.

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Answer:

The value of x is 20 degrees.

Step-by-step explanation:

The three angles of a triangle must equal 180 degrees.

100 + 40 + 2x = 140 + 2x

180 - 140 = 40 (goal)

2(x) = 40

2(20) = 40

A) 20 degrees

Answer:

θ = 36.86°

Step-by-step explanation:

Given that,

The shadow of a 60 foot pole is a 100 feet long.

We need to find the angle of elevation from the end of the shadow to the top of the pole.

Height, h = 60 foot

Hypotenuse, H = 100 feet

Using trigonometry to find it.

\(\sin\theta=\dfrac{\text{Height}}{\text{Hypotenuse}}\\\\\sin\theta=\dfrac{60}{100}\\\\\theta=\sin^{-1}(\dfrac{60}{100})\\\\\theta=36.86^{\circ}\)

So, the angle of elevation is 36.86 degrees.

Length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

The area of Rectangle is length times of width

Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.

Here, the dimensions of the rectangles are the same.

The width of the two rectangles is W=2W+2W=4W

The length of the two rectangles is L=L+L+L=3L

Because the adjacent side has a common length.

3L+4W=200

3L=200-4W

Divide both sides by 3

L=(200-4W)/3

Let us form an equation using the area of rectangle formula:

A=2LW

=2(200-4W)/3.W

A=400-8W²/3

Let us differentiate to get the area to be maximized dA/dW=0

1/3×(400-8W²)=0

1/3(400-16W)=0

400-16W=0

400=16W

Divide both sides by 16

W=25

The width is 25 feet.

Substitute W value in equation to get L value:

L=200-4×25/3

=200-100/3

=100/3

=33.33

The length is 33.33 feet.

Now let us find the maximum area

A=2LW

=2×33.33×25

=1666.66

Hence, length is 33.33 feet and width is 25 feet are dimensions should

be used so that the enclosed area will be a maximum.

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The numbers are 1 and 8.

We have,

Let's assume the lesser number as "x" and the greater number as "8x".

According to the given information, when the lesser number is subtracted from the greater, the result is 2 more than 5 times the lesser number:

8x - x = 5x + 2

Simplifying the expression:

7x = 5x + 2

Subtracting 5x from both sides:

2x = 2

Dividing both sides by 2:

x = 1

So, the lesser number is 1 and the greater number is 8 times that, which is 8.

Therefore,

The numbers are 1 and 8.

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Answer:

Option A

Step-by-step explanation:

       Pick any two points on the line.

       (3 , 0) ⇒ x₁ = 3 & y₁ = 0

        (0,-2) ⇒ x₂ = 0 & y₂ = -2

Find the slope using the formula,

      \(\boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}\)  

                   \(\sf =\dfrac{-2-0}{0-3}\\\\\\=\dfrac{-2}{-3}\\\\\\=\dfrac{2}{3}\)

      Slope-point form of a line: y - y₁ = m(x - x₁)

Substitute slope and the point in the above equation,

              \(y - 0 = \dfrac{2}{3}(x - 3)\\\\ ~~~~~~ y= \dfrac{2}{3}x-\dfrac{2}{3}*3\\\\\\~~~~~~\boxed{ y = \dfrac{2}{3}x-2}\)

This is in slope intercept form: y = mx + b.

For given pair of lines:

Line 1 and Line 2 => parallel

Line 1 and Lin2 3 => parallel

Line 2 and Line 3 => parallel

In this question, we have been given equations of lines.

Line 1: y = -3/2x - 6

Line 2: 2y = -3x + 3

we can write it as,

y = -3/2x + 3/2

Line 3: 6x + 4y = -8

           4y = -6x - 8

            y = -3/2 x - 2

We know that the product of slopes of perpendicular lines is -1.

And the slopes of parallel lines are equal.

By comparing given line s with slope -intercept form of equation of line i.e., y = mx + c

Slope of line 1 = -3/2

slope of line 2 = -3/2

slope of line 3 = -3/2

This means, all lines are parallel to each other.

Therefore, for given pair of lines:

Line 1 and Line 2 => parallel

Line 1 and Lin2 3 => parallel

Line 2 and Line 3 => parallel

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Answer:

40 students are in the class :)

Step-by-step explanation:

35%=14

1%=14/35=0.4

0.4*100=40=100%

Answer:

8 i think

Step-by-step explanation:

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The man still owes R87,726 in taxes.

To calculate the tax amount the man still owes, we need to determine his taxable income first.

Gross income: R500,000

Less: PAYE deductions (17% of gross income): R500,000 * 0.17 = R85,000

Taxable income: R500,000 - R85,000 = R415,000

Next, we can use the tax table information provided to calculate the tax owed based on the taxable income.

Tax owed: R93,135 + 36% of (taxable income - R393,200)

Tax owed: R93,135 + 0.36 * (R415,000 - R393,200)

Tax owed: R93,135 + 0.36 * R21,800

Tax owed: R93,135 + R7,848

Tax owed: R100,983

Finally, we subtract the rebate amount of R13,257 from the tax owed to find the amount the man still owes.

Tax owed - Rebate: R100,983 - R13,257 = R87,726

Therefore, the man still owes R87,726 in taxes.

The correct option is not provided among the given answer choices.

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Answer:

Each person would get 1/6 of the pizza

Step-by-step explanation:

1/3 divided by 2 is 1/6. Do that again and you will get four of 1/6.

The equivalent function for .5=2⁻¹ is: 2x = 1 or log2(0.5) = -1 These are alternative ways of expressing the same relationship between 0.5 and 2⁻¹.

Understanding the Exponential Function

In mathematics, the exponential function is a function that is defined as f(x) = a^x, where 'a' is a constant called the base of the exponential function, and 'x' is the exponent. The exponential function is an important function in mathematics and is used in many different fields, such as finance, physics, and engineering.

To understand the relationship between an exponential function and a power of a number, we can consider the example of 0.5 = 2⁻¹ This means that 2 raised to the power of -1 is equal to 0.5.

To prove this, we can use the definition of the exponential function as f(x) = a^x. In this case, a = 2 and x = -1. So, we have:

f(-1) = 2⁻¹

We can simplify this expression using the property of negative exponents that states that a^-n = 1/a^n. Therefore:

f(-1) = 1/2¹

Simplifying further, we get:

f(-1) = 1/2

So, we see that 2 raised to the power of -1 is indeed equal to 0.5.

In conclusion, understanding the exponential function is important in mathematics and many other fields. The example of 0.5 = 2⁻¹ helps to illustrate the relationship between an exponential function and a power of a number, and how we can use the properties of exponents to simplify expressions involving exponential functions.

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Answer:

27

Step-by-step explanation:

Answer:172 cm²

Step-by-step explanation:

when we use the formula, and we can  solve out is like 172.05 and round to tenth and will have the answer

Formula is 1/2 × p × a  

Answer:

4

Step-by-step explanation:

Step-by-step explanation:

\(y = 3x + 10......eq3 \\ 2(3x + 10) = 6x + 20 \\ 6x + 20 = 6x + 20\)

you can see that coming across that complication where the eqaution is balanced there is no solution for x and y fir those systems of equations.