What is the equation of a line perpendicular to y = 2x - 6 that passes through (5, 4)

Answer:

n=−5

Step-by-step explanation:

0.6(10n+25)=10+5n

Step 1: Simplify both sides of the equation.

0.6(10n+25)=10+5n

(0.6)(10n)+(0.6)(25)=10+5n(Distribute)

6n+15=10+5n

6n+15=5n+10

Step 2: Subtract 5n from both sides.

6n+15−5n=5n+10−5n

n+15=10

Step 3: Subtract 15 from both sides.

n+15−15=10−15

n=−5

Answer:

[tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given:

Two fair number cubes i.e. two dice consisting the numbers 1, 2, 3, 4, 5, 6 on their faces and have equal probability of each number.

The dice are rolled.

To find:

Probability of getting the sum of two numbers as 4.

Solution:

First of all, let us have a look at the total possibilities when two dice are rolled:

([1][1], [1][2], [1][3], [1][4], [1][5], [1][6],

[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],

[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],

[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],

[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],

[6][1], [6][2], [6][3], [6][4], [6][5], [6][6])

These are total 36 possible outcomes.

For getting a sum as 4:

Possible number of favorable cases are 3 (as highlighted in BOLD in above)

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Required probability is:

[tex]\dfrac{3}{36} = \bold{\dfrac{1}{12}}[/tex]

Answer:  see proof below

Step-by-step explanation:

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity:     cos²A + sin²A = 1

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}[/tex]

[tex]\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}[/tex]

[tex]\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}[/tex]

[tex]\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}[/tex]

[tex]\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}[/tex]

[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}[/tex]

                               =  cos A

LHS = RHS:  cos A = cos A   [tex]\checkmark[/tex]

Answer:

the answer is /36

Step-by-step explanation:

3 goes into 36

4 goes into 36

9 goes into 36

Answer:

Below

Step-by-step explanation:

● x-20 = y+20 (1)

● 2(y-22) = x+22 (2)

This is a system of simulataneous equations

Let's simplify the expressions first

● x -20 = y + 20 (1)

Add 20 to both sides

● x -20 + 20 = y+20 +20

● x = y + 40 (1)

● 2(y-22) = x+22 (2)

● 2y - 44 = x +22

Substrat 22 from both sides

● 2y-44-22 = x+22-22

● 2y -66 = x (2)

This is the new system:

● x = y+40 (1)

● x = 2y-66 (2)

Substract (2) from (1)

● x-x = y+40-(2y-66)

● y+40-2y+66 = 0

● -y +106 = 0

● y = 106

Replace y with 106 in (1)

● x = y +40

● x = 106+40

● x = 146

So the solutions are (146,106)

Answer:

The answer is

Step-by-step explanation:

Volume of a sphere is given by

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

where r is the radius

From the question

r = 3 inches

So the volume of the sphere is

[tex]V = \frac{4}{3}( {3)}^{3} \pi[/tex]

[tex]V = \frac{4}{3} \times 27\pi[/tex]

[tex]V = 4 \times 9 \times \pi[/tex]

We have the final answer as

Volume = 36 π cubic inches

Hope this helps you

Answer:

36pi cubic inches.

Step-by-step explanation:

Just took the Pre-Test on Edg (2020-2021)!!

Answer:

14 adults and 5 children

Step-by-step explanation:

Set up a system of equations, where a is the number of adults and c is the number of children:

2.5a + c = 40

a + c = 19

Multiply the bottom equation by -1 to solve by elimination:

2.5a + c = 40

-a - c = -19

1.5a = 21

a = 14

Now, plug in 14 as a  to find the number of children:

a + c = 19

14 + c = 19

c = 5

So, 14 adults and 5 children attended

Answer:

x(5)/(6)y(1)/(2)

Step-by-step explanation:

Hoped I helped

leave a like or rate.

Answer:

a) The standard form of the equation

[tex]y=\frac{16}{x^{2} }[/tex]

Step-by-step explanation:

Explanation:-

    A parabola is the set of all points in a plane that are equidistant from a fixed line and a fixed point (not in a line) in the plane

• The Fixed line is called the directrix of the parabola.

• The Fixed point is called the focus of the parabola.

• A line through the focus and perpendicular to the directrix is called the axis of the parabola.

• The point of intersection of parabola with the axis is called the vertex of the parabola.

Given Focus of the parabola S(0,a)= (0,4)

Given Focus is lies on y-axis and the directrix is parallel to x-axis

Given directrix of the parabola y = -4

Directrix     y = -a

Standard form of the parabola

                                x² = 4ay

                               x² = 4(4)y

                              x² = 16y

                              [tex]y=\frac{16}{x^{2} }[/tex]

Answer:

$91.00

Step-by-step explanation:

From the above question, we obtained the following information.

James charges:

1 compact car = $7.00

1 mid sized car = $10.00

1 SUV = $15.00

On Saturday, he washed:

a) 3 compact cars

1 compact car = $7.00

3 compact cars = ?

= $7.00 × 3

= $21.00

b) 4 mid-sized cars

1 mid- sized car = $10.00

4 mid-sized cars = ?

= $10.00 × 4

= $40.00

c) 2 SUVs.

1 SUV = $15.00

2 SUVs = ?

= $15.00 × 2

= $30.00

How much money did he earn?

$21.00 + $40.00 + $30.00

= $91.00

Therefore, James earned $91.00

Answer: To simplify this problem you combine the like terms in the equation (numbers with the same variables.)

Demo: 12r + -4r = 8r

Answer:

8r + 14s - 7T

Step-by-step explanation:

Hello!

We have to make sure the terms are like terms before we add them.

Like terms are terms with the same variable so we can add r's with r's, t's with t's, etc.

There are two r's and two s's so we can simplify those

12r - 4r = 8r

5s + 9s = 14s

Now put these all together with the T in the original equation to get the answer

8r + 14s - 7T

Hope this helps!

Answer:

D

Step-by-step explanation:

The area of a rectangle is given by the formula:

[tex]A=\ell w[/tex]

So, we are given that the area is:

[tex]x^3-5x^2+3x-15[/tex]

And the width is:

[tex]x^2+3[/tex]

And we want to find the length. To do so, first substitute the expressions into the equation:

[tex]x^3-5x^2+3x-15=(x^2+3)\ell[/tex]

Thus, to find the length, divide by (x²+3):

[tex]\displaystyle \ell = \frac{x^3-5x^2+3x-15}{x^2+3}[/tex]

We can factor the numerator:

[tex]x^3-5x^2+3x-15[/tex]

From the first two terms, factor out a x².

From the third and fourth terms, factor out a 3:

[tex]=x^2(x-5)+3(x-5)[/tex]

Combine:

[tex]=(x^2+3)(x-5)[/tex]

Putting this back:

[tex]\displaystyle \ell = \frac{(x^2+3)(x-5)}{x^2+3}[/tex]

Cancel:

[tex]\ell =x-5[/tex]

Hence, our answer is D.

Answer:

D on Edge 2021 ;))

Step-by-step explanation:

Answer:

5 represent calories from other ingredients

c= 5 1/2 grams

Step-by-step explanation:

Total calories=c grams of carbohydrates + other ingredients

Total calories in granola bite=27

The equation 4c + 5 = 27 represents the relationship between these quantities

1. 5 represent calories from other ingredients

2. Priya said that neither 8 nor 3 could be the solution to the equation

4c + 5 = 27

When the solution is 8

4(8)+5=27

32+5=27

37 =27

Solution 8 gives a higher calories than total calories

When solution is 3

4(3)+5=27

12+5=27

17=27

Solution 3 gives a lower calories than total calories

3. Solution to the equation

4c + 5 = 27

Subtract 5 from both sides

4c+5-5=27-5

4c=22

Divide both sides by 4

c=22/4

=5 2/4

=5 1/2

c= 5 1/2 grams

Answer:

linear

Step-by-step explanation:

hey there,

< Linear equations are constant. They are not like parabolas so they are not curved but instead are straight, which allows them to be constant. >

Hope this helped! Ask me any more questions if you still don't understand!

Answer: The answer is a Linear Function

Step-by-step explanation:

Answer:

1.095, 1.152, 1.153, 1.338, 1.45, 1.729, 1.755, 1.806, 1.935, 1.993

Step-by-step explanation:

Answer:

$122.28

Step-by-step explanation:

Give the following :

Insurance worth = $240,000

Price sold = $225

P(survival) = 0.999572

P(death) = 1 - 0.999572 = 0.000428

If she survives, insurance firm makes $225

If she dies, insurance firm pays $240,000, hence the company losses :

$(225 - 240,000) = $−239775

Expected value (E(x)) = sum of P(i) * X(i)

E(x) = (P(survival) * profit made) + (P(death) * loss incurred)

E(x) = (225 * 0.999572) + (0.000428 * −239775)

= 224.9037 - 102.6237

=$ 122.28

Answer:

$773.3587

Step-by-step explanation:

The probability that the female survives = 0.999572

therefore, probability that female dies = 1-0.999572 = 0.000428

if the female survives the insurance company makes = $225

x=$250

If the female dies the insurance company pays $240,000.

So, the amount with the company = 240000-225 = $ 2390775

Therefore Expected value = 250(0.999572)-2390775(0.000428)= $773.3587

Answer:

2.4 hours

Step-by-step explanation:

To find the number of hours it takes to cook 3 kilograms of meat, we must fist find the rate of the ration we have:

12 : 5

= 12 / 5

= 2.4

This means that if you mulitply this by the value of the weight of meat, you'll get the amount of time it takes to cook that amount of meat.  We can do ths is find the time it takes to find the hours it takes to make 3 ilograms of meat:

x : 3

x = 3 * 2.4 = 7.2

x : 3

= 7.2 : 3

I takes 7.2 hours to cook 3 kilograms of meat.  You can use this process to find all the other hours based on the weight.

I hope this helps!  Tell me if I am wrong!

Answer:

D

Step-by-step explanation:

So we have the equation:

[tex]ax+by+c=0[/tex]

First, let's convert this to slope-intercept form.

Subtract ax from both sides:

[tex]by+c=-ax[/tex]

Subtract c from both sides:

[tex]by=-ax-c[/tex]

Divide everything by b:

[tex]y=-\frac{a}{b}x-\frac{c}{b}[/tex]

We are told that a>0, b<0, and c>0.

In other words, a is positive, b is negative, and c is positive.

The slope of the equation is -a/b.

Since a is positive and b is negative, we will have:

-(+)/(-).

The negatives will cancel out. Therefore, our slope will be positive.

Since our slope is positive, our line must be upwards sloping. Eliminate answers A and C.

Also, our y-intercept is:

-c/b.

c is positive and b is negative. Thus, similarly:

-(+)/(-).

Again, the negatives cancel. This means that the y-intercept must be positive.

Out of B and D, the graph that has a positive y-intercept is D.

D is our answer :)

Answer:

For the first one it would be A. x = -3, 4 because they where f(x) and g(x) intersect.

Step-by-step explanation:

For the second one it would be B. Fuction 1 has the larger maximum at (4,1) because the maximum point for Fuction 1 is at (4,1) becuase that the highest point/vertex it goes.

Answer:

I believe it is A

Step-by-step explanation:

Answer:

x = - 2

Step-by-step explanation:

[tex]5x + 4 = 8x + 10 \\ 5x - 8x = 10 - 4 \\ - 3x = 6 \\ x = \frac{6}{ - 3} \\ x = - 2[/tex]

The solution of the equation 8x + 10 = 5x + 4 will be negative 2.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given below.

8x + 10 = 5x + 4

Simplify the equation, then we have

8x - 5x = 4 - 10

3x = - 6

x = - 6 / 3

x = - 2

The solution of the equation 8x + 10 = 5x + 4 will be negative 2.

More about the solution of the equation link is given below.

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Answer:

f=2.93cm

Step-by-step explanation:

SOH CAH TOA [the length you are finding is adjacent to the angle and opposite to right angle is the hypotenuse, therefore use cosine]

cos(43°)=f/4

[times 4x on both sides it cancels on the left]

4cos(43°)=f

2.93=f

Answer:

[tex]P = 3.5\ million[/tex]

Step-by-step explanation:

Given

Represent 1950 Population with P and 2003 Population with Q

[tex]Q = 19.5\ million[/tex]

Required

Determine the value of P

From the question; we have that

[tex]Q = 2\ million + 5 * P[/tex]

Substitute 19.5 million for Q

[tex]19.5\ million = 2\ million + 5 * P[/tex]

Subtract 2 million from both sides

[tex]19.5\ million - 2\ million= 2\ million - 2\ million + 5 * P[/tex]

[tex]19.5\ million - 2\ million= 5 * P[/tex]

[tex]17.5\ million = 5 * P[/tex]

Divide both sides by 5

[tex]\frac{17.5\ million}{5} = \frac{5 * P}{5}[/tex]

[tex]\frac{17.5\ million}{5} = P[/tex]

[tex]3.5\ million = P[/tex]

[tex]P = 3.5\ million[/tex]

Hence, the 1950 population is 3.5 million

Answer:

im not sure how the data should be interpreted but here is the distribution. It goes up by .416

Step-by-step explanation:

the average of the first 8 games is 24

the average of the 12 games is 24.416

The mean of the data of the given basketball player will increase if she scored 24, 22, 27, and 28 points in her next four games.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given that the number of points scored by a basketball player in the first eight games is 15, 35, 18, 30, 25, 21, 32, and 16. Therefore, the mean of the first 8 games is,

Mean = (15 + 35 + 18 +30 + 25 + 21 + 32 + 16)/8

          = 176/8

          = 22

Now, the player scored 24, 22, 27, and 28 points in her next four games. Therefore, the mean will be,

New Mean = (15 + 35 + 18 +30 + 25 + 21 + 32 + 16 + 24 + 22 + 27 + 28)/12

                  = 277 / 12

                  = 23.0833

Hence, the mean of the data of the given basketball player will increase if she scored 24, 22, 27, and 28 points in her next four games.

Learn more about Mean here:

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Answer:

Density = 5751.66 gram per litre

Step-by-step explanation:

It is given that the density of a certain material 6 pounds per pint.

The conversion from pint to liter is as follows :

1 pint = 0.473 litre

The conversion from pounds to kg is as follows :

1 pound = 453.59 kg

We need to express the density from pounds per pint to grams per liter.

1 pound per pint = 958.611 gram per litre

So,

6 pound per pint = 958.611 × 6 gram per litre

6 pound per pint  = 5751.66 gram per litre

Answer:

The last step says the answer is 5751.66

Answer:

shirts are $32 each and hats are $18 each

Step-by-step explanation:

x = shirts

y = hats

2x + 5y = 154

3x + 4y = 168

use either substitution or elimination

x = $32

y = $18

The price of each shirt is $32 while the price of each hat is $18.

let

the price of each shirt  = x

the price of each hat = y

Eva's purchase will be

Nicole's purchase will be

Combine the equation to find the price of each shirt and hat.

2x + 5y = 154

3x + 4y = 168

2x = 154 - 5y

x = 77 - 5 / 2 y

3x + 4y = 168

3(77 - 5 / 2 y) + 4y = 168

231 - 15 / 2 y + 4y  = 168

168 - 231 = - 7 /2 y

- 63 = - 7 / 2 y

cross multiply

-126 = -7y

y = 18

2x + 5(18) = 154

2x + 90 = 154

2x = 154 - 90

2x = 64

x = 64 / 2

x = 32

Price of each shirt  = $32

price of each hat  = $18

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Answer:

Hello!!!!

The answer is y-6=3/2(x+6)

Step-by-step explanation:

point slope form is y-y1=m(x-x1)

-6 is x1 and 6 is y1

m=3/2

then plug in these values

hope this helps!!!!

Answer:

y-6=3/2(x--6)

Step-by-step explanation:

I am the best at the maths thing

The equation formed using the given data is 195 = x + 12 and your final score is 183 points.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Let's say your final score is x

Given that,

Your final score x is 12 points less than your friend's final score.

So,

x = friend final score - 12

Now,

Friend final score = 195

So,

x = 195 - 12

x + 12 = 195

195 = x + 12

Now,

x = 195 - 12 = 183

Hence "The equation formed using the given data is 195 = x + 12 and your final score is 183 points".

For more about the equation,

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Answer:

17.3825

Step-by-step explanation:

First I figured out the area of the square which is 18×18=324

Then I found out the are of the circle which is 254.47, so 324 - 254.47 = 69.53

Then there are 4 times the shaded are so divided by 4, so 69.53  ÷ 4 = 17.3825

PLEASE GIVE BRAINLIEST!

Answer:

shaded area = 17.38 cm²

Step-by-step explanation:

given:

diameter of circle = 18 cm and = side of square

π = 3.142

shaded area = ( Area of square - Area of circle ) x 1 / 4

Area of square = s² = 18² = 324 ²cm

Area of circle = π d² / 4

                       = 3.142 (18²) / 4

                       = 254.5 cm²

therefore, shaded area = ( 324 cm² - 254.5 cm² ) * 1/4

                                       = 17.38 cm²

Answer:

57

Step-by-step explanation:

-7+2*36-8

-7+72-8

65-8

57

Answer:

18

Step-by-step explanation:

1/3 of 27 is 9 so 2/3 is 18