1/5+3/7 and you will get 50 points

Answer:

the third one

Step-by-step explanation:

Answer:

Step-by-step explanation:

y-7= -4/3 (x+6)

y-7= -4/3x-8

add 7 to both sides

y= -4/3x-1

The equation in slope-intercept form for the given line is 3y = -4x -3

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that a line passes through the point (-6,7) and has a slope of -4/3.

Standard equation of a line = y = mx + c where m is the slope,

Therefore, putting values of x and y to get the value of c

7 = -6*-4/3 + c

c = 7 - 8

c = -1

Equation = y = -4x/3 -1

Or, 3y = -4x -1

Hence, the equation of a line passing through the point (-6,7) and has a slope of -4/3 is 3y = -4x -1

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Answer:

A deduction can only lower your taxable income and the tax rate that is used to calculate your tax. This can result in a larger refund of your withholding. A credit reduces your tax giving you a larger refund of your withholding, but certain tax credits can give you a refund even if you have no withholding.

Step-by-step explanation:

Answer:

[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]

Step-by-step explanation:

From the information given:

Lets first change the given relations into polar coordinates

So, the region of the inner circle into polar coordinates is as follows:

(x - 4)² + y² = 16

x² + y² - 8x = 0

r² - 8r cos θ = 0

r = 8 cos θ

For the outside circle:

x² + y² = 16

r² = 16

Thus, the intersection point are:

64cos²θ = 16

cos²θ = 1/4

θ = -(π/3) , (π/3)

Now: if we are to represent the sketch on a graph, the region of the integration D will be:

[tex]D = \bigg \{ (r,\theta )\bigg |-\dfrac{\pi}{3}\leq \theta \leq \dfrac{\pi}{3}, 4 \leq r \leq 8 cos \theta \bigg \}[/tex]

Therefore, the are of the required region can now be computed as follows:

[tex]A = \int \int _D \ dA[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \int ^{8 \ cos \theta}_{4} \ r dr d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \bigg (\dfrac{r^2}{2} \bigg ) ^{8 \ cos \theta}_{4} \ d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{1}{2} \bigg (64 \ cos ^2 \theta - 16 \bigg ) \ d \theta[/tex]

[tex]A = \int ^{\pi/3}_{-\pi/3} \dfrac{16}{2} \bigg (4 \ cos ^2 \theta - 1 \bigg ) \ d \theta[/tex]

[tex]A = \dfrac{16}{2} * 2 \int ^{\pi/3}_{0} \bigg (4 \bigg ( \dfrac{ 1+ cos 2 \theta}{2} \bigg) - 1 \bigg ) \ d \theta[/tex]

[tex]A = 16 \int^{\pi/3}_{0} (1 + 2 cos 2 \theta ) d \theta[/tex]

[tex]A =16 ( \theta + sin2 \theta )^{\pi/3}_{0}[/tex]

[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) - (0-0) \end {bmatrix}[/tex]

[tex]A = 16 \begin {bmatrix} \bigg (\dfrac{\pi}{3} + \dfrac{\sqrt{3}}{2} \bigg ) \end {bmatrix}[/tex]

[tex]\mathbf{A = \dfrac{8}{3} \bigg (2 \pi + 3\sqrt{3} \bigg ) }[/tex]

The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.

The double integral formula for the area of a given curve is described below:

[tex]A = \iint\,r(\theta) \,dr\,d\theta[/tex] (1)

Where:

We notice that [tex]r \in [4, 8\cdot \cos \theta][/tex] and [tex]\theta \in \left[-\frac{\pi}{3}, \frac{\pi}{3} \right][/tex], then we have the following integral:

[tex]A = \int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \int \limits_{r= 4}^{r = 8\cdot \cos \theta}\,r\,dr\,d\theta[/tex]

Now we proceed to integrate the expression:

[tex]A = \frac{1}{2}\int\limits_{-\frac{\pi}{3} }^{+\frac{\pi}{3} } \,(64\cdot \cos^{2}\theta -16)\,d\theta = 32 \int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \,\cos^{2}\theta \, d\theta - 8\,\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]

[tex]A = 16\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } {\cos 2\theta} \, d\theta + 8\int\limits^{+\frac{\pi}{3} }_{-\frac{\pi}{3} } \, d\theta[/tex]

[tex]A = 8\sqrt{3}+\frac{16\pi}{3}[/tex]

The area of the region is equal to [tex]8\sqrt{3} + \frac{16\pi}{3}[/tex] square units.

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Answer:

Step-by-step explanation:

tan x° = [tex]\frac{3}{4}[/tex] ⇒ x° ≈ 36.87° ≈ 36.9°

Answer:

use it to help you

See the explanation for a 'tip'

Explanation:

Quotient means 'the answer after dividing'.

If you get really stuck this is one (bit long) way of dealing with it.

Firstly lets for the moment forget about the negative and just deal with

-96÷12

Write as 96 12

Notice that both numbers are even so we can divide by 2

96÷2=48

12÷2=6

Again they are both even

48÷2=24

6÷2=3

The two digits of 24 are such that

2+4=6

and 6 is exactly divisible by 3 so 24 is also exactly divisible by 3. So now we can do this:

24÷3=8

3÷3=1

Now we put the negative back in giving −8

Answer: There are  62 tricycles in the shop.

Step-by-step explanation:

Given: Number of wheels in a bicycle = 2

Number of wheels in a tricycle = 3

Let x = Number of bicycles , y = Number of tricycles.

As per given , we have

x+y =120       (i)

2x+3y=302       (ii)

Multiplying 2 on both sides of (i)

2x+2y=240      (iii)

Subtract (iii) from (ii) , we get

y= 62

Put value of y in (i) , we get

[tex]x+62=120\\\\\Rightarrow\ x=120-62\\\\\Rightarrow\ x= 58[/tex]

Hence, there are 58 bicycles and 62 tricycles in the shop.

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, the complete question is:

A rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y 81-x², what are the dimensions of the rectangle with the maximum area? what is the area?

Solution:

Given the parabola:

y = 81 - x²

Let the points (a,0) and (-a, 0) be points on the axis, this points touch the parabola at (a, 81 - a²) and (-a, 81 - a²).

Points (a,0), (-a, 0), (a, 81 - a²), (-a, 81 - a²) form the rectangle.

The length of rectangle = distance between (a,0) and (-a, 0) or between (a, 81 - a²) and (-a, 81 - a²) = 2a

The breadth of rectangle = distance between (a,0) and (a, 81 - a²) or between (-a, 0) and (-a, 81 - a²) = 81 - a²

Area of rectangle (A) = length × breadth = 2a × (81 - a²) = 162a - 2a³

A = 162a - 2a³

The maximum area is at dA / da = 0

dA / da = 162 - 8a² = 0

162 - 6a² = 0

6a² = 162

a² = 27

a = 5.2 units

Length = 2a = 2(5.2) =  10.4 units

Breadth = 81 - a² = 81 - 5.2² = 54 unit

Area = length × breadth = 54 × 10.4 = 561 unit²

Answer:

They make 4 approximately tons of oxygen each year.

Step-by-step explanation:

( 250lbs × 32 ) ÷ 2000 = 4t

250 pounds because each tree makes about 250 pounds of oxygen a year.

× 32 because there are 32 trees, so they'll make 32 times more oxygen than one tree.

÷ 2000 because before that everything was in pounds, and the question asks about tons. There are 2000 pounds in a ton, so you divide by 2000 to get the answer, which is 4 tons.

Answer:You will need to buy 1/2 a pound of cashews and 1/2 a pound of peanuts

Answer:

no image

Step-by-step explanation:

Answer: In order: 25, 15, 67.

Step-by-step explanation:

In picture

Answer:

9a-65

Step-by-step explanation:

simply write 9a+(add the remaining numbers all together)

========================================================

Explanation:

The general equation

y = ax^2 + bx + c

has the vertex (h,k) such that

h = -b/(2a)

In this case, a = -16 and b = 147. This means,

h = -b/(2a)

h = -147/(2*(-16))

h = 4.59375

The x coordinate of the vertex is x = 4.59375

Plug this into the original equation to find the y coordinate of the vertex.

y = -16x^2+147x+118

y = -16(4.59375)^2+147(4.59375)+118

y = 455.640625

The vertex is located at (h,k) = (4.59375, 455.640625)

The max height of the rocket occurs at the vertex point. Therefore, the max height is y = 455.640625 feet which rounds to y = 455.6 feet

Answer:

The value of x is 37.36

Step-by-step explanation:

The given triangle is a right-angled triangle where

Base = 25

Angle = 48°

Hypotenuse = x

As the triangle is a right angled triangle, trigonometric ratios can be used to find the missing value. We can use a ratio which uses base and hypotenuse.

[tex]cos\ 48 = \frac{base}{hypotenuse}\\cos\ 48 = \frac{25}{x}\\0.6691 = \frac{25}{x}\\x = \frac{25}{0.6691}\\x = 37.36[/tex]

Hence ,

The value of x is 37.36

Answer:

When  Item Price * (%) is < or > to $ Off

Step-by-step explanation:

Answer:

I think it is 4 but, im not sure

Answer: 18 miles

explanation: set up a proportion. (2 over 1/9 = x over 1). cross multiply, 2x1=2, then divide 2/(1/9)=18.

Answer:53

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Houses can be either domed or octagonal: True

Answer:

The answer is $0.07 cents per inch

Step-by-step explanation:

If you take 6 feet into inches (72)

and divide the total cost by the amount of inches (5.04 / 72)

You get the answer

Answer:

El Perímetro de un hexágono es igual a la suma de todos sus lados.

Step-by-step explanation:

el perimetro siempre es la suma de los lados de cualquier figura

Answer:

There are 2 given situations:

Plant A and Plant B growing in 3 weeks. Find which plant grows proportional

Plant A

=> 1st week = 18 inches

=> 2nd week = 36 inches

=> 3rd week = 56 inches

=> 18 + 18 = 36 + 20 = 56

Thus, this is not proportional

Plant B

=> 1st week = 18 inches

=> 2nd week = 36 inches

=> 3rd week  = 54 inches

=> 18 + 18 = 36 + 18 = 54 inches

thus, the growth of this plant is proportional

Answer:

1

Step-by-step explanation:

h

Answer:

I know it is 1

Step-by-step explanation:

Answer:  8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The total profit made by the student is 56.8%

The correct answer is D

Given parameters:

final price in which he book was sold = Rs.400

the first profit made by the student = 12% = 0.12

the final profit made by the student = 40% = 0.4

To find:

To find the total profit made by the student, we have to find the initial cost price of the book.

The cost price of the book before the student made the profit of 40%.

Let this cost price = y

100%y + 40%y = 400

140%y = 400

1.4y = 400

[tex]y = \frac{400}{1.4} \\\\y = 285.71[/tex]

This cost price become the new selling price before the student made the profit of 12%.

The cost price of the book before the student made the profit of 12%.

Let this cost price = x

100%x + 12%x = 285.71

112%x = 285.71

1.12x = 285.71

[tex]x = \frac{285.71}{1.12} \\\\x = 255.1[/tex]

This is the initial cost price of the book

The total profit made by the student is calculated as;

[tex]Profit \ \%= \frac{selling \ price - cost \ price }{cost \ price} \times 100\%\\\\Profit \ \%=(\frac{400 - 255.1}{255.1} )\times 100\%\\\\Profit \ \%= 56.8\%[/tex]

Thus, the total profit made by the student is 56.8%

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Answer:

x = 20

Step-by-step explanation:

Exterior angles are equal.

7x - 3 = 6x + 17

Add 3 and subtract 6x to both sides.

x = 20 is the answer.