Find the equation of the line that contains the point (6, -2) and is perpendicular to the line y = - 2x + 8.
O y = -x
Oy=2x-14
O y =
x-5
O y = - 2x + 10

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{16 \dfrac{40}{50}}[/tex]

[tex]\mathsf{= \dfrac{16\times50 + 40}{50}}[/tex]

[tex]\mathsf{= \dfrac{800 + 40}{50}}[/tex]

[tex]\mathsf{= \dfrac{840}{50}}[/tex]

[tex]\mathsf{= 840\div50}[/tex]

[tex]\mathsf{= 16.8}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{16.8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The area of the farm in acres is 864 acres.

An acre is equal to​ 43,560 square​ feet, and there are 5280 feet in a mile.

Therefore,

1 mile = 5280 feet's

The farm has the shape of a rectangle measuring 0.9 miles by 1.5​ miles. Therefore, let's convert to feet's

1 mile = 5280 feet's

0.9 miles = ?

cross multiply

length = 0.9 × 5280 = 4752 feet

1 mile = 5280 feet's

1.5 miles = ?

width = 1.5 × 5280 = 7920 feet's

Hence,

area of the farm = 4752 × 7920

area of the farm = 37635840

Therefore, the area of the farm in acres can be calculated as follows:

43560 ft = 1 acre

37635840 ft = ?

cross multiply

area of farm = 37635840 / 43560

area of the farm = 864 acres.

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Answers:

f(6) = 4

f ' (6) = 1/6

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

Explanation:

f(6) = 4 since the point (6,4) is on the f(x) curve. This is where the tangent is touching.

The tangent line also goes through (0,3)

Let's find the slope of the line through those two points.

[tex](x_1,y_1) = (6,4) \text{ and } (x_2,y_2) = (0,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 4}{0 - 6}\\\\m = \frac{-1}{-6}\\\\m = \frac{1}{6}\\\\[/tex]

The slope of the tangent line is 1/6. This is the value of f ' (6) because the derivative measures the tangent at the given x value. It's useful to determine the instantaneous rate of change.

The cost per item for maximum profit is $7.50 .

The maximum and minimum value of a function f(x) is calculated by finding the first and second derivative of f(x).

The cost to produce x pies is given by the cost function

[tex]C(x)=3x+36[/tex]

The price demand function for each pie is given by

[tex]p(x)=12-0.5x[/tex]

Revenue gained from selling x pies

[tex]R(x)=x\times p(x)\\or,R(x)=x\times(12-0.5x)\\or,R(x)=12x-0.5x^2[/tex]

Now profit function is given by

[tex]P(x)=R(x)-C(x)\\or,P(x)=-0.5x^2+12x-3x-36\\or,P(x)=-0.5x^2+9x-36[/tex]

Now we have to find the maximum profit. We know that for a function

[tex]P(x)=-0.5x^2+9x-36\\P'(x)=-x+9[/tex]

[tex]P''(x)=-1[/tex]

At P'(x)=0

or,-x+9=0

or, x=9

As P''(x)<0 therefore the profit function P(x) is maximum for x at P'(x)=0.

The profit is maximum at x=9

Price to charge per item=12-0.5x

Substituting the value of x we get:

[tex]p(x)=12-(0.5\times 9)\\or,p(x)=12-4.5\\or,p(x)=7.5[/tex]

Therefore the cost per item for maximum profit is $7.50 .

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Step-by-step explanation:

there is no real number solution for the square root of a negative number.

a sqare root multiplied by itself had to deliver exactly the number inside the square root.

so for sqrt(-49), what can be the answer ?

which number multiplied by itself gives -49 ?

it any negative number at that.

because

a × a = a²

and

-a × -a = a² but definitely not -a².

we get a negative number only, when we multiply a positive number with a negative number or vice versa.

the only solution is complex or imaginary (based on the imaginary number i):

i² = -1

i = sqrt(-1)

so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i

but again, no real solution.

Answer:

30x100= 3000

Step-by-step explanation:

Answer:

Step-by-step explanation:

哇，我喜歡吃很多食物，因為我喜歡並喜歡它。

Wa, wǒ xǐhuān chī hěnduō shíwù, yīnwèi wǒ xǐhuān bìng xǐhuān tā.

Answer: 124.12347

Step-by-step explanation:

Answer:

5 is not divisible by 3 and 9 .

Answer:

the answer is 435

Step-by-step explanation:

the change between each line is 105, so we start to add and then you get the resul

The value of A in the number line is the in-between of 225 and 645 so it is 435.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

A horizontal number line is the most common representation and can be extended infinitely in any direction.

Given the number line,

Now if we count the interval of A between 225 and 645 it is 2(same).

So A must be between 225 and 645.

So,

225 - A = A - 645

2A = 870

A = 435

Hence "The value of A in the number line is the in-between of 225 and 645 so it is 435".

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The quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons

From the question, we are to determine how much water is left in the barrel

From the given information,

"The barrel is filled with 18 gallons of water"

and

"Ryan used 9.7 gallons to water his garden in June"

After this time,

The quantity of water that would be left in the barrel will be 18 gallons - 9.7 gallons

= 8.3 gallons

Then,

3 and one eighth gallons in July

3 and one eighth = 3 1/8 = 3.125 gallons

The quantity of water that would be left is 8.3 gallons - 3.125 gallons

= 5.175 gallons

Hence, the quantity of water left in the barrel is 5.175 gallons. The correct option is the second option 5.175 gallons

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Answer:

b

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Take 92 and divide by 3

3*30 = 90

92-90 = 2

There are 2 donuts left over

Answer:

USE AIR MATH!!

Step-by-step explanation:

hope that helps

$690 is the next bill payment will be added for the next billing cycle.

What is rate of interest ?

An interest rate tells you how high the cost of borrowing is, or high the rewards are for saving. So, if you're a borrower, the interest rate is the amount you are charged for borrowing money, shown as a percentage of the total amount of the loan.

Total payment charged = $900

amount paid = $300

amount remained = $600

APR on $600 = 15%

= 600*15/100

= 600*0.15

= $90

Therefore, in the next bill total amount charged is 600 +90 = $690

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Answer:

7.50

Step-by-step explanation:

Finance Charge =.1512×$600=$7.50

$7.50 will be added to his balance next billing cycle, it is the cost he must pay for borrowing $600 from the credit card company this cycle.

answer : 452\12 ×2

452/24

18.83333333 answer

Answer: about 0.41

Step-by-step explanation:

Use calculator

[tex]arcsin=sin^{-1}x\\\\\boxed{sin^{-1}(0.4) = 0.41151684}[/tex]

Answer:

1. y= = 0.5 (2, 0.5)

2. y= 0 (4, 0)

3. y= -0.5 (6, 0.5)

Step-by-step explanation:

To get your answer, you would want to plug in the x-coordinates into the equation and solve for y.

Answer:

Step-by-step explanation:

Mustafa's soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100.

The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending

the dance, which equation can be used to find the number of students needed to make $1,500 in profit?

Answer:

Step-by-step explanation:

This article is about the basic inequality {\displaystyle z\leq x+y}{\displaystyle z\leq x+y}. For other inequalities associated with triangles, see List of triangle inequalities.

Three examples of the triangle inequality for triangles with sides of lengths x, y, z. The top example shows a case where z is much less than the sum x + y of the other two sides, and the bottom example shows a case where the side z is only slightly less than x + y.

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.[1][2] This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality.[3] If x, y, and z are the lengths of the sides of the triangle, with no side being greater than z, then the triangle inequality states that

{\displaystyle z\leq x+y,}z\leq x+y,

with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms):

{\displaystyle \|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,}\|\mathbf {x} +\mathbf {y} \|\leq \|\mathbf {x} \|+\|\mathbf {y} \|,

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

I just answered this.

in short : we rotate each vertex on a circle arc. the center of that circle being P.

so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.

therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.

that is starting at

360/5 = 72°

and then every additional 72°

144°

216°

288°

360°

so, A, D and E are correct

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

Explanation:

The given sequence is 5, 12, 33, 96, 285, ...

The sequence of increases is: 7, 21, 63, 189

Then notice,

Assuming this pattern keeps up, the next increment will be 189*3 = 567

We add this increment to the last term of the original sequence

285+567 = 852

The sequence is now 5, 12, 33, 96, 285, 852, ...

Answer:

[tex]\begin{array}{|l|l|c|c|c|}\cline{1-5} \textbf{Equation} & \textbf{Standard Form} & \textbf{a} & \textbf{b} & \textbf{c}\\\cline{1-5} \text{1.}\:\:x^2+x=20 & x^2+x-20=0 & 1 & 1 & -20\\\cline{1-5} \text{2.}\:\:4x^2-2x=28 \phantom{)))}& 4x^2-2x-28=0 \phantom{)))}& 4 & -2 & -28\\\cline{1-5} \text{3.}\:\:5x^2=225 & 5x^2-225=0 & 5 & 0 & -225\\\cline{1-5} \text{4.}\:\:x^2-x=36 & x^2-x-36=0 & 1 & -1 & -36\\\cline{1-5} \text{5.}\:\:3x^2-4=7x & 3x^2-7x-4=0 & 3 & -7 & -4 \\\cline{1-5}\end{array}[/tex]

Step-by-step explanation:

Standard form of a quadratic equation:

[tex]\boxed{ax^2+bx+c=0}[/tex]

Question 1

Given:

[tex]x^2+x=20[/tex]

Rearrange to standard form by subtracting 20 from both sides:

[tex]\implies x^2+x -20=20-20[/tex]

[tex]\implies x^2+x -20=0[/tex]

Therefore:

Question 2

Given:

[tex]4x^2-2x=28[/tex]

Rearrange to standard form by subtracting 28 from both sides:

[tex]\implies 4x^2-2x-28=28-28[/tex]

[tex]\implies 4x^2-2x-28=0[/tex]

Therefore:

Question 3

Given:

[tex]5x^2=225[/tex]

Rearrange to standard form by subtracting 225 from both sides:

[tex]\implies 5x^2-225=225-225[/tex]

[tex]\implies 5x^2-225=0[/tex]

Therefore:

Question 4

Given:

[tex]x^2-x=36[/tex]

Rearrange to standard form by subtracting 36 from both sides:

[tex]\implies x^2-x-36=36-36[/tex]

[tex]\implies x^2-x-36=0[/tex]

Therefore:

Question 5

Given:

[tex]3x^2-4=7x[/tex]

Rearrange to standard form by subtracting 7x from both sides:

[tex]\implies 3x^2-4-7x=7x-7x[/tex]

[tex]\implies 3x^2-4-7x=0[/tex]

[tex]\implies 3x^2-7x-4=0[/tex]

Therefore:

Answer:

18

Step-by-step explanation:

tbh I kinda forgot how to do this but ill try,

input 3 into the f(x)

4(3)+6=12+6=18

A) The distance that a force of 3 newtons would stretch the rubber band is; 0.015 m

B) The amount of work it takes to stretch the rubber band this far is; 0.0225 J

From Hookes's law, as long as the elastic limit is not exceeded the extension is directly proportional to the force applied.

F = Ke

Where;

F = force

K = force constant

e = extension

Thus,  for a restoring force of magnitude 2 newtons ;

2 N = K(1 × 10⁻²) m

K = 2 N /(1 × 10⁻²) m

K = 200 N/m

a) For a force of 3 newtons, we have;

3N = 200 N/m × a

Where a is the extension in meters

a = 3N/200 N/m

a = 0.015 m

b) The formula to find the work done is;

P.E = ¹/₂Ke²

P.E = ¹/₂ * 200 * 0.015²

P.E = 0.0225 J

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Answer:factors

Step-by-step explanation:

in the equation y= -x-1/2

the slope is -1/1 which can also be shown as -1.

We're given:

If the shop sold " [tex]9\dfrac{9}{10}[/tex]  times as much milk chocolate as white chocolate", we must multiply [tex]9\dfrac{9}{10}[/tex] by the amount of white chocolate sold to find the amount of milk chocolate sold.

Multiply [tex]9\dfrac{9}{10}[/tex] by 9 ounces:

[tex]9\dfrac{9}{10}\times9[/tex]

Convert the fraction into an improper fraction:

[tex]=\dfrac{99}{10}\times9[/tex]

Multiply:

[tex]=\dfrac{891}{10}[/tex]

The shop sold [tex]\dfrac{891}{10}[/tex] ounces of milk chocolate.

Answer:

41

Step-by-step explanation:

because if m=-4 that means (-4)2+6(-4)+9=41