Please help me solve for x (show work)


-4/7x = -1

Answer:

Explained below.

Step-by-step explanation:

(a)

It is provided that the price function for 1000 TVs is,

p (1000) = 400.

Also provided that if rebate of $10 is given then sale increases by 100 per week.

Let x be the number of unit sold per week then (x − 1000) is the increase in the number  of units sold.

Then the price function is:

[tex]p(x)=400-\frac{1}{10}(x-1000)[/tex]

       [tex]=400-\frac{x}{10}+100\\\\=500-\frac{x}{10}[/tex]

Thus, the demand function is, [tex]p(x)=500-\frac{x}{10}[/tex].

(b)

The revenue function is:

[tex]R(x)=x\cdot p(x)[/tex]

        [tex]=x[500-\frac{x}{10}]\\\\=500x-\frac{x^{2}}{10}[/tex]

Maximize the revenue as follows:

      [tex]\frac{d}{dx}(R(x))=0[/tex]

[tex]\frac{d}{dx}[500x-\frac{x^{2}}{10}]=0[/tex]

        [tex]500-\frac{x}{5}=0[/tex]

                 [tex]\frac{x}{5}=500[/tex]

                 [tex]x=2500[/tex]

Observe that R'(x) > 0 for 0 ≤ x < 2500 and R'(x) < 0 for x > 2500. Hence, first  derivative test will lead to the conclusion that maximum occurs at x = 2500.

Compute the value p (2500) as follows:

[tex]p(2500)=500-\frac{2500}{10}=500-250=250[/tex]

Then the rebate to maximize the revenue should be: $400 - $250 = $150.

(c)

The weekly cost function is,

[tex]C(x) = 73000 + 110x[/tex]

Compute the profit function as follows:

[tex]P(x)=R(x)-C(x)[/tex]

        [tex]=500x-\frac{x^{2}}{10}- 73000 - 110x\\\\=390x-\frac{x^{2}}{10}- 73000[/tex]

Compute the marginal profit as follows:

[tex]\text{Marginal profit}=P'(x)\\=\frac{d}{dx}P(x)\\=\frac{d}{dx}[390x-\frac{x^{2}}{10}- 73000]\\=390-\frac{x}{5}[/tex]

Compute the value of x for P'(x) = 0 as follows:

[tex]P'(x)=0\\\\390-\frac{x}{5}=0\\\\x=390\times 5\\\\x=1950[/tex]

Observe that P'(x) > 0 for 0 ≤ x < 1950 and P'(x) < 0 for x > 1950. Hence, first

derivative test will lead to the conclusion that maximum occurs at x = 1950.

Compute the value p (1950) as follows:

[tex]p(1950)=500-\frac{1950}{10}=500-195=305[/tex]

Then the rebate to maximize the profit should be: $400 - $305 = $95.

the answer is 7-7y i think if not the it should be 7+7y

Answer:

20991

Step-by-step explanation:

Answer:

It should take her father four hours to reach her.

Step-by-step explanation:

Since Madison takes an hour to travel 10 miles, by the time she reaches 3 hours, shes at 30 miles. (At this point her father has begun traveling towards her) And since he goes 15 miles per hour, four hours later (for her father), they will both be at the same distance.

(So in 6 hours, Madison goes 60 miles, and in 4 hours her father also goes 60 miles since hes faster)

Please tell me if I did anything wrong!

It will take the time that Madison's dad 8 hours to catch up with her.

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

Let's call the distance from Madison's house to the point where her dad catches up with her "D".

distance Madison traveled = rate × time = 10 mph × 2 hours = 20 miles.

This means that when Madison's dad starts driving, Madison is 20 miles ahead of him.

For Madison's dad, his rate is 15 mph, and the time it takes him to catch up to Madison is "t" hours.

So his distance traveled is:

distance traveled by Madison's dad = 15 mph × t

For Madison, her rate is 10 mph, and she has already traveled for 2 hours. So her distance traveled is:

distance traveled by Madison = 10 mph × (t + 2)

Now, their distances are equal to each other:

15t = 10(t + 2) + 20

Simplifying and solving for "t", we get:

15t = 10t + 40

5t = 40

t = 8

Therefore, it will take Madison's dad 8 hours to catch up with her.

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Answer:

see explanation

Step-by-step explanation:

Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant Δ = b² - 4ac informs us about the nature of the roots.

• If b² - 4ac > 0 then 2 real and distinct roots ( solutions )

• If b² - 4ac = 0 then 2 real and equal roots

• If b² - 4ac < 0 then roots are not real

Given

3x² - 6 = 2x ( subtract 2x from both sides )

3x² - 2x - 6 = 0 ← in standard form

with a = 3, b = - 2, c = - 6 , thus

b² - 4ac = (- 2)² - ( 4 × 3 × - 6) = 4 - (- 72) = 4 + 72 = 76

Since b² - 4ac > 0 then the solution is 2 real and distinct roots

Answer:

#9 x=21

#10 a. QP  b. 8  c. 18

Step-by-step explanation:

#9 use the theorem where the ratio between a midline and the base of the triangle is 1:2

as we know the midline and the base is 1:2

this means

2(4x-65)=2x-4

  4x-65=x-2

    3x=63

      x=21

---------------------------------------------------------------

#10

a. RS|| QP (Remember to write the letters accordingly)

b. 8 (As mentioned before of the ratio 1:2)

c. 18

Answer:

D. $10,909.09

Step-by-step explanation:

The class recovery period for residential rental property each year = 27.5 years

The cost basis for the residential property = $300,000

The amount he will be able to depreciate

= Cost basis/ Number of years

= $300000/ 27.5 years

=$10, 909.090909

Approximately ≈ $10,909.09

The amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

Using this formula

Depreciation=Rental unit amount/ MACRS residential rental property recovery period

Where:

Rental unit amount=$300,000

MACRS Residential rental property recovery period=27.5 years

Let plug in the formula

Depreciation=$300,000/27.5

Depreciation=$10,909.09

Inconclusion the amount he will be able to depreciate  using the class recovery period for residential rental property each year is: D. $10,909.09.

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Answer: 12.96

Step-by-step explanation:

given data:

Poisson distributio = 3.60

solution:

The Poisson distribution expected value is same as Variance.

which is expressed as = SD^2

therefore;

the expected value

= SD^2

= 3.60^2

= 12.96

Answer:

2/10 because if the two fraction

The equivalent fractions of 8/11 = 16/22 , 24/33 , 32/44

The equivalent fractions of 1/10 = 2/20 , 3/30 , 4/40

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the first fraction be represented as A

Now , the value of A = 8/11

Let the second fraction be represented as B

Now , the value of B = 1/10

And , the equivalent fractions of A is given by

A = 8/11 , 16/22 , 24/33 , 32/44

And , the equivalent fractions of B is given by

B = 1/10 , 2/20 , 3/30 , 4/40

Hence , the fractions are solved

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Answer:

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

Step-by-step explanation:

The question is incomplete; However

[tex]A = (-2, -4)[/tex]

[tex]B = (6, 1)[/tex]

Required

Determine coordinates of P

When line segment is divided in ratios, the following formula calculates the coordinates;

[tex]P(x,y) = \{\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\}[/tex]

In this case;

[tex]m:n = 2:1[/tex]

[tex](x_1,y_1) = (-2, -4)[/tex]

[tex](x_2,y_2) = (6, 1)[/tex]

So, the coordinates of P is calculated as thus

[tex]P(x,y) = \{\frac{2 * 6 + 1 * (-2)}{2+1}, \frac{2 * 1 + 1 * (-4)}{2+1}\}[/tex]

[tex]P(x,y) = \{\frac{12 -2}{3}, \frac{2 -4}{3}\}[/tex]

[tex]P(x,y) = \{\frac{10}{3}, \frac{-2}{3}\}[/tex]

Hence, the coordinates of P is

[tex]P(\frac{10}{3}, \frac{-2}{3})[/tex]

The question is incomplete, the points A and B are:

A = (-2, -4)

B = (6, 1)

We want to find a point P in the segment AB such that the ratio of AP to PB is 2:1

We will find that:

[tex]P = (\frac{2}{3} , \frac{7}{3} )[/tex]

The general formula for two points (x₁, y₁) and (x₂, y₂), the coordinates of a point that separates the segment in a ratio j:k is

[tex]P = (\frac{j*x_1 + k*x_2}{j + k} , \frac{j*y_1 + k*y_2}{j + k})[/tex]

So we only need to use that general formula:

[tex]P = P = (\frac{2*(-2) + 1*6}{3} , \frac{2*(-4) + 1*1}{3})\\\\P = (\frac{2}{3} , \frac{7}{3} )[/tex]

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Answer:

1/4x + 3

Step-by-step explanation:

The question said one-third(1/3) not one-fourth(1/4).

1/3x + 4 can also be written as x/3 + 4.

Answer:

1/4x + 3

Step-by-step explanation:

expressions does not represent "four more than one-third x"

1/3x + 4 --- No.

x/3 + 4  --- No.

1/4x + 3 --- Yes. it does not represent 4 + 1/3x. you can tell it by +3

Answer:

Mercury, Venus, Earth, Mars, and Uranus

Step-by-step explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

[tex]\left[\begin{array}{cccc}Planet&R(m)&g(m/s^{2})&v(m/s)\\Mercury&2.43\times10^{6}&3.61&4190\\Venus&6.07\times10^{6}&8.83&10400\\Earth&6.37\times10^{6}&9.80&11200\\Mars&3.38\times10^{6}&3.75&5030\\Jupiter&6.98\times10^{7}&26.0&60200\\Saturn&5.82\times10^{7}&11.2&36100\\Uranus&2.35\times10^{7}&10.5&22200\\Neptune&2.27\times10^{7}&13.3&24600\end{array}\right][/tex]

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s.  So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.

Answer:

AC

Step-by-step explanation:

First, let's find m∠B and m∠C by solving for x. Since the sum of interior angles in a triangle is 180°, we know that:

60 + 3x - 2 + 2x + 7 = 180

5x + 65 = 180

5x = 115

x = 23° so m∠B = 3(23) - 2 = 67° and m∠C = 2(23) + 7 = 53°. The longest side of a triangle is always opposite to the largest angle of the triangle, and since m∠B is the largest, we know that the side opposite to ∠B is the longest. That side is AC.

In triangle ABC, the longest side is AC, since it is opposite the biggest angle ∠B.

According to the angle sum property of a triangle, the sum of the three interior angles is 180°.

In a triangle, the longest side is on the opposite side of the biggest angle, and the shortest side is on the opposite side of the smallest angle.

We are given the angles of the triangle ABC. We are asked to find the longest side in the triangle ABC.

By the angle sum property of a triangle, we know that,

m∠A + m∠B + m∠C = 180°

or, 60° + (3x - 2)° + (2x + 7)° = 180°

or, 5x + 65° = 180°

or, 5x = 180° - 65° = 115°

or, x = 115/5 = 23.

∴ m∠A = 60°.

m∠B = (3x - 2)° = (3(23) - 2)° = (69-2)° = 67°.

m∠C = (2x + 7)° = (2(23) + 7)° = (46 + 7)° = 53°.

∵ m∠B is the largest angle, the side opposite to it, that is, AC is the longest side of the triangle.

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Step-by-step explanation:

Hey, there!!

Let's solve it simply,

angle ONP = 60°+55° { as exterior angle is equal to the sum of opposite interior angle}.

Therefore, angle ONP = 115°.

Now, let's solve for x,

x+ 115°=180° { because the sum of co-interior angle is 180°}.

x= 180°-115°

Therefore, the measure of angle x is 65°.

Hope it helps...

Answer:

[tex]\Huge \boxed{{x=65\° }}[/tex]

Step-by-step explanation:

l and m are parralel lines.

The third angle in the triangle is also x, because of corresponding angles.

Angles in a triangle add up to 180 degrees.

Create an equation and solve for x.

x + 60 + 55 = 180

Add the numbers.

x + 115 = 180

Subtract 115 from both sides.

x = 65

Answer:

D?

Step-by-step explanation:

¯\_(ツ)_/¯

Answer:

399.17 miles

Step-by-step explanation:

Gunnar's car gets 22.4 miles per gallon. His gas tank can hold 17.82 gallons of gas.

Gunnar's car travels with one gallon of gas = 22.4 miles

He can travel with 17.82 gallon of gas = 17.82 × 22.4

                                                             = 399.168 ≈ 399.17 miles

Gunnar can travel 399.17 miles if he uses all of the gas in the gas tank.

Answer:

324 miles divided by 18 gallons = 18 miles per gallon (mpg)  

Therefore, 41 gallons x 18 mpg = 738

Step-by-step explanation:

Answer: A

16 minutes

Step-by-step explanation:

The required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.

The rate of change is defined as the change in value with the rest of the time is called rate of change.

Here,
radius = 55 / 2 = 27.5
Since volume is directly proportional to the cube of the radius,
So,
For maximum volume,
V ∝ R³

and
2/3V = v
2/3R³ = r³
r = 27.5 ∛2/3
r = 24
Now,
the radius increases at a rate of 1.5 feet per minute.
Time to reach a radius of 24 feet,
= 24 / 1.5
= 16 minutes

Thus, the required time to inflate the balloon to Two-thirds of its maximum Volume is 16 minutes.

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Answer:

1.00o2

Step-by-step explanation:

You dont need this explained come on

Answer:

b would be a negative number

Answer:  The sign of b is negative or  -

Step-by-step explanation:

If you multiply two negative numbers you will have a positive number. And if you multiply a positive and negative numbers you will have  a negative answer.

Answer:

C) Both functions are decreasing and both are positive on the interval (0;2)

Step-by-step explanation:

As known the exponent function has no minimum and has no maximum.

Otherwise exponent function can be only or increasing or decreasing for all x.

That means that in case y(x2)>y(x1) and  if x2>x1-  function is increasing.

That means that in case y(x2)<y(x1) and  if x2>x1-  function is decreasing.  

Lets check what is going on with the function f(x)

If x1=0        f(x1)=24

If x2=2        f(x2)=0

So    x2>x1 however f(x2)<f(x1)=> function is decreasing

Similarly g(x)

If x1=0   g(x1)=15

If x2=2   g(x2)=0

So x2>x1 however g(x2)<g(x1) => function is decreasing

So bothfunctions are decreasing.

Because f(x) is decreasing the function meaning with argument x1=0 has max in the interval x∈(0;2) And function meaning has the minimum if argument x2=2.   So the function F(x) in interval (0;2) is changing from 24 to 0 => is positive on the interval (0,2)

The same is with g(x) .  g(x) gonna be positive on the interval (0;2)

Answer:

The answer is A.

Do you need an explanation?

387,500 /100 = 3,875

3,875 * 0.43 = 1,666.25

I multiplied, because, if you divide with a decimal, the number increases, instead of decreasing... hope this helps!

Answer:

p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]

Step-by-step explanation:

Given equations:

2p - 3q = 4        -----------(i)

3p + 2q = 9       ------------(ii)

Let's solve this equation simultaneously using the elimination method

(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;

[2p - 3q = 4]        x 3

[3p + 2q = 9]       x 2

6p - 9q = 12            -------------(iii)

6p + 4q = 18            -------------(iv)

(b) Next, subtract equation (iv) from equation (iii) as follows;

     [6p - 9q = 12]        

 -   [6p + 4q = 18]    

            -13q = -6      -----------------(v)

(c) Next, make q subject of the formula in equation (v)

      q = [tex]\frac{6}{13}[/tex]

(d)  Now substitute the value of q = [tex]\frac{6}{13}[/tex] into equation (i) as follows;

     2p - 3([tex]\frac{6}{13}[/tex]) = 4

(e)  Now, solve for p in d above

Multiply through by 13;

26p - 18 = 52

Collect like terms

26p = 52 + 18

26p = 70

Divide both sides by 2

13p = 35

p = [tex]\frac{35}{13}[/tex]

Therefore, p = [tex]\frac{35}{13}[/tex] and q = [tex]\frac{6}{13}[/tex]

Answer: 192  books

Step-by-step explanation:

2/3 + 1/4 = 11/12

16 remaining books = 1/12

16 x 11 = 176

176 + 16=192

Answer:

ksdljfdacnkjdsfhbjfjkn

Step-by-step explanation:

Answer:

the percent decrease is approximately 47 %

Step-by-step explanation:

Since the quantity started at 170 and then changed to 90, there was clearly a decrease in its value.

We use the following formula to calculate the percent of decrease:

[tex]\%\,decrease = \frac{original-final}{original} \,100\\\%\,decrease = \frac{170-90}{170} \,100\\\%\,decrease = \frac{80}{170} \,100\\\%\,decrease \approx 47\,\%[/tex]

Answer:

21

Step-by-step explanation:

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