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Find the slope of the line passing through the points (1,5) and (4,-2).

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:

none of these unless one of the 45s are 46

Step-by-step explanation:

nearest dollar means no cents so $46.60 and $45.60 are out

58 is over 50 so the two 45s go away

the only option left is none of these or 46 if you accidentally put 45 instead of 46

Answer:

D?

Step-by-step explanation:

¯\_(ツ)_/¯

Answer:

[tex]g=\frac{2\,H}{m+r}[/tex]

Step-by-step explanation:

Starting with :

m g + r g = 2 H

extract "g" as a common factor on the left of the equal sign:

g (m + r) = 2 H

Now, in order to solve for "g" , divide both sides of the equal sign by the binomial (m + r):

g = (2 H )/(m + r)

[tex]g=\frac{2\,H}{m+r}[/tex]

I hope this helps you. Plz mark me as the brainliest.

Answer:

1.26

Step-by-step explanation:

1.008 divided by o.8 =1.26

Answer:

1.26, Dude get a calculator

Step-by-step explanation:

0 1. 2 6 0

8 1 0. 0 8 0

− 0        Listen. Its hard to do long division ona computer.

 1 0      

−   8      

   2 0    

 − 1 6    

     4 8  

   − 4 8  

       0 0

     −   0

         0

Answer:

[tex] x = 6.25 [/tex]

Step-by-step explanation:

Given that ∆DFG ~ ∆RPQ, therefore, [tex] \frac{DF}{PR} = \frac{DG}{QR} = \frac{FG}{QP} [/tex] (similarity theorem).

DF = 10

PR = 8

DG = 5

QR = 4

QP = 5

FG = x

[tex] \frac{10}{8} = \frac{5}{4} = \frac{x}{5} [/tex]

Using [tex] \frac{5}{4} = \frac{x}{5} [/tex] , solve for x

cross multiply:

[tex] 4*x = 5*5 [/tex]

[tex] 4x = 25 [/tex]

[tex] x = \frac{25}{4} [/tex]

[tex] x = 6.25 [/tex]

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:

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:

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:

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:

21

Step-by-step explanation:

tcctvucycyccyctctctchu ycuvuvuvy t r y y g g t g

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:

x =28

Step-by-step explanation:

Divide the numbers

Combine multiplied terms into a single fraction

Eliminate fraction denominators

Simplify

Divide both sides of the equation by the same term

Answer:

Step-by-step explanation:

This is a geometric sequence with first element 1 and common ratio 2:

a(n) = 1*2^(n - 1)

Thus, a(1) = 1

a(2) = 2^(2 - 1) = 2

a(3) = 2^(3 - 1) = 4

a(4) = 2 ^( 4 - 1) = 2^ 3 = 8

a(5) = 2^(5  -1) = 2^ 4 = 16

One month is approximately 30 days.  Therefore,

a(30) = 2^ (30 - 1) = 2^29 = 536870912

Using this pattern, Paulina will "make" $536870.12 vs $20 via Paulina's father's plan.

...... ❤

[tex] \frac{ - 4}{ \: \: 7} x = - 1[/tex]

Now firstly we have to take 7 to right hand side and multiply -1 by 7

[tex] - 4x = - 1 \times 7[/tex]

[tex] - 4x = - 7[/tex]

Now we have to take -4 to the right hand side and divide -7 by -4

[tex]x = \frac{ - 7}{ - 4} [/tex]

As we know that in case of division - and - are cancelled so ,

[tex]x = \frac{7}{4} [/tex]

Hope it helps u mate

Answer:

20991

Step-by-step explanation:

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: 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:

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.

Answer:

1.00o2

Step-by-step explanation:

You dont need this explained come on

Answer:

whole number

hope it helps

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:

Hey there!

30-second ads for 20 days on a day time show.

6200(20)=124000

30-second ads for 5 days on a prime time show.

165000(5)=825000

124000+825000=949000 dollars.

Let me know if this helps :)

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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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:

Y(x) = 10x - 2600

Profit= RS. 1000

Step-by-step explanation:

Amount sold per item=RS. 50.

Cost of manufacturing= RS. 36.5

Distributor charges= Rs 3.5

Daily over head charge= RS.2600

Profit function Y (x)

Y (x) =x(50) -36.5(x) -3.5(x)-2600

Y(x) = (50-36.5-3.5)x-2600

Y(x) = 10x - 2600

If x= 360

Profit Y = 10(360) - 2600

Profit Y = 3600-2600

Profit = 1000

Profit= RS. 1000

Answer:

See below.

Step-by-step explanation:

1)

So we have:

[tex]\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2[/tex]

This can be interpreted as:

"There exists a natural number x and an integer y such that x² is equal to y²."

2)

So we want even numbers are in the set of integers.

[tex]\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}[/tex]

This is interpreted as:

"The set of even numbers (2n such that n is an integer) is in the set of integers"

Answer:

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

Therefore, 41 gallons x 18 mpg = 738

Step-by-step explanation: