The variables x and y vary directly. Use the given values to write an equation that relates x and y

Answer:

the value of x is between -4 and 4

Answer: D

Step-by-step explanation:

[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)}=\frac{\sqrt[3]{2x}}{4x+1}[/tex].

This eliminates A and B.

Also, the domain excludes when the denominator equals 0, which in this case, makes the answer D

Answer: 597

Step-by-step explanation:

The common difference is 5-1=4, so the explicit formula is [tex]a_{n}=1+(n-1)(4)[/tex]

Substituting in n=150,

[tex]a_{150}=1+(150-1)(4)=\boxed{597}[/tex]

Answer:

slope: -1

y-intercept: 6

Step-by-step explanation:

y-intercept is when x is 0 so it's 8 and the slope can be found using the slope formula (y2-y1)/(x2-x1)

(6-8)/(0 - (-2)) = -2/2 = -1

Answer:

B will be the answer...

Step-by-step explanation:

The second equation in system B is only in terms of y, so we need to use elimination to eliminate the x term from the second equation in system A.

To do that, we need to multiply the first equation by 5.

5 (-x − 2y = 7)

-5x − 10y = 35

Add to the second equation.  Notice the x terms cancel out.

(-5x − 10y) + (5x − 6y) = 35 + (-3)

-16y = 32

Combining this new equation with the first equation from system A will get us system B.

-x − 2y = 7

-16y = 32

Answer:

To get system B, the second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution to system A.

Step-by-step explanation:

exact answer

Answer:

  $385.50

Step-by-step explanation:

The amount of commission is found by multiplying the commission rate by the value of the sale.

  1.5% × $25,700 = $385.50

A commission of $385.50 is made on an average car sold.

Answer:

No

Step-by-step explanation:

no because just muiltiplying 7.00 * 8 is 56 not inculuding the 99 cents it is already over 50. The answer is 63.92 so a reasonable estimate would be around $60

Answer:

5/8

Step-by-step explanation:

5/8=0.6.25

0.625> all the other numbers

Answer:

[tex]f(z) = z^2-3z+2[/tex]

[tex]f(x+1) = x^2-x[/tex]

[tex]f(\sqrt{2}+1) = 2-\sqrt{2}[/tex]

Step-by-step explanation:

[tex]f(x+1) = x^2+2x+1-3x-3+2[/tex]

[tex]f(\sqrt{2}+1) = 2+2\sqrt{2}+1-3\sqrt{2}-3+2[/tex]

[tex]a - 4 = ( \sqrt{a} - 2)( \sqrt{a} + 2)[/tex]

[tex] \frac{ \sqrt{a} - 2}{a - 4} = \frac{ \sqrt{a} - 2}{( \sqrt{a} - 2)( \sqrt{a} + 2) } = \frac{1}{ \sqrt{a} + 2 } [/tex]

12.5% is the percentage of numbers randomly generated by Taylor's computer that is less than 0.5.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

The percentage of numbers randomly generated by Taylor's computer are less than 0.5 is given by

P(0≤X≤0.5)

=[tex]\int_{0}^{0.5}\frac{1}{4}dx[/tex]

[tex]=\frac{1}{4}x|^{0.5}_{0}[/tex]

[tex]=\frac{1}{4}(0.5-0)[/tex]

[tex]=0.25(0.5)[/tex]

= 0.125

That is 12.5%

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Based on the upper and lower quartiles of the box plots:

Range for Maths is 60 to 85

Range for Language arts is 60 to 80.

In a box plot, the about half of the data set lies between the upper quartile and the lower quartile which are represented at the beginning and the end of the edges of the box respectively. This makes up 50% of a data distribution.

Thus, for Maths, the Upper and lower quartiles are between 60 to 85, hike that for Language arts are between 60 to 80.

Therefore, 50% of Theos scores for Maths ranges from: 60 to 85, while for Language arts is: 60 to 80.

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Answer:

Step-by-step explanation:

Use interest formula:

Substitute given values and calculate:

Answer:

$ 380

Step-by-step explanation:

We can use the below formula to find the simple interest.

Simple interest = P r t ÷ 100

Here,

P ⇒ Principal ⇒ $ 9500

r ⇒ rate ⇒ 2%

t ⇒ time ⇒ 2 years

Let us solve it now.

Simple interest = P r t ÷ 100

Simple interest = 9500 × 2 × 2 ÷ 100

Simple interest = 38000 ÷ 100

Simple interest = $ 380

The profit-maximizing price of​ e-books relating to​ do-it-yourself topics is $5.35 and the average total cost of producing​ e-books is $4.35.

​

a. Profit-maximizing price

The maximum that the firm can earn is $35,000 at a quantity of 35,000 copies

Fixed cost FC = $140,000

Variable cost vc=$0.35 per book

Total Revenue TR =P XQ

Total Revenue TR= P x 35,000

Total Cost TC = FC + VC XQ

Total Cost TC = 140,000 + (0.35×35,000)

Total Cost TC = 140,000 +$12,250

Total Cost TC = $152,250

Profit = TR- TE

35,000 = 35,000P- $152,250

35,000P=187,250

P=187,250/35,000 copies

P=$5.35

b. Average total cost

Average total cost=Total cost/Quantity

Average total cost= $152,250/35,000 copies

Average total cost=$4.35

Therefore the profit-maximizing price of​ e-books relating to​ do-it-yourself topics is $5.35 and the average total cost of producing​ e-books is $4.35.

​

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The complete question is:

A firm that sells​ e-books - books in digital form downloadable from the Internet​ - sells all​ e-books relating to​ do-it-yourself topics​ (home plumbing,​ gardening, and so​ on) at the same price. At​ present, the company can earn a maximum annual profit of ​$35,000 when it sells 35,000 copies within a​ year's time. The firm incurs a 35​-cent expense each time a consumer downloads a​ copy, but the company must spend ​$140,000 per year developing new editions of the​ e-books. The company has determined that it would earn zero economic profits if price were equal to average total​ cost, and in this case it could sell 40,000 copies. Under marginal cost​ pricing, it could sell 120,000 copies.

In the short​ run, to the nearest​ cent, what is the​ profit-maximizing price of​ e-books relating to​ do-it-yourself topics? ​

At the​ profit-maximizing quantity, to the nearest​ cent, what is the average total cost of producing​ e-books?

The trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)

The height of the tree can be found using trigonometric ratios.

Therefore,

tan ∅ = opposite / adjacent

Hence,

for the higher wire

tan 75 = h / 4

4 tan 75 = h

This can be express as follows:

tan 75 = tan(45 + 30)

Hence,

4 × 3.73205080757 = 14.9282032303 ft = 14.9ft

Hence, the trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)

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Answer:

143°

Step-by-step explanation:

supplementary angles are angles that combine to form a straight line (and we know that a straight line = 180 degrees)

you can think of an angle as needing another angle to "supplement" it into being a full line.

So, we know that one angle = 37°

And that: one angle + supplementary angle = 180 degrees

                 37° + x  = 180°

                - 37           -37

                     x    = 143

So, the measure of this angle's supplement is 143°

hope this helps!!

Answer:

143 degrees

Step-by-step explanation:

180 - 37 = 143

∠A ≅ ∠D , BC≅ EF , AC ≅   DF  , option B , C , F are the correct answer.

CPCTC stands for corresponding parts of congruent triangles are congruent .

This means when two triangles are congruent then the corresponding sides are also congruent.

In the given triangles , Δ ABC ≅ ΔDEF

∠A ≅ ∠D

BC≅ EF

AC ≅   DF

Therefore option B , C , F are the correct options

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Answer:

60°, arms 6

Step-by-step explanation:

let the total arms = n

total generated angles in a regular polygon is = (n-2)×180

now,

(n-2)×180 = 120 n

or, 180n - 360 =120n

or, 60n = 360

or, n = 6

The answers are as follow:

a) y'= -2x/y

b) y' = -4/y

The technique of implicit differentiation allows you to find the derivative of y with respect to x without having to solve the given equation for y.

Given:

x²y+4y=8

On differentiation

applying product rule

2xy+ x²y'  = 0

2xy = - x²y'  

2y = -xy'

y'= -2x/y

b) equation of the tangent line to the graph when x = 2.

y' = -4/y

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Answer:

Values: 3,4,5

Step-by-step explanation:

I hope this helps:)

Answer:

7.5mph

Step-by-step explanation:

Let the average speed of the boat to be x mph.

Total Distance = Avg. Speed x Total Time

60 = ((x+6) + (x-6))(4)

60 = (x+6+x-6)(4)

(2x)(4)=60

2x=60/4

2x = 15

x = 15 /2

x = 7.5mph

Answer:

  15 +√261 ≈ 31.155 mph

Step-by-step explanation:

The time for the trip can be found by dividing the distance by the speed.

__

The relation between time, speed, and distance is ...

  time = distance/speed

The speed for the downstream leg was the sum of the boat speed (b) and 6 mph. The speed for the upstream leg was the difference. So the total trip time was ...

  4 = 60/(b +6) +60/(b -6) . . . total  time is the sum of the times for the legs

__

Multiplying by the product of the denominators, we have ...

  4(b +6)(b -6) = 60(b -6) +60(b +6)

  b² -36 = 30b . . . . divide by 4 and simplify

  b² -30b = 36 . . . . put in a form useful for completing the square

  (b -15)² = 36 +15² . . . . . complete the square

  b -15 = √261 . . . . . . . . take the square root (negative root is extraneous)

  b = 15 +√261 ≈ 31.155 . . . . add 15

The average speed of the boat was about 31.155 mph.

It takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc.

It should be noted that a quadrilateral simply means a shape that has four sides and four angles.

In orde to prove that triangles are similar, we only need to prove corresponding angles congruency.

On the other hand, it takes more to prove that quadrilaterals are similar because there are several quadrilaterals such as rectangle, square, etc. This makes them more elaborate.

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Answer:

50.24 mm^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2  where r is the radius

A = 3.14 ( 4)^2

   = 50.24 mm^2

Answer:

c. 50.24 square millimeters

Step-by-step explanation:

Radius of circle = 4 milimeters.

Area of a circle = πr²

Area = 3.14 × 4² (π = 3.14)

= 50.24 square millimeters

The function among the given option is height of a building in feet, height of the building in inches , Option B is the correct answer.

A function is a law that relates a dependent and an independent variable.

The options mentioned below needs to be studied to determine which forms a function.

Option A , C and D doesn't really form a function ,

For two variables need to be a function then they have to be dependant on each other and have only one output for a given input.

height of a building in feet, height of the building in inches

Height of building in feet = (height of building in inches/12)

so this is a function

Therefore Option B is the right answer.

The missing options are

If the relationships below are given in the form (input, output), which pairing always describes a function?

A) (number of doors in a car, number of cup holders in the car)

B) (height of a building in feet, height of the building in inches)

C) (beverage charge on a bill, total meal charge on the bill)

D) (distance from home during a trip, time elapsed during the trip)

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Answer:

a² b² c² equals mc² and that is the answer

Answer:

A

Step-by-step explanation:

In this case you have to show that 1 + 2 = 180

This way when you show that 2 + 3 = 180, that proves 1 & 3 are congruent.

Answer:

A. 2. ∡1 is supplementary to ∡2 (linear pair theorem)

Step-by-step explanation:

Given the following proof so far, we have:
1. Line a and line b intersect => given

2. ? => ?

3.  ∡3 is supplementary to  ∡2 => linear pair theorem

4.  ∡1 ≅ ∡3 => congruent supplements theorem

Now let's take a look at the reasoning for statement 4, which says that angle 1 and 3 are congruent due to congruent supplements theorem.

In this theorem, if 2 angles are supplementary (add up to 180 degrees) to the same angle, it means those 2 angles are congruent.

Why does this work?
________________________________________________________
Let's say x + y = 180, and z + y = 180

By transitivity (if a = b and b =c, then a=c), x + y is equal to z + y

x + y = z + y

Subtract y from both sides

x = z

________________________________________________________

Statement 3 says  ∡3 is supplementary to  ∡2, and because of congruent supplements theorem being our last reason (where  ∡1 and  ∡3 are congruent), we need to make statement 2 also have ∡1 being supplementary to ∡2, (∡2 is like y in the example above - it's the angle that  ∡1 and  ∡3 are both supplementary to).

This will eliminate choices B (which has  ∡1, but also  ∡4 which isn't necessary), C ( ∡which mentions nothing about  ∡1), and D (which also doesn't mention anything about  ∡1, and which also isn't necessary as we have statement 3 essentially saying the same thing), leaving A as the correct answer.

Answer:

[tex] \dfrac{149}{40} [/tex]

[tex] \dfrac{38}{15} [/tex]

Step-by-step explanation:

[tex] (\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) =  [/tex]

[tex] = (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10}) [/tex]

[tex] = (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20}) [/tex]

[tex] = \dfrac{67}{40} - (-\dfrac{41}{20}) [/tex]

[tex] = \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2} [/tex]

[tex] = \dfrac{67}{40} + \dfrac{82}{40} [/tex]

[tex] = \dfrac{149}{40} [/tex]

[tex] (-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) = [/tex]

[tex] = (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5}) [/tex]

[tex] = 0 + \dfrac{18}{15} + \dfrac{20}{15} [/tex]

[tex] = \dfrac{38}{15} [/tex]

Answer: r = 121.92 cm

              Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

              7587404.65

Step-by-step explanation:

The radius is given. It's the distance from the center of the sphere to the end. The radius is 4 ft. 1 ft is 30.48cm so 4ft is 121.92cm  

(radius) r = 121.92 cm

Volume = 4/3 x 3.14 x [tex]121.92^{3}[/tex]

             = 4/3 x 3.14 x 1812278.18

             = 4/3 x 5690553.49

             = 7587404.65

Answer:

25

Step-by-step explanation:

find the greatest common factor (GCF) of the 3 quantities using prime factorisation.

125 = 5 × 5 × 5

150 = 2 × 3 × 5 × 5

225 = 3 × 3 × 5 × 5

Next, identify those prime factors that the 3 numbers have in common and multiply them.

the common factors are 5 × 5 = 25

then

125 ÷ 25 = 5

150 ÷ 25 = 6

225 ÷ 25 = 9

the 25 students each get 5 apples, 6 oranges and 9 mangoes