A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

Answers

Answer 1
A direct variation has a constant slope, i.e. (y/x)= constant.

Both of the given two points give a slope of (y/x)=14/2=28/4=7, so the equation of the function is
y/x=7, or simply
y=7x

Related Questions

if 2 pounds of strawberries cost 4.50 how much would 3 pounds cost

Answers

6.75$ this my best answer

[tex]\bf \begin{array}{ccll} lbs&\$\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2&4.50\\ 3&x \end{array}\implies \cfrac{2}{3}=\cfrac{4.50}{x}\implies x=\cfrac{3\cdot 4.50}{2}[/tex]

What is the common difference for the arithmetic sequence?

4.7, 6, 7.3, 8.6, 9.9,...

Answers

The common difference is 1.3
It would be 1.3 like the other person said because 6-4.7 is 1.3 and 7.3-6 is 1.3 so that would be the sequence ( Explanation )

You've got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?

Answers

10 minutes : 8 problems
x minutes : 60 problems
10 * 60/8 = 150/2 = 75 minutes for 60 problems
about 75 minutes because if you divide 60 by 8, you get 7.5, 7.5x10=75 so that is your answer



Factor out the coefficient of the variable. The expression 2.2x +4.4 factored is

Answers

2.2(x+2) is the answer

what is r^m divided by r^m equal to.

Answers

1, everything divided by itself is 1

Given f(x) = x^2 - 10x + 22, what is the range of f?

Answers

The range is all the possible y-values.

For a parabola that opens up, it is everything greater than the vertex.

If the vertex is (h,k) then the range is y >= k.

Vertex can be found using completing the square:
[tex]x^2 -10x +22 \\ \\ (x^2 -10x + (\frac{-10}{2})^2) +22 - (\frac{-10}{2})^2 \\ \\ (x^2 -10x+25) +22-25 \\ \\ (x-5)^2 - 3[/tex]
(h,k) = (5,-3)    ------> Range is y >= -3

Vertex may also be found using formula [tex]h = \frac{-b}{2a} [/tex]
a = 1, b = -10, c = 22
[tex]h = \frac{10}{2} = 5[/tex]
[tex]k = 5^2 - 10(5) +22 \\ \\ k = 25 -50+22 \\ \\ k = -3[/tex]
------> Range is y >= -3

f(x)=x2-10x+22 domain of f

Answer: all real numbers

Range of F

Answer: y> -3

Solve for the distance between (522, 1322) and (9000, -1337) to the third decimal.

Answers

[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 522}}\quad ,&{{ 1322}})\quad % (c,d) &({{ 9000}}\quad ,&{{ -1337}}) \end{array} \\\\\\ % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\\\ -------------------------------\\\\ d=\sqrt{(9000-522)^2+(-1337-1322)^2}\\\\\\ d\sqrt{8478^2+(-2659)^2} \\\\\\ d=\sqrt{71876484+7070281}\implies d=\sqrt{78946765} \\\\\\ d\approx 8885.199209922\implies d\approx 8885.199[/tex]

the sum of two numbers is 18 . the difference of the two numbers is -2 find the numbers

Answers

a and b is a numbers 
a + b = 18
a - b = -2

2a = 16
a   = 8

8 + b = 18
b = 10 

Suppose e(x) = 3 and e[x(x − 1)] = 27.5. (a) what is e(x2)? [hint: first verify that e[x(x − 1)] = e[x2 − x] = e(x2) − e(x).]

Answers

52(ex) would be your answer 

Amanda can jog 18 miles in 5 hours. At this rate, how many miles can Amanda jog in 4 hours?

Answers

18 = x
__ __
5 4
x = 18•4 / 5
72/5 = 14.4 final answer

we know that

Amanda can jog [tex]18[/tex] miles in [tex]5[/tex] hours

so

by proportion

Find the number of miles that Amanda  can jog in [tex]4[/tex] hours

[tex]\frac{18}{5} \frac{miles}{hours} =\frac{x}{4} \frac{miles}{hours} \\ \\5*x=18*4 \\ \\x=72/5 \\ \\ x=14.4\ miles[/tex]

therefore

the answer is

[tex]14.4\ miles[/tex]

8 = 4x + 12 what does x equal

Answers

x = -1.   8 = 4x+12
            -4 = 4x
            -1 = x

8 = 4x + 12
1) subtract 12 from both sides.
-4 = 4x
2) divide each side by 4
-1 = x

The formula for the volume of a sphere is Upper V equals four thirds pi r cubedV=
4/3πr3​, where r is the radius of the sphere. The steel ball to the right is in the shape of a sphere and has a diameter of 3030 millimeters.
a. Find the exact volume of the sphere.
b. Find a​ 2-decimal-place approximation for the volume.

Answers

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\quad \begin{cases} r=radius=\frac{diameter}{2}\\ d=diameter\\ ----------\\ d=10\\ r=5 \end{cases}\implies V=\cfrac{4\pi \cdot 5^3}{3}[/tex]


now, that rounded to 2 decimals is just 523.60

After calculating, the volume of the sphere obtained will be equal to V = 1.45 × 10¹⁰ mm³.

What is Volume?

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given data in the question,

The formula for the volume of the sphere is given as,

V = 4/3 π r³  

Diameter = 3030 mm

r = D/2

r = 3030/2

r = 1515 mm

So, the volume will be,

V = 4/3 π (1515³)

V = 1.45 × 10¹⁰ mm³

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The Perez family has a rectangular fish tank how much water will the tank hold if it's length is 3 feet, its width is 2 feet and its height is 3 feet


A) NONE
B) 18 cubic feet
C) 3 cubic feet
D) 6 cubic feet
E) 9 cubic feet

Answers

V = 3 x 2 x 3 = 18
answer
B) 18 cubic feet 

You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over. What fractional portion of the original bowl of salad does each friend receive?

Answers

How many friends are there?

Answer:

[tex]\frac{2}{3x}[/tex]

Where, x = total friends

Step-by-step explanation:

Given,

The part of the salad has eaten = [tex]\frac{1}{3}[/tex]

Total part of the salad = 1,

Thus, the remaining part of the salad = original part - part has eaten

[tex]=1-\frac{1}{3}[/tex]

[tex]=\frac{3-1}{3}[/tex]

[tex]=\frac{2}{3}[/tex]

If there are x friends,

Then the portion of the original bowl of salad received by each friend

[tex]=\frac{\text{Remaining part}}{\text{Total friends}}[/tex] [tex]=\frac{2}{3x}[/tex]

Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found. Find the slope and y-intercept of the line.

Answers

Answer:

m=-63 b=825

Step-by-step explanation:

The slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.

What is the general equation of straight line? What is a mathematical function, equation and expression?straight line : The general equation of a straight line is -

        [y] = mx + c

function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is that Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods.

It is given that a graph has number of days on the x - axis and number of canned goods on the y-axis. The line goes through points (2, 699) and (8, 321). The slope of the line can be written as -

[m] = (321 - 699)/(8 - 2)

[m] = -378/6

[m] = - 63

For the point (2, 699), we can write -

y = - 63x + c

699 = - 63 x 2 + c

699 = -126 + c

c = 699 + 126

c = 835

Therefore, the slope of the line would be - [m] = - 63 and the [y] intercept is - [c] = 835.

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{Complete question -

A graph has number of days on the x-axis and number of canned goods on the y-axis. A line goes through points (2, 699) and (8, 321).

Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found.

Find the slope and y-intercept of the line.}

Find the missing number of each unit rate

Answers

4/2 = 2/1
6/2 = 3/1
12/4 = 3/1
if the last on is negative it would -24/8 = -3/1 if positive 3/1 hope this helps remember you would reduce your fraction
4/2 reduces to 2/1.

12/4 reduces to 3/1

Can you do the remaining problems?

whats the nearest tenth to -61 square root

Answers

well, the square root of a negaitve number will be an imaginary number
that is, i=√-1

so we can write
[tex]\sqrt{-61}=(\sqrt{-1})(\sqrt{61})=(i)(\sqrt{61})[/tex] [tex] \sim (i)(7.81) \sim 7.8i[/tex]
Hello!
the √(-61) is a complex number √61i

But if you wish to find the value of an irrational and imaginary number, I will give you the approximate answer.

[tex] \sqrt{-61} \to \sqrt{-1*61} \to \sqrt{-1} * \sqrt{61} \to i* \sqrt{61} \to i*7,81024...\: \boxed{\approx 7.8i}[/tex]

there are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred

Answers

1,525
In the case of rounding up, the number beside the must be above 5
But, in the case of rounding down, the number beside must be below 5.
The hundred place is the number 5.
The number before the 5 is the number 2
Since 2 is lower than 5, we round it down..
Thus the answer is 1,500

Hope this helps :))

Julia and Kim round the number of pages to the nearest hundred as 1500.

Given that, there are 1,525 pages in a book.

What is the rounding off numbers?

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

In the given number, digit in the tens place is 2, so the number rounded to nearest hundred as 1500.

Therefore, Julia and Kim round the number of pages to the nearest hundred as 1500.

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the circle with center (3,5) and radius 2 has a equation?

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &3&5&2 \end{array} \\\\\\ (x-3)^2+(y-5)^2=2^2\implies (x-3)^2+(y-5)^2=4[/tex]

6578 divided 34

20\5

Answers

0.0037942 is your answer

Answer:

263.56 :)

Step-by-step explanation:

The measure of arc XZ is 28° what is the measure of XYZ

Answers

Arc XZ is marked in red (see the image attachment)
Angle XYZ is marked in blue

It turns out that angle XYZ is exactly half the measure of arc XZ. This is due to the inscribed angle theorem. Angle XYZ is an inscribed angle that cuts off, or subtends, arc XZ.

measure of arc XZ = 28 degrees
measure of angle XYZ = (1/2)*(measure of arc XZ)
measure of angle XYZ = (1/2)*(28 degrees)
measure of angle XYZ = 14 degrees

Answer: D) 14 degrees

Which three statements would produce the truth value F when p is true and q is false?

A. p -> q
B. ~p/\~q
C. p->~q
D. q\/~p
C. p/\~q
please help

Answers

B. If [tex]p[/tex] is true, then [tex]\sim p[/tex] (NOT [tex]p[/tex]) is false; If [tex]q[/tex] is false, then [tex]\sim q[/tex] is true. Then [tex]\sim p\land\sim q[/tex] must be false, because both arguments are not true.

Answer with Step-by-step explanation:

p is true then ~p is false.

q is false then ~q is true.

A. p -> q

if p is true and q is false then this gives false truth value.

Hence, here truth value is F

B. ~p/\~q

if any one of them is false then it gives false truth value.

Hence, here truth value is F(since,~p is false)

C. p->~q

true statement implies a true statement hence, truth value will be true

Hence, here truth value is T(p true implies ~q true)

D. q\/~p

if any one of them is true then compound statement is true.

Hence, here truth value is F(since, ~p and q both are false)

E. p/\~q

if both true then compound statement is also true.

Hence, here truth value is T(since p and ~q both are true)

A geologist have two rocks on a scale that weighs 2 1/2 lbs together rock a was 1/7 of a the total weight how much did rock a weight

Answers

Final answer:

By using the given fraction of rock 'a' against the total weight of two rocks, we can find that rock 'a' weighs approximately 0.357 lbs.

Explanation:

The student's question involves calculating the weight of a rock, given as a fraction of a total weight. In this case, they are talking about a scenario where a geologist uses a scale to weigh two rocks together, with a total weight of 2 1/2 lbs, and rock 'a' is specified to be 1/7 of this total weight. To determine the weight of rock 'a', we simply divide the total weight by 7.

So, 2 1/2 lbs is equivalent to 2.5 lbs (since 1/2 is the same as 0.5). To find the weight of rock 'a', we take this total weight and perform the operation: 2.5 ÷ 7 = 0.357 lbs.

Therefore, rock 'a' weighs approximately 0.357 lbs. Remember, this is an estimation because the weight of the rock is being given as a fraction of the total weight, and actual weights can vary based on factors such as density and volume.

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6-1. let x have a poisson distribution with a mean of 4. find (a) p(2≤x≤5). (b) p(x≥3). (c) p(x≤3).

Answers

The mean of a Poisson distribution coincides with its rate parameter, so [tex]\lambda=4[/tex]. We have a PMF of

[tex]f_X(x)=\dfrac{e^{-4}4^x}{x!}[/tex]

So,

a. [tex]\mathbb P(2\le X\le5)=\dfrac{e^{-4}4^2}{2!}+\cdots+\dfrac{e^{-4}4^5}{5!}\approx0.6936[/tex]

b. [tex]\mathbb P(X\ge3)=\dfrac{e^{-4}4^3}{3!}+\dfrac{e^{-4}4^4}{4!}+\cdots\approx0.7619[/tex]

c. [tex]\mathbb P(X\le3)=\dfrac{e^{-4}4^0}{0!}+\cdots+\dfrac{e^{-4}4^3}{3!}\approx0.4335[/tex]

MARIA WALKED 4.035 KILOMETERES. WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?

Answers

Here's my interpretation:  4 whole km, plus zero tenths of a km, plus 3 hundredths of a km, plus 5 thousandths of a km.

Answer:

[tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]

Step-by-step explanation:

Given : MARIA WALKED 4.035 KILOMETERS.

To Find :WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?

Solution :

Number = 4.035

The numbers after decimals when read from first to last has positions tenth , hundredth , thousandth and so ...

The number before the decimal part has positions ones , tens , hundreds and so on when read from last to first

Now 4 is at ones place

0 is at tenth place

3 is at hundredth place

5 is at thousandth place

So, Expanded form : [tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]

The cost of 5 cds and a $ 12 DVD

Answers

Final answer:

The cost of 5 CDs and a $12 DVD is $62.

Explanation:

The subject of this question is Mathematics. The question asks for the cost of 5 CDs and a $12 DVD. To find the total cost, we need to know the price of each CD and the price of the DVD.

Let's say the price of each CD is $10. The total cost of 5 CDs would be 5 multiplied by $10, which is $50.Adding the cost of the DVD, which is $12, to the cost of the CDs, we get a total cost of $50 + $12 = $62.

Therefore, the cost of 5 CDs and a $12 DVD is $62.

determine the quadratic function of f whose graph is given. The vertex is (1,-3) and the y-intercept is -2

Answers

hmmm the y-intercept is at -2?  what does that mean?  well, is where the graph "intercepts" or touches the y-axis, and when that happens, x = 0, so the point is really ( 0 , -2 ).

and we know where the vertex is at.  Let's assume a vertical parabola, in which case the squared variable is the "x".

[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex \begin{cases} h=1\\ k=-3 \end{cases}\implies y=a(x-1)^2-3 \\\\\\ \textit{now, we also know that } \begin{cases} x=0\\ y=-2 \end{cases}\implies -2=a(0-1)^2-3 \\\\\\ 1=a(-1)^2\implies \boxed{1=a}\qquad thus\implies \begin{cases} y=1(x-1)^2-3\\ \textit{or just}\\ y=(x-1)^2-3 \end{cases} [/tex]

A red candle is 8 inches tall and burns at a rate of 7/10 inch per hour. A blue candle is 6 inches tall and burns at a rate of 1/5 inch per hour. After how many hours will both candles be the same height?

Answers

Answer:

  4 hours

Step-by-step explanation:

The height of the red candle in inches can be modeled by ...

  h = 8 - (7/10)t

where t is the number of hours it burns.

Likewise, the height of the blue candle can be modeled by ...

  h = 6 - (1/5)t

The heights of the two candles will be the same when one expression for height is equal to the other.

  8 - (7/10)t = 6 - (1/5)t

  2 = t(7/10 - 1/5) . . . . . . . . . add (7/10)t -6

  2/(5/10) = t = 4 . . . . . . . . . divide by the coefficient of t

Mr. and Mrs. Zeller close on a 20 year home loan for $150,000. The monthly payment with no points is $1,160, but if they buy a point it is $1,150. What might you infer if Mr.and Mrs. Zeller choose not to buy a point? a. They plan to sell the house at the end of 5 years. b. They plan to sell the house at the end of 15 years. c. They plan to sell the house at the end of 20 years. d. They plan to sell the house at the end of 25 years.

Answers

the answer is A. they plan to sell the house at the end of 5 years

Answer:

the answer is A they plan to sell it in 5 years

Step-by-step explanation:

An object's position is given by x(t) = 5 + 10 t 2. what is its acceleration after 5 s

Answers

Final answer:

The acceleration after 5 seconds is 20 m/s^2.

Explanation:

To find the acceleration, we need to take the second derivative of the position function.

x(t) = 5 + 10t^2

Taking the derivative with respect to time, we get:

v(t) = 20t

Taking the derivative again, we get the acceleration:

a(t) = 20

Therefore, the acceleration after 5 seconds is 20 m/s^2.

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