The depth of a lake, d, varies directly with r, the amount of rainfall last month. if k is the constant of variation, write an equation to represent the situation.

Answers

Answer 1

Answer:
d = kr

Explanation:
We know that the depth (d) varies directly with the amount of rain (r).
This means that as the amount of rain increases, the depth increases and vice-versa.
The depth would depend on r multiplied by a constant of variation (k)

Translating this into equation, we would get the following:
d = kr

Hope this helps :)

Related Questions

To find the length ab of a small lake, a surrounding veyor measured angle acb to 96, ac to be 91 yards, and bc to be 71 yards. what is the approximate length of the lake?

Answers

Using the law of Cosins that states: For any triangle, a, b and c are sides and C is the angle opposite side c
c² = a² + b² − 2ab cos(C)

Applying this in our problem, we get:
AB²= 71²+91²- 2x91x71 cos96
AB²=14627.7 yard²
AB=121 yard

Find 2 positive real numbers that differ by 1 and have a product of 1

Answers

A) x -y =1
B) x * y =1
B) y = 1/x

A) x -(1/x) = 1
Multiplying both sides by "x"
A) x^2 -1 = x
A) x^2 -x -1 = 0

Solving by the quadratic formula
x = 1.618 and
y = .618

Interestingly, the number 1.6180339... is called the "phi ratio" or the "golden ratio".
https://en.wikipedia.org/wiki/Golden_ratio

How much greater is the median number of pairs of shoes in the inventory at the Golf pro Shop than the median number of pairs of shoes in the inventory at the Tennis Pro Shop?

Answers

Answer: 20

To get this answer, you find the median of the golf pro shop data (a = 40) and the median of the tennis pro shop data (b = 20). Then you subtract to get a-b = 40-20 = 20. The median of any box plot is the vertical line inside the box plot.

Answer:

Step-by-step explanation:

A wise man once said, "500 reduced by 3 times my age is 200." What is his age?

Answers

The answer is: " 100 " .
_________________________________________________________

Explanation:
_________________________________________________________

Let "x" represent the numerical value of [the man's age].

500 - 3x = 200 ; Solve for "x" ;

Subtract "500" from each side of the equation:

500 - 3x - 500 = 200 - 500 ;

to get:

- 3x = -300 ;

Now, divide each side of the equation by "-3" ; to isolate "x" on one side of the equation; & to solve for "x" ;

- 3x / -3 = -300 / -3 ;

x = 100 .
_______________________________________________________
The answer is: " 100 " .
_______________________________________________________

Two similar cones have volumes of 8pi and 64pi find the ratios of the radio

Answers

we have that
volume larger cone=64*pi unit³
volume smaller cone=8*pi unit³

we know that
volume larger cone=[scale factor]³*volume smaller cone
[scale factor]³=volume larger cone/volume smaller cone
[scale factor]³=64*pi/(8*pi)-----> 8
[scale factor]=∛8------> [scale factor]=2

Find the ratios of the radio
[radio larger cone/radio smaller cone] is equal to the scale factor
so
[radio larger cone/radio smaller cone]=2
or
[radio smaller cone/radio larger cone]=1/2

Danielle ran 3 1/8 miles on Tuesday and 4 and 1/2 miles on Wednesday and 5 1/4 miles on Thursday how far did Danielle run all together this

Answers

well you would figure out a common denominator for all fractions.

3 1/8

4 1/2

5 1/4

the common denominator would be 8. so multiply all the fractions by the number that would give you 8 on the bottom of the fraction

1/8 x 1 = 1/8

1/2 x 4 = 4/8

1/4 x 2 = 2/8

now you would set up your problem

3 1/8 + 4 4/8 + 5 2/8

first add the fractions

1/8 + 4/8 + 2/8 = 7/8

then add the whole numbers

3 + 4 + 5 = 12

now put the number and fractions together and you have your answer

12 and 7/8

Need help on this as soon as possible!

Answers

Volume of the prism: V= Ab*h
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6

Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4

V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)

Michael, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Michael also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2.20 dollars, Basic Proofreading 2.80 dollars, Extended Proofreading 3.90 dollars, and Deep Editing 12 dollars Maria has a 25-page manuscript. The equation below shows the relationship between the total cost of editing 25 pages, T, and the cost per page, c, if she gets the 5% discount: 25c − 0.05(25c) = T Using the equation, what is the best quality of editing that Maria can get done for a maximum of $66.50?

Answers

Using the equation, the cost per page Maria can afford is
25c -.05(25c) = 66.50
0.95*25*c = 66.50
c = 66.50/(0.95*25) = 2.80

The best quality of editing that Maria can afford is ...
Basic Proofreading

Tracy solved the system of equations by making a substitution for x in the second equation.

What equation did she get as a result of that substitution?

x = –2y – 2
2x + 3y = –6

–2y – 2 = –6
–2y + 1 = –6
–4y – 2 + 3y = –6
–4y – 4 + 3y = –6

Answers

Tracy put (-2y-2) where x is in the second equation. This resulted in
2(-2y-2) +3y = -6
After eliminating parentheses, Tracy had
-4y -4 +3y = -6

The 4th selection is appropriate:
-4y - 4 + 3y = -6

Suppose you want to build a rectangular sandbox where the width is 5 feet less than the length and the diagonal is 5 feet longer than the length. what are the dimensions of the sandbox?

Answers

Let L = length
W = L - 5 ←5 feet less than (reverse order - ) the length (L)
D = L + 5
These 3 lengths form a right triangle with D being the hypotenuse, c.
Using the Pythagorean Theorem, a² + b² = c²
L² + (L - 5)² = (L + 5)²
L² + L² - 10L + 25 = L² + 10L + 25
L² - 20L = 0
L = 0 (can't use this answer) or L = 20 (this is a usable answer)
Dimensions of the sandbox 20 ft by 15 ft
Length = 20 ft
Width = 15 ft
Diagonal = 25 ft

In the figure, what is the value of x?

Answers

1. C 2. B 3. D 4. B 5. C

Answer:x=90 °

Step-by-step explanation:

In any circle the exterior angle formed is half of the major arc - minor arc .

Angle formed by tangents or secants = [tex]\frac{1}{2}(Major arc - minor arc )[/tex]

The sum of measure of arcs inany circle is 360°.

Minor arc is given as x°.So Major arc = 360-x.

Substituting the given values in the formula :

[tex]x=\frac{1}{2}(360-x-x)[/tex]

[tex]x=\frac{1}{2}(360-2x)[/tex]

x=180-x

Adding x both sides we have:

2x=180.

Dividing both sides by 2.x= 90.

The domain of this graph is {x | x≥−2}.

True.
False.

Answers

The correct answer is: [B]: " True ".
_____________________________________________________
Note: From visual inspecton of the graph shown — [Note: all images attached refer to the same graph.] :

→ We can see that when "x = -2" ; there is only one value for "y" ; and then the "line" of the graph stops for any coordinate corresponding to any "x-value" LESS THAN "-2" ;

→ and that there are corresponding "y-coordinates" corresponding to any "x-value that is equal to "-2" and "GREAT THAN "-2" .
_________________________________________________________

The domain of the graph is {x|x>= - 2}

So the answer is TRUE

Which of the following equations could be used to solve the given equation?

9x + 26 + 7x - 17 = 2x + (-3x) + 5x

16x + 9 = 0
16x + 9 = 4x
16x + 11 = 4x

Answers

If we simplify like terms on left and right sides we gwt

16x + 9 = 4x

Its B

Answer: The correct option is (B) [tex]16x+9=4x.[/tex]

Step-by-step explanation: We are given to select the correct equation that could be used to solve the following equation :

[tex]9x+26+7x-17=2x+(-3x)+5x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find the correct equation, we need to simplify the given equation (i).

From equation (i), we get

[tex]9x+26+7x-17=2x+(-3x)+5x\\\\\Rightarrow (9+7)x+(26-17)=2x-3x+5x\\\\\Rightarrow 16x+9=(2-3+5)x\\\\\Rightarrow 16x+9=4x.[/tex]

Thus, the required equation is [tex]16x+9=4x.[/tex]

Option (B) is CORRECT.

HELP ASAP PLEASE!1!! Determine the factors of a2b + 2a2 + 3b + 6. (b + 3)(a2 + 2) (b + 2)(a2 + 3) (ab + 2)(a + 3) (ab + 3)(a + 2)

Answers

The answer is (b+2)(a²+3).
Hope this helps!

Answer:

B. (b + 2)(a2 + 3)

Step-by-step explanation:

Please help !!

Question posted below

Answers

4 (6) - 3 (4)
24 - 12 = 12

One of the angles of a parallelogram is equal to 40°. Find the rest of the angles.

Answers

angles a and b must add up to 180 degrees. So the angles are 40, 140, 40, 140

The angles of parallelogram are 40°, 140°, 40°, 140°.

What is parallelogram?

A parallelogram is a type of quadrilateral. It is a two-dimensional figure with four sides. The most important properties of a parallelogram are that the opposite sides are parallel and congruent and the opposite angles are also equal.

For the given situation,

One angle of parallelogram = 40°

Let the unknown angle be 'x'

The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees.

⇒ [tex]40+x=180[/tex]

⇒ [tex]x=140[/tex]

The opposite interior angles are equal.

Hence we can conclude that the angles of parallelogram are 40°, 140°, 40°, 140°.

Learn more about the parallelogram here

https://brainly.com/question/25999877

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help a brother out lol

Answers

We know that [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex]; to find [tex]( \frac{g}{f} )(x)[/tex] we are going to divide [tex]g(x)[/tex] by [tex]f(x)[/tex]:
[tex]( \frac{g}{f} )(x)= \frac{x^2-6}{3x+1} [/tex]
Since the denoinatorcan't be zero:
[tex]3x+1 \neq 0[/tex]
[tex]x \neq - \frac{1}{3} [/tex]

We can conclude that the correct answer is A. [tex]\frac{x^2-6}{3x+1} [/tex] [tex]x \neq - \frac{1}{3}[/tex]

A sum of money is divided among peter paul and jane in ratio 13:12:7 calculate how much paul gets if amount peter gets more than jane is 78$

Answers

First we define variables:
x: Money Peter receives
y: Money Paul receives
z: Money Jane receives
We write the system of equations:
x / y = 13/12
x / z = 13/7
x = z + 78
Solving the system we have:
x = $ 169
y = 156 $
z = 91 $
Answer:
Paul gets 156 $

Assuming the cost of cement blocks is $75 per 1,000, how much will it cost for the blocks to build a wall 7ft. tall by 20 ft. long if the block is 6 inches thick and 10 blocks are needed for 1 cubic foot.

Answers

First, we are going to convert the thick of the block from inches to feet. To do that we are going to take advantage of the fact that 1 foot=12 inches to create a multiplier:
[tex]6in* \frac{1ft}{12in} =0.5ft[/tex]

Since the thickens of the wall will be equal to the thickness of each block, the thick of the all is 0.5 feet.
Now, to find the volume of the wall, we are going to use the formula:
[tex]V_{w}=hlt[/tex]
where
[tex]V_{w}[/tex] is the volume of the wall
[tex]h[/tex] is the height of the wall
[tex]l[/tex] is the length of the wall
[tex]t[/tex] is the thickness of the wall
We know for our problem that the wall is 7ft. tall by 20 ft. long, so [tex]h=7ft[/tex] and [tex]l=20ft[/tex]. We also know from our previous calculation that the thickness of the wall is 0.5ft, so [tex]t=0.5ft[/tex]. Lets replace those values in our formula:
[tex]V_{w}=hlt[/tex]
[tex]V_{w}=(7ft)(20ft)(0.5ft)=70ft^3[/tex]

Now we know that the volume of the wall is 70 cubic feet. We also know that 10 blocks are needed for 1 cubic foot, so to find the total numbers of blocks needed, we are going to multiply the volume of the wall by the number of blocks needed for 1 cubic foot:
[tex]TotalBlocks=70ft^3* \frac{10blocks}{1ft^3 } =700 blocks [/tex]

Finally, to find the total cost, we are going to multiply the number of blocks needed by the cost of 1000 blocks:
[tex]TotalCost=700blocks* \frac{75}{1000} =52.5[/tex]

We can conclude that the cost of the wall will be $52.5

2/3 (a-b) =c, solve for a

Answers

[tex]\dfrac{2}{3}(a-b)=c\ \ \ \ |\cdot3\\\\2(a-b)=3c\\\\2a-2b=3c\ \ \ \ |+2b\\\\2a=3c+2b\ \ \ \ |:2\\\\\boxed{a=\dfrac{3c+2b}{2}}[/tex]

Which number is irrational A)25.23 B) 8 C)square root of 48

Answers

Ans:- √48

Reason:

=> √48 = √(2×2×2×2×3) = 4√3

As, we know√3 is irrational therefore √48 is also irrational no.

Hope this helps!

Hello there, and thank you for posting your question here on brainly.

Short answer: C.

Why?

When a number is irrational, that means it goes on forever. It can't be A, because we know the end is .23. It can't be B because that is just a whole number. The only one that would make sense is answer choice C. √48.

Hope this helped you! ♥

If a population has a birth rate of 40 individuals per 1,000 per year and a death rate of 30 individuals per 1,000 per year, how will the population change each year

Answers

It will increase by 10 individuals per 100 per year

Bruno is designing his next skateboard. the skateboard store has 333 types of grip tape, 131313 types of decks, 777 types of trucks, 4 types of bearings, and 2 types of wheels. how many different skateboards can bruno create

Answers

Did u make this up? Because there are would be loads

Answer:

2184 is what i got.

Step-by-step explanation:

triangle ABC is similar to Triangle XYZ. AB=5x+25, BC=7x+44, YZ=29, XZ=45, XY=14 Find x

Answers

Answer: The fraction -109/47 (see note below)

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

Explanation:

Triangle ABC is similar to Triangle XYZ. This means that
AB/BC = XY/YZ
is one proportion we can form

Plug in the given expressions and then isolate x
AB/BC = XY/YZ
(5x+25)/(7x+44) = 14/29
29(5x+25) = 14(7x+44)
29(5x)+29(25) = 14(7x)+14(44)
145x+725 = 98x+616
145x-98x = 616-725
47x = -109
x = -109/47

note: its possible your teacher made a typo since we got a negative fraction here. I would ask your teacher to double check.

Find the surface area of the equilateral triangular pyramid.

Answers

C is the correct answer

good luck

Answer:

i think the answer is C.

GOOD LUCK!!!

Broderick answered 21 of the 25 questions on his history test correctly. What decimal represents the fraction of problems he answered incorrectly?

Answers

THE ANSWER IS 0.84 I just multiplied 25 and 21 by four to get 84 over 100 to easily convert to a decimal.
84 hundredths

Bryant collects a set of 20 data representing the lengths of worms he found in the garden. The variance of the set of measurements is 36. What is the standard deviation from the mean? millimeters

Answers

Answer:

6 millimeters

Explanation:

The standard deviation is the square root of the variance.

Since the variance is 36, the standard deviation would be

√36 = 6

Answer:6

Step-by-step explanation:

Factor the trinomial below.
x2 – 14x + 45

A. (x – 3)(x + 15)
B. (x – 5)(x + 9)
C. (x – 5)(x – 9)
D. (x – 3)(x – 15)

Answers

Hi there!

The answer is C.
[tex] {x}^{2} - 14x + 45 = (x - 9)(x - 5)[/tex]

To find our answer we are looking for 2 integers. The sum of the integers must be -14 (since it must be equal to the number before the variable x). The product of both integers must be 45. Now we can conclude we are looking for the numbers -9 and -5.

[tex] - 9 + - 5 = - 9 - 5 = - 14 \\ - 9 \times - 5 = 45[/tex]

(Remember that multiplying 2 negatives makes you end up with a positive.)

~ Hope this helps you!

WILL MARK BRAINLIEST!!

Given: x - 5 > -10.

Choose the solution set.

{x | x R, x < -15}

{x | x R, x > -5}

{x | x R, x < 5}

{x | x R, x > 15}

Answers

Answer:

{x | x R, x > −5}

Step-by-step explanation:

x - 5 > -10

+ 5 + 5

__________

x > −5

I am joyous to assist you anytime.

classify 4x^5+2x^4-5x^3+12 by number of terms

Answers

That is 4 terms long.

The polynomial 4x⁵ + 2x⁴ - 5x³ + 13 has a degree of five and a quadrinomial (four terms).

What is a polynomial?

Polynomial is an expression that involves only the operations of addition, subtraction, multiplication of variables.

Polynomials can be classified based on degree as linear, quadratic, cubic and so on. Polynomials can also be classified based on number of terms.

The polynomial 4x⁵ + 2x⁴ - 5x³ + 13 has a degree of five and a quadrinomial (four terms).

Find out more on polynomial at: https://brainly.com/question/2833285

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