Mathematics High School

At the local grocer, the prices for apples are the following: 9 ounces for $1.89 or 1 pound for $2.49. How much will you save per pound, by buying the least expensive? Round to the nearest cent.

A.) $0.87
B.) $0.10
C.) $0.60
D.) $0.21

Answers

Answer 1

Answer: Option 'A' is correct.

Explanation:

Cost of  9 ounces of apples = $1.89

Cost of 1 ounce of apple is given by

[tex]\frac{1.89}{9}=\$0.21[/tex]

Now, if he bought 1 pound of apple,

Cost of 1 pound of apple = $2.49

Cost of 16 ounces = $2.49

(∵ 1 pound = 16 ounces)

Cost of 1 ounce of apple is given by

[tex]\frac{2.49}{16}=\$0.156[/tex]

So, Second option is the least expensive if he bought 1 pound of apple for $2.49

Then, he will save which is given by

[tex]0.21-0.156=0.054\times 16=$0.87\ per pound[/tex]

Hence, option 'A' is correct.

Answer 2

Final answer:

You will save $0.87 per pound by purchasing apples at the price per pound rate ($2.49) compared to the 9-ounce rate ($1.89 for 9 ounces), with the savings calculated by converting the 9-ounce price to a per pound rate and comparing it to the given per pound price.

Explanation:

To determine how much you will save per pound by buying the least expensive option for apples, first convert the price for 9 ounces into the equivalent price per pound. Since there are 16 ounces in a pound, you need to calculate the price per ounce and then multiply by 16 for the pound equivalence. The price per ounce for the first option is $1.89/9 ounces = $0.21 per ounce. Hence, the price per pound would be $0.21 per ounce × 16 ounces/pound = $3.36 per pound.

Now compare the price per pound of both options. The specified price per pound is $2.49, and the calculated price per pound for the 9-ounce option is $3.36. The savings per pound when buying the least expensive option ($2.49 per pound) would be $3.36 - $2.49 = $0.87 per pound, rounded to the nearest cent.

Therefore, the correct answer is (A) $0.87.

Related Questions

Find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3). (answer in slope-intercept form)

Answers

First, we can add 12 to both sides to get..
y=2x+4 
To get a perpendicular line, we have to take the reciprocal of the current slope and turn it to the opposite sign (ex: if it is positive, make it negative, if it is negative, make it positive) 
y= -(1/2)x+4
To make sure it passes through the points (2,3) we substitute x=2 and y=3 (x,y) 
3= -(1/2)2 +4
3= (-1) + 4
3=3
Now we know the equation is working
y= -(1/2)x + 4

The equation of the line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3) is y = (-1/2)x + 4.

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 to find the equation of a line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3).

The given equation is -

y - 12 = 2x - 8

y = 2x - 8 + 12

y = 2x + 4

Assume the equation of the line to be -

y = mx + c

Now -

m = -1/2                              {m (1) x m (2) = - 1 → for perpendicular lines}

So, the equation can be written as -

3 = - 1/2 x 2 + c

c = 3 + 1

c = 4

Therefore, the equation of the line perpendicular to y - 12 = 2x – 8 that passes through the point (2, 3) is y = (-1/2)x + 4.

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In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b

Answers

Answers are: 
a^5b^3
b^8
a^4b^4
a^8
ab^7
(there are 5 answers)

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

The exponents for the variable terms must add to 8, which is the original outer exponent of the expression given (3a+4b)^8

For something like a^8, we don't have any other exponent so we don't have to worry about it. If you wanted, you can think of a^8 as a^8b^0 and then note how 8+0 = 8. So the rule still applies

For ab^7, we would write it as a^1b^7 and the rule works here as well (1+7 = 8). 

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

Something like a^2b^3 is a non-answer because the exponents add to 2+3 = 5
Same goes for ab^8 = a^1b^8 because we have the exponents add to 1+8 = 9
And for a^6b = a^6b^1 we have the sum of exponents being 6+1 = 7

The [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms and this can be determined by using the arithmetic operations.

Given :

Expression  ---  [tex]\rm (3a + 4b)^8[/tex]

The following calculation can be used in order to determine the possible variables from the given expression.

The given expression can be written as:

[tex]\rm (3a + 4b)^8=(3a+4b)^2(3a+4b)^2(3a+4b)^2(3a+4b)^2[/tex]

[tex]\rm (3a + 4b)^8=(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)[/tex]

Now, further simplify the above expression.

[tex]\rm (3a + 4b)^8=(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)[/tex]

So, from the above calculation, it can be concluded that [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms.

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A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?

Answers

Solution:
To evaluate for P(0.372<x<0.428) we shall proceed as follows:
z-score is given by:
z=(x-μ)/σ
thus when x=0.372:
z=(0.372-0.4)/0.028
z=-1
thus
P(x<0.372)=P(z<-1)=0.1587

when x=0.428
z=(0.428-0.4)/(0.028)=1
P(x<0.428)=P(z<1)=0.8413
thus
P(0.372<x<0.428) =P(z<1)-P(z<-1)=0.8413-0.1587=0.6826
Final answer:

To find the percentage of observations between two values in a normal distribution, we can convert the values to z-scores and use a z-table to find the corresponding areas. In this case, the percentage of observations between 0.372 and 0.428 is 68.26%.

Explanation:

To find the percentage of observations that will lie between 0.372 and 0.428 in a normal distribution with a mean of 0.40 and standard deviation of 0.028, we need to find the area under the curve between these two values.

Using a standard normal distribution table or z-table, we can convert the values to z-scores by subtracting the mean and dividing by the standard deviation. The z-score for 0.372 is (0.372 - 0.40) / 0.028 = -1, and the z-score for 0.428 is (0.428 - 0.40) / 0.028 = 1.

By looking up the corresponding area for these z-scores in the z-table, we find that the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. To find the percentage between -1 and 1, we subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826 or 68.26%.

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WILL MAKE BRAINLIEST!!!!!!!The arc length of a sector is equal to twice the radius. Express the arc length s as a function of the area a of the sector.
s=

Answers

The area of a circular sector is . 

==>  
Since r = s/2, it follows that , or , or 
.

The arc length as a function of the area of the sector is  l=2√A.

What is the area of a sector?

Area of a sector = 1/2 * arc length(l) * radius(r)

[tex]A=[/tex] [tex]\frac{1}{2} l*r[/tex]......(1)

It is given that the arc length of a sector is equal to twice the radius.

This means [tex]l=2r\\[/tex]

So, [tex]r=\frac{l}{2}[/tex]

Putting the value of r in (1)

[tex]A = \frac{l^{2} }{4}[/tex]

[tex]l^{2} =4A[/tex]

[tex]l=2\sqrt{A} \\[/tex]

So, the required function is l=2√A

Hence, the arc length as a function of the area of the sector is  l=2√A.

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EASY 14 POINTS, PLEASE HELP ASAP.

Go into a dark room with a flashlight and face the beam toward a wall. Change the flashlight's distance from the wall as well as the way you hold the flashlight. Which conic sections can you form? Explain.

Describe how you formed different conic sections with your flashlight. Take and upload digital pictures as needed. Look at other students' descriptions and pictures and tell whether you agree with them.

What other simple tasks can you do in your home to form any of the conic sections? Again, describe these and/or take pictures to share with other students.

Answers

Well really it would have to depend on the flashlight. Is it an led bulb or a regular bulb?

Well really it would have to depend on the flashlight. Is it an led bulb or a regular bulb?

Complete the equation of the line through (-6,5) and (-3,-3) Use exact numbers. y=

Answers

(-6,5) and (-3,-3) 
slope = (5+3)/(-6 + 3) = 8/-3 = -8/3

y = mx + b
b = y - mx
b = -3 - (-8/3)(-3)
b = -3 - 8
b = -11

equation
y = -8/3 x - 11

hope it helps

The equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.

What is the equation of a line passing through two points?

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are given below.

(-6,5) and (-3,-3)

Then the equation of the line passing through the points (-6,5) and (-3,-3) will be

[tex]\rm (y + 3) = \left (\dfrac{-3-5}{-3+6} \right ) (x + 3)[/tex]

Simplify the equation, then the equation of the line will be

y + 3 = -(8/3)(x + 3)

y = -(8/3)x - 8 - 3

y = -(8/3)x - 11

Then the equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.

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BRAINLIESTTT ASAP!

please help

Answers

Width = x
Length = 2x+1

1/2 the permiter = l + w

1/2 perimeter = 176 /2 = 88
 so we have x + 2x+1 = 88

combine like terms:
3x +1 = 88

subtract 1 from both sides:
3x = 87
 divide both sides by 3
x = 87 / 3 = 29

with = 29 feet
 length = 29 x 2 = 58 +1 = 59 feet

check: 59 +59 +29+29 = 176


Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of them said they play football. Twenty of them said they do not play baseball or football.

Enter your answers in the boxes to complete the two-way table based on the given data.

Answers

The two-way table is attached.

We start out placing 31 in the Total column beside the Don't Play Baseball row.  We then place 16 in the Total row under the Play Football column.  20 goes in the Don't Play Baseball row under the Don't Play Football column.

Since there are 31 people that do not play baseball, and 20 of them don't play football, this leaves us with 31-20=11 that do not play baseball and play football.

There are 58 people total, so this goes in the Total row under the Total column.

There are 58 people, and 31 of them do not play baseball; this leaves us 58-31=27 total that play baseball.

16 total people play football, and 11 of them don't play baseball.  This leaves us 16-11=5 people that play football and play baseball.

There are 58 people, and 16 of them play football; this leaves us 58-16=42 total that don't play football.

42 people don't play football, and 20 of them don't play baseball; this leaves us 42-20=22 people that don't play football and play baseball.

5 people play baseball and play football, and 22 people play baseball and don't play football; this gives us 5+22=27 people total that play baseball.

if it takes 18 gallons of gas to go 400 miles how many gallons would it take to go 300 miles

A. 5.5 gallons

B. 13.5 gallons

C. 16.6 gallons

D. 22.2 gallons

E. 24 gallons

Answers

We will use the ratio and proportion method ( an equation formed with two ratios that are equal) to solve the question “if it takes 18 gallons of gas to go 400 miles,  how many gallons would it take to go 300 miles?”

Let x= the number of gallons for the gas  to go 300 miles

18:400=X:300

400x=300*18

400x=5400

X=5400/400

X=13.5 so the answer is B.

Answer:

B

Step-by-step explanation:

its 13.5 gallons

If you answer 110 questions and get a 94% how many did you get wrong

Answers

STEP 1:
Set up a ratio.

x= number correct out of 110

x/110= 94/100
cross multiply

(x * 100)= (110 * 94)
100x= 10,340

divide both sides by 100
x= 103.4


STEP 2:
subtract number correct in step 1 from total number of questions

=110 - 103.4
=6.6 questions wrong


ANSWER: There were exactly 6.6 questions wrong on the test. Since you cannot have a partial question (unless otherwise stated), but only whole questions, round up to 7 whole questions wrong.

Hope this helps! :)

A bag contains 6 red, 7 blue, and 5 green coins. If 3 coins are randomly selected in succession, what is the probability of selecting a red coin, then a blue coin, and then a green coin, if replacement occurs each time?

Answers

Total coins = 6 + 7 + 5 = 18
Red = 6
Blue = 7
Green = 5

P(Red, then blue, then green) = (6/18)(7/18)(5/18) = 35/972

Answer: 35/972
[tex]|\Omega|=18^3=5832\\ |A|=6\cdot7\cdot5=210\\\\ P(A)=\dfrac{210}{5832}=\dfrac{35}{972}\approx3.6\%[/tex]

If each person takes up 2.5 square feet of space, how many people can fit in an elevator that is 8 feet by 6 feet? Round to the nearest person.


2.5


19


38


48

Answers

First you would want to get the area of the elevator
To get that you would multiply 8x6=48
So now since each person takes 2.5 square feet you would divide 48 by 2.5
48/2.5=19.2
19.2 rounded to the nearest whole number is 19 
Your final answer is 19..

can someone please explan how I got this wrong?
Solve for x in the triangle
using laws of cosine

Answers

[tex]\bf \textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)cos(C)\implies c = \sqrt{a^2+b^2-(2ab)cos(C)} \\\\\\ \cfrac{a^2+b^2-c^2}{2ab}=cos(C)\implies cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C\\\\ -------------------------------\\\\ \begin{cases} x=24\\ a=25\\ b=19 \end{cases}\implies cos^{-1}\left(\cfrac{25^2+19^2-24^2}{2(25)(19)}\right)=\measuredangle x \\\\\\ cos^{-1}\left( \cfrac{41}{95} \right)=\measuredangle x\implies 64.432194^o\approx \measuredangle x[/tex]

Frazier has $1,200 in savings. He works because he is saving money for college, and he earns $9 an hour. If Frazier saves 25 percent of his net pay, after 20 percent is taken out for tax, identify the expression which represents Frazier's savings.

A) 1.8x + 1,200
B) 3.6x + 1,200
C) 7.2x + 1,200
D) 9x + 1,200

Answers

the correct answer is A..!! I think...:(



Answer:  The correct option is (A) [tex]1.8x+1200.[/tex]

Step-by-step explanation:  Given that Frazier is saving money for college and has $1200 in savings. He earns $9 per hour. He saves 25% of his net pay after 20% taken out for tax.

We are to identify the expression that represents Frazier's savings.

Let, x represents the number of hours for which Frazier works.

So, the net pay of Frazier = $ 9x.

Since 20% of the net pay is taken out for tax, so total pay of Frazier after taking out tax is given by

[tex]I_t=9x-20\%\times 9x=9x-\dfrac{20}{100}\times 9x=9x-\dfrac{9x}{5}=\dfrac{36x}{5}.[/tex]

Now, Frazier's savings from his net pay is given by

[tex]I_s=25\%\times \dfrac{36x}{5}=\dfrac{25}{100}\times \dfrac{36x}{5}=\dfrac{9x}{5}=1.8x.[/tex]

Since Frazier has $1200 already in savings, so the equation representing Frazier's savings will be

[tex]1.8x+1200.[/tex]

Thus, the required equation is [tex]1.8x+1200.[/tex]

Option (A) is CORRECT.

Consider the function f(x)=(x-9)/(x^3-81x)

Find the vertical asymptote(s) of f(x)

Answers

Answer:

Its A

x=0, -9

Step-by-step explanation:

just got it correct

Final answer:

The function f(x)=(x-9)/(x^3-81x) has three vertical asymptotes at x = 0, x = 9, and x = -9.

Explanation:

To find the vertical asymptote(s) of the function f(x) = (x-9)/(x^3-81x), we need to determine the values of x for which the denominator equals zero. Setting the denominator equal to zero and solving for x, we get:

x^3 - 81x = 0x(x^2 - 81) = 0x(x - 9)(x + 9) = 0

Therefore, the function has three vertical asymptotes at x = 0, x = 9, and x = -9.

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How to find two numbers that sum equal 15 and product are maximized?

Answers

x - the first number15 - x - the second numberx(15 - x) - the product of the our numbers 
f(x) = -x^2 + 15x

The maximum value is in the vertex of parabola (h; k).
For ax² + bx + c:
[tex]h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{b^2+4ac}{4a}[/tex]
We have: a = -1; b = 15; c = 0
substitute:
[tex]h=\dfrac{-15}{2\cdot(-1)}=\dfrac{15}{2}=7.5[/tex]
15 - 7.5 = 7.5
Answer: 7.5 and 7.5.

Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?

Answers

The answer is 1,000 miles

Please help asap, 70 points, THREE questions (:

Answers

[tex]9x^2=17\ \ \ |:9\\\\x^2=\dfrac{17}{9}\to x=\pm\sqrt{\dfrac{17}{9}}\\\\\boxed{Answer:\ x\approx-1.37\ \vee\ x=1.37}[/tex]


[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ the\ equation\ has\ 2\ solutions\\if\ \Delta=0\ then\ the\ equation\ has\ 1\ solution\\if\ \Delta < 0\ then\ the\ equation\ has\ no\ solution[/tex]

[tex]x^2+5x+7=0\\a=1;\ b=5;\ c=7\\\\Delta=5^2-4\cdot1\cdot7=25-28=-3 < 0\\\\\boxed{Answer:\ 0}[/tex]


[tex]5y^2-8y=2\ \ \ |-2\\\\5y^2-8y-2=0\\\\a=5;\ b=-8;\ c=-2\\\\b^2-4ac=(-8)^2-4\cdot5\cdot(-2)=64+40=104\\\\\sqrt{b^2-4ac}=\sqrt{104}\approx10.198\\\\y_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ y_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\y_1=\dfrac{-(-8)-10.198}{2\cdot5}\approx-0.22\\\\y_2=\dfrac{-(-8)+10.198}{2\cdot5}\approx1.82\\\\\boxed{Answer:\ 1.82,\ -0.22}[/tex]

Answer:

the answer for number 1 is 1.82

Step-by-step explanation:

Let 40 x 55 = n. Which of the choices shown is also equal to n?
A) (550 x 40)
B) (4 x 50) + (40 x 5)
C) (50 x 40) + (50 x 40)
D) (10 x 55) + (10 x 55) + (10 x 55) + (10 x 55)

Answers

D) (10 x 55) + (10 x 55) + (10 x 55) + (10 x 55)

use distributive rule to factor out 55:
55 (10+10+10+10) = 55×40

Simplify 72x6 y7 z .

Answers

Nothing further can be done to this topic

Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+20x-12=0

Answers

For this case we have the following function:
 x ^ 3-9x ^ 2 + 20x-12 = 0
 Rewriting we have:
 (x-6) * (x-2) * (x-1) = 0
 Therefore, the solutions are given by:
 Solution 1:
 x-6 = 0
 x = 6
 Solution 2:
 x-2 = 0
 x = 2
 Solution 3:
 x-1 = 0
 x = 1
 Answer:
 x = 6
 x = 2
 x = 1

Answer:

D= 1,2,or 6

Step-by-step explanation:

What are the trigonometric ratios of a right triangle ABC that has its right angle at C? AC=12 and BC=5

Answers

There are 3 trigonometric ratios:
Sine = opposite/hypotenuse, 
Cosine = adjacent/hypotenuse and
tangent = opposite/adjacent
Since in the question we have not been given the hypotenuse, we calculate it first. 
So, hypotenuse = √(12²+5²) = √(144+25) = √169 = 13.

Now we can find the trigonometric ratios; 
Sin A = Cos B = 5/13
Sin B = Cos A = 12/13
Tan A = 5/12
Tan B= 12/5  

 

A class has 24 boys and 16 girls. on a test the class mean was 75. the mean of the girls' score was 72. what was the mean of the boys' scores?

Answers

24+16=40
40*75=3000
16*72=1152
3000-1152=1848
1848/24=77

The mean of the boys' scores was 77.

What is arithmetic mean?

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.

We have been given that the class has 24 boys and 16 girls.

And the class mean was 75

The total number of students in the class was:

24 + 16 = 40

Total scored by 40 students = 40 × 75 = 3000

Number of girls = 16 and their mean = 72

Total scored by girls = 16 × 72 = 1152

The difference between the scores will give the total score of boys:

⇒ 3000 - 1152 = 1848

Number of boys = 24

Their mean will be 1848 / 24

So the mean of the boys' scores = 77

Therefore, the mean of the boys' scores was 77.

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Anyone know this? Will give brainiest

Answers

I believe the answer is C,
Hope this helps

Anyone know this geometry question? 10 min left! Will give brainiest

Answers

Angle 3 and angle 6 are corresponding angles, which means they are equal. In order for the lines to remain parallel, angle 3 and angle 6 would need to remain equal. If something is done to angle 6, then it would have to be done to angle 3 as well in order to keep the angles equal. So, if angle 6 is doubled, angle 3 would also have to be doubled. 

The answer is B. m< 3 would need to double.

Hope this helps =)

The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)

Answers

x(t)=3t
y(t)=4t^2+1

Time (seconds):

Where is the ship after 10 seconds?
t=10→Position: Point: P=(x(t), y(t))=(x(10), y(10))=?

t=10→x(10)=3(10)→x(10)=30
t=10→y(10)=4(10)^2+1=4(100)+1=400+1→y(10)=401

Position: P=(x(10), y(10))=(30, 401)

Answer: Option C.) (30, 401) 

Selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red pens

Answers

What? That’s not possible because there’s no blue pens. If that’s the awnser?

A city has a population of 260,000 people. Suppose that each year the population grows by 6.75% . What will the population be after 7 years? Use the calculator provided and round your answer to the nearest whole number.

Answers

Final answer:

The population of the city after 7 years will be approximately 393,574.

Explanation:

To find the population after 7 years, we'll use the formula for exponential growth:

P = P0(1 + r)t

Where P is the future population, P0 is the initial population, r is the growth rate as a decimal, and t is the number of years.

In this case, P0 = 260,000, r = 6.75% = 0.0675 (decimal form), and t = 7.

Plugging in these values, we have:

P = 260,000(1 + 0.0675)7

Using a calculator, the population after 7 years is approximately 393,574.

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Please Help!!!


Let ​ x2−12x=61 .​ What values make an equivalent number sentence after completing the square?

Answers

I did the math and there were two answers 1. 15.849 2. 3.849

The given equation is [tex] x^2-12x=61 [/tex]. Add 36 to both the sides of the equation, then

[tex] x^2-12x+36=61+36 [/tex].

The equation becomes,

[tex] x^2-12x+6^2=97\\
(x-6)^2=97 [/tex]

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:
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 :)
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