The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 square feet. Let y represent the number of square yards and x the number of square feet. Then y varies directly with x.What is the constant of variation?

Answers

Answer 1

Answer: Let y represent the number of square yards
Let x the number of square feet.
Then y varies directly with x.

y = kx
where k is the constant of variation.
y = 3 yards^2
x = 27 feet^2

3 = k(27)
k = 3/27
k = 1 yard^2 /9 feet^2

So the constant of variation is 1 yard^2 /9 feet^2.

Answer 2

Answer:

Answer:

constant of variation is 1/9 and equation is y=1/9x

Step-by-step explanation:

3/27 = 1/9

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A certain brand of coffee comes in two sizes. A 10.15-ounce package costs 2.98. A 27.8 -ounce package costs 8.99. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Find the arithmetic mean between 7 and 23
1/3 (n+1)+2=1/6 (3n-5)

Five more than four times a number is greater than seven

Answers

Answer:

5+ 4x > 7, x > 1/2

Step-by-step explanation:

How would I write 8.21 as a mixed number?

Answers

we know that

A mixed number is a number consisting of a whole number and a proper fraction

we have

$8.21$

$8.21=8+0.21=8+(21)/(100)=8(21)/(100)$

therefore

the answer is

$8(21)/(100)$

The value of mixed number of number 8.21 is,

⇒ 8 (21 / 100)

We have to given that;

A number is,

⇒ 8.21

Now, We can simplify as;

⇒ 8.21

⇒ 8.21 × 100 / 100

⇒ 821 / 100

⇒ 8 21/100

Therefore, The value of mixed number of number 8.21 is,

⇒ 8 (21 / 100)

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The number of girls at Sky High School is 60 greater than the number of boys. If there are 1250 students all together, how many girls are there all together?

Answers

$girls : x\nboys : y \n \n x= y+60 \nx+y=1250 \n\nsubstitution : \n \n y+60+y=1250 \n 2y=1250-60\n2y=1190 \ \ / :2 \n y= 595 \n \n x=595 +60=655 \n \nAnswer : \ there \ is \ 655 \ \ girls \ and \ 595 \ boys$

595 in boys and i think 655 in girls

The measure of central angle RST is radians. What is the area of the shaded sector? 4Pi units squared8Pi units squared
16Pi units squared
20Pi units squared

Answers

Answer:

" $8\pi$ units squared"

Step-by-step explanation:

The image of the circle is attached.

The shaded area of the circle is basically HALF of the whole circle. If we can get the area of the circle, we will halve it, to get our answer for area of shaded region.

Area of circle is given as:

$A=\pi r^2$

Where

A is area

r is the radius

Looking at the pic, the radius is "4", so we substitute and find area of circle:

$A=\pi r^2\nA=\pi (4)^2\nA=\pi (16)\nA=16\pi$

THe shaded area is HALF of that, so:

Area of Shaded = $(16\pi)/(2)=8\pi$ sq. units.

Answer is " $8\pi$ units squared"

Answer:

its 8

Step-by-step explanation:

i got it right

3) Dori created a 2 letter code to get into her waterproof iPad. She only used the letters ABC and D because she was afraid she might forget the combination. Well, Dori forgot anyway and now wants to make a list of all possible combinations so she can get back in A Make a list of all the possible 2 letter codes.

Answers

Answer:

AA, AD, AC, AB (or flipped)

BB, BD, BC, BA (or flipped)

CD, CA, CB, CC (or flipped)

DA, DC, DD, DB (or flipped)

Step-by-step explanation:

Find the first five terms of the sequence defined by each of these recurrencerelations and initial conditions.
a) an = 6an-1, a0 = 2
b) an = −2an-1, a0 = −1
c) an = an-1 – an-2, a0 = 2, a1 = −1

Answers

a) The first five terms of the sequence are 2, 12, 72, 432, 2592.
b) The first five terms of the sequence are -1, 2, -4, 8, -16.

c) The first five terms of the sequence are 2, -1, -3, -2, 1.

To find the first five terms of the sequence defined by each of these recurrence relations and initial conditions, we will use the given recurrence relation and initial conditions to find the next terms in the sequence.

a) an = 6an-1, a0 = 2

The first term is given as a0 = 2. We will use the recurrence relation to find the next terms.
a1 = 6a0 = 6(2) = 12
a2 = 6a1 = 6(12) = 72
a3 = 6a2 = 6(72) = 432
a4 = 6a3 = 6(432) = 2592

So, the first five terms of the sequence are 2, 12, 72, 432, 2592.

b) an = −2an-1, a0 = −1

The first term is given as a0 = -1. We will use the recurrence relation to find the next terms.
a1 = -2a0 = -2(-1) = 2
a2 = -2a1 = -2(2) = -4
a3 = -2a2 = -2(-4) = 8
a4 = -2a3 = -2(8) = -16

So, the first five terms of the sequence are -1, 2, -4, 8, -16.

c) an = an-1 – an-2, a0 = 2, a1 = −1

The first two terms are given as a0 = 2 and a1 = -1. We will use the recurrence relation to find the next terms.
a2 = a1 - a0 = -1 - 2 = -3
a3 = a2 - a1 = -3 - (-1) = -2
a4 = a3 - a2 = -2 - (-3) = 1

So, the first five terms of the sequence are 2, -1, -3, -2, 1.

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