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neonofarm [45]
3 years ago
7

A proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordere

d pair (4, 3) is on the graphed line.
Part A: What is the price of 1 pound of potatoes? Show your work, including the proportion you used to determine the price. (8 points)
Part B: What does the ordered pair (8, 6) on the graph represent? Explain in words. (2 points)
Mathematics
1 answer:
Ronch [10]3 years ago
8 0

Part A

We have x = 4 and y = 3 paired up together.

This says that 4 pounds of potatoes cost $3

The price per pound (aka unit price) is y/x = 3/4 = 0.75 dollars = 75 cents.

Answer: 75 cents per pound

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

Part B

The ordered pair (8,6) means x = 8 and y = 6 pair up together.

So in this case, 8 pounds of potatoes cost $6.

notice how y/x = 6/8 = 3/4 = 0.75 dollars = 75 cents here as well. So we get the same unit cost.

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.
Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

Hypotenuse:37.56

Other\ Legs: 26.56

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

y = 11 + x

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

y^2 = x^2 + x^2

y^2 = 2x^2

This gives:

(11+x)^2 = 2x^2

Open bracket

121 + 22x + x^2= 2x^2

Collect like terms

2x^2 - x^2 -22x - 121 = 0

x^2 -22x - 121 = 0

Using quadratic formula:

x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}

x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}

x = \frac{-(-22)\±\sqrt{968}}{2*1}

x = \frac{22\±31.11}{2}

Split

x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\

x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}

x can not be negative.

So:

x = \frac{53.11}{2}

x = 26.56

Recall that:

y = 11 + x

y = 11 + 26.56

y = 37.56

Hence, the dimensions are:

Hypotenuse:37.56

Other\ Legs: 26.56

6 0
3 years ago
Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown. A (–1, 1) B (1, 1) C (1,
yaroslaw [1]

Answer:

the transformation was 90° at the origin

Step-by-step explanation:

the transformation was 90° at the origin

5 0
4 years ago
Read 2 more answers
Can anyone help me please?
vovangra [49]

Answer:

- 6

Step-by-step explanation:

The given statement implies that the slope of line formed by (5, r) is (3, -2) is -2, as they lie on the same line.

Slope(using these pts) = (y2 - y1)/(x2 - x1)

=> - 2 = (-2 - r)/(3 - 5)

=> -2 = (-2 - r)/(-2)

=> (-2)(-2) = (-2 - r)

=> 4 = -2 - r

=> r = - 2 - 4

=> r = - 6

4 0
3 years ago
Read 2 more answers
(a) A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected and the amount of g
rewona [7]

Answer:

In average, houses in the particular area use 119,6 therms of gas during the month of January.

Step-by-step explanation:

The μ formula is:

μ= ΣXi/N

ΣXi= is the sum of each xi. xi is each observation in the sample.

N= Total number of observations.

For this case:

ΣXi= 125+103+118+ 109+ 122+ 82+ 99+ 138+ 151+ 149

ΣXi= 1196

N= 10

μ= 1196/10

μ= 119,6

In average, houses in the particular area use 119,6 therms of gas during the month of January.

5 0
4 years ago
Find the perimeter 8ft 11ft
Irina18 [472]
8x2=16 and 11x2=22 all you have to do is add 16+22 and that gives you 38 i hope this helped
4 0
3 years ago
Read 2 more answers
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