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RSB [31]
2 years ago
14

Marie pays $2.50 for 5 pencils. Use the drop-down menus to explain how to determine and

Mathematics
1 answer:
irinina [24]2 years ago
8 0
1:division
2:y=2.50/x
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Paulina swims 5 miles down a creek with a current for 2 hours. It takes her 4
Westkost [7]

Answer: her swimming speed = 1.875 mph

Speed of current = 0.625 mph

Step-by-step explanation:

Let x represent her swimming speed.

Let y represent the speed of the current.

Paulina swims 5 miles down a creek with a current for 2 hours. Since this is faster, it means that she swam with the current. Her total speed would be (x + y) mph

Distance = speed × time

Therefore,

5 = 2(x + y)

dividing both sides by 2, it becomes

2.5 = x + y- - - - - - -1

It takes her 4 hours to swim the same 5 miles back to her original destination against the

same current. It means that her total speed was (x - y) mph

Distance covered would be

5 = 4(x - y)

Dividing both sides by 4, it becomes

1.25 = x - y- - - - - - - 2

Adding equation 1 to equation 2, it becomes

3.75 = 2x

x = 3.75/2

x = 1.875

Substituting x = 1.875 into equation 1, it becomes

2.5 = 1.875 + y

y = 2.5 - 1.875

y = 0.625

4 0
2 years ago
Josephine bought 8 packets of biscuits. Each packet had a mass of 500 g
Nataly_w [17]

Answer: 985 g

Step-by-step explanation:

Total mass = 8 × 500g = 4000g

Let the three new packs be X, Y, and Z, for first, second, and third pack respectively.

4000g = X + Y + Z

let's put X and Z in terms of Y, since we're trying to solve for the second pack.

X = 2Y, and Z = Y + 60

Therefore,

4000 = X + Y + Z

4000 = 2Y + Y +Y + 60

4000 = 4Y +60

4000 - 60 = 4Y

3940 = 4Y

3940 ÷ 4 = Y

985g = Y = mass of the second pack

7 0
2 years ago
When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent?
stira [4]
Note that (5π)/6 radians = 150°. Therefore the given angle is in quadrant 2.

Refer to the figure shown below.

Reference angles are measured relative to the horizontal axis.
Therefore the reference angle in each quadrant is π/6 radians or 30°.
Denote the reference angle as θ'.
Then, in quadrant 1,
cos θ' = √3/2,  sin θ' = 1/2,  tan θ' = √3.

Because we are in quadrant 2,
  sin θ' = π/6;
  sin(5π/6) is positive, but cos (5π/6) and tan (5π/6) are negative.

 Answer:
5π/6 is in quadrant 2.
The reference angle, θ' = π/6.
sin(5π/6) is positive, cosine and tangent are negative.

3 0
2 years ago
Read 2 more answers
Circle J is located in the first quadrant with center (a, b) and radius s. Felipe transforms Circle J to prove that it is simila
iVinArrow [24]
The correct answer for the question that is being presented above is this one: "c. translate circle J by (x-a, y-b) and dilate by a factor of t/s." Circle J is located in the first quadrant with center (a, b) and radius s. Felipe transforms Circle J to prove that it is similar to any circle centered <span>at the origin with radius r.</span>
3 0
2 years ago
With an 18% discount, Joan was able to save $13.23 for a coat. What was the original price of the coat?
strojnjashka [21]
Hi there!

First we need to realise that the 18% discount equals John's savings. Therefore 18% of the original price is $13.23.

When we know 18% of the price, we can also find 1% of the total price.

18% = $13.23
Divide both sides by 18.

1% = $0.735
To find the total price, which equals 100%, we know only need to multiply both sides by 100.

100% = $73.50.
Therefore, the original price for the coat is $73.50.

~ Hope this helps you!
5 0
2 years ago
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