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3 years ago

Find two positive numbers whose difference is 8 and whose product is 1505.

Mathematics

1 answer:

likoan [24]3 years ago

6 0

Answer:

The two positive numbers are 35 and 43.

Step-by-step explanation:

Let the two positive numbers be x and x + 8.

It is given that their product is 1505.

Therefore, x(x + 8) = 1505

$x^{2} +8x=1505$

$x^{2} +8x-1505=0$

$x^{2} +43x-35x-1505=0$

x(x + 43) - 35(x + 43) = 0

(x + 43)(x - 35) = 0

x = -43, x = 35

Since, the numbers are positive, x = 35 is only valid.

The other number is x + 8 = 35 + 8 = 43.

Hence, the required positive numbers are 35 and 43.

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F(x)=8x^3+125 find the zeros

eduard

Answer:

x = -5/2, (5+5i√3)/4, (5-5i√3)/4

6 0

3 years ago

It is estimated that approximately 8.1% of Americans are afflicted with diabetes. Suppose that a certain diagnostic evaluation f

denis23 [38]

Answer:

Multiple answers

Step-by-step explanation:

Considering that 8.1% of Americans have the disease:

If our theoretical group is of 10,000. We know that the 8.1% of our group have diabetes, so we multiplify 10,000 × .081(the percentaje) = 810. This is the total of adults in our group that have diabetes.

Now:

Test Positive:

We know that the test correctly diagnoses 95% of adults with diabetes. In our case the total of adults with diabetes is 810, so we multiplify 810 × .95(percentaje) = 769.50.
We know too that the test incorrectly diagnoses 3.5% of the adults. In our case the total of adults with diabetes is 810, so we multiplify 810 × .035(percentaje) = 28.35.
The total of adults the test diagnoses positive with diabetes should be the correctly and incorrectly we calculate previously. 769.50 + 28.35 = 797.85

Test Negative:

The total of test negative diagnoses should be the total of our group less the positive diagnoses. 10,000 - 797.85 = 9,202.15

Total do not have diabetes:

The total of adults do not have diabetes is the total of our group less the total of adults in our group that have diabetes. 10,000 - 810 = 9190

We expect that only the 95% of test positive for diabetes have the disease.

810 × .95(percentaje) = 769.50.

We expect that only the 5% (100% - 95% of test positive) of the 8.1% of americans afflicted with diabetes of negative test actually have the disease. 8.1 × .05(percentaje) = .40%, 9,202.15 ×.004(percentaje) = 36.80.

The 3.5% of Americans who test positive will not have the disease because this is the percentaje that the test incorrectly diagnoses.

4 0

3 years ago

Please find the what x equals 1) x/6=3/9 2) 9/12=x/8 3) 3/9=x/12 4) x/12=6/8

pychu [463]

$1)\\\dfrac{x}{6}=\dfrac{\not3^1}{\not9_3}\\\\\dfrac{x}{6}=\dfrac{1}{3}\qquad\text{multiply both sides by 6}\\\\x=\dfrac{1}{\not3_1}\cdot\not6^2\\\\\boxed{x=2}\\\\2)\\\dfrac{x}{8}=\dfrac{\not9^3}{12\!\!\!\!\!\diagup_4}\\\\\dfrac{x}{8}=\dfrac{3}{4}\qquad\text{multiply both sides by 8}\\\\x=\dfrac{3}{\not4_1}\cdot\not8^2}\\\\x=3\cdot2\\\\\boxed{x=6}$

$3)\\\dfrac{x}{12}=\dfrac{\not3^1}{\not9_3}\\\\\dfrac{x}{12}=\dfrac{1}{3}\qquad\text{multiply both sides by 12}\\\\x=\dfrac{1}{\not3_1}\cdot12\!\!\!\!\!\diagup_4\\\\\boxed{x=4}\\\\4)\\\dfrac{x}{12}=\dfrac{\not6^3}{\not8_4}\\\\\dfrac{x}{12}=\dfrac{3}{4}\qquad\text{multiply both sides by 12}\\\\x=\dfrac{3}{\not4_1}\cdot12\!\!\!\!\!\diagup_3\\\\x=3\cdot3\\\\\boxed{x=9}$

8 0

3 years ago

2. A lunch stand makes s.75 profit on each chef's salad and $1.20 profit on each Caesar salad. On a typical weekday, it sells be

kow [346]

Let's let

x = the number of chef salads, x>=0

y = the number of Caesar salads, y>=0

The constrains are:

40 <= x <= 60

35 <= y <= 50

x + y <= 100

The objective function here is F(x, y) = 0.75x + 1.20y

The corner points are (40, 35), (60, 35), (60, 40), (50, 50) and (40, 50).

F (40, 35) = 0.75*40 + 1.20*35 = $72

F (60, 35) = 0.70*60 + 1.20*35 = $84

F (60, 40) = 0.75*60 + 1.20*40 = $93

F (50, 50) = 0.75*50 + 1.20*50 = $97.50

F (40, 50) = 0.75*40 + 1.20*50 = $90

Thus, we conclude to maximize the profit 50 Chef and 50 Caesar salads should be prepared.

8 0

4 years ago

While working at the drugstore, Sam earns $9 per hour. How many hours will it take Sam to earn $18? Write your result in the spa

Goryan [66]

Answer:

2 hours

Step-by-step explanation:

Each hour, Sam earns $9

So 2 hours, Sam will earn 2 * $9 = $18

Thus, Sam will earn $18 in 2 hours working at the drugstore.

3 0

4 years ago