What is the range of 90, 72, 150, 43, 84, 91, 65, 48?<br> 105<br> 106<br> 107

Find two positive numbers satisfying the given requirements. the product is 192 and the sum of the first plus three times the se

Zepler [3.9K]

<h3>Given</h3>

Two positive numbers x and y such that xy = 192

The values that minimize x + 3y

<h3>Solution</h3>

y = 192/x . . . . . solve for y

f(x) = x + 3y

f(x) = x + 3(192/x) . . . . . the function we want to minimize

We can find the x that minimizes of f(x) by setting the derivative of f(x) to zero.

... f'(x) = 1 - 576/x² = 0

... 576 = x² . . . . . . . . . . . . multiply by x², add 576

... √576 = x = 24 . . . . . . . take the square root

... y = 192/24 = 8 . . . . . . . find the value of y using the above equation for y

The first number is 24.

The second number is 8.

6 0

3 years ago

The Clark family must pay $2,820 in property tax on their home this year. The house payment $752 per month. What is their paymen

Harlamova29_29 [7]

It's actually easier than it seems. if the tax is paid in equal payments every month and the total throughout a year (12 months) is $2,820, you have to find out how much they pay every month
so divide the total by the number of months
2,820/12=235
they pay $235 in taxes every month
to find out the total of the taxes and the house payment, just add the monthly tax and the monthly house payment.
235+752
and your answer is the sum

8 0

3 years ago

Read 2 more answers

An ant has a mass of approximately 4 × 10–3 grams and an elephant has a mass of approximately 8 x 106 grams. About how many time

Butoxors [25]

Ant's mass: 4 x 10 - 3
Elephant's mass: 8 x 106

First, we should evaluate these expressions by using PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. From P to S is the order that we must follow these steps.

So first for the ant's mass, we have to multiply first since the M comes before the S, resulting in 40 - 3 grams.
Next we have to subtract, leading us to getting 37.

For the elephant since there is only one operation, all we have to do is multiply, which equals 848.

In order to see how many times larger the elephant is than the ant, we have to divide the elephant's mass by the ant's.
848/37 = 22.9

Since you only want an approximate answer, you can put down 23 or even go a bit more vague and put down 20.

5 0

3 years ago

In the isosceles △ABC m∠ACB=120° and AD is an altitude to leg BC . What is the distance from D to base AB , if CD=4cm?

snow_lady [41]

If ΔACB is an isosceles triangle, then ∠A ≅ ∠B and AC ≅ CB

Since ∠C = 120° and ∠A + ∠B + ∠C = 180°, then ∠A = 30° and ∠B = 30°

Next, look at ΔADB. ∠A + ∠D + ∠B = 180°, so ∠A + 90° + 30° = 180° ⇒ ∠A = 30°

Now look at ΔADC. Since ∠A = 30° in ΔACB, and ∠A = 60° in ΔADB, then ∠A = 30° in ΔADC <em>per angle addition postulate.</em>

Now that we have shown that ΔADB and ΔADC are 30-60-90 triangles, we can use that formula to calculate the side lengths.

CD = 4 cm (given) so AC = 2(4 cm) = 8 cm

Since AC ≅ BC, then BC = 8 cm. Therefore, BD = 4 + 8 = 12 <em>by segment addition postulate.</em>

Lastly, look at ΔBHD. Since ∠B = 30° and ∠H = 90°, then ∠D = 60°. So, ΔBHD is also a 30-60-90 triangle.