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AVprozaik [17]
3 years ago
5

A diver is currently at an elevation of -380 feet. Write an absolute value statement to express the diver's distance, in feet, f

rom sea level. Then, interpret the result in this situation by explaining what this means for the diver.
Mathematics
1 answer:
algol133 years ago
5 0

Answer:

The absolute value function:

f(x) = |x|

is defined as:

f(x) = x              if x ≥ 0

f(x) = -x             if x < 0.

Then, knowing that the elevation of the diver is -380 ft

We can write the absolute value of the distance as:

|-380ft| = -(-380ft) = 380ft

This means that the diver is at a distance of 380 ft from sea level. (And because we know that the sign is negative, we can conclude that he is 380ft below sea level).

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LenKa [72]

Answer:

  • x - 4y = 22

Step-by-step explanation:

<u>Given line:</u>

  • x - 4y = 20

<u>Convert the equation into slope-intercept form:</u>

  • x - 4y = 20
  • 4y = x - 20
  • y = 1/4x - 5

It has a slope of 1/4.

Parallel lines have equal slopes.

<u>Find the parallel line lines that passes through the point (2, - 5):</u>

  • y = 1/4x + b

<u>Substitute x and y values to work out the value of b:</u>

  • - 5 = 1/4*2 + b
  • - 5 = 1/2 + b
  • b = - 5 - 1/2
  • b = - 11/2

<u>The line is:</u>

  • y = 1/4x - 11/2

<u>Covert this into standard form:</u>

  • y = 1/4x - 11/2
  • 4y = x - 22
  • x - 4y = 22

7 0
2 years ago
Read 2 more answers
. Write the following expression in factored form using the greatest common factor.<br> 50a3 + 10a2
Tanya [424]

The factors of  50a³  are  1,  2,  5,  10,  25,  50,
   and their products with a, a² and a³ .

The factors of  10a²  are  1,  2,  5,  10,
    and their products with 'a' and a² .

Their common factors are  1, 2, 5, 10,
       and their products with 'a' and a².

Their greatest common factor is  10a² .

(Another way to spot it, easily, is to remember this helpful factoid:

                 If the smaller number is a factor of the larger number,
                 then the smaller number is their greatest common factor.

Using the greatest common factor, then . . .

           50a³ + 10a²  =     10a²(5a + 1) .

3 0
3 years ago
A class is going on a field trip to see a movie. Each ticket is $8.00. The number of students, n, who will receive a $8.00 ticke
garik1379 [7]
The equation would be 8n=c

Hope this helps!
6 0
3 years ago
You and your family left the house for a vacation at 8 A.M. You promptly fell asleep in the
poizon [28]

Answer:

201 miles.

Step-by-step explanation:

If you've traveled 124 miles in 2 hours, than in one hour must've been 62 miles. 62 multiplied by 3 is 186, which is how much miles have been traveled in 3 hours. Plus the 15 minutes would probably be 201 miles. Hope this helps!

8 0
3 years ago
Read 2 more answers
A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex
Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general  equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

I=P*r*t

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

x+y=50000

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

x+y=50000\\12500+y=50000\\y=50000-12500=37500

Therefore, the loan at 8% is $37500

5 0
3 years ago
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