A radio station receives 3815 phone calls in 35 min. How many calls does it get in 1 hr? Show Your Work.

Given that a rectangle with length $3x$ inches and width $x + 5$ inches has the property that its area and perimeter have equal

scoray [572]

Answer:

First, we need to know how to calculate the area and the permiter of a rectangle.

To calculate the area, we multiply base by height and to calculate the perimeter, we sum all sides.

Knowing this, we can say that the area is 3x * (x+5) and the perimiter is 3x + 3x + x + 5 + x + 5, as we know both are the same, we write it as an equation:

$3x * (x+5) = 3x + 3x + x + 5 + x + 5$

Now we solve the equation:

$3x^2 +15x = 6x + 2x + 10$

$3x^2+15x =8x + 10$

$3x^2+15x-8x-10=0$

$3x^2+7x-10=0\\\\x_1=\frac{-10}{3}\\x_2 = 1$

As the negative result doesn't have sense, we only pick the second one: 1.

If x = 1, then area would be 3*6 = 18 square inches and perimeter 3+3+6+6 = 18 inches

7 0

2 years ago

Read 2 more answers

What are the solution(s) to the quadratic equation 40 − x2 = 0?

Anni [7]

X = 20
First, you move the 40 to the other side.
-2x=-40
Then, you divided -40 by -2.
x= -40/-2
x= 20
x is 20 because the negatives cancel out making it positive.

4 0

2 years ago

Read 2 more answers

Trapezoid A B C D is shown. Sides A B and D C are parallel. Sides A D and B C are congruent. Angle B is (3 x) degrees and angle

photoshop1234 [79]

Answer: The value of x in trapezoid ABCD is 15

Step-by-step explanation: The trapezoid as described in the question has two bases which are AB and DC and these are parallel. Also it has sides AD and BC described as congruent (that is, equal in length or measurement). These descriptions makes trapezoid ABCD an isosceles trapezoid.

One of the properties of an isosceles trapezoid is that the angles on either side of the two bases are equal. Since line AD is equal to line BC, then angle D is equal to angle C. It also implies that angle A is equal to angle B.

With that bit of information we can conclude that the angles in the trapezoid are identified as 3x, 3x, 9x and 9x.

Also the sum of angles in a quadrilateral equals 360. We can now express this as follows;

3x + 3x + 9x + 9x = 360

24x = 360

Divide both sides of the equation by 24

x = 15

Therefore, in trapezoid ABCD

x = 15

4 0

2 years ago

Read 2 more answers

Tara owes $14,375 in credit card debt. The interest accrues at a rate of 5.3%. She is also borrowing $570 each month for rent fr

siniylev [52]

Answer:

$(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$

$29619.13

Step-by-step explanation:

a. Tara has $14375 in credit card debt and the interest rate is 5.3%.

Now, if f(t) represent the amount of money Tara have in credit card debt, where t is the number of years after after interest begins to accrue, then

$f(t) = 14375 (1 + \frac{5.3}{100})^{t}$ ......... (1)

Again Tara borrows $570 each month for rent from her parents without any interest.

If g(x) represent the amount of money Tara owes to her parents, where t represents the number of years passed,then we can write

g(t) = 570 × 12t = 6840t ........ (2)

Therefore, $(f + g)(t) = f(t) + g(t) = 14375 (1 + \frac{5.3}{100})^{t} + 6840t$

b. So, for t = 2 years,

$(f + g)(t) = 14375 (1 + \frac{5.3}{100})^{2} + 6840 \times 2$ = $29619.13

So, Tara has to repay $29619.13 if she continues this way without any repayment for 2 years. (Answer)

7 0

2 years ago

In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy] unitsize(2 cm); pair D, E,

sergey [27]

Answer:

Step-by-step explanation:

The answer to this question is 12+6sqrt3.

This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.

The square root of 108 simplified=6sqrt3.

Then you add them together and get 12+6sqrt3.

5 0

2 years ago