Lisa purchased a prepaid phone card for $25 . Long distance calls cost 12 cents a minute using this card. Lisa used her card only once to make a long distance call. If the remaining credit on her card is $19.96 , how many minutes did her call last?

The centroid theorem, the value of x is: 2.5.

According to the centroid theorem, the centroid of a triangle is two-thirds of the distance from each midpoint to each vertex.

Given:

BD = 4x + 5

BF = 9x

Thus:

BD = 2/3(BF)

Replace 4x + 5 = 2/3(9x) with

4x + 5 = 6x

4x - 6x = -5

-2x = -5

x = 5/2

x = 2.5

As a result of the centroid theorem, the value of x is: 2.5.

Complete question:

Point D is the centroid of △ABC. Use the given information to find the value of x.

BD=4x+5 and BF=9x

x=

The statement that is always true for any parallelogram is that the diagonals bisect each other.

The statement that is always true for any parallelogram is b. "the diagonals bisect each other". To bisect means to divide into two equal parts. In a parallelogram, the diagonals (the line segments connecting opposite corners) will always divide each other into two equal parts. This can be proven by using properties of parallel lines and alternate interior angles.

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Answer:

d

Step-by-step explanation:

Side = 11 cm, side = 5 cm, side = 5 cm

Answer:

D.Domain: (-∞,∞) Range: (-2,∞)

is the right answer.

Step-by-step explanation:

Given is a function as

[tex]f(x) = 3|x+7|-2[/tex]

This is an absolute value function hence the minimum value of

|x+2|=0

Hence the range cannot be below -2

For maximum no limit

[tex]Range = [-2,\infty)[/tex]

Domain can be any real value

Hence option d is correct answer.

Answer:

A) domain: (-∞, ∞) range: (-∞, ∞)

Step-by-step explanation:

width = x

length = 2x+8

area = l x w

x(2x+8)=120

2x^2+8x−120=0

x^2+4−60=0

(x+10)(x−6)=0

x=−10 and x=6

 width has to be a positive number

Width = 6 inches.

Answer:

Look at how many factors it has.

If it has 2, it's prime.

If it has 3 or more, it's composite.

Step-by-step explanation:

I hope it helps!

To solve for log base 5 of x + log base 5 of (4x-1), combine the two logarithms using the property that the sum of logarithms is equal to the logarithm of the product: log base 5 of x + log base 5 of (4x-1) = log base 5 of (x(4x-1)).

To solve the logarithmic expression log5(x) + log5(4x-1), we can combine the two logarithms using the property that the sum of logarithms is equal to the logarithm of the product. This gives us:

log5(x) + log5(4x-1) = log5(x(4x-1))

So the solution to the expression is log5(x(4x-1)).

Answer:

OptionC

Step-by-step explanation:

Given that the correlation coefficient (r) between the number of miles driven x and the number of gallons of gasoline used y is 0.925

Coefficient of determination = square of r

= 0.8556

=85.6%

Hence the percent of the variation in the number of gallons of gasoline can be explained by differences in the number of miles driven is 85.6%

Option C

There are 42 dimes and 14 nickels there if the collection of dimes and nickels is worth $5.60

First, we need to convert dimes and nickel to pennies to have:

1 dime = 10 pennies

1 nickel = 5 pennies

Since the ratio of dimes to nickels is 3:2, this shows that we have 30  dimes and 10 pennies

Total pennies  = 30 + 10 = 40 pennies

Since the total collection of dimes and nickels is worth $5.60, this means that the total collections in pennies are 560 pennies ($1 is 100 pennies)

Number of pennies for the ratio of 30 = 30/40 * 560

Number of pennies for the ratio of 30 = 420

Number of dimes = 420/10 = 42 dimes

Number of pennies for the ratio of 10 = 10/40 * 560

Number of pennies for the ratio of 10 = 140

Number of nickel = 140/10 = 14 nickels

Hence there are 42 dimes and 14 nickels there if the collection of dimes and nickels is worth $5.60

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Given that one inlet pipe can fill an empty pool in 4 hours. The outlet pipe can empty the pool in 8 hours. We know that rate x time = work done.

Rate = work done / time

Rate of inlet pipe = ¼ hours.

Rate of outlet pipe = 1/8 hours

Here 1 represent the work completed.

Let x be the time taken to fill the pool by the inlet pipe if the drain is left.

Work done by inlet pipe – work done by outlet pipe = 1 work completed.

x/4 – x/8 = 1.

To solve the rational equation, first we clear the fractions by multiplying it with LCD (4,8)=8 to each item.

8(x/4) – 8(x/8) = 8(1)

2x – x = 8

X = 8

Time taken for the pipe to fill the pool if the drain is left open = 8 hours

Answer:

There are 15 dimes and 22 quarters in the jar.

Step-by-step explanation:

Deangelo has $7 worth of dimes and quarters in a jar.

Let he has d number of dimes and q number of quarters in a jar.

0.10d + 0.25q = 7 -------(1)

He has 7 more quarters than dimes.

q = d + 7 -------(2)

We replace the value of y from equation 2 in the equation 1

0.10d + 0.25(d + 7) = 7

0.10d + 0.25d + 1.75 = 7

0.35d = 7 - 1.75

0.35d = 5.25

d = [tex]\frac{5.25}{0.35}=15[/tex] dimes

Now we put this value in the equation number 2

q = 15 + 7 = 22

Therefore, number of dimes and quarters are 15 and 22 respectively.

Area = l*w = 72

L = 72/w

Perimeter = 2l+ 2w

44 = 2(72/w) +2w

22 = 72/w +w

W^2-22w +72 =0

(w-18) (w-4) = 0

W = 18

L = 4

A decimal is a way of expressing numbers that are not whole numbers, but rather include a fractional or decimal part. The decimal equivalent of the base-6 number 12345 is 1415.

To convert a base-6 number to decimal, we multiply each digit by its corresponding weight and add the products together. The weights are 6 to the power of the digit's position, starting from the rightmost digit.

For example, to convert the base-6 number 12345 to decimal, we would do the following:

(1 * 6^4) + (2 * 6^3) + (3 * 6^2) + (4 * 6^1) + (5 * 6^0)

= 1296 + 72 + 18 + 24 + 5

= 1415

Therefore, the decimal equivalent of the base-6 number 12345 is 1415.

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