Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $13 monthly fee and charges an additional $0.17 for each minute of calls. The second plan has a $23 monthly fee and charges an additional $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer:

Step-by-step explanation:

(Tangent Length)^2 = y*(y + 11)   You are going to have to use the quadratic formula on this.

Tangent Length = 7

7^2 = y * (y + 11)

49 = y^2 + 11y  

0 = y^2 + 11y - 49

a = 1

b = 11

c = - 49

When you solve this quadratic equation you get

x1 = 3.40 which is the answer you go with.

x2 = -14.40 which can't be used. A negative length has no meaning.

(6, 7) and (-3, -2)

1. Find the slope.

m = slope

m = (-2 -7)/(-3 -6)

m = -9/-9

m = 1

2. Plug the slope and one of the points into the equation y - y_1 = m(x - x_1).

y - 7 = 1(x - 6)

3. Solve for y.

y - 7 = x - 6

y = x - 6 + 7

y = x + 1

Answer is choice D.

The answer is A: -1/2

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x + 6y = 9 into this form

Subtract 6x from both sides

6y = - 3x + 9 ( divide all terms by 6 )

y = - [tex]\frac1}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{1}{2}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2 → C

Step-by-step Answer:

Given:

Bill : 3 minutes / apple

Frank : 5 minutes / 2 apples, or 2.5 minutes / apple.

So in 15 minutes, Bill eats 5 apples, and Frank eats 15/2.5 = 6 apples for a total of 11 apples.

To eat completely at least 12 apples, it would take 15 minutes + 1 apples, which means 17.5 minutes, with Bill having eaten 5 5/6 apples, and Frank having eaten 7 apples, exactly.

So the minimum time to eat 12 apples would be 17.5 minutes.

Note: at 18 minutes, they would have eaten 13 1/5 apples.

Answer:

$36

Step-by-step explanation:

Answer:

b 1/6

Step-by-step explanation:

the probability of the dice rolling on five or six is 2 out of 6. the probability that the coin will

The probability that the number cube will show a number greater than 4 and the coin will land with tails up  [tex]\frac{1}{6}[/tex].

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes

Probability of getting number greater than 4 on dice i.e., of getting 5 and 6 on the dice= [tex]\frac{2}{6} =\; \frac{1}{3}[/tex]

Now, along with probability of getting tails on the coin =[tex]\frac{1}{2}[/tex]

So, the combined probability of both the instance is= [tex]\frac{1}{3}[/tex] x [tex]\frac{1}{2}[/tex]

                                                                                      = [tex]\frac{1}{6}[/tex]

So, the Probability is  [tex]\frac{1}{6}[/tex].

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Answer:

128.605m^2

Step-by-step explanation:

because the kite has equal sides you can simply just do 8.5m x 10.2m+8.5m x 4.93m :D

Answer: 2,000

Step-by-step explanation: 22,000 - 20,000 = 2,000

Angie’s current equity on her car is 2,000

Answer:

[tex]\$2,000[/tex]

Step-by-step explanation:

Equity is defined by difference between total value of the asset and total liabilities.

Value of Angie's car is [tex]\$22,000[/tex] and she owes [tex]\$20,000[/tex] which means:

Total value of asset (car) = [tex]\$22,000[/tex]

Total liability = [tex]\$22,000[/tex]

∴ Equity = [tex]22000 - 20000 = 2000[/tex]

Hence Angie's current equity is [tex]\$2,000[/tex]

Answer:

  tan(x) = -1 ±√5

Step-by-step explanation:

This is a quadratic equation in tan(x). Let z = tan(x). Then the equation is ...

  z² = 4 - 2z

  z² +2z = 4 . . . . . . . add 2z

  z² + 2z + 1 = 5 . . . . add 1 to complete the square

  (z +1)² = 5 . . . . . . . . write as a square

  z +1 = ±√5 . . . . . . . square root

  z = -1 ±√5 = tan(x) . . . . . subtract 1; use definition of z

Answer:

1/12 hour

Step-by-step explanation:

Subtract 3/4 hr from 5/6 hr:  use the LCD 12:

Subtract 9/12 from 10/12 hr:  The difference is 1/12 hr.

Steve watched TV 1/12 hour longer on Tuesday than on Monday.  That's 5 minutes.

Answer:

B. 2

Step-by-step explanation:

[tex] \frac{2(x + 1)}{x + 5} = 1 - \frac{1}{x + 5} [/tex]

Multiply two sides by (x+5), we have

[tex](x + 5) \frac{2(x + 1)}{x + 5} = (x + 5) - (x + 5) \frac{1}{x + 5} [/tex]

so

[tex]2(x + 1) = x + 5 - 1 \\ = > \: 2x + 2 = x + 4 \\ = > x = 2[/tex]

Answer:

  B.  2

Step-by-step explanation:

You can add 1/(x+5), then multiply by (x+5), then subtract (x+3).

[tex]\dfrac{2(x+1)+1}{x+5}=1 \qquad\text{add 1/(x+5)}\\\\2x+3=x+5 \qquad\text{multiply by x+5}\\\\x=2 \qquad\text{subtract x+3}}[/tex]

_____

Sometimes you have to try several methods to find the easiest. One "always works" method is to subtract one side of the equation so you have something that equals zero. Here that would look like ...

[tex]\dfrac{2(x+1)}{x+5}-1+\dfrac{1}{x+5}=0 \qquad\text{subtract the right side}\\\\\dfrac{2(x+1)-(x+5)+1}{x+5}=0 \qquad\text{use a common denominator}\\\\\dfrac{x-2}{x+5}=0 \qquad\text{simplify}\\\\x=2 \qquad\text{the value of x that makes the numerator 0}[/tex]

Answer:

∠D = 13°

Step-by-step explanation:

∠A and ∠D are vertical angles and thus are congruent, hence

x - 2 = - 3x + 58 ( add 3x to both sides )

4x - 2 = 58 ( add 2 to both sides )

4x = 60 ( divide both sides by 4 )

x = 15

∠D = x - 2 = 15 - 2 = 13°

Answer:   36 months

Step-by-step explanation:

total for car        $26,800

down payment - $  1,600

amount leased   $25,200

700 monthly divided into $25,200

700/25200 = 36

Answer:

0.8 and 1.6 miles respectively

Step-by-step explanation:

The two benches divide the length of the path into thirds.  The length of each third is 2.4 miles / 3, or 0.8 mile.

The first bench is at 0.8 mile from the beginning, and the second is at 2(0.8 mile), or 1.6 mile from the beginning.

Answer:

x = 5.5

Step-by-step explanation:

Given 2 secants intersecting the circle from a point outside the circle then

The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is

x(x + 14) = 6(6 + 12)

x² + 14x = 6 × 18 = 108 ( subtract 108 from both sides )

x² + 14x - 108 = 0 ← in standard form

with a = 1, b = 14 and c = - 108

Using the quadratic formula to solve for x

x = ( - b ± [tex]\sqrt{b^2-4ac}[/tex] ) / 2a

  = ( - 14 ± [tex]\sqrt{14^2-(4(1)(-108)}[/tex] ) / 2

  = ( - 14 ± [tex]\sqrt{196+432}[/tex] ) / 2

  = ( - 14 ± [tex]\sqrt{628}[/tex] ) / 2

  x = [tex]\frac{-14-\sqrt{628} }{2}[/tex] or x = [tex]\frac{-14+\sqrt{628} }{2}[/tex]

  x = - 19.5 or x = 5.5 ( to 1 dec. place )

However x > 0 ⇒ x = 5.5

Answer:

0

Step-by-step explanation:

-3x +4y = 20      Multiply this equation by 2.

======================

6x + 3y = 15

-6x + 8y = 40    Notice that -3 becomes -6, 4 becomes 8 and 20 becomes 40

=====================  Add

11y  = 55               The xs have disappeared. Divide by 11

y = 55/11

y = 5

=====================

6x + 3y = 15

6x + 3*5 = 15

6x + 15 = 15

6x = 15 - 15

6x = 0

6x/6 = 0/6

x =0

Answer:

0

Step-by-step explanation:

Answer:

Explanation:

The relative frequency can be measured as a ratio (proportion) or as a percentage.

As a ratio, the relative frequency is the number of times that the desired outcome is observed (either theoretically or experimentally) divided by the total number of  possible outcomes (theoretically) or  observed (experimentally).

As a percentage, the relative frequency is the ratio multiplied by 100.

This shows it mathematically:

                                       = sum of all (n) frequencies / number of events =

                                       = number of events / number of events = 1

As a percentage, total relative frequency = 1 × 100 = 100

In a relative frequency distribution, the sum of relative frequencies should equal 100% if expressed in percentages, or 1 if expressed in proportions. This signifies that all the data has been accounted for.

After constructing a relative frequency distribution, whether that is summarizing IQ scores of college students or analyzing other data sets, the sum of the relative frequencies will depend on the format in which they are expressed. The sum differs based on whether percentages or proportions were used.

If percentages are used to express the relative frequency, the sum of all percentages should be 100%. This indicates that 100% of the given data set has been account for in the distribution. This is true for all relative frequency distributions, not just those involving IQ scores.

If proportions are used, then the sum of all proportions should equal 1. A proportion is a part-to-whole comparison, where the total or whole is represented by the number 1.

So, the correct answer to your question is A. If percentages are used, the sum should be 100%, if proportions are used, the sum should be 1.

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ANSWER

B. –4, –3, 0, 5

EXPLANATION

The general formula for the sequence is:

[tex]f(n)=n(n-2) - 3[/tex]

To find the first term we substitute n=1

[tex]f(1)=1(1 - 2) - 3 = - 4[/tex]

To find the second term, we substitute n=2

[tex]f(2)=2( 2-2) - 3 = - 3[/tex]

To find the third term,we put n=3;

[tex]f(3)=3(3-2) - 3 = 0[/tex]

To find the fourth term, we put n=4

[tex]f(n)=4(4-2) - 3 = 5[/tex]

The correct choice us B

Answer:

B

Step-by-step explanation:

Answer:

A. TRUE

Step-by-step explanation:

To verify if that value 5 is a solution, you place it in the equation instead of 'x' and see if the equality is respected at the end.

The equation is: x² - 6x + 5 = 0

Now, let's replace x by 5:

5² - 6 (5) + 5 = 0

25 - 30 + 5 = 0

-5 + 5 = 0

0 = 0

Since 0 = 0 is true, the value 5 is a valid solution for this equation.

If we had tried with 6, it would have ended with

36 - 36 + 5 = 0

5 = 0

So, 6 is NOT a solution.

Answer:

Segment JK is congruent to segment to GH ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the meaning of congruent triangles

- When two triangles are congruent then they will have exactly the

  same three sides and exactly the same three angles

- Congruent triangles have same areas and same perimeters

- Ex: If Δ ABC ≅ Δ XYZ, then their corresponding sides are congruent

 and their corresponding angles are equal

 side AB ≅ side XY , side BC ≅ side YZ , side AC ≅ side XZ

 angle A ≅ angle X , angle B ≅ angle Y , angle C ≅ angle Z

* Lets solve the problem

∵ Δ FGH ≅ Δ IJK

- The corresponding sides are:

# FG and IJ

# GH and JK

# FH and IK

∵ The corresponding side of GH is JK

∵ The corresponding sides are congruent

∴ GH ≅ JK

∴ Segment JK is congruent to segment to GH

Answer: y = 5/2x + 6

Step-by-step explanation:

y - y₁ = m(x - x₁)

y - (-9) = 5/2(x- (-6))

y + 9 = 5/2(x+ 6)

y +9 = 5/2x + 15

y = 5/2x + 15 - 9

y = 5/2x +6

Answer:

32 ft

Step-by-step explanation:

find the area of the large rectangle:

30 x 16 = 480

find the area of the small rectangle:

10 x 8 = 80

subract the small rectangle from the big rectangle to get the area of the shaded region:

480 - 80 = 400

now plug this area and the height into the equation for triangle area:

A = bh/2

400 = b(25)/2 multiply both sides by 2

2(400) = 2(25b/2)

800 = 25b divide both sides by 25

800/25 = 25b/25

32 = b

For this case we have that the area of the shaded region is given by the subtraction of the large rectangle minus the small rectangle.

[tex]A_ {sr} = 30 * 16-10 * 8\\A_ {sr} = 480-80\\A_ {sr} = 400[/tex]

Thus, the area of the shaded region is [tex]400 \ ft ^ 2[/tex]

If the triangle must have the same area and a height of 25, then we have:

[tex]400 = \frac {1} {2} b * 25\\400 = 12.5b[/tex]

Dividing between 12.5 on both sides of the equation:

[tex]b = 32[/tex]

Thus, the base of the triangle is 32.

Answer:

32

Answer:

10

Step-by-step explanation:

you can add the short section (AB) and the longer section (BC) to get AC which is 3+7=10

According to basic geometric principles, the length of a continuous straight line is the sum of the lengths of its segments. Therefore, if AB = 3 and BC = 7, then AC = AB + BC, which equals 10.

In Mathematics, specifically in geometry, when we talk about points and lines, if AB = 3 and BC = 7, then the whole length of the line AC, which includes AB and BC, is simply the sum of AB and BC. Therefore, AC = AB + BC.

To calculate it, just add these two lengths together, 3 + 7, which equals 10. So, AC = 10.

This is a fundamental principle in math that when you have a continuous straight line divided into segments, the total length of the line is equal to the sum of the lengths of its segments. This can be easily visualized if you imagine a ruler, with AB being the first 3 units, and BC being the next 7 units. The total length AC represents all 10 units.

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Step-by-step Answer:

Customer is allowed to choose any five, where order does not count.

This means that there are 11 toppings to choose from for the first one, 10 for the second, 9 for the third, 8 for the fourth, and 7 for the last for a total of 11*10*9*8*7 = 11!/6! choices.

Since order does not count, we have over-counted by 5!, so the final answer should be 11!/(6!*5!) choices.

Mathematically, this number is represented by

C(11,5) = 11!/(6!5!) = 462, and is read

"Combination of 5 choices out of 11", or simply "11 choose 5".

The answer is A: y=96 The maximum number of moose that the forest can sustain at one time.

Answer:  A) y = 96,

The maximum number of moose the forest can sustain at one time.

Step-by-step explanation:

The horizontal asymptote (H.A.) is the value of y that the graph cannot cross.

Since the degree of the numerator equals the degree of the denominator, divide their coefficients to find the H.A.

[tex]y=\dfrac{60}{0.625}\\\\\\\large\boxed{y=96}[/tex]

Answer:

  B.  The original purchase total must be at most to $44 before the discounts are applied.

Step-by-step explanation:

Solve the inequality by adding $10, then dividing by 0.8.

  0.8x -$10 ≤ $25.20

  0.8x ≤ $35.20 . . . . . . . . add $10

  x ≤ $35.20/0.8 . . . . . . . divide by 0.8

  x ≤ $44 . . . . . . . . . the before-discount purchase must be at most $44

Answer:

68

Step-by-step explanation:

The first differences of the given terms are ...

8 -5 = 3

11 -8 = 3

These are the same value, so we see this sequence is an arithmetic sequence with a common difference of 3. The first term is 5.

The explicit formula for the n-th term is ...

an = a1 +d(n -1)

We know a1=5, d=3, and we want to find the value for n=22. Hence ...

a22 = 5 +3(22 -1) = 5 +63 = 68

The 22nd term is 68.

Answer:

Third option and  sixth option

Step-by-step explanation:

It is important to remember that, by definition, "Excluded values"  are all those values that make the denominator equal to 0.

You need to substitute -5 into each rational expression:

[tex]\frac{x+5}{x-5}=\frac{x+5}{(-5)-5}=\frac{x+5}{-10}[/tex]

[tex]\frac{x^2-5}{x^2+5}=\frac{x^2-5}{(-5)^2+5}=\frac{x^2-5}{30}[/tex]

[tex]\frac{x-3}{x^2-25}=\frac{x-3}{(-5)^2-25}=\frac{x-3}{0}[/tex]

[tex]\frac{x^2-25}{2x^2+5}=\frac{x^2-25}{2(-5)^2+5}=\frac{x^2-25}{55}[/tex]

[tex]\frac{2x+1}{x^2+25}=\frac{2x+1}{(-5)^2+25}=\frac{2x+1}{50}[/tex]

[tex]\frac{(x-2)(x-5)}{(x+3)(x+5)}=\frac{(x-2)(x-5)}{(x+3)((-5)+5)}=\frac{(x-2)(x-5)}{0}[/tex]

Answer:

A

Step-by-step explanation:

5 of the 150 want to take the cruise, so:

p = 5/150

p = 0.03

Answer A.

Answer:

Option A

Step-by-step explanation:

Due to budget constraints they cannot survey all 800 people in the senior class so they randomly select 150 people from the class and ask them their preference.

Out of 150 students, 5 want to go to cruise to Bermuda.

So, the proportion becomes:

[tex]\frac{5}{150}=\frac{1}{30}[/tex]

= 0.033

So, option A is the answer.

Fine two pints that cross the x and Y axis to use to find the slope.

Slope is the change in Y over the change in x.

(-2,0) (0,3)

Slope = 3-0  /  0- -2 =  3/2

The slope is 3/2 and the Y - intercept is where it crosses the Y axis when X is o, which is 3

The answer is B.

Answer:

B.  m = 3/2; y-int = 3.

Step-by-step explanation:

The y intercept is the point where the line crosses the y-axis. That is  3.

The slope m = rise / run.

So if we take  the y-intercept and the x intercept it is 3/2.