A telephone company charges a fixed monthly rate plus a rate per minute of usage. The company charges $135 for 100 minutes of usage and $375 for 500 minutes of usage. An equation can be written to show the relationship between the total minutes used (x) and the total monthly charges (y). Which of the following best describes the steps to draw the graph of y against x?Draw a graph which joins the points (135, 100) and (375, 500) and has a slope = 0.6
Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6
Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 1.67
Draw a graph which joins the points (135, 100) and (375, 500) and has a slope = 1.67

Answers

Answer 1

Answer: Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6

The ordered pairs are: (100, 135) and (500, 375)

The first number is the number of minutes of usage and the second number is the charge of the month.

The slope is: ( 375 -135) / (500 - 100) = 240/400 = 0.6

Answer 2

Answer:

Answer:

Draw a graph which joins the points (100, 135) and (500, 375) and has a slope = 0.6

Step-by-step explanation:

Data

x: total minutes used

y: total monthly charges

x | y

100 | $135

500 | $375

That can be expressed as coordinates (x, y), so the points are (100, 135) and (500, 375).

The slope is computed with two points (x2, y2) and (x1, y1) as follows:

slope = (y2 - y1)/(x2 - x1)

Replacing with data

slope = (375 - 135)/(500 - 100) = 0.6

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Find the sum or difference. (3a – 3a^2) + (5 + 8a)A: a^2 + 11a + 5

B: –3a^2 + 11a + 5

C: 3a^2 + 11a + 5

D: –3a^2 + 11a – 5

Answers

Answer: B = –3a^2 + 11a + 5

For difference, the answer is

-3a^2 -5a -5

Step-by-step explanation:

(3a – 3a^2) + (5 + 8a)

To find the sum or difference, we will open the brackets.

To look for l the sum, we add

3a – 3a^2 + 5 + 8a

Collecting like terms,

= -3a^2 +8a + 3a +5

= -3a^2 + 11a + 5

Option B is the right answer.

To look for the difference, we subtract.

(3a – 3a^2) - (5 + 8a)

Opening the brackets

3a – 3a^2 - 5 - 8a

Collecting like terms

-3a^2 + 3a -8a -5

= -3a^2 -5a -5

The options available corresponds only to what we got for the sum, so

-3a^2 + 11a + 5 is the answer

Answer: B. -3a^2 + 11a + 5

1.) Remove parentheses.

3a−3a^2 +5+8a

2.) Collect Like Terms.

(3a+8a) - 3a^2+5

3.) Simplify.

11a - 3a^2+5

-3a^2 + 11a + 5

Lisa has a certain amount of money. She spent 39 dollars and has 3/4th of the original amount left. How much money did she have originally

Answers

If $\frac { 3 }{ 4 }$ is left, that means $\frac { 1 }{ 4 }$ was spent. So $\frac { 1 }{ 4 }$ of the total amount is equal to 39.. Let's say x to the total amount. $\frac { 1 }{ 4 } \cdot x=39\n x=4\cdot 39\n x=156\n$

$156, $39 is 1/4 of the money so 39 * 4 = 156

The diameter of a round dinner plate is 10 inches. What is the area of the plate? A. 314 square inches
B. 39.25 square inches
C. 39.25 inches
D. 78.5 square inches

Answers

The area of table is 78.5 square inches.

What is area?

A figure's area is the amount of space it takes up in two dimensions. To put it another way, it is the number that tells how many unit squares cover the surface of a closed figure. Square units, such as square inches, square feet, and so on, are the standard measurement for area.

Given the diameter of dinner plate = 10 inches

shape of plate is circular

area of circle is πr²

where r is radius

r = d/2 = 10/2 = 5 inches

A = πr²

A = 3.14(5)²

A = 3.14 x 25

A = 78.5 square inches

Hence area is 78.5 square inches.

Learn more about area;

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A=πrˆ2
Since the diameter is 10 inches, the radius must be half of that: 10/2=5.
A=π(5)ˆ2
A=25π
A=25π or 78.54 inches

a rectangular field with a area of 8000m2 is enclosed by 400m of fencing. determine dimensions to nearest tenth of a metre

Answers

$field:x\ *\ y\n\n \left\{\begin{array}{ccc}x\cdot y=8000\n2x+2y=400&/:2\end{array}\right\n\left\{\begin{array}{ccc}x\cdot y=8000\nx+y=200&\to x=200-y\end{array}\right\n\nsubstitute\ to\ x\cdot y=8000\n\n(200-y)\cdot y=8000\n\n-y^2+200y-8000=0\n\n\Delta=b^2-4ac;\ \Delta=200^2-4\cdot(-1)\cdot(-8000)=40000-32000=8000\n\ny_1=(-b-\sqrt\Delta)/(2a);\ y_2=(-b+\sqrt\Delta)/(2a)$

$\sqrt\Delta=√(8000)=√(1600\cdot5)=40\sqrt5\n\ny_1=(-200-40\sqrt5)/(2\cdot(-1))=(-200-40\sqrt5)/(-2)=100+20\sqrt5\approx144.7\ (m)\n\ny_2=(-200+40\sqrt5)/(2\cdot(-1))=(-200+40\sqrt5)/(-2)=100-20\sqrt5\approx55.3\ (m)\n\nx_1\approx200-144.7=55.3\ (m)\n\nx_2\approx200-55.3=144.7\ (m)\n\nAnswer:Dimension of the field is:55.3m\ *\ 144.7m$

Find two condecutive odd integers such that the smaller one is twelve more than one-third the larger

Answers

Let be x and x + 2 two consecutive odd integers;
You have the equation : x = 12 + ( x + 2 ) / 3 ;
(3x) / 3 = 36 / 3 + ( x + 2 ) / 3 ;
(3x) / 3 = ( 38 + x ) / 3 ;
3x = 38 + x ;
2x = 38 ;
x = 19 ;
The numbers are 19 and 21 .

What is the solution to the equation 1/2 (x-12) + 4 = 1/3 (6x-15)?