The table gives the probabilities that orphaned pets in animal shelters in six cities are one of the types listed.

Graph the line y = kx +1 if it is known that the point M belongs to it: M(1,3)

tigry1 [53]

Answer:

$M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ . Please see attachment below to know the graph of the line.

Step-by-step explanation:

From Analytical Geometry we know that a line is represented by this formula:

$y=k\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$k$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

If we know that $b = 1$ , $x = 1$ and $y = 3$ , then we clear slope and solve the resulting expression:

$k = \frac{y-b}{x}$

$k = \frac{3-1}{1}$

$k = 2$

Then, we conclude that point $M(x,y) = (1,3)$ belongs to the line $y = 2\cdot x +1$ , whose graph is presented below.

3 0

1 year ago

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lo

miv72 [106K]

you could use this equation to help you solve it;

x + (x + 42) = 138

the first step is to combine like terms;

2x = 138 -42

2x = 96

X = 96/2

X = 48

we already solved for x now substitute it in the equation I gave you.

48 + (48 + 42) = 138

48 + 90 = 138

hope it helped...if you have any concerns just let me know:)

3 0

2 years ago

Which of the following slopes show that the set of points C(1, 1), D(3, -4), E(5, 8) are not collinear?

MArishka [77]

C is the answer you want

8 0

2 years ago

Read 2 more answers

A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil contained in 1 mile (5280 feet) of a pipeli

8_murik_8 [283]

1)volume of the pipeline

The pipeline is a cylinder, therefore;
Volume (cylinder)=πr²h
r=radius
h=height of the cylinder

diameter=6 in*(1 ft / 12 in)=0.5 ft
raius=diameter / 2=0.5 ft / 2=0.25 ft.
height=5280 ft

Volume (pipeline)=π(0.25 ft)²(5280 ft)=330π ft³≈1036.73 ft³.

2) we calculate the number of barrel
1 mile of oil in this pipeline is 330π ft³ of oil.

1 barrel of crude------------------5.61 ft³
x----------------------------------330π ft³

x=(1 barrel*330π ft³) / 5.61 ft³=184.8 barrels

3) we calculate the price.

1 barrel---------------$100
184.8 barrels---------- x

x=(184.8 barrels * $100) / 1 barrel=$18,480

Solution: ≈$18,480

6 0

1 year ago

Holly plays tennis on the school tennis team. She can hit a tennis ball really high in the air. She learned that the quadratic e

Gala2k [10]

Answers:

A. x = 8 seconds

B. y = 80 feet . We know because it is the peack of the graph.

C. x = 3 s, x=5 s

Step-by-step explanation:

To easily solve this three part problem, we use a graphing tool to plot the equation that describes the height of the tennis ball over time, after it was hit by a tennis racket. Please, see the attached graph for clarification.

y = -5x^2 + 40*x

(the equation must have the minus sign, otherwise it makes no sense for the problem)

Where,

y = height of the tennis ball in feet,

x = seconds after the ball is hit with the racket

Question A

How long does it take for the ball to hit the ground?

By examining the graph, we need to find the points where the graph intersects with the x-axis.

This is equivalent to making y = 0 in the equation and solving for x

0 = -5x^2 + 40*x

We get two solutions, but time must be positive so, x > 0

The graph shows that when x = 8 seconds, y = 0

-5(8)^2 + 40*(8) = 0

Question B

What is the highest point reached during the flight of the ball? how do you know?

By examining the graph, we need to find the point where the graph has maximum amplitude.

The point corresponds to (4,80), y = 80 feet at x = 4 seconds

We know because it is the maximum peak of the plot. Please see attached picture for reference.

Question C

When was the ball exactly 75 feet off the ground?

We look for y = 75 feet in the plot.

This corresponds to x = 3 seconds and x=5 seconds

This can also be found analytically

75 = -5x^2 + 40*x

75 = -5(3)^2 + 40*(3)

3 0

1 year ago

Read 2 more answers