MATHEMATICS HIGH SCHOOL

Which correctly describes how the graph of the inequality 5x + 2y ≥ 13 is shaded? (1 point) Above the solid line Below the solid line Above the dashed line Below the dashed line

Answers

Answer 1

Answer:

Answer:

The graph of inequality $5x+2y\geq 13$ is above the solid line.

Step-by-step explanation:

Step-by-step explanation:

An inequality on a coordinate plane consist of a boundary line and an area in which each point is a possible solution.

* If the inequality has a sign or , then the line will be a solid line and its point are included in the solution.

* If the inequality has a sign '>' or '<' , then the line will be a dotted line and its point are not included in the solution.

Given: The linear inequality: $5x+2y\geq 13$

Then, the equation of the boundary line is; 5x+2y =13 ......[1]

we can write this as;

$2y = -5x+13$

Divide by 2 we get;

$y = -(5)/(2) x + (13)/(2)$ ......[2]

Compare this boundary line equation with the general point slope intercept line i.e, y = mx+b where m is the slope and b is the y-intercept.

Therefore, the slope of the this line is, m = $-(5)/(2)$

and a y-intercept (b) = $(13)/(2)$ = 6.5

To find x -intercept:

Substitute y =0 in to solve for x;

$5x+0 =13$

Simplify:

$x =(13)/(5) = 2.6$

Therefore, the x-intercept is 2.6

Now,

Plot $y = -(5)/(2) x + (13)/(2)$ ( as a solid line because $y\geq$ included equal to)

and shade the area above as $5x+2y\geq 13$ as shown below in the graph

Answer 2

Answer: The answer is above the solid line.
Tip: On problems like these, go to the website, desmos.com, press the big red button that says "Start Graphing", and you can graph any equation by typing it in on the side and it show you the graph to get the answer!

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Prove the identity
2sin^2x - 1 = sin^2x - cos^2x

Answers

Hello,

sin² x-cos² x=sin² x-(1-sin² x)=2sin² x-1
==============================

From the trigonometric identity:

$cos^(2)x + sin^(2) x$ =1
Making $sin^(2)$ x the subject we get:
$sin^(2)$ x=1- $cos^(2)$ x
On evaluating the left hand side and replacing $sin^(2)$ x with 1- $cos^(2)$ x;
2(1- $cos^(2)$ x)-1
This gives

=2-2 $cos^(2)x$ -1
=1-2 $cos^(2)$ x
From the identity in $cos^(2)$ x+ $sin^(2)$ x=1, replace 1 in the equation to get;
$cos^(2)$ x+ $sin^(2)$ x-2 $cos^(2)$ x
= $sin^(2)$ 2x- $cos^(2)$ x

Which of the following is not equivalent to the formula d = rt?

Answers

The second choice ... r = dt ... is not equivalent to the formula ' d = rt ' .

Each of the other choices IS equivalent to it.

Question:In the equation P = 2x + 7, P represents the price, in dollars, of tickets to a concert x hours after they go on sale. When will the price exceed $20.00?

1. Describe in words how the equation can be used to solve the problem.

2. Draw a graphical representation of the price equation, and illustrate how a solution could be found that way.

Answers

Let

P-------> the price in dollars of tickets

x------> the number of hours

we know that

$P=2x+7$ -------> equation A

When will the price exceed $20.00?

Part 1) Describe in words how the equation can be used to solve the problem

Substitute the value of P equal to $\$20.00$ in the equation A and find the value of x

For $P=\$20.00$

substitute in equation A

$20=2x+7$

$2x=20-7$

$2x=13$

$x=6.5\ hours$

therefore

the answer Part 1) is

the price exceed $\$20.00$ when the time exceed $6.5\ hours$

Part 2) Draw a graphical representation of the price equation, and illustrate how a solution could be found that way.

using a graphing tool

Draw the equation of the lines

$P=2x+7$

$P=20$

the solution is the intersection both graphs

see the attached figure

the solution is the point $(6.5, 20)$

that means

for $x=6.5\ hours$

$P=\$20.00$

1. This equation can be used to help solve the problem by plugging in numbers for x. Whatever answer for x gives a price that is more than $20.00 is the answer for the number of tickets that have to be sold in order to exeed $20.00.

2. This equation has the same format as an equation in slope intercept form. This makes it easy to graph.The y intercept will be 7 and the slope is 2. Using this information, it is easy to graph the equation and find a solution. The graph should look like the image I attached to this answer.

For f (x), evaluate the following:
a, f(0)
b. f(6)

Show all of your work

Answers

Answer:

a). f(0) = 4

b). f(6) = 8

Step-by-step explanation:

a). When x < 5, piecewise function to be considered,

f(x) = x + 4

Since, x = 0 is less than x = 5

f(0) = 0 + 4

f(0) = 4

b). When 5 ≤ x < 7,

Piecewise function to be considered,

f(x) = 8

Therefore, for x = 6,

f(6) = 8

A firefighter climbed up to the middle of a ladder to see if there was any fire on the second floor of a building and there was none; he then climbed up 10 more steps and saw some smoke so he came back down 14 steps and waited for 5 seconds to check his equipment. He then climbed 20 steps all the way to the top of the ladder and got off on the roof. How many steps are there on the ladder?