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4 years ago

Which system is represented by the graph?

Mathematics

1 answer:

Georgia [21]4 years ago

8 0

Answer:

The system that is represented by the graph is (a) $y=3x-2\\y=3x-1$ .

Step-by-step explanation:

The Slope-Intercept Form of the equation of a straight line is given by:

$y = mx + b$

the slope is given by $m$ and the y-intercept is given by $b$ .

The slope of a line is a number that measures its "steepness" and its given by:

$Slope=m=\frac{\:change \:in \:y}{\:change \:in \:x}=\frac{y_2-y_1}{x_2-x_1}$

The y-intercept is where a line crosses the y-axis of a graph (0, b).

From the graph, we can see that the y-intercept is -1 for the blue line and -2 for the orange line.

The blue line appears to go through the points (0,-1) and (1, 2) and the slope is

$m=\frac{2+1}{1-0}=\frac{3}{1}=3$

The orange line appears to go through the points (0,-2) and (1, 1) and the slope is

$m=\frac{1+2}{1-0}=\frac{3}{1}=3$

So, the system that is represented by the graph is

$y=3x-2\\y=3x-1$

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Solve for the unknown angle measures of the polygon. The measures of 13 of the 14 angles of a 14−gon add up to 2,040°. What must

Jet001 [13]

Answer: The measure of fourteenth angle is 120°.

Step-by-step explanation:

Since we have given that

Total number of angles in 14 gon = 14

Sum of measures of 13 angles = 2040°

As we know that sum of all angles in 14 gon would be

$(14-2)\times 180^\circ\\\\=12\times 180^\circ\\\\=2160^\circ$

So, the measure of fourteenth angle would be

$\sum_{x=1}^{13}+x_{14}=2160^\circ\\\\2040^\circ+x_{14}^\circ=2160^\circ\\\\x_{14}^\circ=2160-2040\\\\x_{14}^\circ=120^\circ$

Hence, the measure of fourteenth angle is 120°.

6 0

3 years ago

1. Joshua has a ladder that is 12 ft long. He will lean the ladder against a vertical wall. For safety reasons, he wants the ang

marishachu [46]

Let h=height where top of ladder touches wall and x be distance from wall to bottom of ladder...

tana=h/x

a=arctan(h/x) and a≤75

arctan(h/x)≤75 now taking tan of both sides :P

h/x≤tan75 now we have an ugly x value that we need to get rid of:

Using the pythagorean theorem we know:

144=x^2+h^2, x^2=144-h^2, x=√(144-h^2) now we can use this in our inequality for x

h/√(144-h^2)≤tan75

h^2/(144-h^2)≤(tan75)^2

h^2≤144(tan75)^2-h^2(tan75)^2

h^2+h^2(tan75)^2≤144(tan75)^2

h^2(1+(tan75)^2)≤144(tan75)^2

h^2≤[144(tan75)^2]/(1+(tan75)^2)

h^2≤134.353829

h≤11.5911

So he cannot have the top of the ladder 11.8 ft above the ground and not exceed a 75° angle with the ground.

I worked it the hard way just to go through the process. However we could have used a simple trig function to see that maximum height of the top of the ladder....

sin75=h/12

h=12sin75

h≈11.59 ft. That would be the maximum height given that we did not want to exceed 75° with the ground.

7 0

3 years ago

98 prime or composite

insens350 [35]

A prime number is a number that has no factors except ' 1 ' and itself.

If I can find any factors of 98 besides 1 and 98, then 98 is not prime.

The factors of 98 are 1, 2, 7, 14, 49, and 98 .

I guess 98 is not prime.
98 is composite.

3 0

4 years ago

Read 2 more answers

The ages of three family children can be expressed as consecutive integers. the square of the age of the youngest child is 4 mor

sukhopar [10]

Let the middle child be x
youngest child = x - 1
Oldest child = x + 1

(x - 1)^2 = 8(x + 1) + 4
x^2 - 2x + 1 = 8x + 8 + 4
x^2 - 10x - 11 = 0
(x - 11) * (x + 1) = 0

X = - 1 makes no sense. How can a middle child be - 1 years old?
x = 11

The youngest child is 10
The middle child is 11
The oldest child is 12

Check
=====
10^2 = 100
(8*12) + 4
96 + 4 = 100 So the results have been checked.

3 0

3 years ago

Subtract using a number line. 12−(−5) Select the point on the number line to plot the answer.

andreev551 [17]

It 17 but you didn't give me a number line

7 0

4 years ago

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