Anybody know the answer?

Consider this system of equations. x + 2y = 5, –x + 3y = 6 The x- and y-intercepts of the first equation are found below. x-in

vichka [17]

Answer:

Part 1) The x-intercept is the point (-6,0)

Part 2) The y-intercept is the point (0,2)

Step-by-step explanation:

we know that

The x-intercept is the value of x when the value of y is equal to zero

The y-intercept is the value of y when the value of x is equal to zero

we have

$-x+3y=6$

Part 1) Find the x-intercept

For y=0

substitute the value of y in the linear equation and solve for x

$-x+3(0)=6$

$-x=6$

$x=-6$

The x-intercept is the point (-6,0)

Part 2) Find the y-intercept

For x=0

substitute the value of x in the linear equation and solve for y

$-(0)+3y=6$

$3y=6$

$y=2$

The y-intercept is the point (0,2)

7 0

3 years ago

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Find the exact value of cos theta, given that sin thetaequalsStartFraction 15 Over 17 EndFraction and theta is in quadrant II.

vova2212 [387]

Answer:

$cos \theta = -\frac{8}{17}$

Step-by-step explanation:

For this case we know that:

$sin \theta = \frac{15}{17}$

And we want to find the value for $cos \theta$ , so then we can use the following basic identity:

$cos^2 \theta + sin^2 \theta =1$

And if we solve for $cos \theta$ we got:

$cos^2 \theta = 1- sin^2 \theta$

$cos \theta =\pm \sqrt{1-sin^2 \theta}$

And if we replace the value given we got:

$cos \theta =\pm \sqrt{1- (\frac{15}{17})^2}=\sqrt{\frac{64}{289}}=\frac{\sqrt{64}}{\sqrt{289}}=\frac{8}{17}$

For our case we know that the angle is on the II quadrant, and on this quadrant we know that the sine is positive but the cosine is negative so then the correct answer for this case would be:

$cos \theta = -\frac{8}{17}$

5 0

3 years ago

A $500 couch is marked up 20%. What is the new price of the couch?

Aleks04 [339]

Pretty sure the answer is $600

Hope this helps

6 0

3 years ago

3.16 x 10 with the power of 3

DENIUS [597]

Answer:

3160

Step-by-step explanation:

3.16 x 10^3

10^3 = 1000

so you move the decimal point three times to the right

I hope this helps

8 0

3 years ago

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When truckers are on long-haul drives, their driving logs must reflect their average speed. Average speed is the total distance

KengaRu [80]

Answer:

0.500 hour

Step-by-step explanation:

Givens

Distance

Total Distance on the highway = 3hr * 60 miles / hr = 180 miles
Distance in the city = 20 miles
Total Distance = 180 + 20 = 200 miles

Time

Time on the highway = 3 hours
Time in the city = x

Formula

d /t = r

Solution

Average rate = 57.14
Total Distance / Total Time = average rate
200 / (3 + x) = 57.14 Multiply both sides by 3 + x
200 = 57.14 * (3 + x) Remove the brackets
200 = 57.14*3 + 57.14x Multiply the factors on the right
200 = 171.42 + 57.14x Subtract 171.42 from both sides.
200 - 171.42 = 171.42 - 171.42 + 57.14x So the subtraction
28.58 = 57.14x Divide by 57.14
28.57/57.14 = x
x = 0.500 hour Answer

3 0

3 years ago

Read 2 more answers