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puteri [66]
2 years ago
11

Slope-intercept form graph and solve the system of equations y=2x+8 -x+y=6

Mathematics
1 answer:
omeli [17]2 years ago
3 0

Answer:

y=mx+b

y=2x+8

y=x+6

Step-by-step explanation:

y=2x+8          y=x+6

slope:2          slope:1

y-int:8            y-int:6

x.     y             x.     y

0.    8             0.    6

1.     10            1.     7

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Sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).
Sever21 [200]
\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta

\sin\alpha=\dfrac{21}{29}\implies \cos^2\alpha=1-\sin^2\alpha=\dfrac{400}{841}

Since \alpha lies in quadrant II, we have \cos\alpha, so

\cos\alpha=-\sqrt{\dfrac{400}{841}}=-\dfrac{20}{29}

\cos\beta=\dfrac{15}{17}\implies\sin^2\beta=1-\cos^2\beta=\dfrac{64}{289}

\beta lies in quadrant I, so \sin\beta>0 and

\sin\beta=\sqrt{\dfrac{64}{289}}=\dfrac8{17}

So

\sin(\alpha-\beta)=\dfrac{21}{29}\dfrac{15}{17}-\left(-\dfrac{20}{29}\right)\dfrac8{17}=\dfrac{475}{493}
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2 years ago
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A ball is thrown straight out at 80 feet per second from an upstairs window that's 15 feet off the ground. Find the ball's horiz
Alex73 [517]

Answer:

Step-by-step explanation:

In order to find the horizontal distance the ball travels, we need to know first how long it took to hit the ground. We will find that time in the y-dimension, and then use that time in the x-dimension, which is the dimension in question when we talk about horizontal distance. Here's what we know in the y-dimension:

a = -32 ft/s/s

v₀ = 0 (since the ball is being thrown straight out the window, the angle is 0 degrees, which translates to no upwards velocity at all)

Δx = -15 feet (negative because the ball lands 15 feet below the point from which it drops)

t = ?? sec.

The equation we will use is the one for displacement:

Δx = v_0t+\frac{1}{2}at^2 and filling in:

-15=(0)t+\frac{1}{2}(-32)t^2 which simplifies down to

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t=\sqrt{\frac{-15}{-16} } so

t = .968 sec (That is not the correct number of sig fig's but if I use the correct number, the answer doesn't come out to be one of the choices given. So I deviate from the rules a bit here out of necessity.)

Now we use that time in the x-dimension. Here's what we know in that dimension specifically:

a = 0 (acceleration in this dimension is always 0)

v₀ = 80 ft/sec

t = .968 sec

Δx = ?? feet

We use the equation for displacement again, and filling in what we know in this dimension:

Δx = (80)(.968) +(0)(.968)^2 and of course the portion of that after the plus sign goes to 0, leaving us with simply:

Δx = (80)(.968)

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3 years ago
Kirsten has to walk 2 3/4km to school. How far has she walked when she halfway? Give your answer in metres.
evablogger [386]

Answer:

375 m

Step-by-step explanation:

\frac{3}{4}  \times 1000 = 750

From halfway

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2 years ago
What is m∠8 if m∠4 = 50°?
r-ruslan [8.4K]

Answer:

D) 50°. You got parallel lines cut by a traversal, so angles 4 and 8 are congruent because they're corresponding angles.

Step-by-step explanation:

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3 years ago
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