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Nimfa-mama [501]
3 years ago
14

Solve by substitution ANSWER NOW

Mathematics
1 answer:
Maslowich3 years ago
5 0
Y = -5x + 9
y = 5x + 7

5x + 7 = -5x + 9
5x + 5x = 9 - 7
10x = 2
x = 2/10 reduces to 1/5

y = 5x + 7
y = 5(1/5) + 7
y = 1 + 7
y = 8

solution is (1/5,8)
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Suppose that on a coordinate plane a hexagon is reflected across the x-axis. Compare the area of the original hexagon to the are
kap26 [50]

Reflection along x-axis is just a swapping of left and right sides. It does not change the size or area of the hexagon.

Hence, the correct option is B.

4 0
3 years ago
CALCULUS - Find the values of in the interval (0,2pi) where the tangent line to the graph of y = sinxcosx is
Rufina [12.5K]

Answer:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

Step-by-step explanation:

We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.

Since the tangent line is horizontal, this means that our derivative at those points are 0.

So, first, let's find the derivative of our function.

y=\sin(x)\cos(x)

Take the derivative of both sides with respect to x:

\frac{d}{dx}[y]=\frac{d}{dx}[\sin(x)\cos(x)]

We need to use the product rule:

(uv)'=u'v+uv'

So, differentiate:

y'=\frac{d}{dx}[\sin(x)]\cos(x)+\sin(x)\frac{d}{dx}[\cos(x)]

Evaluate:

y'=(\cos(x))(\cos(x))+\sin(x)(-\sin(x))

Simplify:

y'=\cos^2(x)-\sin^2(x)

Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':

0=\cos^2(x)-\sin^2(x)

Now, let's solve for x. First, we can use the difference of two squares to obtain:

0=(\cos(x)-\sin(x))(\cos(x)+\sin(x))

Zero Product Property:

0=\cos(x)-\sin(x)\text{ or } 0=\cos(x)+\sin(x)

Solve for each case.

Case 1:

0=\cos(x)-\sin(x)

Add sin(x) to both sides:

\cos(x)=\sin(x)

To solve this, we can use the unit circle.

Recall at what points cosine equals sine.

This only happens twice: at π/4 (45°) and at 5π/4 (225°).

At both of these points, both cosine and sine equals √2/2 and -√2/2.

And between the intervals 0 and 2π, these are the only two times that happens.

Case II:

We have:

0=\cos(x)+\sin(x)

Subtract sine from both sides:

\cos(x)=-\sin(x)

Again, we can use the unit circle. Recall when cosine is the opposite of sine.

Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.

At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).

At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.

Therefore, our solution set is:

\{\frac{\pi}{4}, \frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\}

And we're done!

Edit: Small Mistake :)

5 0
2 years ago
What kind of equations have the greatest outputs?
stepladder [879]

Answer:

Exponential

Step-by-step explanation:

8 0
3 years ago
4a-b<br> Evaluate the expression when a=5 and b=-7
stepladder [879]

Answer:

27

Step-by-step explanation:

So first we need to plug in 5 as the variable a and -7 as the variable b

4(5)-(-7)

Next we multiply the 4 and the 5 together to get 20

4(5) = 20   or    4 x 5 = 20

20-(-7)

Now we subtract negative 7 from 20

20-(-7) = 27

This can also be written as 20 plus 7 as a mathematical rule states: two negatives make a positive. So:

20-(-7) = 20 + 7

Both of these are equivalent in every sense of the word and give us our final answer of 27

8 0
3 years ago
Read 2 more answers
4. The Bulldog Theater charges $9.10 for each adult ticket and $7.75 for each student ticket. Mrs. Williams purchased 7 tickets
zhuklara [117]

Answer:

Two adult tickets and 5 student tickets

Step-by-step explanation:

Let a=adult tickets   Let s=student tickets

You know that each adult ticket is $9.10 and each student ticket cost $7.75. At the end, it cost $56.95 for both students and adults so the first equation should be 9.10a+7.75s=56.95. To get the second equation, you know that Mrs. Williams purchased 7 tickets in total that were both students and adults. Therefore, the second equation should be a+s=7. The two equations are 9.10a+7.75s=56.95

a+s=7.

Now, use substitution to solve this. I will isolate s from this equation so the new equation should be s=-a+7. Plug in this equation to the other equation, it will look like this 9.10a+7.75(-a+7)=56.95. Simplify this to get 9.10a-7.75a+54.25=56.95. Simplify this again and the equation will become 1.35a=2.70. Then divide 1.35 by each side to get a=2. This Mrs. Williams bought two adult tickets. Plug in 2 into a+s=7, it will look like this (2)+s=7. Simplify this and get s=5. This means Mrs. Williams bought five adult tickets. Therefore she bought 2 adult tickets and 5 student tickets.

Hope this helps

4 0
3 years ago
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