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3 years ago

Help plssssssssssssssssssssss

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

7 0

Answer:

Then the solution is (4, 6).

Step-by-step explanation:

Let's use the substitution method:

First multiply the second equation by 4, obtaining 4y = -2x + 32.

Now substitute (-2x + 32) for 4y in the first equation:

3x + (-2x + 32) = 36, or

3x - 2x + 32 = 36. or

x = 4.

If x = 4, then the second equation yields y = (-1/2)(4) + 8, or

y = -2 + 8, or y = 6

Then the solution is (4, 6).

Check, using the first equation:

Does 3(4) + 4(6) = 36? Does 12 + 24 = 36? YES

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Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

6 0

3 years ago

These are the first six terms of a sequence with a1= - 3: - 3, 8, 19, 30, 41, 52, … Find a recursive formula for this sequence t

ad-work [718]

Answer:

$a(n+1)=a(n)+11$

Step-by-step explanation:

The difference between two consecutive elements is 11.

$8=-3+11\\19=8+11\\30=19+11\\41=30+11\\52=41+11\\$

Hence $a(n+1)=a(n)+11$

6 0

3 years ago

The lines below are parallel. If the slope of the green line is -2, what is the slope of the red line?

IgorLugansk [536]

Parallel lines have equal slopes, so if green line has slope = -2 then, red line's slope would be equal to -2

In short, Your Answer would be Option A

Hope this helps!

5 0

3 years ago

Read 2 more answers

Empat sebutan pertama suatu jajang aritmetik ialah 3x-1,4x,5x+1,4.cari

wariber [46]

Here, A.P. is 3x-1, 4x, 5x+1, 4

i) Common difference (d)
(5x-1) - 4x = x - 1
It would be same as 4 - (5x-1) = 4-5x+1 = 5-5x
Now, x - 1 = 5 - 5x
5x + x = 5 + 1
6x = 6
x = 6/6
x = 1

So, Common difference would be 1

ii) Eight term will be: a + (n-1)d = 2 + (8-1)2 = 2+7(2) = 2+14 = 16

So, eight term would be 16

Hope this helps!

3 0

3 years ago

if <img src="https://tex.z-dn.net/?f=h%28x%29%3D4x%5E%7B2%7D%20-16" id="TexFormula1" title="h(x)=4x^{2} -16" alt="h(x)=4x^{2} -1

spayn [35]

Ummmmmmmmmmmm theeeee answerrrrrr isssssss 11,13

4 0

3 years ago