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2 years ago

7

What is the angle of rotation of the figure? 300

1 answer:

Dennis_Churaev [7]2 years ago

4 0

Answer:

The angle of the figure is 90°

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The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.

skad [1K]

Since we know the sequence is quadratic, we expect the $n$ -th term to have the general form

$x_n = an^2 + bn + c$

Plug in the first 3 known values of the sequence to form a system of equations.

$x_1 = 3 = a + b + c$

$x_2 = 12 = 4a + 2b + c$

$x_3 = 25 = 9a + 3b + c$

Eliminating $c$ gives

$(4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9$

$(9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11$

Eliminating $b$ gives

$(4a + b) - (3a + b) = 11 - 9 \implies a = 2$

Solving for $b,c$ , we get

$4a + b = 11 \implies b = 11-4\cdot2 = 3$

$a+b+c=3 \implies c=3-2-3 = -2$

So, the $n$ -th term of the sequence is

$x_n = \boxed{2n^2 + 3n - 2}$

7 0

2 years ago

A scuba diver was swimming at a depth of 8 meters below the surface of the water. He saw an eel swimming 3 meters above him and

Trava [24]

You have to do 8-3
and 8-3=5
so the answer is 8-3=5

6 0

3 years ago

Read 2 more answers

The train station clock runs too fast and gains 7 minutes every 4 days. How many minutes and seconds will it have gained at the

Olegator [25]

16 minutes and 15 seconds.

4x2=8 8 days = 14 minutes
7/4=1.75= 2 minutes 15 seconds= total of 16min 15sec

3 0

3 years ago

Read 2 more answers

The volume of a cone is 50 pi cubic feet. Its height is 6 feet. In feet, what is the radius of the cone? Round the answer to the

prohojiy [21]

Answer:

The radius of the cone is $5\ ft$

Step-by-step explanation:

we know that

The volume of a cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

In this problem we have

$V=50\pi\ ft^{3}$

$h=6\ ft$

substitute in the formula and solve for r

$50\pi=\frac{1}{3}\pi r^{2}(6)$

Simplify

$25=r^{2}$

square root both sides

$r=5\ ft$

6 0

3 years ago

Read 2 more answers

2x+3x^2(4x-5)<br> please helpppp asap

Aliun [14]

Here's my step-by-step explanation:

We're just gonna factor.

If your teacher has spoken of FOIL, then he/she has probably said that it means First Outer Inner Last and that it helps with distributing problems like these.

Right, so let's get to it.

$2x+3x^2 (4x-5)\\2x(4x-5)+3x^2(4x-5)\\2x(4x) + 2x(-5) + 3x^2(4x) + 3x^2(-5)$

Can you see the FOIL method being spread out here? Let's keep going.

$2x(4x) + 2x(-5) + 3x^2(4x) + 3x^2(-5)\\8x^2 + (-10x) + 12x^3 + (-15x^2)\\12x^3 + 8x^2 - 15x^2 -10x\\12x^3 -7x^2 -10x$

Hope this helps, and let me know if I made a mistake! ^_^

7 0

3 years ago