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2 years ago

Describe how to determine whether the parabola y = 3x2 + 3x + 6 is opening upward.

Mathematics

1 answer:

qaws [65]2 years ago

4 0

Answer:

Opening upward

Step-by-step explanation:

Standard equation of parabola is:

y = ax² + bx + c

The parabola is opening upward if a > 0 and opening downward if a < 0

The given parabola has a = 3 > 0, therefore it is opening upward

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2. Suppose (220)_b and (251)_b are the squares of consecutive integers. Determine b.

Andrei [34K]

Let $x$ and $x+1$ be these consecutive integers. For some base $b$ , we can write

$(x_{10})^2=220_b=2b^2+2b$

$((x+1)_{10})^2=251_b=2b^2+5b+1$

$x^2=2b^2+2b$

then

$x^2+1=2b^2+2b+1$

Now,

$x^2+2x+1=2b^2+5b+1$

$2x+2b^2+2b+1=2b^2+5b+1$

$\implies2x=3b$

Squaring both sides gives

$4x^2=9b^2$

and so

$4(2b^2+2b)=9b^2$

$\implies8b^2+8b=9b^2$

$\implies b^2-8b=0\implies\boxed{b=8}$

(because the base has to be non-zero)

3 0

2 years ago

Find the missing length of the triangle. 10 in. 16 26 in.

Yanka [14]

Answer:

Step-by-step explanation:

26x26=676

10x10=100

676/100=576

The square root of 576 is 24.

8 0

2 years ago

two angles are complementary.one angles measure is 79 degrees. What is the measure of the other angle

dalvyx [7]

Complementary means the two angles add up to 90 degrees. Do 90 - 79 to find the other angle.

It's 11 degrees.

5 0

3 years ago

Which expression shows the prime factorization of 36?

Svetradugi [14.3K]

36....we need to break this down...12 * 3 = 36
12 * 3....we can break this down because 12 is not prime...4 * 3 = 12
4 * 3 * 3...we can break the 4 down because it is not prime
2 * 2 * 3 * 3 <==== prime factorization

6 0

2 years ago

Solve 5x − 4 = 7 for x using the change of base formula log base b of y equals log y over log b.

Sauron [17]

Answer:

5.209 or A

Step-by-step explanation

5^x-4=7

reserve 4

log sides

x-4 log5 and log7

x-4=log7/log5

+4 or number of your equation

x=log5/log7 +4

use calculator

get answer

5.209

EDIT: Got a 100 on the test this is correct

5 0

2 years ago