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2 years ago

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PLEASE ANSWER ALL THE QUESTIONS IM LOSING MY SANITY

1 answer:

alex41 [277]2 years ago

4 0

Hypotenuse-Leg (HL) Theorem. If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.

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The function f(x) = x2 + 6x + 3 is transformed such that g(x) = f(x − 2). Find the vertex of g(x).

garri49 [273]

Answer:

(-1,-6)

Step-by-step explanation:

$f(x)=x^2+6x+3$

$g(x)=f(x-2)$

$g(x)=(x-2)^2+6(x-2)+3$ (Replaced x in f with (x-2))

$g(x)=x^2-4x+4+6x-12+3$ (Used $(x+b)^2=x^2+2bx+b^2$ and distributive property)

$g(x)=x^2-4x+6x+4-12+3$ (Gathered like terms)

$g(x)=x^2+2x-5$ (Simplified)

The vertex of a parabola occurs at $(\frac{-b}{2a},g(\frac{-b}{2a})$ .

Let's find $\frac{-b}{2a}$ first.

$\frac{-2}{2(1)}=-1$

Now we can obtain $g(\frac{-b}{2a})$ which is $g(-1)$ in this case:

$g(x)=x^2+2x-5$

$g(-1)=(-1)^2+2(-1)-5$

$g(-1)=1-2-5$

$g(-1)=-1-5$

$g(-1)=-6$ .

The vertex is (-1,-6).

6 0

2 years ago

For the geometric sequence of a1=2 and r=2 find a5

Brrunno [24]

Answer:

$a_5 = 32$

Step-by-step explanation:

The nth term for the geometric sequence is given by:

$a_n = a_1 \cdot r^{n-1}$

where,

$a_1$ is the first term

r is the common ratio

n is the number of terms.

As per the statement:

For the geometric sequence of $a_1=2$ and r=2

We have to find $a_5$

for n = 5;

$a_5=a_1 \cdot r^{n-1}$

Substitute the given values we have;

$a_5 = 2 \cdot 2^4 = 2 \cdot 16$

⇒ $a_5 = 32$

Therefore, the value of $a_5$ is, 32

3 0

3 years ago

Frank's bank charges a variable finance rate of 1.5 percent on purchases up to $100, and one percent for purchases over $100. If

Brilliant_brown [7]

Answer:

Hi there, $4.04 should be his finance charge.

Step-by-step explanation:

4 0

2 years ago

The total cost of an $85.73 meal with a 20% tip

kkurt [141]

Answer:

$102.876

Step-by-step explanation:

multiply 85.73 by 120% bc there is the price of the meal and 20% of the original price

4 0

2 years ago

Read 2 more answers

What is the prime factorization for 900 i just need the answer i got to turn in in like 2 minute

Tomtit [17]

Answer:

Factors (2 x 2 x 3 x 3 x 5 x 5 = 900). It can also be written in exponential form as 22 x 32 x 52.

Step-by-step explanation:

4 0

2 years ago