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3 years ago

Brainliest if you are correct

Mathematics

2 answers:

frez [133]3 years ago

4 0

Answer:

D) $log_2(x)+3log_2(9)$

Step-by-step explanation:

Given: $log_2(9x^{3})$

Use Exponent Rule: $3log_2(9x)$

Use Addition Rule: $log_2(x)+3log_2(9)$

PtichkaEL [24]3 years ago

3 0

D............................

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The parabola described by the equation -1/16(x-3)^2 + 4 = y has the directrix at y=8. What is the focus of the parabola?

slamgirl [31]

Answer:

(3, 0)

Step-by-step explanation:

A parabola is the locus of a point such that the distance from a fixed line called directrix and the distance from a fixed point called focus is constant.

The equation of a parabola with a vertex at (h, k) with axis of symmetry parallel to the y axis is given as:

$4p(y-k)=(x-h)^2$

The directrix is at y = k - p, and focus is at (h, k + p).

Given an equation -1/16(x-3)^2 + 4 = y, expressing it in standard form is:

$-\frac{1}{16}(x-3)^2+4=y\\\\(y-4)= -\frac{1}{16}(x-3)^2\\\\-16(y-4)=(x-3)^2\\\\$

Comparing with the standard form:

The center = (h, k) = (3, 4)

Also, -16 = 4p

p = -4

Directrix is at y = k - p = 4 - (-4) = 8

Directrix is at y = 8

The focus is at (h, k + p) = (3, 4 + (-4)) = (3, 0)

The focus is at (3, 0)

3 0

3 years ago

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial inve

pentagon [3]

Answer:

Brian has $776 more account in his account than Chris.

Step-by-step explanation:

Compound interest Formula:

$A=P(1+r)^t$

$I$ = A-P

A= Amount after t years

P= Initial amount

r= Rate of interest

t= Time in year

Given that,

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years.

Here P = $10,000 , r= 4%=0.04, t=10 years

The amount in his account after 10 years is

$A=10000(1+0.04)^{10}$

=$14802.44

≈$14802

Five years after Brian's investment,Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

Here P = $10,000 , r= 7%=0.07, t=5 years

The amount in his account after 5 years is

$A=10000(1+0.07)^{5}$

=$14025.51

≈$14026

From the it is cleared that Brian has $(14802-14026)=$776 more account in his account than Chris.

6 0

3 years ago

a bakery sells 17 cups of coffee for every 3 cups of hot chocolate they sell. At the end of the day the bakery sold 406 more cof

tester [92]

Answer:

Step-by-step explanation:

4 0

3 years ago

What are some expressions that are equivalent to 6(m+2+ m)

Maurinko [17]

Answer:

12m + 12 is one equivalent expression

Step-by-step explanation:

This can be found by distributing the numbers as shown below:

6(m + 2 + m)

6m + 12 + 6m

12m + 12

8 0

3 years ago

Read 2 more answers

Prove that if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

hammer [34]

It is proved that the if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

According to the statement

we have to prove that the if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

And for this proof we use the contradiction

So,

Proof by contradiction is a common proof technique that is based on a very simple principle: something that leads to a contradiction can not be true, and if so, the opposite must be true.

So for this purpose,

Assume a is even, so a = 2k for some integer k. Now let a and b be integers such that a divides b and a + b is odd.

Since a divides b, b = an for integer n, and in turn b = 2nk, which means b is even and hence a + b is also even. But this contradicts our initial assumption, so a must be odd.

So, It is proved that the if a and b are nonzero integers, a divides b, and a b is odd, then a is odd.

Learn more about integers here

brainly.com/question/17695139

#SPJ4

7 0

2 years ago