Match the base to the height

Pls help me answer this !!

krek1111 [17]

We want our exponential function to look like

y = ab^x.

Let a = the initial y-value.

Our initial value is the first number given for f(x). So, a = 3.

Let b = the number that is needed to go from 3 to 6 to 12 to 24 to 48.

We find b by division.

So, b = the next number divided by the previous.

So, b = 6/3 = 2.

We now plug in our values into the general formula above.

y = ab^x

Answer: y = (3)(2)^x

4 0

3 years ago

11. What is the location of the vertex of the parabola defined by f(x) = −3x2 − 18x − 35 and in what direction does the parabola

lbvjy [14]

11. The given parabola has equation: $f(x)=-3x^2-18x-35$

We complete the square to have the function in the vertex form: $f(x)=-3(x^2+6x)-35$

$f(x)=-3(x^2+6x+9)+3*9-35$

$f(x)=-3(x^2+6x+9)+27-35$

$f(x)=-3(x+3)^2-8$

The vertex is (-3,-8), the graph opens down because a=-3<0

Ans: B. Vertex: (−3, −8), opens downward

12. We know the graph of $y=x^2$ is a parabola that opens up and has its minimum point at the origin.

The range of this function is $y\ge 0$

A straight line that has its y-intercept below the x-axis (y=3x-6) will not intersect $y=x^2$ and hence will form a system with no solution.

Ans: D. y equals x squared, y equals 3x minus 6

14. We want to find the zeros of $x^2+21x=5x-63$

$x^2+21x-5x+63=0$

$x^2+16x+63=0$

The factored form is $(x+7)(x+9)=0$

$x=-7\:or\: x=-9$

Ans: C. x = −7, −9

15. The given quadratic expression is $6x^2-17x+10$

We split the middle term to obtain:

$6x^2-12x-5x+10=0$

We factor by grouping to get:

$6x(x-2)-5(x-2)=0$

$(x-2)(6x-5)=0$

Ans: D. 6x − 5

8 0

4 years ago

Read 2 more answers

Find the mean of the following data set. 42, 45, 58, 63 42 47 52

vredina [299]

You have to add all the numbers and then with that sum divide it by the number of numbers. In this case it would be 42+45+58+63+42+47+52=349. Now divide that by the numbers of numbers which in this case is 7, ~49.85(answer).

8 0

3 years ago

Read 2 more answers

A scientist claims that 4% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of

oksano4ka [1.4K]

Answer:

The probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%=0.00427

Step-by-step explanation:

We are given that

$\mu_{\hat{p}}=p=4%=0.04$

n=662

We have to find the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%.

q=1-p=1-0.04=0.96

$\sigma_{\hat{p}}=\sqrt{p(1-p)/n}$

$\sigma_{\hat{p}}=\sqrt{\frac{0.04(1-0.04)}{662}}$

$\sigma_{\hat{p}}=0.0076$

Now,

$P(\hat{p}>0.06)=1-P(\hat{p}$

$=1-P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}$

$=1-P(Z$

$=1-0.99573$

$P(\hat{p}>0.06)=0.00427$

Hence, the probability that the proportion of airborne viruses in a sample of 662 viruses would be greater than 6%=0.00427

7 0

3 years ago

An airline finds that if it prices a cross-country ticket at $200, it will sell 300 tickets per day. It estimates that each $20

olya-2409 [2.1K]

We can write that as a function:

$f(n)=(200 -20n) * (300 + 50n)\\f(n)=60000+10000n-6000n-1000n^2\\f(n)=-1000n^2+4000n+60000\\$

where $n$ is the number of price reductions. We can see that it is a quadratic function which has the biggest value at P = (p, q). It means that p is the number of reductions which results in the biggest profit.

$p=\frac{-b}{2a}=\frac{-4000}{-2000}=2$

It means that it's the best to make 2 price reductions for the company. The tickets should be sold for $200 - 2 * $20 = $160. It results in 2 * 50 more tickets sold which is 300 + 100 = 400.

Answer:

Ticket price: $160

Number of tickets: 400

6 0

3 years ago