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3 years ago

What is the y-value of the vertex of the function f(x) = –(x + 8)(x – 14)?

2 answers:

8 0

so we want to know the vertex point of the equation f(x)=-(x+8)(x-14). First lets simplify the equation: f(x)=-x^2+6x+112. Now lets calculate the vertex by transforming the function to the form: f(x)=a(x-h)^2 + k where h and k are vertex coordinates. So: f(x)= (-x^2+6x+9)+121=-(x-3)^2+121 and the vertex point is (3,121).

Romashka [77]3 years ago

4 0

Answer:

D.121

Step-by-step explanation:

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Write 600 as a product of it's primse factors

givi [52]

Answer:

2*2*2*3*5*5

2^3 *3* 5^2

Step-by-step explanation:

600 = 60*10

These are not prime so keep going, breaking 60 and 10 down

= 6*10 * 5*2

6 and 10 are not prime so keep going ( 5 and 2 are prime)

= 3*2 * 5*2 * 5*2

All of the numbers are prime, so we normally write them in order from smallest to largest

2*2*2*3*5*5

We can write with exponents

2^3 *3* 5^2

8 0

2 years ago

If f(x)=3 x -1 and g(x)=0.03x^3-x+1 an approximate solution for the equation f(x)=g(x) is

lubasha [3.4K]

Answer:

x ≈ {-11.789, +0.501, 11.288}

Step-by-step explanation:

The cubic g(x) - f(x) = 0 has three real solutions. It can be rewritten as ...

$g(x)-f(x)=0\\\\0.03x^3-x+1-(3x-1)=0\\\\0.03x^3-4x+2=0$

Since the solutions are irrational, they are best found using a spreadsheet or graphing calculator. My favorite graphing calculator shows the approximate solutions below.

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Comment on the problem statement

Your expression for f(x) is ambiguous in that many Brainly questions have the exponentiation indicator replaced by a blank: 3 x -1 often means 3^x -1 and sometimes means 3^(x-1). We have taken the expression at face value and have assumed it is a linear expression. If otherwise, the problem is basically worked the same way: write a function h(x) = g(x) - f(x) and look for solutions to h(x) = 0. Graphing can be useful.

3 0

3 years ago

A man can drive a motorboat 70 miles down the Colorado River in the same amount of time that he can drive 40 miles upstream. Fin

pochemuha

The speed of the current is 40.34 mph approximately.

SOLUTION:

Given, a man can drive a motorboat 70 miles down the Colorado River in the same amount of time that he can drive 40 miles upstream.

We have to find the speed of the current if the speed of the boat is 11 mph in still water. Now, let the speed of river be a mph. Then, speed of boat in upstream will be a-11 mph and speed in downstream will be a+11 mph.

And, we know that, $\text{ distance } =\text{ speed }\times \text{ time }$

$\begin{array}{l}{\text { So, for upstream } \rightarrow 40=(a-11) \times \text { time taken } \rightarrow \text { time taken }=\frac{40}{a-11}} \\\\ {\text { And for downstream } \rightarrow 70=(a+11) \times \text { time taken } \rightarrow \text { time taken }=\frac{70}{a+11}}\end{array}$

We are given that, time taken for both are same. So $\frac{40}{a-11}=\frac{70}{a+11}$

$\begin{array}{l}{\rightarrow 40(a+11)=70(a-11)} \\\\ {\rightarrow 40 a+440=70 a-770} \\\\ {\rightarrow 70 a-40 a=770+440} \\\\ {\rightarrow 30 a=1210} \\\\ {\rightarrow a=40.33}\end{array}$