All categories

3 years ago

PLEASE HELP!!

Mathematics

2 answers:

cluponka [151]3 years ago

8 0

Answer:

$x\in(-\infty,-2)\cup(5,\infty)$

Step-by-step explanation:

The duadratic function $g(x)=x^2+20$ begin to exceed the linear function $f(x)=3x+30$ when $g(x)>f(x)$

Solve this inequality:

$x^2+20>3x+30\\ \\x^2-3x+20-30>0\\ \\x^2-3x-10>0\\ \\x^2-5x+2x-10>0\\ \\x(x-5)+2(x-5)>0\\ \\(x-5)(x+2)>0$

This inequality is equivalent to

$\left[\begin{array}{l}\left\{\begin{array}{l}x-5>0\\x+2>0\end{array}\right.\\ \\\left\{\begin{array}{l}x-5-2\end{array}\right.\\ \\\left\{\begin{array}{l}x$

Answer: $x\in(-\infty,-2)\cup(5,\infty)$

VMariaS [17]3 years ago

5 0

Answer:

x=5

Step-by-step explanation:

We are given that

$f(x)=3x+30$

$g(x)=x^2+20$

We have to find the positive integer value of x for which the quadratic function g(x) begin to exceed the linear function f(x).

$g(x) > f(x)$

$x^2+20 > 3x+30$

$x^2+20-3x-30 >0$

$x^2-3x-10 > 0$

$(x-5)(x+2) > 0$

$x-5 > 0$

$x > 5$

$x+2 > 0$

$x >-2$

Interval ( $5,\infty)$

Therefore , g(x) exceed f(x) in the interval ( $5,\infty)$ .

g(x) begin to exceed the linear function at x=5

You might be interested in

Please help me out I need it done ASAP

irinina [24]

Your answer will be letter c

7 0

3 years ago

Which is the graph of the step function f(x)? f(x) = StartLayout Enlarged left-brace 1st row 1st column negative 1 2nd column x

Andrews [41]

Answer:

its B

Step-by-step explanation: just took test

5 0

2 years ago

Can someone plz help me with Algebra 2....... :) Will give Brainliest!!

Anarel [89]

Using logarithms property of log(x)+log(y)=log(xy)
so here, you can sum the equation to;
$log((x+6)*(x-6))=2$
so you can simply say that;
$log_{8}((x+6)( x-6))=2$
and by multiplying (x+6)*(x-6)
$log_{8}(x^2-36)=2$
and as you know also that;
$a^{b}=c$ is same as $log _{a}c=b$
so you can simply state it as;
$8^2=x^2-36
64=x^2-36
64+36=x^2
x^2=100
x=10$
And you can check your work by substituting with 10 instead of x in the original function.
Hope this helps!

6 0

3 years ago

Measure Math | Welcome, HAILEE KNOTT

grandymaker [24]

Answer: $15\times\frac{1}{2}$

Explanation:

Multiplying by 1/2 is the same as dividing by 2.

For example, if you have 10 slices of cake and 2 friends, then each friend gets 10/2 = 5 slices. We could also say $10\times \frac{1}{2} = 5$

The fraction 1/2 converts to the decimal form 0.5, which means $10 \times \frac{1}{2} = 10*0.5$

3 0

2 years ago

Somebody please help so I can pass, please

ASHA 777 [7]

First, we are going to find the vertex of our quadratic. Remember that to find the vertex $(h,k)$ of a quadratic equation of the form $y=a x^{2} +bx+c$ , we use the vertex formula $h= \frac{-b}{2a}$ , and then, we evaluate our equation at $h$ to find $k$ .

We now from our quadratic that $a=2$ and $b=-32$ , so lets use our formula:
$h= \frac{-b}{2a}$
$h= \frac{-(-32)}{2(2)}$
$h= \frac{32}{4}$
$h=8$
Now we can evaluate our quadratic at 8 to find $k$ :
$k=2(8)^2-32(8)+56$
$k=2(64)-256+56$
$k=128-200$
$k=-72$
So the vertex of our function is (8,-72)

Next, we are going to use the vertex to rewrite our quadratic equation:
$y=a(x-h)^2+k$
$y=2(x-8)^2+(-72)$
$y=2(x-8)^2-72$
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.

We can conclude that:
The rewritten equation is $y=2(x-8)^2-72$
The x-coordinate of the minimum is 8

8 0

3 years ago

Read 2 more answers