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Len [333]
3 years ago
12

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

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What two numbers add to make 36 with one of the numbers being exactly twice the other?
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Answer:

12 and 24

Step-by-step explanation:

2 numbers, x in this case, with one being twice the other, one of them will be 2x, equals 36. Your equation would look like this: 2x+x=36. Simplify it to get 3x=36, divide the 3 and you get 12. 12 will be your small number then multiply by 2 to get your large one, 24.

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Ellie practices piano 2/3 h per day, several days each week. She practiced piano 32 2/3 hours during the summer. What equation c
SVEN [57.7K]

hello :)

so let me just give you the answer first:

2/3 * d = 32 2/3

here is why

so since the sentence said 2/3 PER day, then d (the number of days) multiplied by the time spent each day playing piano should give you how much time was spent in total over the certian number of days.

the 32 2/3 is just the amount of time ellie spent (as you have said)

so, this equation would be the correct one.

i hope this helped you out! please vote me for brainliest and have splendid day!

4 0
3 years ago
Write an equation of the line through each pair of points in slope-intercept form.
ASHA 777 [7]

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

7 0
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