Find the area of the figure.
Area: __ m2
(Please help I am not good at area)

The vertex of the given function [tex]f(x)= -4(x-2)^2+100[/tex] is (2, -25). the y-intercept is (0,-21). the x-intercept are (-3,0) and (7,0).

The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function.

The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis,

where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.

We have the function,

[tex]f(x)= -4(x-2)^2+100[/tex]

On simplifying, we get,

[tex]f(x)= x^2 - 4x -21\\\\f(x) = (x+3)(x-7)[/tex]

Now, the factors of the given functions are (x+3) and (x - 7).

We have,an intercept form of the function is .

[tex]f(x) = (x+3)(x-7)[/tex]

Now, we know that,

Value of x-coordinate of the vertex is -b/2a

= 4 / 2

= 2

x = 2

Then,

[tex]f(2)= 2^2 - 4(2) -21\\\\f(2)= -25[/tex]

So, the vertex of the function is (2, -25).

Further, we know that 'the y-intercept of a function is the point where the function crosses the y-axis'.

So, when x=0, we have,  i.e. f(0) = -21

Thus, the y-intercept is (0,-21)

Also, 'the x-intercept of a function is the point where the function crosses x-axis'.

Then, for f(x)=0, we have  i.e.  i.e. x= -3 and x= 7

Thus, the x-intercept are (-3,0) and (7,0).

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Answer:

152.5

Step-by-step explanation:

Answer:

(-4, 2), (-1, -3), (2,0), (4,3).

Answer:

96

Step-by-step explanation:

12 ÷ 3 = 4 (therefore he is saving $24 four times in 12 weeks)

24 × 4 = 96

Answer:

97 degrees

Step-by-step explanation:

supplementary angles are 2 angles that add up to 180 degrees

so

180- 83 = 97

[tex]\boxed{\sf 97~degrees}\boxed{explanation~below}[/tex]

         [tex]\sf 180 - 83 = 97deg.[/tex]

Answer:34a

Step-by-step explanation:

because 6a-4=2a

4a+28=32a

2a+32a=34a

Answer:

A

Step-by-step explanation:

10-7= 7-4= 3

That's it!

Answer:

[tex]\sf 2\sqrt{2}[/tex]

Step-by-step explanation:

First find h(10)

   h(x) = 2x - 8

   h(10) = 2*10 - 8

           = 20 - 8

           = 12

[tex]\sf g(x)=\sqrt{x-4}\\\\ g(h(10) = g(12) = \sqrt{12-4}\\[/tex]

                         [tex]\sf = \sqrt{8}\\\\ = \sqrt{2*2*2}\\\\ = 2\sqrt{2}[/tex]

Answer:

X= -6 & x= 14

Step-by-step explanation:

The factors are -14 and 6, these numbers are multiplied to get -84 and added to get -8.

Therefore the new equation is:

x^2 -14x +6x -84 = 0

factorize: x (x -14) 6 (x - 14)

So: (x+6) (x-14) = 0

x = -6 and 14

Answer:

Lisa played 4.35 hours over the weekend :)

Step-by-step explanation:

Answer:

$239.68

Step-by-step explanation:

Given

Solving

Step-by-step explanation:

In an interdependent world, nations tend to cooperate more with each other. Some even argue that big wars are less likely to happen because countries need each other. The downside is that nations tend to have less autonomy when it comes to making major decisions.

Step-by-step explanation:

f(x) = y= -x²-x+6

When y is max, f'(x) = 0

f'(x) = -2x-1

Equating to 0,

-2x-1= 0

x= -1/2

Put the value of x in f(x)

y = -(-1/2)² -(-1/2) +6

= -1/4+1/2+6

= 6+1/2

y= 13/2

Answer:

39364

Step-by-step explanation:

You can simplify the equation to make 4(1+3+9...) The nth term is therefore [tex]3^{n-1}[/tex] so u can substitute that into the equation so 4([tex]3^{n-1}+ 3^{n} + 3^{n+1}[/tex]..). This would simplify to 4([tex]3^0 +3+3^2[/tex]+[tex]3^3+3^4+3^5+3^6+3^7+3^8[/tex]). By simplifying this, you can make it so 4([tex]2^2+6^2+18^2+42^2+81^2[/tex]) = 4(4+36+324+2916+6561) =39364

Answer:

$2.39

Step-by-step explanation:

to find the cost of 1 pound , divide the cost of 4 pounds by 4

$9.56 ÷ 4 = $2.39

Answer:

she is 66

Step-by-step explanation:

you multiply the age she as when you were born with 3 and get 66

ur wlcm :)

brainliest?

Answer:

  a +7d = 11

Step-by-step explanation:

The sum of an arithmetic series is given by the formula ...

  Sn = (n/2)(2·a1 +d(n -1))

where n is the number of terms, a1 is the first term, and d is the common difference.

__

Here, you are given n=15, S = 165, a1=a, and asked to find a relation for 'a' and 'd'. Substituting the known values, we have ...

  165 = (15/2)(2a +d(14))

  11 = a +7d . . . . . . . . simplify and divide by 15

We have found the relation to be ...

  a +7d = 11 . . . . . as required

The values of CotD and SinC from the information given in the task content are; 15/8 and 15/17 respectively.

It follows from the task content that the right triangle has tanC = 15/8 and cosD=15/17.

On this note, it follows from Pythagoras theorem that the other value are as follows;

Hence, it follows that the values of cotD and sinC are; 15/8 and 15/17 respectively.

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Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

Answer:

  x = 6

Step-by-step explanation:

We assume your functions are ...

In general, mixed polynomial and exponential functions have no algebraic solution. That means we need to solve f(x) = g(x) using a table of values, or by graphing.

__

Attached is a graphical solution. It shows the largest value of x for which f(x) = g(x) is x=6.

Check: f(6) = 1/2(2^6) = 32 = g(6) = 5(6) +2

__

Additional comment

We can start with f(x) = g(x) and subtract g(x) from both sides of the equation. This gives ...

  f(x) -g(x) = 0

Many graphing calculators readily identify the zeros of a function or expression. We have used that fact to find the two values of x where these functions are equal: ≈0.32 and 6.

For x>6, the exponential function increases without bound, so the graphs never cross again. Likewise, for x < -0.32, the linear function decreases without bound, so the graphs never cross again.

The lower value of x where the graphs cross is an irrational number near −0.319886722135.

Answer:

Step-by-step explanation:

unknown length=√(13²-12²)=√(169-144)=√25=5

B

yes

a numerical expression is a mathematical statement involving only numbers and one or more operation symbols. and a algebraic expession is an expressions that includes at least one variable and at least one operation. Order of operation goes (), exponent, divison, multiplication, addtion and subratcion

Answer: Choice C

f(x) = x+5

===========================================

Explanation:

The input x = -3 has 5 added to it to get x+5 = -3+5 = 2

The diagram shows the "-3" in the input oval pointing to "2" in the output oval.

Through similar steps, we have the input -2 map to the output 3. Also, the input 0 points to the output 5.

The input -5 should map to 0, but 0 isn't in the output list. So we ignore -5 in the input oval.

A. The rolls of groovy wallpaper is needed to cover the apartment bedroom. 9 rolls

B.The cost to re-wallpaper the apartment room $143.10

Based on the question, we have to assume there are no windows and no doors in that bedroom... to calculate how much less wallpaper we really need, and we cover completely from the floor to the ceiling.

A. If one rolls covers 50 sq ft, how many rolls do we need?

First, let's calculate the perimeter of that room, which is 16'x10'.

P = 16 + 10 + 16 + 10 = 52 feet of perimeter.

Now, the walls are 8 feet high... so, let's see just how big is the area to cover.

A = 52 feet * 8 feet = 416 sq feet to cover all walls.

Since we know each roll covers 50 sq ft, we will need:

416 / 50 = 8.32 rolls.

When talking about quantity you need to buy or to fill something, you always have to round up to the next unit.  Because you usually can't buy a portion of a unit and if you round it down, you'll miss material to cover your walls.

So, we will need 9 rolls.

B. Total cost, based on $15.90 per roll.

We already know we need 9 rolls... so how much will it cost us?

C = 9 * $15.90 = $143.10

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Answer:

the answer is A

Step-by-step explanation:

Given x2-2y= stock value

and

2x+5y= purchases

stock value must stay at or more than 6000

while purchases must stay under 2000

Answer: C and D

Step-by-step explanation:

√36 = ±6

Answer:

2

Step-by-step explanation:

The point being shown is 4,2 so the constant of proportinality is just a simple multiplication problem 2x2=4 so 2 is the answer.

Answer:

108

Step-by-step explanation:

five times a number x decreased by 2 can be expressed as by 5x- 2

Step-by-step explanation:

If we let the width be w, then the length is w+3.5.

This means that w(w+3.5)=11

w^2 + 3.5w - 11 = 0

2w^2 + 7w - 22 = 0 (multiply both sides by 2)

(2w+11)(w-2)=0

w = -11/2 or w = 2 (disregard w = -11/2 as distance is positive)

This means that w=2, and thus the length is 2+3.5=5.5

Answer:

0.625

Step-by-step explanation:

5/8th simplified is just 5 divided by 8

5/8 = 0.625

hope this helps!

Turn to decimals

Done!