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baherus [9]
4 years ago
14

Rewrite the function by completing the square. h(x)= 4 x^{2} -36 x +81

Mathematics
1 answer:
noname [10]4 years ago
6 0

Answer:

4(x-4.5)^2

Step-by-step explanation:

h(x)=4x^2-36x+81

=4(x^2-9x)+81

=4(x^2-9x+20.25)-(4)(20.25)+81

=4(x-4.5)^2

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In Bluepoint, the average low temperature for January was 40 °F. The average low in February was 27% lower. What was the average
yarga [219]

The average low temperature for January was 40 °F - 100%.

The average low in February was x °F - 27% lower, that is 100%-27%=73%.

Write a proportion:

\dfrac{40}{x}=\dfrac{100}{73},\\ \\x=\dfrac{73\cdot 40}{100},\\\\x=29.2

Answer: the average low in February was 29.2 °F.

5 0
4 years ago
Write an inequality to describe the region. The solid upper hemisphere of the sphere of radius 5 centered at the origin
dusya [7]

Answer:

x^2 + y^2 + z^2 \le 25 for z \ge 0

Step-by-step explanation:

Given

r = 5 --- radius

Required

Determine the inequality of the region

The inequality of a region of a sphere is determined using:

x^2 + y^2 + z^2 \le r^2

Substitute 5 for r

x^2 + y^2 + z^2 \le 5^2

x^2 + y^2 + z^2 \le 25

Solving further: <em>The question says only the upper hemisphere is considered.</em>

This implies that:

z \ge 0

<em>So, the equation is:</em>

x^2 + y^2 + z^2 \le 25

z \ge 0

5 0
3 years ago
Rewrite y= (square root all) 9x+45 (non sqrt) -2 to make it easy to graph using a translation. describe the graph
iVinArrow [24]

Answer:

(i)

shifted left side by 5 units

(ii)

vertically stretch by 3 units

(iii)

shifted vertically downward by 2 units

Step-by-step explanation:

we are given

y=\sqrt{9x+45} -2

we can also write as

y=\sqrt{9(x+5)} -2

we can factor out 9

y=3\sqrt{(x+5)} -2

Firstly, we will identify parent function

y=\sqrt{x}

step-1:

We can see that there is x+5 in place of x

so, f(x) will be shifted left side by 5 units

step-2:

3 is multiplied to sqrt

so, it is vertically stretch by 3 units

step-3:

-2 is added to y-value

so, it is shifted vertically downward by 2 units

Graph:


3 0
4 years ago
You invest 1300 in a bank with an interest rate of 8.5% how much money will you have in 12 years ?
densk [106]

Answer:

3460

Step-by-step explanation:

Lots and lots and lots and lots of math. :p

Basically just add 8.5% to each number 12 times

5 0
3 years ago
If a = 15 ft, b = 20 ft, and c = 25 ft, what is the total area of the porch? Assume that the wooden part is a right triangle and
Sergeu [11.5K]
First do 25x25 then tell me


7 0
4 years ago
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