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ollegr [7]
2 years ago
15

Rewrite the function to complete the square f(x) = x^2 + 4x + 41

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
7 0

tot 8/8

Step-by-step explanation:

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How many liters of 60% alcohol solution should be added to 40 liters of a 20% alcohol solution to make a 50% solution?
kolbaska11 [484]

Answer:

120 liters of 60% alcohol solution is needed

Step-by-step explanation:

Let's assume

x liters of 60% alcohol solution  is added

so, we  get solution as

=\frac{60}{100}\times x

=0.6x

we are given

40 liters of a 20% alcohol solution is

=40\times\frac{20}{100}

=40\times\frac{20}{100}

=8

so, total alcohol solution is

=8+0.6x

now, we can find total solutions

total solutions is

=x+40

now, it is making 50% solution

so, we get

\frac{8+0.6x}{x+40} =\frac{50}{100}

now, we can solve for x

\left(8+0.6x\right)\cdot \:100=\left(x+40\right)\cdot \:50

800+60x=50x+2000

10x=1200

x=120

So,

120 liters of 60% alcohol solution is needed

4 0
2 years ago
How do I solve this?
Korvikt [17]

The interior angles of any triangle always sum to 180°.

In the triangle, angles C and D are labeled congruent, so the missing angle has measure

180° - 2 (6x - 5)°

This angle is supplementary to the one labeled (11x + 1)°, which means

180° = (11x + 1)° + (180° - 2 (6x - 5)°)

Solve for x :

180° = (11x + 1)° + 180° - 2 (6x - 5)°

0 = (11x + 1)° - 2 (6x - 5)°

0 = (11x)° + 1° - (12x)° + 10°

(12x - 11x)° = 1° + 10°

x° = 11°

x = 11

5 0
2 years ago
Are the decimals 0.4 and 0.40 equal?
zepelin [54]
0.4 and 0.40 are equal. That zero on the hundredths place does not matter.
3 0
3 years ago
Read 2 more answers
what is the smallest number of degrees needed to rotate a regular pentagon around its center onto itself
Serhud [2]
Since a pentagon has five identical sides, rotating it by (360 degrees/5) will result in the same image. 360/5=72 degrees
8 0
3 years ago
What is a, the initial amount, for the function: f(x) = 300(1.16)*?
jeka94
<h3>Answer:   300</h3>

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

Explanation:

One general template of exponential functions is

f(x) = a*(b)^x

The 'a' is the initial amount, which in this case is a = 300

----------------------

Extra info:

The b is the base of the exponential, which is b = 1.16

The value of b is helpful to determine if you have exponential growth or decay, and how much of either. Because b = 1.16 is greater than 1, it indicates exponential growth. The rate of growth is found by solving 1+r = 1.16 to get r = 0.16, which leads to 16% growth.

6 0
3 years ago
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