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2 years ago

HELP

Mathematics

1 answer:

adelina 88 [10]2 years ago

8 0

Answer:

$(x-6)^2=8$

Step-by-step explanation:

$x^2-12x+32=4$

$x^2-12x+32+4=4+4$

$x^2-12x+36=8$

$(x-6)^2=8$

Basically, you need to add a number to both sides so that you can reduce the left side to a square. In this case, you add 4.

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Alexa worked 30 hours last week and earned $450. Her pay has now been increased by 20%. Which equation describes her new rate of

vesna_86 [32]

Answer:

$p=18h$

$p=\dfrac{450}{30}\cdot 1.2\cdot h$

Step-by-step explanation:

If Alexa worked 30 hours last week and earned $450, then her hourly payment is

$\dfrac{\$450}{30}=\$15.$

Her payment has now been increased by 20%, so her hourly payment becomes

$\$15\cdot 1.2=\$18.$

If she worked h hours, then she earned $\$18h.$ If her new payment is p, then

$p=18h$

$p=\dfrac{450}{30}\cdot 1.2\cdot h.$

4 0

3 years ago

A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns,

guajiro [1.7K]

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation $A=45e^{-0.05t}$ .

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate $A=15$ and solve for t as:

$15=45e^{-0.05t}$

$\frac{15}{45}=\frac{45e^{-0.05t}}{45}$

$\frac{1}{3}=e^{-0.05t}$

Now we will switch sides:

$e^{-0.05t}=\frac{1}{3}$

Let us take natural log on both sides of equation.

$\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})$

Using natural log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})$

$-0.05t\cdot (1)=\text{ln}(\frac{1}{3})$

$-0.05t=\text{ln}(\frac{1}{3})$

$t=\frac{\text{ln}(\frac{1}{3})}{-0.05}$

$t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}$

$t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}$

$t=-\text{ln}(\frac{1}{3})\cdot 20$

$t=-(\text{ln}(1)-\text{ln}(3))\cdot 20$

$t=-(0-\text{ln}(3))\cdot 20$

$t=20\text{ln}(3)$

Therefore, it will take $20\text{ln}(3)$ years for area of the glacier to decrease to 15 square kilo-meters.

6 0

3 years ago

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 1, 3, 9, 27

r-ruslan [8.4K]

a geometric sequence is a bunch of numbers where you can get from a number to the next number by multiplying the previous number by a certain number

might be confusing so here's an example

1,2,4,8,16

each term is multiplied by 2 to get next term, that number that each term is multiplied by is called the common ratio

formula for geometric sequence is

$a_n=a_1(r)^{n-1}$

where $a_n$ is nth term

$a_1$ is first term

r is teh common ratio

n=which term

in our example

1,3, 9, 27, 81

each term is being multiplied by 3 so it is a geometric sequence and thus r=3

also first term is 1 so $a_1=1$

so the formula is $a_n=1(3)^{n-1}$ or in function notation $f(n)=1(3)^{n-1}$

7 0

3 years ago

Read 2 more answers

Write 460,053 in expanded form

Marianna [84]

400,000 60,000
0,000
000
50
3

6 0

3 years ago

Read 2 more answers

Factorization prima de 1024

Tamiku [17]

1024
/ \
32 32
/ \ / \
8 4 8 4
/\ /\ /\ /\
(2) 4 (2) (2)(2) 4 (2) (2)
/\ /\
(2)(2) (2)(2)

2x2x2x2x2x2x2x2x2x2 or 2^10

*(There wasn’t a little 10 to use so I just put 2^10 which is two to the tenth power)

3 0

3 years ago