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maw [93]
4 years ago
15

Can someone please clearly and correctly work out Q19? Would appreciate it a lot! :)

Mathematics
1 answer:
DiKsa [7]4 years ago
6 0
x^{2} +10x+30
I always start by moving the last term to the other side
x^{2} +10x=-30
To complete the square you take term 'b' , divide it by 2 then square it
( \frac{10}{2} )^2 = 25
We have to add 25 to what we have and what you do to one side you have to do to the other
x^{2} +10x+25=-30+25
x^{2} +10x+25=-5
Now we factor what is on the left side of the equation
(x+5)^2=-5
The last step is to move our right side of the equation back over 
(x+5)^2+5 - which is your answer :)))


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Inverse of f(x)=2^x+6
hodyreva [135]
F(x)=2^x+6

let f(x) = n
f^-1(n) = x
x = 2^n + 6
x - 6 = 2^n
2^n = x - 6
log 2^n = log (x-6)
n log 2 = log (x-6)
n = (x-6)/2
f^-1(x) = (x-6)/2
4 0
3 years ago
F(x)=x^2-3x-2 is shifted 4 units left. The result is g(x) what is g(x)
grandymaker [24]

To solve this problem you must apply the proccedure shown below:

1. If the function f(x)=x^{2}-3x-2 is shifted 4 units left, this means that you must substitute the value of x by x+4 to find g(x), as following:

f(x+4)=(x+4)^{2}-3(x+4)-2

2. Now, expand the function:

f(x+4)=x^{2} +8x+16-3x-12-2\\ f(x+4)=x^{2} +5x+2

3. Then, you have that g(x) is:

g(x)=x^{2} +5x+2

Therefore, the answer is: g(x)=x^{2} +5x+2

3 0
4 years ago
Carmita bought 20 pizzas for a party, An hour after the party started, 2/7 of the pizzas had been eaten. How many pizzas had bee
lora16 [44]

Answer: 5 5/7

Step-by-step explanation:

Number of pizza bought = 20

Fraction of pizza ate = 2/7

Therefore, the number of pizzas that have been eaten will be:

= Fraction of pizza eaten × Number of pizza bought

= 2/7 × 20

= 40/7

= 5 5/7

Therefore, 5 5/7 pizza have been eaten

4 0
3 years ago
Figure out the pattern, and write the next number.<br> 2,6,21,88
bija089 [108]
Answer:
a5=445

Explanation:
a of n=(a+1)*n
a1=2
I found the pattern to add 1 to the previous number and then multiply it by its number in the sequence. Apologies for the terrible format of my recursive formula.
Proof of pattern:
(2+1)*2=6
(6+1)*3=21
(21+1)*4=88
a5=(88+1)*5=445
6 0
3 years ago
pls help...1.The given right rectangular prism is composed of small cubes. Find the following is the volume of the prism and the
marusya05 [52]

Answer:

1. 1.3778  2. 0.0089

Step-by-step explanation:

to find the volume of the whole rectangle prism you would have to do the volume formula since it is a 3d shape. VOLUME FORMULA, LxWxH.

so 1x0.83x1.66= 1.3778

you can always convert the fraction into decimal to help you calculate the problem.

i don't know if this is correct but i give it a try, so if the whole volume of the triangle is 1.3378 than you can divide that by the the number of small cubes it has inside.

it is 5 by 10 so there are 150 cubes in total.

1.3378 divided by 150=0.0089

im confident about the 1st but not so much with the second

7 0
3 years ago
Read 2 more answers
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