There are 50 rabbits on a farm. They are increasing at the rate of 12% every month. How many months will it be until there are 1000 rabbits?

Answers

Answer 1

Answer: Given:
50 rabbits
12% increase per month.

Solve for the increase per month. (multiply 50 by 12%)
50 x 12%= n
50 X .12= 6
6 rabbits per month is increased.
We will solve for the total number of months it will be when the number of rabbits reached up to 1000.
1000-50 +6=n
n=1000-50
6
n = 950 ÷ 6
n= 158.33.... months or 158 months and 10 days.

Since there are 50 rabbits already in the farm, we will subtract 50 from 1000. Every month the rabbits increased 12 % which is 6 (12% of 50) so, we will divide 950 (1000-50=950) by 6. The result is 158.33... months or 158 months and 10 days or .33 month.
158 months x 6= 948 rabbits (950-948=2)
Since 6 rabbits are increased per month, we need to calculate the two rabbits to make up 950.
2 rabbits ÷ 6 rabbits per month =.33 or 33% of the total increased.
33% of 30 days (1 month) =9.9 days or 10 days when rounded off.

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If given f(x) = x 4 and g(x) = –2x2 3x – 1, what is (f – g.(x)?
a. (f –
g.(x) = –2x2 4x – 3
b. (f –
g.(x) = –2x2 – 2x 5
c. (f –
g.(x) = 2x2 2x 5
d. (f –
g.(x) = 2x2 – 2x 5

Answers

f(x) = x + 4
g(x) = -2x^2 + 3x - 1
(f - g)(x) = f(x) - g(x) = x + 4 - (-2x^2 + 3x - 1) = x + 4 + 2x^2 - 3x + 1 = 2x^2 - 2x + 5

Answer:

$2x^2-2x+5$

Step-by-step explanation:

Given,

$f(x)=x+4$

$g(x)=-2x^2+3x-1$

$(f-g)(x)=f(x)-g(x)$ ( Subtraction of two functions )

$=(x+4)-(-2x^2+3x-1)$ ( By substituting values )

$=x+4+2x^2-3x+1$ ( Distributive property )

$=2x^2-2x+5$ ( Combining like terms )

Hence,

$(f-g)(x)=2x^2-2x+5$

Option d is correct.

One half of the birds at a pet store were yellow. Tara buys one. Then 1/3 of the birds left are yellow. How many yellow birds were left at the store before Tara bought them?

Answers

$x-the\ number\ of\ yellow\ birds\ at\ the\ beginning,\ \ \ x>0\n \n (x-1)/(2x) = (1)/(3) \n \n3\cdot(x-1)=2x\cdot1\n \n3x-3=2x\ \ \ \Rightarrow\ \ \ 3x-2x=3\ \ \ \Rightarrow\ \ \ x=3\n \n Ans.\ the\ number\ of\ yellow\ birds\ at\ the\ beginning\ is\ 3$

Complete the pairs of corresponding parts if △ RST ≅ △ TXY. ∠ R =
∠ XYT
∠ XTY
∠ TXY

Answers

Solution:

Given: △ RST ≅ △ TXY

We are given ΔRST and ΔTXY are congruent to each other.

If two triangles are congruent to each other then their corresponding parts are equal.

Please see the attachment of two triangles.

∠R is corresponding to ∠T

∵ ∠R=∠T By CPCT

∠XYT is corresponding to ∠STR

∵ ∠XYT=∠STR By CPCT

∠XTY is corresponding to ∠SRT.

∵ ∠XTY=∠SRT By CPCT

∠TXY is corresponding to ∠RST

∵ ∠TXY=∠RST By CPCT

CPCT: Congruent part of congruence triangle.

So, two triangles are similar. Ordering of letters matters when you are writing this down. So, RST~TXY, then ∠R = ∠T, or ∠TRS = ∠YTX = ∠XTY

Use the problem 34.65 ÷ 10³

Answers

34.65 / 10^3
34.65 / 1000

0.03465

Answer: when following PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction,) the answer comes out to 34.65 / 1000. The answer after that is 0.03465.

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