A^3+a+a^2+1 2a^2+2ab+ab^2+b^3------------------------------- * ----------------------------------
a^3+a^2+ab^2+b^2 a^3+a+a^2b+b

Answers

Answer 1

Answer: $(a^3+a+a^2+1)/(a^3+a^2+ab^2+b^2) \cdot (2a^2+2ab+ab^2+b^3)/(a^3+a+a^2b+b) =(a(a^2+1)+1(a^2+1))/(a^2(a+1)+b^2(a+1)) \cdot (2a(a+b)+b^2(a+b))/(a(a^2+1)+b(a^2+1)) =\n\n=((a^2+1)(a+1))/((a+1)(a^2+b^2)) \cdot ((a+b)(2a+b^2))/((a^2+1)(a+b)) = (2a+b^2)/(a^2+b^2)$

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solve this problem as a quadratic equation. The difference between two positive numbers is 5. Their product is 104 find the numbers.

Answers

let's call the smaller number x:

y-x=5
xy=104

y-x=5 can be rewritten as y=x+5

Substituting this into the second equation gives:

x(x+5)=104
x^2+5x=104
x^2+5x-104=0

Then simply solve as a quadratic:

x^2+13x-8x-104=0
x(x+13) -8(x+13)=0
(x-8)(x+13) = 0

x=8,-13

the question said the numbers are positive, so x=8

if x=8,

y=x+5
y=13

So the two numbers are 8 and 13.

The best way to do this is to find the factors of 104. For this I got 1, 2, 4, 8, 13, 26, 52 and 104. From this, you are then able to look at the two that have a difference of five, which in this case, is 8 and 13. You should then double check that when these are multipled, they are equal to 104, which they are. I'm not 100% sure if this is the answer that you are looking for, but the two numbers are 8 and 13

Find two consecutive positive even numbers the sum of whose squares is 340

Answers

consecutive even means
x and x+2 since they are 2 apart

sum of squares is 340
x^2+(x+2)^2=340
expand and add
x^2+x^2+4x+4=340
2x^2+4x+4=340
divide both sides by 2 to make it easier
x^2+2x+2=170
minus 170 bot sides
x^2+2x-168=0
facotr
(x-12)(x+14)=0
set each to zero
x-12=0
add 12
x=12

x+14=0
minus 14
x=-14
but they has to e positive to disregard

x=12
x+2=14

numbers are 12 and 14

A pentagonal prism is cut by a plane perpendicular to the base. What is the shape of the cross section that is formed?a pentagon with one pair of equal sides
a trapezoid with one pair of parallel sides
a rectangle
a triangle
a hexagon

Answers

The correct answer is:

a rectangle

Explanation:

In a right pentagonal prism, the bases are pentagons and the lateral faces are rectangles.

If we take a cross-section perpendicular to the base, this same cross-section will be parallel to the lateral faces. This means it will be the same shape as the lateral faces, which is a rectangle.

Answer:

rectangle

Step-by-step explanation:

edemuntum gang

I NEED HELP ASAP!!!!!!!!!!!!!!!!Mrs. Baxter deposits $2,000 in an account that earns 5% simple interest. How much is Mrs. Baxter's investment worth after 8 years?

I need the formula, work, and solution.

Answers

Answer:

3200 i think

Step-by-step explanation:

2,000/5=400

400x8=3200

A group of students surveyed chose baseball and soccer as their favorite sport in the ratio 3:8 A) if 132 students were surveyed, find the number of students that chose soccer as there favorite sport

B) if 56 students chose soccer as their favorite sport, find the number of students that chose baseball as their favorite sport.

Answers

$3x-\ those\ who\ chose\ baseball\n8x-\ those\ who\ chose\ soccer\n\na)\n3x+8x=132\n\n11x=132\ \ \ | divide\ by\ 11\n\nx=12\n\n8x=8*12=96\n\n96\ chose\ soccer.\n\n\b)\n8x=56\ \ \ | divide\ by\ 8\n\nx=7\n\n3x=3*7=21\n\n21\ chose\ baseball.$

Final answer:

Using ratios, we determine that out of 132 students, 96 chose soccer. If 56 students chose soccer, then 21 students chose baseball.

Explanation:

This question deals with the concept of ratios. The ratio of students who chose baseball to those who chose soccer is given as 3:8. This means that the total number of parts is 3 (for baseball) + 8 (for soccer) = 11.

A) If 132 students were surveyed, we can determine the number of students who chose soccer by first finding the value of each 'part' in the ratio. This is done by dividing the total number of students (132) by the total number of parts (11) which equals 12 students per 'part'. As soccer was chosen by 8 'parts' of students, the number of students is 8 * 12 = 96.

B) If 56 students chose soccer, represented by 8 'parts', then each 'part' corresponds to 56 / 8 = 7 students. The number of students who chose baseball, represented by 3 'parts', is then 3 * 7 = 21.