MATHEMATICS HIGH SCHOOL

Which category does each card go into?

Answers

Answer 1

Answer:

Answer:

See attached

Step-by-step explanation:

The answer is attached

Infinitely many solutions

E2, E8, E10

One solution

E1, E7, E12

No solution

E3, E6, E11

Answer 2

Answer:

Step-by-step explanation:

E3, E6, E11, E7: no solution

E1, E12 : 1 solution

E2, E8, E10 : infinite solutions

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What is X divided by 2?
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The prism can be cut into three pyramids with the shaded faces congruent. If the shaded faces are considered as bases, then all three pyramids have the same height, h. Therefore the pyramids have equal volumes. What is the volume of each pyramid?A) ⅓BtB) ⅓AhC) ⅓ArD) ⅓At

Prove the identity
cos(A+B+C)=cosAcosBcosC-cosAsinBsinC-sinAcosBcosC-sinAsinBcosC

Answers

Hello !

cos (a+b) = cos a cos b - sin a sin b
sin (a+b) = sin a cos b + sin b cos a

cos (a+b+c) = cos (a+(b+c))
cos (a+b+c) = cos a cos (b+c) - sin a sin (b+c)
cos (a+b+c) = cos a (cos b cos c - sin b sin c) - sin a (sin b cos c + sin c cos b)
cos (a+b+c)=cos a cos b cos c - cos a sin b sin c - sin a sin b cos c - sin a cos b sin c

What two numbers multiply to 10 and add to -29 ?

Answers

xy=10
x+y=29

subtract x from both sides for second equation

y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x= $\frac{-b+/- \sqrt{b^(2)-4ac} }{2a}$

so
x^2+29x+10=0
a=1
b=29
c=10
x= $\frac{-29+/- \sqrt{(-29)^(2)-4(1)(10)} }{2(1)}$
x= $(-29+/- √(841-40) )/(2)$
x= $(-29+/- √(801) )/(2)$
x= $(-29+/- 3√(89) )/(2)$

x= $(-29- 3√(89) )/(2)$ or $(-29+ 3√(89) )/(2)$
those are the 2 numbers
aprox=-28.65 and -0.349

There are none.
You can prove this by graphing.
xy = 10
y = 10/x

x + y = -29
y = -x - 29

On the graphing calculator, type in
Y1 = 10/x
Y2 = -x - 29

As you can see the two do not intersect.

A savings account accrues interest at a rate of 3.0% yearly. If someone opens an account with $2,500, how much money would the account have after 5 years?

Answers

$3\%=(3)/(100)=0,03\n\n First\ year:2500+2500*0,03=2500+75=2575\n\nSecond\ year:\ 2575+2575*0,03=2575+77,25=2652,25\n\nThird\ year:\ \ 2652,25+2652,25*0,03=2652,25+79,5675=\n\n2731,8175\n\n Fourth\ year: 2731,8175+2731,8175*0,03=2731,8175+81,954525\n\n=2813,772025\n\nFifth\ year:\ 2813,772025+2813,772025*0,03=\n\n2813,772025+84,41316075=2898,18518575\$$

What is the solution of the equation? 3 = b + 3
A. 0
B. 1
C. 9
D. 6

Answers

A would be the answer
you have to combine like terms
so subtract 3 from each side and then you are left with b=0

Find the area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards long. Round your answer to the nearest tenth.

Answers

Answer:

Step-by-step explanation:

area=6×11.4×13÷2=444.6 yd²

To break even in a manufacturing business, income or revenue R must equal the cost of production C. The revenue R from selling x number of computer boards is given by R=40x, and the cost C of producing them is given by C=30x+1000. Find how many boards must be sold to break even. Find how much money is needed to produce the break-even number of boards.

Answers

Answer:

To find the number of boards that must be sold to break even, we need to set the revenue equal to the cost and solve for x.

Given:

Revenue R = 40x

Cost C = 30x + 1000

Since the break-even point is when revenue equals cost, we have the equation:

40x = 30x + 1000

To solve for x, we subtract 30x from both sides of the equation:

40x - 30x = 30x + 1000 - 30x

Simplifying:

10x = 1000

Dividing both sides by 10:

x = 100

Therefore, to break even, 100 computer boards must be sold.

To find the amount of money needed to produce the break-even number of boards, we substitute the value of x into the cost equation:

C = 30x + 1000

C = 30 * 100 + 1000

C = 3000 + 1000

C = 4000

Therefore, $4000 is needed to produce the break-even number of boards.

Step-by-step explanation:

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