A student bought 1 box of crayons and 5 reams of paper for $54. She bought 5 boxes of crayons and 3 reams of paper $50. what is the cost of each box of crayons and each ream of paper?

Answers

Answer 1

Answer: lets solve it using a system of equations, c is the price of crayons and p the price of reams of paper, so we have:
1c + 5p = 54
5c + 3p = 50
those equations represent the situation. Lets solve the system multiplying the first equation by -5 and adding it to the second, we have:
-5c - 25p = -270
5c + 3p = 50
---------------------
0 - 22p = - 220
22p = 220
p = 10
and now substitute in the original equation:
1c + 5p = 54
1c + 5(10) = 54
c = 4

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Justin was asked to write equations based on the triangle below. So far he has come up with the following equations: Which of the following would be another correct equation?

Answers

Answer:

C: tan 60 = √3

Step-by-step explanation:

Let the adjacent part of the triangle be x and let the opposite side be y.

Thus, from trigonometric ratios;

x/10 = cos 60

We are given cos 60 = ½

Thus;

x/10 = ½

x = ½ × 10

x = 5

Similarly;

y/10 = sin 60

Now,from trigonometric relationship we know that; sin 60 = cos 30. Thus;

y/10 = cos 30

We are given cos 30 = (√3)/2

Thus;

y/10 = (√3)/2

y = 10 × (√3)/2

y = 5√3

Since it is a right angle triangle with one angle being 60°, it means the other one is 30° since sum of angles in a triangle is 180°.

Thus;

5/(5√3) = tan 30°

1/√3 = tan 30

Similarly;

5/10 = sin 60°

sin 60° = ½

Also;

tan 60 = (5√3)/5

tan 60 = √3

Also;

sin 30 = 5/10

sin 30 = ½

Looking at the options, the only correct one is Option C

Moira borrowed $4,500 from her grandfather to pay for her first year of college. Three years later, she repaid the $4,500 a long with an interes of $143. What was the annual interes rate?

Answers

Answer: The annual interest rate is 1.06%

Step-by-step explanation: This is a simple interest computation.

The formular for a simple interest is given as;

I = (P ×R × T)/100

Where I represents the interest paid,

P represents Principal borrowed at the beginning

R represents the rate at which the interest is calculated

T represents the Time measured in number of years

If the interest is calculated as I = (P×R×T)/100, we should first of all make R the subject of the formular;

Multiply both sides by 100

100I = P×R×T

Divide both sides of the equation by P and T

(100I)/(P × T) = R

Now we can insert the values into the rearranged formular

(100 × 143)/(4500 × 3) = R

14,300/13,500 = R

143/135 = R

1.0592592593 = R

Therefore, R which is the rate of interest equals approximately 1.06%

Anthropologists can estimate the height of a woman by measuring the length of her radius bone (from the wrist to the elbow). The length of the radius bone b is given by b=0.26h-18.85 where h is the height (in centimeters) of the woman. How do you solve the equation?

Answers

b = 0.26 h - 18.85,
where b is the length of the radius bone and h is the height.
To find the equation for height of a woman, you can solve the equation for h.
0.26 h = b + 18.85
h = ( b + 18.85 ) / 0.26
h = ( 100 b + 1,885 ) / 26
Then you can plug in the length of the radius bone in this equation.

What percent is 33 of 96?

Answers

1. We assume, that the number 96 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 96 is 100%, so we can write it down as 96=100%.
4. We know, that x is 33% of the output value, so we can write it down as x=33%.
5. Now we have two simple equations:
1) 96=100%
2) x=33%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
96/x=100%/33%

34, basically just divide 33 and 96

The value of a two-digit number exceeds twice the sum of its digits by 19. The tens digit is two less than the units digit. Find the number.

Answers

Answer with Step-by-step explanation:

Let the ones digit of the number be y

and tens digit of the number be x.

The tens digit is two less than the units digit.

i.e. x=y-2

The value of the number exceeds twice the sum of its digits by 19.

i.e. 10x+y=2(x+y)+19

10(y-2)+y=2(y-2+y)+19

10y-20+y=2(2y-2)+19

11y-20=4y-4+19

11y-4y=20-4+19

7y=35

dividing both sides by 7, we get

y=5

Putting value of y in x=y-2, we get

x=3

10x+y=10×3+5

=35

Hence, the two digit number is:

DIFFERENTIAL EQUATIONS
Solve the differential equations.
dy = 4 − x
/
dx

Answers

anti derivative of 4 is 4x
anti derivative of -x is -1/2 x^2

so y = 4x - (1/2)x^2 + C
(can't forget constants when doing anti derivatives xD)

is this what you need?

*edit
Anti-derivative of a Constant [just a number] becomes (constant)*x
for example integral of 5 = 5x + C

Then there is a Power Rule for integrals
integral of (x)^n = 1/(n+1) *(x)^(n+1) + C
for example: integral of x^2 = 1/(2+1) * (x)^(2+1) + C = (1/3)*x^3 + C

We have dy/dx = (4-x) dx which is a first order linear ODE

dy = (4-x) dx. Now integrating both sides we get:

y = 4x - 1/2 x^2 + C

which is the answer. Note we only wrote +c once since we can combine arbitrary constants under addition and subtraction with each other.

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