MATHEMATICS HIGH SCHOOL

Kim burns 85 calories per hour hiking how many calories will Kim burn in "h" hours? Identify and explain the independent and dependent variables of this situation

Answers

Answer 1
Answer: The independent variable is the hours and the dependent variable is the calories Kim burns in h amount of hours

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HIGH SCHOOL

Which is an example of an algebraic expression? A. 2k + 25 B. z – 8 = 44 C. 3 + 7 = 10 D. 76 – 10

Answers

B. would be a great example of an algebraic expression 

Please mark as brainliest answer

Options a and b are the algebraic expressions
HIGH SCHOOL

A rectangular piece of cardboard, whose area is 216 square centimeters, is made into an open box by cutting a 2-centimeter square from each corner and turning up the sides. if the box is to have a volume of 224 cubic centimeters, what should the original dimensions of the cardboard start with

Answers

Let the length of the original cardboard be x and width be y.
Area=xy=216
thus y=216/x
after cutting 2 cm from the edges, the dimensions will be:
(x-4) cm by (216/x-4) by 2 cm
thus the volume will be:
V=L×W×H
V=(216/x-4)×(x-4)×2=224
thus solving for x we get:
x=12 or x=18
Hence:
length=18cm width=12 cm

Answer:

Length: 18 cm

Width: 12 cm

Step-by-step explanation:

A better explanation for this is the following:

First we know that the area of the card is 216 cm². This can be expressed as:

A = L * W   so

216 = L * W  (1)

Now, let's change the variables here, we will denote the Length as "x" and the width as "y". Then (1) can be rewritten as:

216 = xy   (2)

Now, we know that in order to make the open box, it was cut from each corner of the card, 2 cm², and the volume of the box is 224 cm³. According to this, we know that the volume of the box is:

V = L' * W' * H (3)

The Height of the box would be the 2 cm that were cut and L' and W' would be x and y. However, as the Length and Width has been cut, then the expression for both of them is the following

For the Length:

L' = x - 4

For the Width:

W'= y - 4

Replacing in expression (3):

224 = 2 * (x-4) * (y-4)

112 = (x-4)(y-4)  (4)

Now, in (2) we can solve either x or y to make a new expression and then, do the same in (4), and thus, we can actually solve for one of the dimensions. In this case, we will solve for y first, so let's solve for y in (2) and (4):

216 = xy

y = 216/x (5)

Solving now for y, from (4):

112/x-4 = y - 4

y = (112/x-4) + 4 (6)

So now, all we have to do is equal (5) and (6), and in that way we can find the value of x:

216/x = (112/x-4) + 4

216/x = 112 + 4(x-4) / (x-4)

216(x-4) = x(112 + 4x - 16)

216x - 864 = 112x + 4x² - 16x

4x² - 120x + 864 = 0 (7)

From here, we can either do the general expression and solve for x, or we can just factorize (7) and get the 2 values of x at once. In this case let's use the general expression. Although is longer, but we will get the correct result using this method so:

4x² - 120x + 864 = 0    (Divide by 4 all terms)

x² - 30x + 216 = 0  (8)

the general equation:

x = -b ±√b² - 4ac / 2a

From (8), we know that a = 1, b = -30, c = 216. Replacing:

x = 30 ± √(-30)² - 4*1*216 / 2

x = 30 ±√900 - 864 / 2

x = 30 ± 6 / 2

x1 = 30 + 6 / 2 = 18

x2 = 30 - 6 / 2 = 12

So the values for the Length and width are:

L = 18 cm

W = 12 cm

If you put this numbers into equations (2) and (4):

216/18 = 12

(18-4)(12-4) = 112

MIDDLE SCHOOL

Amos has 93 cents two of his coins are quarters what is the largest number of nickels he might have

Answers

Amos can have 8 nickels, and he will have 3 cents left 

93 - 50 = 43

5 goes into 43 eight times

5x8 = 40

Hope this helps!
2 are quarters
quarters are worth 25 cents each
2*25=50
50 cents are quarters
93-50=43 cents that aren't quarters

now if we want max number of nickles
how many times can 5 go into 43
43/5=8 and a remainder of 3
so 8 times


max number is 8 nickles
MIDDLE SCHOOL

the perimeter of a triangle is 34 units. its width is 6.5 units. write an equation to determine the length (l) of the rectangle

Answers

Perimeter = length of the 3 sides of the triangle ie 34units

Since width we are given 6.5 units

We have to find the remaining 2 sides:

Formula of Triangle for Perimeter

P = a + b + c (sum of sides)

simplify: P= a + 2b (its an isosceles)

34 = 6.5 + 2b

34 - 6.5 = 2b

27.5 = 2b

Só b = 13.75 units each length of triangle

Relationship between triangle and rectangle

= rectangle has four right angles, so a triangle has an angle of half since it bisects the edges (ie 45*)

Use Trig Ratios to find L

SOHCAHTOA

we want adjacent ( L)

13.75 sin 45

L = 9.72

Thus your equation is

Equation used to find Triangle × Trig ratios

P = a + 2b
sin 45

Where L is length of rectangle
a is width of triangle

L =(P - a +2b)× sin 45

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