MATHEMATICS HIGH SCHOOL

The Kahn's Family lives in a house that has a backyard in the shape of an isosceles trapezoid and a triangle. The area of the backyard can be expressed as the sum of the area of the triangle and the area of the trapezoid, which is 1/2bh+1/2(p+q)L The base and the height of the triangle are represented by b and h, respectively. The bases of the trapezoid are p and q, and the height of the trapezoid is L. 2 Rearrange the formula to find the length of base as a function of the lengths of the other sections of the backyard.

Answers

Answer 1

Answer:

This is solved the way any 2-step linear equation is solved:

subtract the term not containing the variable of interest, then
divide by the coefficient of that variable.

... A = (1/2)bh + (1/2)(p+q)L

... A - (1/2)(p+q)L = (1/2)bh . . . . . subtract the term on the right

... (A -(1/2)(p+q)L)/(1/2·h) = b . . . .divide by (1/2)h, the coefficient of b

... b = (2A -(p+q)L)/h . . . . . . . . . . simplify

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4 1/2 - 2 2/3
Simplest form

Answers

convert the mixed number to an improper fraction
9/2 - 2 2/3
9/2 - 8/3
11/6

simplest form:
1 5/6

Can someone solve this differentiation question.

Answers

We clearly see on the graph that :
A. f is increasing on (2,6) and (8,10) (the derivative is >=0)
B. f is decreasing on (0,2) and (6,8) (the derivative is <=0)
C. f has two relative minima : one at x=2 and one at x=8 (the derivative changes signs there from negative to positive)
D. f has two relative maxima : one at x=6 and one at x=10(the derivative changes signs there from positive to negative)
E. f is concave up when f' is increasing i.e. on (0,4) and (7,9)
F. f is concave down when f' is decreasing i.e. on (4,7) and (9,10)
G. the points of inflexion of f are the points at which f' has an horizontal tangent, thus they are at x=4, x=7 and x=9
H. see the picture attached

A). The function is increasing where its derivative is positive.
Its derivative is positive from 2 to 6, and from 8 to 10.

B). The function is decreasing where its derivative is negative.
Its derivative is negative from 0 to 2, and from 6 to 8.

C). The function has a relative minimum where its derivative is zero
and changing from negative to positive.
Its derivative is zero and changing from negative to positive at 2 and 8.

D). The function has a relative maximum where its derivative is zero
and changing from positive to negative.
Its derivative is zero and changing from positive to negative at 6 and 10.

E). The function is concave up between consecutive relative maxima.
The interval between consecutive relative maxima is 6 < x < 10 .

F). The function is concave down between consecutive relative minima.
The interval between consecutive relative minima is 2< x < 8 .

G). The function has points of inflection where its second derivative is
zero, that is, where its first derivative is a relative minimum or a relative
maximum.
Its first derivative is a relative minimum or maximum at x = 0, 4, 7, and 9 .

H). Good luck on the sketch !

Simplify the expression 63 + 5(4 − 2)

Answers

Answer: 226

Step-by-step explanation:

6^3 + 5(4 - 2 )

6^3 + 5 x 2

6 x 6 x 6 = 216

226 + 5 x 2

5 x 2 = 10

216 + 10 = 226

Answer:

The answer is 226

Step-by-step explanation:

How do you make a dollar using only 30 coins

Answers

Well you could use 15 pennies, 7 dimes, and 3 nickels to make a dollar. It is only 30 coins and it makes a dollar.

U would use

25 pennies , 2 quarters , 1 nickel and one dime

That is 30 coins used and makes a dollar ...

( give Jennifer credit if u like sense she figured it) :)

Write the equation in slope-intercept form. What are the slope and y-intercept? -11x + 9y = -12

Answers

-11x + 9y = -12
9y = -12 + 11x
y = -12/9 + 11/9x

y = (11/9)x - 4/3

Y-intercept is -4/3
Slope or m is 11/9

Translate this expression:
8 less than y

Answers

Answer:

Step-by-step explanation:

y-8

Answer:

y - 8

Step-by-step explanation:

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