MATHEMATICS HIGH SCHOOL

Find the maximum/minimum value of the function y = x2 - (5/3)x + 31/36.A. 1/6

B. 5/6

C. 25/36

D. 10

Answers

Answer 1
Answer:

Answer:

A

Step-by-step explanation:

Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 ), then

minimum/ maximum value is the y- coordinate of the vertex.

The x- coordinate of the vertex is

x_(vertex) = - (b)/(2a)

y = x² - (5)/(3) x + (31)/(36) ← is in standard form

with a = 1 and b = - (5)/(3) , thus

(x)/(vertex) = - (-(5)/(3) )/(2) = (5)/(6)

Substitute this value into y

y = ((5)/(6) )² - (5)/(3) ((5)/(6) ) + (31)/(36)

   = (25)/(36) - (25)/(18) + (31)/(36) = (1)/(6)

Since a > 1 then the vertex is a minimum, thus

minimum value = (1)/(6) → A

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Rewrite f(x) = –2(x − 3)2 + 2 from vertex form to standard form. pleae help.

Answers

f(x) = -2(x - 3)² + 2
f(x) = -2(x - 3)(x - 3) + 2
f(x) = -2[x(x - 3) - 3(x - 3)] + 2
f(x) = -2[x(x) - x(3) - 3(x) - 3(-3)] + 2
f(x) = -2(x² - 3x - 3x + 9) + 2
f(x) = -2(x² - 6x + 9) + 2
f(x) = -2(x²) - 2(-6x) - 2(9) + 2
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2/3 of a some of money is 48p. What is 5/8 of the sum of money?

Answers

Let the sum of money be x
so 2/3 of x = 48p
so x = 48*3/2 = 72p
so 5/8 of the sum of money = 5/8*72 = 45p

Last year, manuel saved $50 per month . this year, he increases his monthly savings by 25%. he plans to buy a smart phone for $375. at this rate, how long will it take him to save enough money to buy the smart phone if he starts saving for it this year?

Answers

First multiply 50 and .25 to find out how much extra he is saving, $12.5 Then add that to 50 to get $62.5. Divide $375 by $62.5 to get 6. It will take 6 months to save the money. Hope this helps!

In ΔCDE, the measure of ∠E=90°, ED = 28, CE = 45, and DC = 53. What ratio represents the tangent of ∠C?

Answers

Answer:

3/5

Step-by-step explanation:

prependicular / hypotenuse

sin C=ED/CD

=3/5

Which is an example of an statement that is accepted without proof?A) Parallel Postulate
B) Pythagorean Theorem
C) Betweenness Theorem
D) Right Angle Congruence Theorem

Answers

A. Parallel Postulate
That type of statement is accepted without any proof

Help with question 9 please

Answers

Volume of a prism = Bh

B = area of the base
h = height

B = 1/2 (base1 + base2) x height
B = 1/2 (9+6) x 8
B = 1/2 (15) x 8
B = 4 x 15
B = 60

Volume = 720
720 = B x h
720 = 60 x h
h = 12

So the height or length is 12mm.

Surface Area = 2B + 2P

Where 
B is the area of the base
P is the perimeter of the base

We already know that B= 60

P = 9 + 10 + 6 + 8
P = 33

So

SA = 2*60 + 2*33
SA = 120 + 66
SA = 186

The surface area is equal to 186mm^2.
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