A midwestern music competition awarded 35 ribbons. The number of blue ribbons awarded was 3 less than the number of white ribbons. the number of red ribbons was 2 more than the number of white ribbons. How many of each kind of ribbon was awarded....white?, blue?, red?

Answers

Answer 1

Answer: 35 total ribbons

x = white ribbons
x-3 = blue ribbons
x+2 = red ribbons

35= x+x-3+x+2
35= 3x -1
36 =3x
12 = x
12 white ribbons
9 blue ribbons
14 red ribbons

12+14+9 = 35

Answer 2

Answer: White 12
Blue 9
Red 14
I did it without paper so I'm not sure but it works :D

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How to find the area of the 45-45-90 triangle with a hypotenuse of 24?

Answers

The area of a triangle is 1/2(base x height) .

The two legs of this triangle are equal. If you position it properly,
one of them is the base, and the other one is the height.

Since it's a right triangle, A² + B² = C²

But A = B and C = 24 .

2A² = (24)²

A² = (24)² / 2

But since A=B, A² is also (base x height) of the triangle.
Area is just 1/2 of it.

Area = 1/2(24²/2) = (24)²/4 = (24/2)² = (12)² = 144 .

$45^o-45^o-90^o\ triangle\ is\ a\ half\ of\ the\ square\ (look\ at\ he\ picture).\n\nThe\ square\ is\ a\ rhombus\nthen\ area\ equal\ the\ half\ of\ multiply\ diameters:\n\nA_{\fbox{}}=(d^2)/(2)\n\nA_\Delta=(1)/(2)A_{\fbox{}}\Rightarrow A_\Delta=(1)/(2)\cdot(d^2)/(2)=(d^2)/(4)\Rightarrow A_\Delta=(24^2)/(4)=(576)/(4)=144.$

What is the derivative of e^(2x)

Answers

Answer:

$\displaystyle (d)/(dx)[e^\big{2x}] = 2e^\big{2x}$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = e^\big{2x}$

Step 2: Differentiate

Exponential Differentiation [Derivative Rule - Chain Rule]: $\displaystyle (d)/(dx) = e^\big{2x} \cdot (d)/(dx)[2x]$
Basic Power Rule [Derivative Property - Multiplied Constant]: $\displaystyle (d)/(dx) = e^\big{2x} \cdot 2$
Simplify: $\displaystyle (d)/(dx) = 2e^\big{2x}$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Given f(2) = 12, which of the following could be an equation of the function?A.
f(x) = 8x – 2
B.
f(x) = 4x + 4
C.
f(x) = 6x – 4
D.
f(x) = –4x – 4

Answers

Answer is B. f(x) = 4x + 4 When we use x=2 in this function f(2) = 4(2) + 4 f(2)= 8 + 4 f(2) = 12 So the answer is B.

Solve: |x + 9| User: Evaluate 5|7 - 9| - 2.
-12
0
1
8

Answers

Solve:

$[x+9]$ - there is nothing to simplify

======================================

Evaluate:

$5(7-9)-2$

= $35 -45-2$

= $-10-2$

= $-12$

or

$5(7-9)-2$

= $35 -45-2$

= $35-47$

= $-12$
------------------------------------------
So, -12 is the answer.

The figure shown is a rectangle. If you draw a new rectangle in which the dimensions are doubled, what is the relationship between the PERIMETERS of the two rectangles?A) The perimeter of the new rectangle is twice that of the original rectangle.
Eliminate
B) The perimeter of the new rectangle is one-half that of the original rectangle.
C) The perimeter of the new rectangle is four times that of the original rectangle.
D) The perimeter of the new rectangle is one-fourth that of the original rectangle.

Answers

the answer is A, sorry if you can't read it quite well

Find the sum of 5m + 3n + p, -5p + 3n, and 2n - m.-4m + 8n - 4p

4m + 8n + 4p

4m - 8n - 4p

4m + 8n - 4p

Answers

After grouping our like pairs we are left with this: 4m, 8n, -4p

The answer is D) 4m+8n-4p

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