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charle [14.2K]
3 years ago
14

WILL GIVE 100 POINTS AND BRAINLIEST FOR BEST ANSWER

Mathematics
1 answer:
coldgirl [10]3 years ago
4 0

Answer:

Step-by-step explanation:-16x^2 + 24x + 16 = 0.

A. Divide by 8:

-2x^2 + 3x + 2 = 0, A*C = -2*2 = -4 = -1 * 4. Sum = -1 + 4 = 3 = B, -2x^2 + (-x+4x) + 2 = 0,

(-2x^2-x) + (4x+2) = 0,

-x(2x+1) + 2(2x+1) = 0,

(2x+1)(-x+2) = 0, 2x+1 = 0, X = -1/2. -x+2 = 0, X = 2.

X-intercepts: (-1/2,0), (2,0).

B. Since the coefficient of x^2 is negative, the parabola opens downward. Therefore, the vertex is a maximum.

Locate the vertex: h = Xv = -B/2A = -24/-32 = 3/4, Plug 3/4 into the given Eq to find k(Yv). K = -16(3/4)^2 + 16(3/4) + 16 = 19. V(h,k) = V(3/4,19).

C. Choose 3 points above and below the vertex for graphing. Include the points calculated in part A which shows where the graph crosses the x-axis.

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You have $814 that you want to share equally between 5 charities.
kifflom [539]

Answer:

give each charity $60

Step-by-step explanation:

$814 to divide equally to 5 charities.

From 814  if we give   -100,  -100, -100, -100, -100, we have left 314 to split in 5

the most useful next step is to give each charity $60

From $814  if we give   -100, -100, -100, -100, -100

                                         -60, -60, -60, -60, -60  

we have left now:

814 -5*100 -5*60 = 814-500-300 = $14 left to split among the 5 charity.

6 0
2 years ago
The ratio of dogs to cats is 2 to 3. There are 15 pets total. How many dogs are there? How many cats are there?
ElenaW [278]
So there are 2 dogs to every 3 cats (put into words)

in order to reach 15 total multiply both 2 and 3 by 3

2x3 = 6
3x3 = 9

so there are 6 dogs and 9 cats
6 0
2 years ago
Hello again! This is another Calculus question to be explained.
podryga [215]

Answer:

See explanation.

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

Functions

  • Function Notation
  • Exponential Property [Rewrite]:                                                                   \displaystyle b^{-m} = \frac{1}{b^m}
  • Exponential Property [Root Rewrite]:                                                           \displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}

<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

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

Derivative Property [Addition/Subtraction]:                                                         \displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 \displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)

Step-by-step explanation:

We are given the following and are trying to find the second derivative at <em>x</em> = 2:

\displaystyle f(2) = 2

\displaystyle \frac{dy}{dx} = 6\sqrt{x^2 + 3y^2}

We can differentiate the 1st derivative to obtain the 2nd derivative. Let's start by rewriting the 1st derivative:

\displaystyle \frac{dy}{dx} = 6(x^2 + 3y^2)^\big{\frac{1}{2}}

When we differentiate this, we must follow the Chain Rule:                             \displaystyle \frac{d^2y}{dx^2} = \frac{d}{dx} \Big[ 6(x^2 + 3y^2)^\big{\frac{1}{2}} \Big] \cdot \frac{d}{dx} \Big[ (x^2 + 3y^2) \Big]

Use the Basic Power Rule:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} (2x + 6yy')

We know that y' is the notation for the 1st derivative. Substitute in the 1st derivative equation:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 6y(6\sqrt{x^2 + 3y^2}) \big]

Simplifying it, we have:

\displaystyle \frac{d^2y}{dx^2} = 3(x^2 + 3y^2)^\big{\frac{-1}{2}} \big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]

We can rewrite the 2nd derivative using exponential rules:

\displaystyle \frac{d^2y}{dx^2} = \frac{3\big[ 2x + 36y\sqrt{x^2 + 3y^2} \big]}{\sqrt{x^2 + 3y^2}}

To evaluate the 2nd derivative at <em>x</em> = 2, simply substitute in <em>x</em> = 2 and the value f(2) = 2 into it:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = \frac{3\big[ 2(2) + 36(2)\sqrt{2^2 + 3(2)^2} \big]}{\sqrt{2^2 + 3(2)^2}}

When we evaluate this using order of operations, we should obtain our answer:

\displaystyle \frac{d^2y}{dx^2} \bigg| \limits_{x = 2} = 219

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

Unit: Differentiation

5 0
2 years ago
Can someone please help. It’s fine if the answer not correct at least you tried. But could anyone help because I can’t figure ou
egoroff_w [7]

WAR is given as 57 degrees.

If you draw a line from W to R, the angle WRA would also be 57 degrees.

57 + 57 = 114

The measure of AR = 180 -114 = 66 degrees.

5 0
3 years ago
Read 2 more answers
Find the simply interest earned on an investment of $15,000 at a rate of 5.25% for two years.
uysha [10]
Ill show you step by step.

This is what the equation should look like 

Y=Initial value(1+/- Increasing or Decreasing value)^2 Which stands for time

So Y=15,000(1+.0525)^2

So you need to do 1.0525 to the 2nd power Which equals 1.10775625

So now you need to do 15,000(1.10775625)
------------------------------------------------------------------------------------
Which equals <span>16616 rounding to the nearest Ones

16616.3 rounding to the nearest tenth</span>
3 0
3 years ago
Read 2 more answers
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