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zlopas [31]
3 years ago
14

Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

Mathematics
1 answer:
Art [367]3 years ago
6 0
                   maybe -6
i could be wrong 
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The position function for a free-falling object is s(t) = -16t^2 + vt +5. A ball is thrown upward from the top of a 400-foot bui
mixer [17]

Answer:

6.21 seconds

Step-by-step explanation:

The position function of a free-falling object is,

s(t) = -16t^2+v_0t+s_0

Where,

s_0 = initial height of the object,

v_0 = initial velocity of the object,

Here,

s_0=400\text{ feet}

v_0=35\text{ feet per sec}

Hence, the height of the ball after t seconds,

s(t)=-16t^2+35t+400

When s(t) = 0,

\implies -16t^2+35t+400=0

t=\frac{-35\pm \sqrt{35^2-4\times -16\times 400}}{2\times -16}

t=\frac{-35\pm \sqrt{1225+25600}}{-32}

\implies t\approx -4.02\text{ or }t\approx 6.21

∵ Time cannot be negative,

Hence, after 6.21 seconds the ball will reach the ground.

4 0
3 years ago
Angle mIJK=180, angle mIJU = 3x-7, and angle mUJK=17x + 7 find angle mIJU
Andrej [43]

Answer:

The measure of angle IJU is 20 degrees.

Step-by-step explanation:

In order to find that, we need to add the two angles together and set equal to 180 degrees. Then we can solve for x.

(3x - 7) + (17x + 7) = 180 ----> Combine like terms

20x = 180 -----> Divide by 20

x = 9

Now that we have this, we can stick the value into the equation and solve for IJU.

IJU = 3x - 7

IJU = 3(9) - 7

IJU = 27 - 7

IJU = 20

3 0
3 years ago
5x + 3 - 2x = 12 + 7x - 2 solution ??? SOMEONE HELPPP PLEASE !!
tensa zangetsu [6.8K]

Answer:

x = -7/4

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  

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtract Property of Equality

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

5x + 3 - 2x = 12 + 7x - 2

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Combine like terms:                                                                                        3x + 3 = 7x + 10
  2. [SPE] Subtract 3x on both sides:                                                                    3 = 4x + 10
  3. [SPE] Subtract 10 on both sides:                                                                      -7 = 4x
  4. [DPE] Divide 4 on both sides:                                                                         -7/4 = x
  5. Rewrite:                                                                                                           x = -7/4

<u>Step 3: Check</u>

<em>Plug in x into the original equation to verify it's a solution.</em>

  1. Substitute in <em>x</em>:                     5(-7/4) + 3 - 2(-7/4) = 12 + 7(-7/4) - 2
  2. Multiply:                                -35/4 + 3 + 7/2 = 12 - 49/4 - 2
  3. Add:                                      -23/4 + 7/2 = 12 - 49/4 - 2
  4. Add:                                      -9/4 = 12 - 49/4 - 2
  5. Subtract:                               -9/4 = -1/4 - 2
  6. Subtract:                               -9/4 = -9/4

Here we see that -9/4 does indeed equal -9/4.

∴ x = -7/4 is the solution to the equation.

8 0
3 years ago
A binomial probability distribution has p = .20 and n = 100.
AleksAgata [21]

Answer:

Mean = 0.2(100) = 20

Variance = 0.2×0.8×100 = 16

Standard deviation = 4

Yes, np > 5 & nq > 5

3 0
3 years ago
Read 2 more answers
Evaluate the determinant for the following matrix [144] [522] [155]
WARRIOR [948]
Matrix :

1    4    4

5    2    2

1    5    5

=> Determinant =

1 * (2*5 - 2*5) - 4 * (5*5 - 1*2) + 4 * ( 5*5 - 2*1)

= 1*(10 - 10) - 4*(25 - 2) + 4*(25 -2) = 1*0 + 4* 23 + 4*(25 - 2) = 0 - 4*23 + 4*23 = 0

Answer: 0
8 0
3 years ago
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