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rosijanka [135]
3 years ago
7

Great Free Practice Problems

Mathematics
2 answers:
Firdavs [7]3 years ago
3 0

Answer:

1) 38

2) 56

3) 86

4)  37

5) 6 i think

6) 93

Step-by-step explanation: sorry if any of these are wrong

Alex73 [517]3 years ago
3 0

Answer:

The answer is 38. Sorry if it's wrong.

You might be interested in
Divide using synthetic division. ( x^4-12x^2-9)/(x+3)
Firdavs [7]

Answer:

x^3 - 3x^2 - 3x + 9 + (-36/(x+3))

OR

x^3 - 3x^2 - 3x + 9 - (36/(x+3))

Step-by-step explanation:

First set the divisor equal to 0:

x + 3 = 0

Subtract 3 from both sides

x = -3

This is what you'll divide the dividend by in synthetic division.

Take the coefficents of each term in the dividend. Do not forget the 0 placeholders:

x^4 + 0x^3 - 12x^2 + 0x -9

Coefficents: 1. 0.  -12. 0 -9.

Please see the image for the next steps.

The remainder is -36. Put the remainder over the divisor and add it to the polynomial (shown in image)

-36/(x+3)

6 0
3 years ago
Solve the following equation for x<br><br> 10=2-4(ax-3)
likoan [24]

Answer:

\large\boxed{x=\dfrac{1}{a}}

Step-by-step explanation:

2-4(ax-3)=10\qquad\text{subtract 2 from both sides}\\\\-4(ax-3)=8\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4(ax-3)}{-4}=\dfrac{8}{-4}\\\\ax-3=-2\qquad\text{add 3 to both sides}\\\\ax-3+3=-2+3\\\\ax=1\qquad\text{divide both sides by}\ a\neq0\\\\x=\dfrac{1}{a}

7 0
2 years ago
Use the unique factorization of integers theorem to prove the following statement. If n is any positive integer that is not a pe
anyanavicka [17]

Answer:

no

Step-by-step explanation:

3 0
3 years ago
Can someone help me with this, please?<br>No links or false answers, please​
VARVARA [1.3K]

The exact value is found by making use of order of operations. The

functions can be resolved using the characteristics of quadratic functions.

Correct responses:

  • \displaystyle 1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7} =\frac{9}{14}
  • x = -4, y = 12
  • When P = 1, V = 6
  • \displaystyle x = -3 \ or \ x = \frac{1}{2}

\displaystyle i. \hspace{0.1 cm} \underline{ f(x) = 2 \cdot \left(x - 1.25 \right)^2 + 4.875 }

ii. The function has a minimum point

iii. The value of <em>x</em> at the minimum point, is <u>1.25</u>

iv. The equation of the axis of symmetry is <u>x = 1.25</u>

<h3>Methods by which the above responses are found</h3>

First part:

The given expression, \displaystyle \mathbf{ 1\frac{4}{7} \div \frac{2}{3} -1\frac{5}{7}}, can be simplified using the algorithm for arithmetic operations as follows;

  • \displaystyle 1\frac{4}{7} \div \frac{2}{3} - 1\frac{5}{7} = \frac{11}{7}  \div \frac{2}{3} - \frac{12}{7} = \frac{11}{7} \times \frac{3}{2} - \frac{12}{7} = \frac{33 - 24}{14} =\underline{\frac{9}{14}}

Second part:

y = 8 - x

2·x² + x·y = -16

Therefore;

2·x² + x·(8 - x) = -16

2·x² + 8·x - x² + 16 = 0

x² + 8·x + 16 = 0

(x + 4)·(x + 4) = 0

  • <u>x = -4</u>

y = 8 - (-4) = 12

  • <u>y = 12</u>

Third part:

(i) P varies inversely as the square of <em>V</em>

Therefore;

\displaystyle P \propto \mathbf{\frac{1}{V^2}}

\displaystyle P = \frac{K}{V^2}

V = 3, when P = 4

Therefore;

\displaystyle 4 = \frac{K}{3^2}

K = 3² × 4 = 36

\displaystyle V = \sqrt{\frac{K}{P}

When P = 1, we have;

\displaystyle V =\sqrt{ \frac{36}{1} } = 6

  • When P = 1, V =<u> 6</u>

Fourth Part:

Required:

Solving for <em>x</em> in the equation; 2·x² + 5·x  - 3 = 0

Solution:

The equation can be simplified by rewriting the equation as follows;

2·x² + 5·x - 3 = 2·x² + 6·x - x - 3 = 0

2·x·(x + 3) - (x + 3) = 0

(x + 3)·(2·x - 1) = 0

  • \displaystyle \underline{x = -3 \ or\ x = \frac{1}{2}}

Fifth part:

The given function is; f(x) = 2·x² - 5·x + 8

i. Required; To write the function in the form a·(x + b)² + c

The vertex form of a quadratic equation is f(x) = a·(x - h)² + k, which is similar to the required form

Where;

(h, k) = The coordinate of the vertex

Therefore, the coordinates of the vertex of the quadratic equation is (b, c)

The x-coordinate of the vertex of a quadratic equation f(x) = a·x² + b·x + c,  is given as follows;

\displaystyle h = \mathbf{ \frac{-b}{2 \cdot a}}

Therefore, for the given equation, we have;

\displaystyle h = \frac{-(-5)}{2 \times 2} = \mathbf{ \frac{5}{4}} = 1.25

Therefore, at the vertex, we have;

k = \displaystyle f\left(1.25\right) = 2 \times \left(1.25\right)^2 - 5 \times 1.25  + 8 = \frac{39}{8} = 4.875

a = The leading coefficient = 2

b = -h

c = k

Which gives;

\displaystyle f(x) \ in \ the \ form \  a \cdot (x + b)^2 + c \ is \ f(x) = 2 \cdot \left(x + \left(-1.25 \right) \right)^2 +4.875

Therefore;

  • \displaystyle \underline{ f(x) = 2 \cdot \left(x -1.25\right)^2 + 4.875}

ii. The coefficient of the quadratic function is <em>2</em> which is positive, therefore;

  • <u>The function has a minimum point</u>.

iii. The value of <em>x</em> for which the minimum value occurs is -b = h which is therefore;

  • The x-coordinate of the vertex = h = -b =<u> 1.25 </u>

iv. The axis of symmetry is the vertical line that passes through the vertex.

Therefore;

  • The axis of symmetry is the line <u>x = 1.25</u>.

Learn more about quadratic functions here:

brainly.com/question/11631534

6 0
2 years ago
Read 2 more answers
Comment if you know the answer please
pochemuha
I think it 0.07 but dont count onmy answer 
3 0
3 years ago
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