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Angelina_Jolie [31]
3 years ago
5

Simplify the expression (q^2)(2q^4)

Mathematics
1 answer:
Akimi4 [234]3 years ago
4 0

Answer:

2q^6

Step-by-step explanation:

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What is -7 as a decimal<br><br> If u don’t know the answer don’t answer
Rainbow [258]

Answer:

-7.0

Step-by-step explanation:

Just add a decimal like any other positive number.

If its a fraction, just say -7/1.

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There are 20 students at lunch. 1/5 of the students are in the hall. How many students are in the hall
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on monday 3.11 inches of rain fell and on tuesday 0.81 inch of rain fell. on wensday,twice as much rain fell as tuesday. How muc
pshichka [43]

Answer:

5.54 inches of rain

Step-by-step explanation:

Monday - 3.11

Tuesday - 0.81

Wednesday - 0.81 x 2= 1.62

3.11 + 0.81 + 1.62=5.54 inches

4 0
2 years ago
(08.07 HC)
andreev551 [17]

Answer:

\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}

\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

C)  See attachment.

Step-by-step explanation:

Given function:

f(x)=2x^2-x-10

<h3><u>Part A</u></h3>

To factor a <u>quadratic</u> in the form  ax^2+bx+c<em> , </em>find two numbers that multiply to ac and sum to b :

\implies ac=2 \cdot -10=-20

\implies b=-1

Therefore, the two numbers are -5 and 4.

Rewrite b as the sum of these two numbers:

\implies f(x)=2x^2-5x+4x-10

Factor the first two terms and the last two terms separately:

\implies f(x)=x(2x-5)+2(2x-5)

Factor out the common term  (2x - 5):

\implies f(x)=(x+2)(2x-5)

The x-intercepts are when the curve crosses the x-axis, so when y = 0:

\implies (x+2)(2x-5)=0

Therefore:

\implies (x+2)=0 \implies x=-2

\implies (2x-5)=0 \implies x=\dfrac{5}{2}

So the x-intercepts are:

x=-2, \:\:x=\dfrac{5}{2}

<h3><u>Part B</u></h3>

The x-value of the vertex is:

\implies x=\dfrac{-b}{2a}

Therefore, the x-value of the vertex of the given function is:

\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}

To find the y-value of the vertex, substitute the found value of x into the function:

\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}

Therefore, the vertex of the function is:

\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)

<h3><u>Part C</u></h3>

Plot the x-intercepts found in Part A.

Plot the vertex found in Part B.

As the <u>leading coefficient</u> of the function is positive, the parabola will open upwards.  This is confirmed as the vertex is a minimum point.

The axis of symmetry is the <u>x-value</u> of the <u>vertex</u>.  Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is <u>symmetrical</u>.

Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).

5 0
2 years ago
2^5×8^4/16=2^5×(2^a)4/2^4=2^5×2^b/2^4=2^c<br>A=<br>B=<br>C= <br>Please I'm gonna fail math
aleksley [76]

9514 1404 393

Answer:

  a = 3, b = 12, c = 13

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

  (a^b)^c = a^(bc)

___

You seem to have ...

  \dfrac{2^5\times8^4}{16}=\dfrac{2^5\times(2^3)^4}{2^4}\qquad (a=3)\\\\=\dfrac{2^5\times2^{3\cdot4}}{2^4}=\dfrac{2^5\times2^{12}}{2^4}\qquad (b=12)\\\\=2^{5+12-4}=2^{13}\qquad(c=13)

_____

<em>Additional comment</em>

I find it easy to remember the rules of exponents by remembering that <em>an exponent signifies repeated multiplication</em>. It tells you how many times the base is a factor in the product.

  2\cdot2\cdot2 = 2^3\qquad\text{2 is a factor 3 times}

Multiplication increases the number of times the base is a factor.

  (2\cdot2\cdot2)\times(2\cdot2)=(2\cdot2\cdot2\cdot2\cdot2)\\\\2^3\times2^2=2^{3+2}=2^5

Similarly, division cancels factors from numerator and denominator, so decreases the number of times the base is a factor.

  \dfrac{(2\cdot2\cdot2)}{(2\cdot2)}=2\\\\\dfrac{2^3}{2^2}=2^{3-2}=2^1

5 0
2 years ago
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