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stiks02 [169]
2 years ago
7

The binomial 5x – 4 is a factor of 10x2 – 23x + 12. What is the other factor?

Mathematics
1 answer:
SVETLANKA909090 [29]2 years ago
6 0
Method\ 1^o\\10x^2-23x+12=(5x-4)(ax+b)\\\\10x^2-23x+12=5ax^2+5bx-4ax-4b\\\\10x^2-23x+12=5ax^2+(5b-4a)x-4b\\\\therefore\\\\  \begin{array}{ccc}(1)\\(2)\\(3)\end{array}\left\{\begin{array}{ccc}5a=10\\5b-4a=-23\\-4b=12\end{array}\right\\\\(1)\ divide\ both\ sides\ by\ 5\to a=2\\(3)\ divide\ both\ sides\ by\ (-4)\to b=-3\\check\\subtitute\ the\ values\ of\ "a"\ and\ "b"\ to\ (2):\\5\cdot(-3)-4\cdot2=-15-8=-23\ /correct/\\\\Answer:\boxed{2x-3}


Method\ 2^o\\10x^2-23x+12=10x^2-8x-15x+12\\=2x\cdot5x-2x\cdot4-3\cdot5x-3\cdot(-4)\\=2x(5x-4)-3(5x-4)=(5x-4)\boxed{(2x-3)}
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murzikaleks [220]
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6 0
2 years ago
Identify the vertical shift, maximum and minimum values of each function
Delicious77 [7]

ANSWER

Vertical shift: 6 units up

Maximum value: 9

Minimum value: 3

EXPLANATION

The given since function is

y = 3(2 -  \sin(x))

Expand and rewrite to obtain,

y = 6 - 3 \sin(x)

Or

y =- 3 \sin(x) + 6

The vertical shift is 6 units up.

The maximum value is 6+3=9.

The minimum value is -3+6=3

5 0
3 years ago
Look at the graph shown below:
sleet_krkn [62]

Answer:

the answer is C

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3 0
3 years ago
What are the x-intercepts of the equation?<br> <img src="https://tex.z-dn.net/?f=r%28x%29%20%3D%20x-1%2Fx%2B4" id="TexFormula1"
cestrela7 [59]

Answer:

<u>The only x-intercept is x = 1</u>

Step-by-step explanation:

The equation is:

r(x)=\frac{x-1}{x+4}

We can substitute y for r(x), to write in the notation:

r(x)=\frac{x-1}{x+4}\\y=\frac{x-1}{x+4}

To get y-intercept, we put x = 0

and

To get x-intercept, we put y =0

We want to find x-intercepts here, so we substitute 0 into y and solve for x. Shown below:

y=\frac{x-1}{x+4}\\0=\frac{x-1}{x+4}\\0(x+4)=x-1\\0=x-1\\x=1

<u>The only x-intercept is x = 1</u>

3 0
3 years ago
If fence poists are to be placed in a row 7 feet apart, how many posts are needed for 210 feet of fence?
ollegr [7]

Answer:

31

Step-by-step explanation:

210 ft ÷ 7 ft = 30

There are 30 7-ft lengths of fence.

Think of putting a post at the end of each 7-ft length. That means you need 30 posts. Now you must add 1 post for the beginning.

Answer: 31

8 0
2 years ago
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