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suter [353]
3 years ago
5

Factor the polynomials 23−162

Mathematics
1 answer:
masha68 [24]3 years ago
3 0

Answer:

-139

Step-by-step explanation:

23-162=

-139

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4(2*2 + 3) - 2*2 = -(3*2 - 1) + 29
Kay [80]

Answer:

24=24

Step-by-step explanation:

4(4+3) - 4 = -(6-1) + 29

4 * 7 -4 = -5 + 29

24 = 24

5 0
1 year ago
Read 2 more answers
Simplify the expression<br><br> -4 + 3 + 5 =
xenn [34]

Answer:

4

Step-by-step explanation:

-4+3=-1

-1+5=4

8 0
2 years ago
In class, Julie was asked to create a scenario for the linear function shown. She came up with the following: .Joe planned a hik
Law Incorporation [45]

Answer:

1. Julie’s scenario doesn't match the linear function graphed, because the graphed function is f(x)=-3x+12 and must be f(x)=-5x+12

2. She has counted the slope of the line incorrect.

3. She can write f(x)=-5x+12 and draw the line with the x-intercept will be at (2.4,0) and y-intercpt ar (0,12).

Step-by-step explanation:

If Joe parked 12 miles away from the cabin and after one hour, he was still 7 miles from the cabin, then he had walked 12 - 7 = 5 miles per hour.

The initial positon of Joe is at point (0,12) (after 0 hours passed, Joe was 12 miles from the cabin). The line must pas through the point (1,7) ( after one hour, he was still 7 miles from the cabin ).

Find the slope:

\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-12}{1-0}=-5

So, the slope of the linear function should be -5 (not -3).

Then the equation of the function is

f(x)=-5x+12

1. Julie’s scenario doesn't match the linear function graphed, because the graphed function is f(x)=-3x+12 and must be f(x)=-5x+12

2. She has counted the slope of the line incorrect.

3. She can write f(x)=-5x+12 and draw the line with the x-intercept will be at (2.4,0) and y-intercpt ar (0,12).

5 0
3 years ago
Replace ... with ≥ or ≤ so that the derived inequality will be true for any value for x: x^2-16x+64 ... 0
ankoles [38]

Answer:

≥

..................................................

8 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
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