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Mice21 [21]
2 years ago
12

There are 10 guests at Alexandra's party. If each guest will be served exactly pint of

Mathematics
1 answer:
Aleksandr-060686 [28]2 years ago
3 0

Answer

10 pints or 11 if she has one too:)

Step-by-step explanation:

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(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
Simplify the following:<br> 3x+2y+7-5x+7y
const2013 [10]
<span>3x+ 2y+7 -5x+7y
= -2x + 9y + 7

hope it helps</span>
3 0
3 years ago
Read 2 more answers
What is the correct solution to (x+2)(x+5)​
elena-s [515]

Answer:

x^2+7x+10

Step-by-step explanation:

multiply the first by first and first by second

multiply the second by first and second by second

7 0
3 years ago
5/12 expressed as a decimal fraction is? (Round to the nearest thousandths)
Makovka662 [10]

Answer:

5/12 = 0.416666667 if you round up to the nearest thousandths it would be 0.417

7 0
3 years ago
Read 2 more answers
Graph the given equation: y=2x+1
lions [1.4K]
So your slope is 2 and your Y-intercept is 1.

To graph it, start at 0 and go up to number 2.
8 0
3 years ago
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