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3 years ago

Which of the following is a integer -5/4, and 2?

Mathematics

1 answer:

Annette [7]3 years ago

6 0

Only 2. Integers have to be a whole number. It can be a positive whole number or negative whole number.

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For every batch of cookies Carla's made , her brother ate 2 cookies. If Carla's brother ate a total of 6 cookies, how many batch

spayn [35]

Step-by-step explanation:

number of the total cookies ÷ the nber her brother ate

6÷2=3

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3 years ago

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DIA [1.3K]

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3 years ago

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7 0

3 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:

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

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:

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

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:

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

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

What is the solution for the following system of equations?<br><br>5x + 7y = 3<br><br>2x + 3y = 1

spayn [35]

<span>A) 5x + 7y = 3
B) 2x + 3y = 1

Multiplying Equation B by -2.5
</span><span>B) -5x -7.5y = -2.5 Then adding this to Equation A)
A) 5x + 7y = 3</span>

-.5y = .5
y = -1

Since
<span>2x + 3y = 1 then
2x -3 = 1
then x = 2

</span>

6 0

3 years ago