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3 years ago

5

Joel made some muffins he gave 1/4 of the muffins to a neighbor. He took 3/8 of the muffins to school. What fraction of the muff

in is left?

1 answer:

geniusboy [140]3 years ago

4 0

3/8 of the muffin is left

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Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?

BaLLatris [955]

Answer:

$Vertex = (\frac{1}{2},\frac{7}{4})$

Step-by-step explanation:

Given

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

Required

The vertex

We have:

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

First, we express the equation as:

$f(x) = a(x - h)^2 +k$

Where

$Vertex = (h,k)$

So, we have:

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

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

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

$f(x) = x^2 - x + (-\frac{1}{2})^2+2 -(-\frac{1}{2})^2$

$f(x) = x^2 - x + \frac{1}{4}+2 -\frac{1}{4}$

Expand

$f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2 -\frac{1}{4}$

Factorize

$f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2 -\frac{1}{4}$

Factor out x - 1/2

$f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+2 -\frac{1}{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}$

$f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}$

Compare to: $f(x) = a(x - h)^2 +k$

$h = \frac{1}{2}$

$k = \frac{7}{4}$

Hence:

$Vertex = (\frac{1}{2},\frac{7}{4})$

8 0

3 years ago

Read 2 more answers

Using this diagram, select the pair of lines that must be parallel.

Bas_tet [7]

Answer:

The answer would be D: d || f.

Step-by-step explanation:

Since the angles 4 and 7 are parallel, it would make sense for the lines that the angles are on to be parallel as well.
It just so happens that line d and line f are completely parallel to each other and angles 4 and 7 are on the lines. So the answer would be D.

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3 years ago

What is the value of x

jok3333 [9.3K]

Answer:

60

Step-by-step explanation:

x = (1/2)(172 - 52)

x = (1/2)(120)

x = 60

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3 years ago

Find the area. The figures are not drawn to scale.

ludmilkaskok [199]

Answer and step-by-step explanation:

If it is a rectangle, the formula is:

L * W

Fill in the values:

4*6.9

Then solve.

27.6

So, if it is a rectangle, the answer is (C), 27.6 Inches squared.

If it is a triangle, the the formula is:

(B*H)/2

Fill in the values:

4*6.9/2

Simplify:

27.6/2

Then solve.

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So, if it is a triangle, the answer is (A), 13.8 Inches squared

Hope this helps!

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2 years ago

What is -3/4 +7/2 in simplest form

Gwar [14]

Answer: 11/4

or 2.75

Step-by-step explanation:

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3 years ago