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3 years ago

The equation of a parabola is y=x^2–4x+13. Write the equation in vertex form.

Mathematics

2 answers:

Korolek [52]3 years ago

5 0

Answer:

y = (x - 2)² + 9

Step-by-step explanation:

To obtain the equation in vertex form use the method of completing the square.

Add/ subtract ( half the coefficient of the x- term)² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 + 13

= (x - 2)² + 9 ← in vertex form

weqwewe [10]3 years ago

3 0

Answer:

vertex form : y=(x-2)^2+9

Step-by-step explanation:

To convert a parabola from standard form y=x^2-4x+13 to vertex form, we complete the square.

first, complete the square using the x-terms, use the constant term to adjust and make a perfect square.

y= x^2-4x+4 + 9

Factor the first three terms on the right-hand side.

y=(x-2)^2 + 9

the resulting express is then the vertex form, which means that

the vertex is at (x-2) = 0, x=2, and at y=9.

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Is 5 in the solution set of x+3>8

Irina-Kira [14]

Answer:

It 5 would not be x

Step-by-step explanation:

If 5 was x, then it would be equivalent, because 5+3 = 8. I hope this helped.

8 0

3 years ago

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Rewrite the equation so that none of the values have a denominator and then solve the equation.

DiKsa [7]

Answer:

The answer in the explanation

Step-by-step explanation:

we have

$\frac{1}{3}x-5=\frac{5}{2}x-\frac{2}{3}$

Step 1

Determine the least common denominator (LCD) of all fractions in the equation

The LCD is equal to

$(3)(2)=6$

Step 2

Multiply both sides of the equation by 6 to remove the fractions

$6[\frac{1}{3}x-5]=6[\frac{5}{2}x-\frac{2}{3}]$

$2x-30=15x-4$

Step 3

Solve for x

Group terms

$15x-2x=-30+4$

Combine like terms

$13x=-26$

$x=-2$

5 0

3 years ago

A right circular cylinder has a height of 19 3/4 ft and a diameter 1 2\5 times its height.

alexira [117]

Answer:

Volume of cylinder is 34833.21 ft³

Step-by-step explanation:

Given : A right circular cylinder having height $19\frac{3}{4}$ ft and diameter $\frac{12}{5}$ times its height.

Given : diameter $\frac{12}{5}$ times its height that is

diameter $\frac{12}{5}$ times $19\frac{3}{4}$ that is

Diameter = $\frac{12}{5} \times \frac{79}{4}$

Diameter = $\frac{237}{5}$ ft

Radius is half of diameter,

Radius = $\frac{1}{2} \times \frac{237}{5}=\frac{237}{10}$ ft

$\text{Volume of Cylinder}=\pi r^2h$

Substitute the values, we get,

$\text{Volume of Cylinder}= \pi (\frac{237}{10})^2 \times \frac{79}{4}$

$\text{Volume of Cylinder}= \times 3.14 \times (23.7)^2 \times 19.75$

$\text{Volume of Cylinder}=34833.21$

Thus, volume of cylinder is 34833.21 ft³

6 0

3 years ago

Different hotels in a certain area are randomly selected, and their ratings and prices were obtained online. Using technology, w

mash [69]

Answer:

Option C) The symbol y represents the predicted value of price.

Step-by-step explanation:

We are given the following in the question:

We find a regression equation with x representing the ratings and y representing price.

The equation has a slope of 130 and a y-intercept of 350.

Comparing with the slope intercept form:

$y = mx + c\\\text{where m is the slope and c is the y intercept}$

Thus, we can write the equation as:

$y = 130x + 350$

Here, y is the predicted variable that is the price, c is the price of hotel when a rating of 0 is given.

Thus, symbol y represents:

C) The symbol y represents the predicted value of price.

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4 years ago

An older TV screen was 26 centimeters wide. The newer model increased the screen size by 6 percent. How wide is the new TV Scree

Artist 52 [7]

Answer:

27.56 cm

Step-by-step explanation:

→ Identify the multiplier

( 100 + 6 ) ÷ 100 = 1.06

→ Multiply by the length

26 × 1.06 = 27.56

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2 years ago

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