The perimeter of a rectangle is 24 feet. The length is 3 feet less than twice the width. The width is:

Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?

densk [106]

Answer:

$A.\ y = x^2 - 6x + 13$ is the correct answer.

Step-by-step explanation:

We know that vertex equation of a parabola is given as:

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

where $(h,k)$ is the vertex of the parabola and

$(x,y)$ are the coordinate of points on parabola.

As per the question statement:

The parabola opens upwards that means coefficient of $x^{2}$ is positive.

Let $a = +1$

Minimum of parabola is at x = 3.

The vertex is at the minimum point of a parabola that opens upwards.

$\therefore$ $h = 3$

Putting value of a and h in the equation:

$y = 1(x-3)^2+k\\\Rightarrow y = (x-3)^2+k\\\Rightarrow y = x^2-6x+9+k$

Formula used: $(a-b)^2=a^{2} +b^{2} -2\times a \times b$

Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.

Comparing $y = x^2 - 6x + 13$ and $y = x^2-6x+9+k$

13 = 9+k

k = 4

Please refer to the graph attached.

Hence, correct option is $A.\ y = x^2 - 6x + 13$

3 0

2 years ago

Read 2 more answers

139°<br> (17x + 3)<br> answer

nasty-shy [4]

Answer:

x= 8

Step-by-step explanation:

17x + 3 = 139

17x = 136

x = 8

6 0

2 years ago

Explain how to use what you know about whole number division to check your work when you divide with fractions.

serious [3.7K]

A fraction is a way to describe a part of a whole. A fraction can be a proper fraction, an improper fraction, or a mixed fraction.

<h3>What is a Fraction?</h3>

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

A fraction consists of two whole numbers, a number that is above the fraction line which is the Dividend, while the number that is below the fraction line is known as the denominator and is the divisor. The result or the answer which we get when we solve the fraction is the factor or can be said, it is the quotient of the operation.

Suppose there is a fraction, a/b which is equal to c, then,

a is the dividend, b is the divisor, and c is the quotient.

Learn more about Fraction:

brainly.com/question/1301963

#SPJ1

4 0

1 year ago

What is the difference between a $20,000 and a $30,000 annual salary over a lifetime

Lelu [443]

10,000 dollars is the answer

7 0

3 years ago

Kayleigh babysat for 11 hours this week that was 5 fewer than 2/3 as manyas she baby sat last week, h write an equation to repre

mars1129 [50]

Answer:

10.5 hours

Step-by-step explanation:

To find the number of hours she babysat last week subtract 5 from 11 which is 7 hours. 7 hours is equal to 2/3 of the many hours. If she babysat h hours last week then solve for h using 2/3 h = 7.

Solve the equation by multiplying each side by the reciprocal.

3/2 * 2/3h = 7*3/2

h = 21/2

h = 10.5 hours

3 0

3 years ago