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10 months ago

Which pair of equations generates graphs with the same vertex?

Mathematics

2 answers:

puteri [66]10 months ago

6 0

Answer:

The pair of equations that generates graphs

with the same vertex is :

y = –4x² ; y = 4x²

Step-by-step explanation:

A quadratic function can be written in the form f(x) = a(x – h)² + k, where a, h, and k are constants.

It’s graph is a parabola which has a vertex at (h, k).

• The graph of the equation y = – (x + 4)² = – [x – (–4)]² + 0

has a vertex at (-4 , 0).

On the other hand ,The graph of the equation y = (x – 4)² = (x – 4)² + 0

has a vertex at (4 , 0).

Therefore , the two equations generate graphs with different vertices.

• The graph of the equation y = –4x² = –4 (x –0)² + 0

has a vertex at (0 , 0).

On the other hand ,The graph of the equation y = 4x² = 4 (x –0)² + 0

has a vertex at (0 , 0).

Therefore , the two equations generate graphs with the same vertex.

• The graph of the equation y = – x² – 4 = – (x – 0)² + (– 4)

has a vertex at (0 , -4).

On the other hand ,The graph of the equation y = x² + 4 = (x – 0)² + 4

has a vertex at (0 , 4).

Therefore , the two equations generate graphs with different vertices.

• The graph of the equation y = (x – 4)² = (x – 4)² + 0

has a vertex at (4 , 0).

On the other hand ,The graph of the equation y = x² + 4 = (x – 0)² + 4

has a vertex at (0 , 4).

Therefore , the two equations generate graphs with different vertices.

zvonat [6]10 months ago

5 0

Answer:

Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

a general line is represented by the equation:

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1 year ago

What is equivalent to 32/40

WARRIOR [948]

4/5 is a fraction equivalent to 32/40. This is in simplest form.
Another fraction that is equivalent to 32/40 is 16/20.

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3 years ago

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Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard devia

padilas [110]

Answer:

Option(A) is correct

Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

Step-by-step explanation:

The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58

the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:

Highest = 97

Lowest = 71

Range = highest value - Minimum value

Range = 97 - 26 = 71

$Range= 71$

mean of the data is the summation of all the numbers in the data set divided by the number of given samples.

Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11

= 647/11

$Mean value =58.7$

Now to find the variance of the data set by using below formular

σ²=[ (xᵢ -mean)²]/n-1

[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10

$Variance=546$

Now, we will calculate standard deviation by taking square root over variance

σ =√(variance)

σ =√(546)

$Standard deviation= 23.4$

Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,

Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.

5 0

2 years ago

Use the identity (x+y)(x−y)=x2−y2 to find the difference of two numbers if the sum of the numbers is 12 and the difference of th

Natalka [10]

Answer:

The difference of two numbers using identity $(x+y)(x-y)=x^2-y^2$ is 4.

Step-by-step explanation:

Given: The sum of the numbers is 12 and the difference of the squares of the numbers is 48.

To find the difference of two numbers using identity $(x+y)(x-y)=x^2-y^2$

Let the two numbers be a and b, then

Given that the sum of the numbers is 12

that is a + b = 12 .........(1)

Also, given the difference of the squares of the numbers is 48.

that is $a^2-b^2=48$ ..........(2)

Using given identity $(x+y)(x-y)=x^2-y^2$

We have $(a+b)(a-b)=a^2-b^2$

Substitute the known values, we have,

$12(a-b)=48$

Divide both side 12 , we have,

$(a-b)=4$

Thus, the difference of two numbers using identity $(x+y)(x-y)=x^2-y^2$ is 4.

8 0

3 years ago

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