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Ann [662]
3 years ago
7

Write a quadratic function with a graph that meets the following conditions: x-intercepts at (2, 0) and (6, 0) with a minimum at

(4, -8)
Mathematics
1 answer:
Darya [45]3 years ago
5 0
The minimum is the vertex
y=a(x-h)^2+k
(h,k) is vertex
given
(4,-8)
y=a(x-4)^2-8
find a
given
(2,0) and (6,0)
find a

0=a(2-4)^2-8
0=a(2)^2-8
0=4a-8
8=4a
divide 4
2=a

other one
0=a(6-4)^2-8
0=a(2)^2-8
0=4a-8
8=4a
divide 4
2=a


the function is
y=2(x-4)²-8 or expanded
y=2x^2-16x+24
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If the mean of 25, 28, a, 30 and 32 is 27, then find the value of a.
Anna11 [10]

Answer:

a = 20

Step-by-step explanation:

The mean is calculated as

mean = \frac{sum}{count}

          = \frac{25+28+a+30+32}{5}  = \frac{115+a}{5}

Then

\frac{115+a}{5} = 27 ( multiply both sides by 5 to clear the fraction )

115 + a = 135 ( subtract 115 from both sides )

a = 20

6 0
3 years ago
If A= (6,11), B= (1,5), and C= (7,0), show by means of slopes that ABC is a right triangle. Name the hypotenuse.
nexus9112 [7]

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

<h3>Right angled triangle</h3>

A right angles triangle is a triangle that has 3 sides and angles with one of its angles to be 90 degrees.

For the given coordinates to be a right angled triangle, one of the line must be perpendicular to the other and for two lines to be perpendicular, the product of its slope must be -1.

Find the slopes of AB, BC and AC

Slope of AB = 5-11/1-6
Slope of AB = -6/-5 = 6/5

Slope of BC = 0-5/7-1
Slope of BC = -5/6

Slope of AC = 0-11/7-6
Slope of AC = -11/1. = -11

Take the product of AB and BC
AB * BC = 6/5 * -5/6
AB * BC = -1

Since the product of AB and BC is -1, hence the ABC is a right triangle and the length AC is the hypotenuse

Learn more on right angle triangle here: brainly.com/question/22790996

#SPJ1

6 0
2 years ago
The cost of renting a bus for a field trip was split evenly among 20 students. At the last minute, 10 more students joined the t
dexar [7]

By solving a linear equation, we will see that the total cost for renting the bus is $90.

<h3>What was the total cost of renting the bus, in dollars?</h3>

Let's say that the total cost is C.

When there are 20 students, each student should pay:

p = C/20

When the other 10 students are added (for a total of 30) each student pays:

p' = C/30.

We know that the cost for each of the original 20 students decreased by $1.50, so:

p' = p - $1.50

Then we have 3 equations to work with:

p = C/20

p' = C/30.

p' = p - $1.50

Now we can replace the first and second equations into the third one:

C/30 = C/20 - $1.50

Now we can solve this linear equation for C:

C/20 - C/30 = $1.50

C*( 1/20 - 1/30) = $1.50

C*(30/600 - 20/600) = $1.50

C*(10/600) = $1.50

C*(1/60) = $1.50

C = 60*$1.50 = $90

So the total cost for renting the bus is $90.

If you want to learn more about linear equations:

brainly.com/question/1884491

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4 0
2 years ago
If rectangle is 8 feet long and (7+x) feet wide. what is the area of the rectangle in square feet?
Ksivusya [100]

if the length is 8ft and the width is (7+x) then the area would be 56+8x, if x is unknown.

5 0
3 years ago
Marguerite is building a box from strips of wood.she needs 78 pieces of wood that are each 29 centimeters long.the wood comes in
dolphi86 [110]
Each strip is 29 cm

------------------------------------------------------
Change the m to cm
------------------------------------------------------
6 m = 600 cm

------------------------------------------------------
Find the number of strips for 1 6m-board
------------------------------------------------------
Find the number of strips that can be cut from the 6m board.

600 ÷ 29 = 20 pieces remainder 20cm

So we can only cut 20 pieces of 29 strips from one 6m board.

------------------------------------------------------
Find number of boards needed 
------------------------------------------------------
70 ÷ 20 = 3.5 

We need 3.5 of the 6m boards.

Since she can't have half a board, she has to buy 4 pieces of the board.

------------------------------------------------------
Answer: 4 pieces of the 6m board.
------------------------------------------------------ 

7 0
3 years ago
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