Answers
Answer:
"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the [tex]x[/tex]-coordinate of the quadratic function, and then substituting that value into the function."
Step-by-step explanation:
Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a polynomial of degree 2, which is a fancy way of saying that something is a quadratic), the [tex]x[/tex]-coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.
In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve [tex](x-3)(x-7)=0[/tex], which gives [tex]x-3=0 \vee x-7=0[/tex] (the 'V' stands for 'or'). We can take the average of the two roots to get the [tex]x[/tex]-coordinate of the minimum point of the graph (which, in this case, is [tex]x=\frac{3+7}{2} = \frac{10}{2} = 5[/tex]).
Having the [tex]x[/tex]-coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the [tex]y[/tex]-coordinate of the extremum.
Related Questions
What is the value of the digit 8 in the number 14.812?
Answers
Answer:
the tenth or 0.1
Find the Area Of This Figure.
Answers
to find area of rectangle L x W
it comes out to be 18
to find area of trapezoid 1/2 BxH
so it comeS out to be 6
add them together and get 24
Answer:
42in
Step-by-step explanation:
First divide up the shape.
The bottom will cut off to form a 6x3 rectangle which will have an area of 18in. Next is the top portion which is a trapezoid. You can figure out the area two ways. You can divide it further into two triangles and a rectangle. Or you can use the trapezoid formula. In this case I feel like dividing it. So since the top is 2 inches the bases of the two side triangles must be 2 due to the bottom base of the whole shape being 6. (1/2*2*6)*2 = 12in. Lastly the center rectangle is 2*6 (got 6 from 9-3) which is also 12. So the top half added together 12+12 equals 24in. When adding both top and bottom portions (18+24) you get 42in.
Sierra has a recipe she wants to make. She has to use eggs and sticks of butter. The ratio for these ingredients is 12 to 4 to make 4 batches. What will the equivalent ratio be if she wants to make 2 batches?
Answers
Find c.
Round to the nearest tenth:
Answers
Answer:
it'd be 95
Step-by-step explanation:
that's the nearest 10th
you are given that 4a - 2b =10 and a + c = 3. write an expression in a, b and c that is equal to 23. give your answer in its simplest form.
Answers
a + c = 3 so a = 3 - c and c = 3 - a
4(3 - c) - 2b = 10
12 - 4c - 2b = 10
-4c -2b = -2
2c - b = 1
That’s all I have so far :/
Five times a number decreased by 8 is less than 37. Write an algebraic inequality to represent this situation. Then solve algebraically & graph.
Answers
Answer:
5x - 8 < 37 and x < 9
Step-by-step explanation:
again, sorry if it's wrong.
5x - 8 < 37
+8 +8
5x < 45
---- -----
5 5
x < 9
What is the length of side s of the square shown below?
45
90°
A. 2-2
B. 2
C. 42
O D. v2
E. 1
O F. 4
Answers
Answer:
D. √2
Step-by-step explanation:
Solve for x by applying trigonometric ratio.
Reference angle = 45°
Hypotenuse = 2
Adjacent side = s
Thus:
Cos (45) = adj/hyp
Cos (45) = s/2
2×Cos(45) = s
2 × √2/2 = s (cos (45) = √2/2)
√2 = s
s = √2
is a symbol for Zero used in the Roman numerations systems
Answers
Answer:
no
Step-by-step explanation:
the word they used for zero is nulla meaning none
What is the value of x? (5 points)
A right angle is shown divided into two parts. The measure of one part of the right angle is 10 degrees. The measure of the other part is 2x
Answers
The angle is broken into to parts, 10 degrees and 2x.
90 = 2x + 10
Subtract 10:
80 = 2x
Divide by 2:
x = 40
Round the fraction to the nearest whole number. 7 3 8
Answers
Answer:
9
Step-by-step explanation:
A cylinder has a base diameter of 6 centimeters and a height of 15 centimeters. What is its volume in cubic centimeters, to the nearest tenths place?
Please help
Answers
Step-by-step explanation:
V
≈
424.12
cm³
d
Diameter
cm
h
Height
cm
Jon had 45 dollars in his account. He made 7 dollars
per hour at his job. At the end of the week he had 150
dollars in his account. How many hours did he work?
Answers
PLEASE HELP ASAP I’LL GIVE BRAINLEST ITS ALEKS ALGEBRA 2 MATH
Answers
145 - 5d
5d = 145, set equal
29 days to lay all the track
b)
5*19 = 95
145-95 = 50
After 19 days, they have 50 miles to go.
Answer:
Step-by-step explanation:
(a)
well since they can lay 7 miles of track every day, the formula i make for the amount of track there is left to lay is:
L=196-Ld
where l is the length of track remaining, L is the length of track they can lay in one day and d is the number of days.
so we replace L for 7 and d for 17 and we get:
L=196-7x17
which works out to be 77 miles of track remaining to lay.
(b)
well since we want them to have 0 length of track remaining, and they can lay 7 miles of track a day, we can work out d. let's give the formula a bash to get:
d=196-l/L
we then replace l with 0 and L with 7 and get:
d=196/7
which works out to be 28. so it will take 28 days or 4 weeks for the railroad crew to lay 196 miles of track.
GIVING BRAINLIEST TOO BEST ANSWERED
Solve for p.
−4.5 + p/6 = −18.9
A
p=−117.9
B
p = −108.9
C
p = −86.4
D
p = 140.4
Answers
Answer:
c p = -86.4
aww man I got to explain too I used this app called math - way they will explain it
what is 3x4x19x39x4x9x11x10x20squared-10473408000 tee-hee
Answers
Answer:
A seizure and a half
Step-by-step explanation:
Answer:
495962981439552000
A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips etc.). No car had more than three defects. Here is the probability distribution for the number of appearance defects in a new car. X: number of defects 0 1 2 3 P(x) 0.61 0.21 0.11 0.07 Find the expected number of appearance defects in a new car. Do not round.
Answers
Answer:
The expected number of appearance defects in a new car is 0.64.
Step-by-step explanation:
To find the expected number of appearance defects in a new car, we multiply each outcome by its probability.
We have that:
0.61 probability of 0 defects
0.21 probability of 1 defect
0.11 probability of 2 defects
0.07 probability of 3 defects
0.61*0 + 0.21*1 + 0.11*2 + 0.07*3 = 0.64
The expected number of appearance defects in a new car is 0.64.
You want to find the width, AB, of a river. You walk along the edge of the river 100 ft and mark point C. Then
you walk 22 ft further and mark point D. You turn 90° left and walk until your location, point A, and point C are
collinear. You mark point E at this location, as shown.
(a) Suppose DE = 42 ft. What can you conclude about the width of the river? Explain. Your explanation
should include the approximate width and how you got this answer.
(b) Can you conclude that △ and △ are similar? Why or why not?
Answers
Answer:
I have been trying to figure this one out, I'm sorry but i don't know the answer
Step-by-step explanation:
i hate math
MATH SEND HELP THANKS BAES
Answers
4,5 and 3,6
alternate exterior:
1,8 and 2,7
same side interior:
4,6 and 3,5
corresponding angles:
1,6
2,5
4,7
3,8
:)
What is equivalent to (9f + 12)*4)
Answers
Answer:
10
Step-by-step explanation:
According to her running log, Alexa averaged 4 Miles per week last month and 50%less this month. How much did she average this month?
Answers
Answer:
2 miles per week
Step-by-step explanation:
If she averaged 50% less this month, that means her average this month is half of 4.
Divide 4 by 2
4/2
= 2
So, she averaged 2 miles per week this month
43 POINTS IF U DO THIS! + ILL MARK BRAINLIEST!
Answers
Answer:
The second one
210 lbs
Step-by-step explanation:
The difference between 7 and 4 is 3
90/3 = 30
30 times 7 = 210
Answer:
Second Diagram
Step-by-step explanation:
If an organism has 35% of cytosines, how
many adenines will it have?
35%
15%
25%
Answers
Answer:
Unknown
Step-by-step explanation:
Since you have 35 C, you will have 35 G. Without knowing the number of thymine, the number of adenine is unknown .
That is all the information you can get from this. Just because there are 35 C and G, there doesn't have to be an equal number of A and T
Answer: 15%
Step-by-step explanation: I just did it
Write the equation in Point-Slope Form of a line that has a slope of 3/4 and passes through point (-4, -12).
Answers
Answer:
The equation in Point-slope form of a line that has a slope of 3/4 and passes through the point (-4, -12) is:
[tex]y+12=\frac{3}{4}\left(x+4\right)[/tex]
The graph of the equation line is also attached below.
Step-by-step explanation:
Given
Slope m = 3/4Point (-4, -12)To determine
We have to determine the equation in Point-Slope Form.
We know that the Point-slope form of a line equation is defined as
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
[tex]m[/tex] is the slope of the line[tex]\left(x_1,\:\:y_1\right)[/tex] is the pointIn our case:
Slope m = 3/4(x₁, y₁) = (-4, -12)substituting the values m = 3/4 and the point (x₁, y₁) = (-4, -12) in the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-\left(-12\right)=\frac{3}{4}\left(x-\left(-4\right)\right)[/tex]
Apply rule: [tex]-\left(-a\right)=a[/tex]
[tex]y+12=\frac{3}{4}\left(x+4\right)[/tex]
Therefore, the equation in Point-slope form of a line that has a slope of 3/4 and passes through the point (-4, -12) is:
[tex]y+12=\frac{3}{4}\left(x+4\right)[/tex]
The graph of the equation line is also attached below.
30 PTS
Please make sure its easy to understand
Answers
work: Write all numerators above the least common denominator: -8+2+5/20
*Calculate the sum or difference: -1/20
Please see image below. What is the value of X in the figure to the right? What is the measure of angle DGC in the figure to the right?
Answers
Answer:
x = 50
DGC: 130 degrees
Step-by-step explanation:
x and the angle next to the angle x-10 are vertical angles are equal, so that means the two angles that add up to 90 are x and x-10.
x + x - 10 = 90
2x - 10 = 90
2x = 100
x = 50
The measure of angle DGC is:
180 - x
180 - 50
130
On August 20, 1989, in Cologne, West Germany, Said Aouita of Morocco also established a world record when he ran the 3000. m run in 7 minutes, 29.45 seconds. What was his average speed (in m/s) for the race? Remember to include your data, equation, and work when solving problem
PLS HURRY I HAVE TO TURN THUS IN!!!!!
Answers
Answer:
Average speed of Aouita = 6.68 meter per second.
Step-by-step explanation:
To create a world record Aouita ran a distance = 3000 m
He took the time to cover this distance = 7 minutes 29.45 seconds
= (7×60) + 29.45 seconds
= 449.45 seconds
Since, formula for the average speed is given by,
Average speed = [tex]\frac{\text{Total distance covered}}{\text{Total time taken}}[/tex]
Therefor, average speed of Aouita = [tex]\frac{3000}{449.45}[/tex]
= 6.675
≈ 6.68 meter per second
Average speed of Aouita was 6.68 meter per second.
Answer:
6.67 m/s
Step-by-step explanation:
7 * 60 = 420
420 + 29.45 = 449.45
V = 3000. / 449.45= 6.67 m/s
What is the exact circumference of a circle with a radius of 15 cm?
O 10 cm
O 15 cm
O 30 cm
O 60 cm
Answers
Answer:
Step-by-step explanation:
None of the choices is correct.
Circumference= 2πr = 30π cm
What is the slope and y-intercept of the line y - 2x = 8
Answers
Answer:
Slope is 2x and y-intercept is 8
Step-by-step explanation:
First you have to get y all by itself on the left side of the equal sign. To do that, you must add 2x on both sides. You will get: y=2x+8.
Answer:
Slope= 2
Y-intercept= (0,8)
3. Five more than a number is below 17. Use n
for the number.
Answers
Answer:
n + 5 = below 17
Step-by-step explanation:
Answer:
n+5<7
Step-by-step explanation:
n+5<7
This is just what I think the problem is asking. Since it asks for 5 more than a number(it doesn't specify what number), then it doesn't matter what number it is. It didn't say that the number is 17, which means that the equation is probably an unequality sentence.
97.28 ÷ 19
PLEASE HELP PLEASE PLEASE HURRY HELP ME PLEASE
Answers
lol
Answer:
5.12
Step-by-step explanation: