Answer:
The Graph of a Quadratic Function
A quadratic function is a polynomial function of degree 2 which can be written in the general form.
Step-by-step explanation:
Example: Graph: f(x)=−x2−2x+3.
Solution:
Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).
f(x)f(0)===−x2−2x+3−(0)2−2(0)+33
The y-intercept is (0,3).
Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.
f(x)000x+3x======−x2−2x+3−x2−2x+3x2+2x−3(x+3)(x−1)0−3orx−1x==Set f(x)=0.Multiply both sides by −1.Factor.Set each factor equal to zero.01
Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).
Step 3: Determine the vertex. One way to do this is to first use x=−b2a to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.
x====−b2a−(−2)2(−1)2−2−1
Substitute −1 into the original function to find the corresponding y-value.
f(x)f(−1)====−x2−2x+3−(−1)2−2(−1)+3−1+2+34
The vertex is (−1,4).
Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.
x −2 y 3f(−2)=−(−2)2−2(−2)+3=−4+4+3=3Point(−2,3)
Our fifth point is (−2,3).
Step 5: Plot the points and sketch the graph. To recap, the points that we have found are
y−intercept:x−intercepts:Vertex:Extra point:(0,3)(−3,0) and (1,0)(−1,4)(−2,3)
Answer:
Given a rectangle with length of (2x+9)cm and width of (3x+1)cm.Two squares, each with sides x cm is removed from the rectangle.The remaining shape has an area of 83cm².Find the value of length and width of the rectangle.
Answer: The length is 13cm and the width is 7cm
Step-by-step explanation:
For a rectangle of length L and width W, the area is:
A = W*L
In this case we have:
L = (2*x + 9) cm
W=(3*x + 1) cm
Then the area of the rectangle is:
A = (2*x + 9)*(3*x + 1) cm^2
A = (6*x^2 + 2*x + 27*x + 9) cm^2
A = (6*x^2 + 29*x + 9) cm^2
now we remove two squares with sides of x cm
The area of each one of these squares is (x cm)*(x cm) = x^2 cm^2
Then the area of the figure will be:
area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2
area = (4*x^2 + 29*x + 9) cm^2
Now we know that the area of this shape is 83 cm^2, then we need to solve:
83 cm^2 = (4*x^2 + 29*x + 9) cm^2
0 = (4*x^2 + 29*x + 9) cm^2 - 83 cm^2
0 = (4*x^2 + 29*x - 74) cm^2
Then we need to solve:
0 = 4*x^2 + 29*x - 74
Here we can use Bhaskara's equation, the solutions of this equation are given by:
[tex]x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)} }{2*4} = \frac{-29 \pm 45}{8}[/tex]
Then the two solutions are:
x = (-29 - 45)/8 = -9.25 (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).
The other solution is:
x = (-29 + 45)/8 = 2
x = 2
Then the length and width of the rectangle are:
Length = (2*2 + 9)cm = 13 cm
Width = (3*2 + 1)cm = 7cm
Please help i dont know the answer and this is due today
Q Nine divided by the product of a number and Five
Q2 The product of a sum and diffrence of x and y
Step-by-step explanation:
Q Nine divided by the product of a number and Five
Let the number = x
product of a number and Five = x * 5 = 5x
The expression is given as;
[tex]\frac{9}{5x}[/tex]
Q2 The product of a sum and difference of x and y
Sum of x and y = x + y
Difference of x and y = x - y
The expression is given as;
(x + y) * ( x -y)
x^2 + xy - xy - y^2
x^2 - y^2
The sink started with 20ml of water and increases at 3ml per min. If the sink is currently holding 75ml, how many minutes have passed? Which equation would you use to solve for m (minutes passed)?
Answer:
18.78 minutes is my opinion
Step-by-step explanation:
3 ml is filled in 1 minute
1 ml is filled in 1/3 minutes
20 ml is filled in 1/3*20 minutes
=6.22
75 ml is filled in 1/3*75 minutes
=25
25-6.22=18.78
Compare | -3| And 1
PLS
Answer:
|-3| > 1
Step-by-step explanation:
Well |-3| = 3
3 > 1
1 < 3
(you can replace 3 for |-3| in those up there^)
19) The sales tax on a $105 digital camera is $7.15. What is the sales tax rate? (Round your answer to the nearest tenth.)
Answer:
the answer is 6 percent
hope it was help full mark me as braniest
Question 1 (4 points)
Which statement is true?
F 21 and 22 are alternate interior angles.
G21 and 23 are corresponding angles.
H 23 and 26 are alternate exterior
angles.
J Z3 and 27 are same-side interior
angles.
14.The volume of a cube whose edge is 3x is _______.
FASTT!!!
Answer:
[tex]27x^3[/tex]
Step-by-step explanation:
What is the range of this data set?
3.7, 18.5, 2.7, 13.8, 7.5, 15.2, 10.1, 7.6, 17.8
14.1
15.8
17.8
18.5
Answer:the answer is 15.8
Step-by-step explanation:
The product of two consecutive positive integers is 26 more than ten times the largest of the two numbers.
1. Write an equation to represent the situation above.
Answer:
x(x+1)=10(x+1)+26
Step-by-step explanation:
Let the two consecutive positive integers be x and x+1.
The product of these two integers is x(x+1).
The largest of the two numbers is x+1.
By given, x(x+1)=10(x+1)+26.
The Diamond Rule says two factors, m and n, must multiply to get to the top number and add to
get to the bottom number.
What are the possible values for m and n?
Answer: -3 and -6
Step-by-step explanation: I took the quiz
Write an equation that could be used to find the value of x using the interior angles of ∆BDC, then solve it.
9514 1404 393
Answer:
x = 16
Step-by-step explanation:
Either or both of the right triangles can be used to find x. Or, triangle ABC could be used. All numbers are assumed to be degrees.
Using ∆ABD
55 +90 +2x+3 = 180
2x = 32 . . . . . . subtract 148
x = 16
Using ∆BCD
50 +90 +2x+8 = 180
2x = 32 . . . . . . subtract 148
x = 16
Using ∆ABC
55 +(2x +3) +50 +(2x +8) = 180
4x = 64 . . . . . . . subtract 116
x = 16
pls pls help ill give brainliest. the red is not part of it it was just how i screenshot it
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
Answer:
5.5 ft
Step-by-step explanation:
therefore if you cut 11 in half you get 5.5
Given the triangle below, which of the following equations correctly represents the relationship between a, b, and c?
Answer:
C. c^2=a^2+b^2-2abcos(90°)
Step-by-step explanation:
This is the law of cosine.
Answer:
C, you're welcome :)
Step-by-step explanation:
Max is asked to prove that LM=MN Here is hs proof.
This is not a correct proof explain why
Answer:
Its not true because:
Step-by-step explanation:
if you divide by M, with M not being 0, ypu have the equation L=N which is false
Jessie spent a total of 14.00 to purchase a gift and have it gift-wrapped and mailed. The cost for the postage was $2.25, and she knows the gift itself cost $9.50.
Answer:
she spent 11.75$ total
Step-by-step explanation:
9.50+2.25=11.75
What is 12x^2 + 53x + 20 written as a product?
Answer:
(12x+5)(x+4)
Step-by-step explanation:
Which of the expressions have like terms? select all that apply
A. 14m + mn
B. 2y + 2x + 4
C. -3/4m + 8m + m
D. 4 - 3p
E. 5.75t + 7.75t - t
F. 8xy - 6xy
Answer:
C, E and F
Step-by-step explanation:
As,
C. - 3/4 m + 8m + m. [Like terms of m]
= 29/4 m + m
= 33/4 m
E. 5. 75t + 7.75 t - t. [Like terms of t]
= 13.5t - t
= 12 . 5t
F. 8xy - 6xy. [Like terms of xy]
= 2xy
For the rotation − 104 3 ∘ −1043 ∘ , find the coterminal angle from 0 ∘ ≤ θ < 36 0 ∘ 0 ∘ ≤θ<360 ∘ , the quadrant and the reference angle.
9514 1404 393
Answer:
co-terminal: 37°1st quadrantreference angle: 37°Step-by-step explanation:
-1043°/360° ≈ -2.9
Adding 3×360° will give a co-terminal angle in the range 0-360°:
-1043° +1080° = 37°
This co-terminal angle is in the first quadrant. It is also the reference angle.
which statement is incorrect?
Where exactly are the alleged statements?
June had aphids in 30% of her rose bushes. She had 40 bushes. How many plants must she release ladybugs on to eat the aphids and save the roses?
Answer::
Step-by-step explanation:
Shalini blusex batting scores were 13144 155 142 167 172 what was his score
What property of operations can be used to justify that the two expressions in this equation are equivalent? 6x^2 +4x=4x + 6x^2
Answer:
Commutative
Step-by-step explanation:
There are four basic property of operations to solve an algebraic expressions. They are associative, commutative, distributive and identity.
The expression given is : [tex]$6x^2 + 4x=4x+6x^2$[/tex]
So the given algebraic expression is a commutative property of operations. The commutative property states that when any two numbers are added in an expression the sum of the numbers are the same regardless of the order of the numbers that are added.
Thus the sum of the above expression will be same in which ever order the numbers are added.
plz answer these quickly anyone plz answer
Answer:
1.perimeter=πr/2=3.16×6/2=18.96/2cm=9.48cm
2.perimeter =
πd/2+2×5=3.16×17/2+10=36.86cm
evaluate the expression
I 13 I + I -2 I
Answer:
15
Step-by-step explanation:
Apply absolute rule: | a | = a, a ≥ 0
| 13 | = 13
= 13 + | -2 |
| -2 | = 2
= 13 + 2
= 15
A state university locks in costs for a student once a student starts attending the university. The total cost is $23,500. A student has the following help in covering the costs of school. An academic scholarship of $8,200. Other scholarships and grants of $7,400. Grandparents pay $1,000. What is the amount that the student will need to save every month in order to pay off the remaining costs in 10 months?
Answer:
Answer is 690 every month
Step-by-step explanation:
The total cost is $23,500
Scholarship:8200$
2nd scholarship:7400$
Grandparents: 1000$
23,500-8,200-7400-1000=6900÷10=690
He will have to save up 690 every month for 10 months
Write the fraction as a decimal.
Round to the nearest hundredth.
7/18~ [?]
Answer:
0.39
Step-by-step explanation:
7/18= 3.888888888
round up
0.39
Write 5.9 as a mixed number.
Answer:
[tex]5\frac{9}{10}[/tex]
good luck, i hope this helps :)
Answer:
5 9/10
Step-by-step explanation:
6.
Do the following conversions:
a.2 GB = ---------------- Kb
b.
2×10 MB = ------------------- B
please answer the question fastly
Answer:
a) 2000000 kilobytes
b)20 000 000 bytes
How many sides does the thirtieth figure have?
Answer:
8.
Step-by-step explanation:
multiples of 3 for every shape.
What is the circumference of a circle with a diameter of 85 feet?
feet
(Use 3.14 for P.)
Answer:
266.9 feet
Step-by-step explanation:
Find the radius
85 ÷ 2 = 42.5
Find the circumference
2 × 3.14 × 42.5 = 266.9 feet
