Answers
9514 1404 393
Answer:
A. f(x) = (x -3)² -1
B. vertex: (3, -1); axis of symmetry: x=3; x-intercepts: {2, 4}; y-intercept: 8
C. see attached for a graph
Step-by-step explanation:
A. Put the function in vertex form by completing the square. Start by putting parentheses around the terms containing x.
f(x) = (x² -6x) +8
Now, identify the coefficient of x (-6) and square half of that. (-6/2)² = 9. Add this value inside parentheses, and subtract this value outside parentheses.
f(x) = (x² -6x +9) +8 -9
Rewrite the trinomial in parentheses as a square. The constant in the binomial will be the value you squared in the previous step.
f(x) = (x -3)² -1 . . . . . vertex form; a(x -h)²+k for vertex (h, k)
__
B. The vertex and the axis of symmetry can be read from the equation. Here, the vertex is (3, -1). The axis of symmetry is the vertical line through the vertex: x = 3. The x-intercepts are found by solving f(x) = 0.
f(x) = 0
(x -3)² -1 = 0
(x -3)² = 1 . . . . . add the opposite of the 'k' value
x -3 = ±√1 . . . . take the square root. We need both signs.
x = 3 ± 1 . . . . . add 3 to get x by itself. These are the x-intercepts.
x = 3-1 = 2 and x = 3+1 = 4
The x-intercepts are 2 and 4, points (2, 0) and (4, 0).
The y-intercept is the value of f(0). It is the constant in the original form of the function. f(0) = 8 . . . . y-intercept
__
C. The graph is attached. The various points above are marked, and the axis of symmetry is shown.
Related Questions
simplify the following 7+(_10)
Answers
Answer:
7 or -3
Step-by-step explanation:
its -3 only if the number you typed was ( -10 ) because i can't really tell if that dash is supposed to be there or not.
steps for 7 :
7 + (10)
7 + 1 ‧ 0
7 + 0
7
steps for -3 :
7 + ( -10 )
7 - 10
-3
Write the following whole number as it’s English word equivalent
Answers
Answer:
eight hundred seventy five thousand five hundred eighty four
Step-by-step explanation:
please help asap!!!!
Answers
Answer:
C
Step-by-step explanation:
yeyeyeye
True or false this number is written in scientific notation?
.2486 x 10^12
Answers
Answer:
It Is TrueIt is true because scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
can soemone help meee i give brainlistt
Answers
Answer:
140.74
Step-by-step explanation:
1.area of right triangle
1/2*b*h=1/2*20*18=180
2.area of semi circle
1/2*pi*r^2=1/2*pi*5^2=39.26
r= d/2
180-39.26=140.74
then do 180-(25pi/2) which equals to about 140.73009
y/8 = 40, y = 5
is this correct? yes or no
Answers
Answer: No, the correct answer is 320.
Step-by-step explanation: To solve for Y, simplify both sides of the equation, then isolate the variable.
Step 1: Multiply both sides by 8.
[tex](\frac{y}{8} )\times(8)=(40)\times(8)=320[/tex]
Therefore, your answer is incorrect, the correct answer is 320.
Ben earns $12,800 a year. About 15% is taken out for taxes. How much is taken out for taxes?
Answers
Answer:
$1920
Step-by-step explanation:
to find a percent of a number, divide the percent by 100 then multiply by the value:
Please use the picture below to find our what x equals
Answers
Answer:
45 degrees
Step-by-step explanation:
Answer:
60 degrees
Step-by-step explanation:
The full angle is supplementary (180 degrees) so you just do
180-(90+30)
180-120
x=60
help please i need you
Answers
Answer:-10hy-4h
Step-by-step explanation:
h*-10y and h*-4
One card is selected from a deck of cards. Find the probability of selecting a black card or a king.
Answers
Answer:
30/52
Step-by-step explanation:
Find the area of each regular polygon. Round to the nearest tenth.
A= _ In2 ?
Answers
Answer:
Area of the square = 225.0 in²
Step-by-step explanation:
Given polygon is a regular polygon that means given quadrilateral has all sides equal in measure.
And a quadrilateral with all sides equal is known to be a square.
Therefore, area of a square = (Side)²
= (15)²
= 225
≈ 225.0 in²
I need an answer for this it’s due today plss
Answers
Answer:
128
Step-by-step explanation:
2^4/2^-3
= 2^7
=128
(12+34)×2.3= (talk to me please please please)
Answers
Answer:
90.2
Step-by-step explanation:
thx for the follow!!!
Answer:
105.8 is the answer
Step-by-step explanation:
105.8
The width of a rectangle is 14 inches less than its length. The area of the
rectangle is 51 square inches. Find the dimensions of the rectangle.
Answers
please help me with this
Answers
Answer: The last option, or D
Step-by-step explanation:
35x−35y+21
Graph a line with a y-intercept of 3 and containing the point (2, 5).
To graph a line, plot two points on the line.
Answers
Answer:
Let me know if you'd like me to clarify something. Good luck
Which fraction does point A show?
A.3/7
B.3/4
C.8/5
D.7/4
Answers
Answer:
d 7/4
Step-by-step explanation:
Question 8
8a) What is the area of the figure below? Select the
best answer.
Answers
Answer:
Try looking this up on the internet or something, I will suggest some sites,
Slader, and math -
way
Answer: 3.8 square kilometers.
Step-by-step explanation:
Area of a triangle = (base × height) ÷ 2.
The base of this triangle is 2km
The height of this triangle is 3.8km
2 × 3.8 ÷ 2 = 3.8km²
The solution to a system of linear equations could be...
Answers
Answer:
a b e f h
Step-by-step explanation:
Work out the value of 54
18 − 6
Answers
5418-6= 5412
Hope this helps
(40 POINTS) Let x = price of a standard ticket, y = price of a matinee ticket, and z = price of a senior ticket.
150x + 80y + 12z = 2,466
380x + 95y + 48z = 5,419
210x + 130y + 60z = 3,960
220x + 225y = 4,445
540x + 270y = 8,370 → y = −2x + 31
x = 11
The solutions to the system mean:
A.) Eleven tickets were sold on Friday. Nine tickets were sold on Saturday. Eight tickets were sold on Sunday.
B.) Eleven standard tickets were sold. Nine matinee tickets were sold. Eight senior tickets were sold.
C.) The price of a standard ticket is $11. The price of a matinee ticket is $9. The price of a senior ticket is $8.
Answers
Answer:
C. The price of a standard ticket is $11. The price of a matinee ticket is $9. The price of a senior ticket is $8.
Answer:
The answer is C
Step-by-step explanation:
what are two fractions that equal -7/10?
Answers
Answer:
-14/20
-21/30
Step-by-step explanation:
-7/10
-7x2=-14 and -10x2=-20
-14/20
-7/10
-7x3=-21 and -10x3= -30
-21/30
Help please :>
Convert 108 km/hr into m/s
Answers
Answer:
hello :) the answer is 30 m/s
Answer:
30m/s
Step-by-step explanation:
Convert km to m:
108 —> 108000
Convert hr to s
1 —> 3600
Now put them back into their place in the fraction: 108000/3600
Simply the fraction: 30m/s
PLEASE SHOW WORK ILL GIVE BRAINLIEST DUE TODAY!!!
14 + 18 ÷ 2 x 18 – 7
15 x 10 + 12 ÷ 3 + 9
8 x 4 + 9 – 9 + 18
2 - 1 + 5 x 4 x 11
60 – 9 x 8 ÷ 8 x 6
(10 ÷ 5)3 + 100 – 9 x 11
3 x 8 x 2 – 42 + 5
14 ÷ 2 -1 + 3
Answers
Answer:
1.) 169
2.) 63
3.) 50
4.) 221
5.) 6
6.) 501
7.)11
8.) 9
Step-by-step explanation:
sorry i dont have time for the explanation. :( i hope i helped you still
In ΔJKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°. Find all possible values of ∠K, to the nearest 10th of a degree.
Answers
Given:
In ΔJKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°.
To find:
The value of ∠K to the nearest 10th of a degree.
Solution:
According to the Law of Sine:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
We have, In ΔJKL, k = 4.1 cm, j = 3.8 cm and ∠J=63°.
Using the Law of Sine, we get
[tex]\dfrac{j}{\sin J}=\dfrac{k}{\sin K}[/tex]
[tex]\dfrac{3.8}{\sin (63^\circ)}=\dfrac{4.1}{\sin K}[/tex]
[tex]3.8\sin K=4.1\sin (63^\circ)[/tex]
[tex]\sin K=\dfrac{4.1\sin (63^\circ)}{3.8}[/tex]
[tex]\sin K=0.961349[/tex]
[tex]K=\sin^{-1}(0.961349)[/tex]
[tex]K=74.0182[/tex]
[tex]K\approx 74.0[/tex]
Therefore, the measure of angle K is 74.0 degrees.
A group of friends were working on a student film that had a budget of $1300. They used $546 of their budget on props. What percentage of their total budget did they spend on props?
Answers
Answer:
42
Step-by-step explanation:
trust me i had the same answer and it was right
4 divided by 2 (2/5) ???
Answers
Answer:
as decimal = 2
as fraction = 1/2
Write an equation of the line that passes through (1,5) and is parallel to the line y=-4x+2.
Answers
9514 1404 393
Answer:
y = -4x +9
Step-by-step explanation:
The same slope-intercept equation can be used, but with a different y-intercept. That new y-intercept can be found from the given point (x, y) using the formula ...
b = y -mx
b = 5 -(-4)(1) = 9
So, the equation with the new y-intercept is ...
y = -4x +9
the perimeter of a square is 7.2 meters how long is each side ?
Answers
Answer:
1.8 meters
Step-by-step explanation:
7.2÷4= 1.8
Answer:
1.8 m
Step-by-step explanation:
let side be 'a'.
perimiter of a square = 4(a)
7.2 = 4(a)
7.2/4 = a
therefore, a = 1.8 m.
Three times a larger number is 30 more than 5 times a smaller number. The sum of the larger number and 5 times the smaller number is 50
Answers
Answer: Smaller number = 6
Larger number = 20
Step-by-step explanation:
Let the smaller number be x.
Let the larger number be y.
Three times a larger number is 30 more than 5 times a smaller number. This will be:
3 × y = (5 × x) + 30
3y = 5x + 30 ...... i
The sum of the larger number and 5 times the smaller number is 50. This will be:
y + 5x = 50 ...... ii
From equation ii
y + 5x = 50.
y = 50 - 5x ...... iii
Put the value of y = 50 - 5x into equation i
3y = 5x + 30
3(50 - 5x) = 5x + 30
150 - 15x = 5x + 30
150 - 30 = 5x + 15x
120 = 20x
x = 120/20
x = 6
The smaller number is 6
Note that y + 5x = 50
y + 5(6) = 50
y + 30 = 50
y = 50 - 30
y = 20
The bigger number is 20
