I need help with these questions for Working with Standard and Vertex Forms of the Quadratic Function, the first image is the instructions for the questions and the rest of the images have been labelled and put in order of the questions:
Answers
9514 1404 393
Answer:
3 (7e) f(x) = -3(x +2)^2 +1; D: (-∞, ∞); R: (-∞, 1]
4 (8) g(x) = 4(x -3)^2 -5; x = 3; (3, -5); min: -5; D: (-∞, ∞); R: [-5, ∞)
5 (10) A(175) = 31,250 m^2
Step-by-step explanation:
Q3. (7e) f(x) = -3x^2 -12x -11 = -3(x^2 +4x) -11 = -3(x^2 +4x +4) -11 +3(4)
f(x) = -3(x +2)^2 +1
Domain: all real numbers; Range: y ≤ 1
Expanded: -3(x^2 +4x +4) +1 = -3x^2 -12x -11
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Q4. (8a) g(x) = 4(x^2 -6x) +31 = 4(x^2 -6x +9) +31 -4(9)
g(x) = 4(x -3)^2 -5
8b) x = 3 . . . axis of symmetry
8c) (3, -5) . . . coordinates of vertex
8d) minimum: -5 (parabola opens upward from vertex, which is the minimum)
8e) any quadratic has a domain of "all real numbers"
8f) the range is upward from the minimum: y ≥ -5
8g) see attached
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Q5. (10) A(x) = 700x -2x^2 = -2(x^2 -350x +30625) +2(30625)
A(x) = -2(x -175)^2 +31,250
The maximum area that can be enclosed is 31,250 square meters.
_____
Additional comment
The process of "completing the square" can be done using the following steps. (a) Factor out the leading coefficient from the variable terms; (b) determine the linear term coefficient inside parentheses, and add the square of half of it inside parentheses; (c) add the opposite of the same quantity outside parentheses (make sure the leading coefficient is properly factored in; (d) rewrite the parentheses as a square, and collect terms outside parentheses. In the final form a(x -h)^2 +k, the vertex is (h, k).
Related Questions
Alina bought groceries that cost a total of $45.00. What is a 13% tax for that total?
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+sales tax if 13% = 5.85
Total price =50.85
There are 10 water birds swimming in a pond. If
there are 6 ducks and 4 geese at the pond, what
fraction of the birds are geese?
Simplify your answer as much as you can.
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Answer:
2/5
Step-by-step explanation:
Total water birds=10
ducks=6
geese=4
fraction of geese=4/10
=2/5
Question 3
3 pts
(06.04)
What is the value of 6 + 2x when x = 5? (3 points)
04
0 13
016
O 40
Please answer fast!
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Answer:
C its 16
Step-by-step explanation:
i would not give the wrong answer
2. Subtract: 7 - 2.5
1
o
5
O
5.5
5.0
4
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HELP FOR THE LOVE OF JESUS HELP ME IF YOU LOVE JESUS OR ANY GOD YOU BELIEVE PLEASE HELP
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Answer:
28
Step-by-step explanation:
24/6=4
11-4=7
4(7)=28
I hope this helps..
your answer would be a. 28
1. Find the degree of the polynomial.
5n^20 p^2 x^6
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Answer:
6
Step-by-step explanation:
Simplify the expression (3.5x - 2.7y) + (-12.8x + 15.8y)
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Answer:
−9.3x + 13.1y
Step-by-step explanation:
Answer: Its -9.3x+13.1y :)
Step-by-step explanation:
Graph 16x+8y=24 on a coordinated plane?
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Answer:
To find the x-intercept, substitute in 0 for y and solve for x .To find the y-intercept, substitute in 0 for x and solve for y . x-intercept(s): ( 3/2, 0) y-intercept(s): ( 0 , 3 )
Which of the following statements about JK and JL is true? 13 12 10 5 L(7.4) K(-4,2) 2 J(2, 1) 1 2 3 4 5 6 7 -7-6-5-4-3-2-1 O A. JL is longer than JK. O B. JK is 7 units long. O C. JK and JL are the same length. D. JK is longer than JL.
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Answer:
I think It´s C
Step-by-step explanation:
Identify the coefficients in the expression below.
10x + 19
**pls help fast!!!
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Answer:
10
Step-by-step explanation:
the Coefficient in an expression is the number before the variable. In this case, since the variable is x, and the number before it is 10, the coeficcient is 10.
domain and range help
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(-Infinity,Infinity) and [0, Infinity)
Please shows step by step if possible for I can understand this.
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Answer:
f(4)=52
Step-by-step explanation:
First, you substitute the x's with 4, so it would be
f=3*4^2+2*4-4
f=48+8-4
f=52
Hope this helps
BC = 36; D = 15. What is the value of BD - AC.
B
A
BD - AC =
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Answer:
BD - AC = 0
Step-by-step explanation:
Given that:
BC = 36 , CD = 15 and BD = x
As these are forming right angled triangle,
Using Pythagorean theorem,
[tex](BD)^2+(CD)^2=x^2\\(36)^2+(15)^2 = x^2\\1296 + 225 = x^2\\1521 = x^2\\[/tex]
Taking square root on both sides
[tex]\sqrt{x^2}=\sqrt{1521}\\x=39[/tex]
As the given shape is rectangular, the sides parallel to each other will have same values.
AB = 15 , AD = 36 and AC = x
[tex](15)^2+(36)^2 = x^2 \\225 + 1296 = x^2 \\1521 = x^2 \\x = 39[/tex]
Now,
BD - AC = 39 - 39 = 0
Hence,
BD - AC = 0
If you help me I’ll give brainliest and 20 points only answer if you know pls and thank you
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Answer:
(2/3)^4 and (4/9)^2
Step-by-step explanation:
PLZ HELP THERS WAY MORE SORRYJUST CLICK AND SEE
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Answer:
A
Step-by-step explanation:
ueid8duenofbenxochikwbdicv
need help please due in 10 minutes!!!Thank you soo much if you answer it
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Answer:
D 115
Step-by-step explanation:
180-65=115
180 cuz it's a straight line
2x^4=50 solve by factoring
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Answer:
2(x4 − 25) = 0
Step-by-step explanation:
Paula asks a classmate to be her partner for a class project, and he agrees to work with her. Next, her friend Nick picks a partner, too. Are these two events dependent or independent?
A dependent
B independent
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Practice :
1. Find a line that is parallel to f(x) = 2x +3 and passes through (0,-4).
2. Find through line that is perpendicular to f(x) = 2x+3 and passes through (0,-4)
Answers
Answer:
1)The equation of the Parallel line is 2x -y -4=0
2) The equation of the perpendicular line of the given line x+2y+8=0
Step-by-step explanation:
Step(i):-
Given function f(x) = 2x+3 and passes through (0,-4)
Let y =f(x) = 2x+3
y = 2x+3
⇒ 2x -y +3=0
The equation of the parallel line of the given line 2x - y +k =0
This line is passes through the point (0,-4)
⇒ 2 (0) -(-4)+k=0
4 +k=0
⇒ k =-4
The equation of the Parallel line is 2x -y -4=0
2)
Step(ii):-
Given function f(x) = 2x+3
Let y = 2 x + 3
2x - y +3=0
The equation of the perpendicular line bx -ay +k=0
The equation of the perpendicular line of the given line -x-2y +k =0
This line is passes through the point (0,-4)
⇒ (0) -2(-4)+k=0
8 +k=0
⇒ k =-8
The equation of the perpendicular line of the given line -x-2y -8 =0
The equation of the perpendicular line of the given line x+2y+8=0
Hank made 6 out of 8 foul shots ,while Nelly made 8 out of 20 foul shots (A) Who scored the most baskets? (B) Compare Hank and Nelly to determine whose son is more accurate
Answers
Answer:
(A) Hank
(B) Hank
Step-by-step explanation:
Hank made 6 out of 8 foul shots Nelly made 8 out of 20 foul shots
(A) Who scored the most baskets?
Converting the shots to decimal
Hank = 6/8 = 3/4 = 0.75
Nelly = 8/20 = 1/4 = 0.40
The person who scored the most baskets is Hank
(B) Compare Hank and Nelly to determine whose son is more accurate
Determining who is more accurate,
Hank = 6/8 = 3/4
This means out of every 4 shots, Hank scored 3
Nelly = 8/20 = 1/4
This means out of every 4 shots, Nelly scored 1
Therefore, Hank is more accurate
The points represented by the (x, y) coordinate pairs in the
table below all lie on line k.
X
1
2.
3
4
5
у
3
1
- 1
-3
-5
What is the slope of line k?
A
-2
B
-3
C
2
D
5
Answers
Step-by-step explanation:
For every increase in the x-value by 1,
the y-value decreases by -2.
(From 3 to 1 and from 1 to -1)
Hence, slope of line k
= Rise/Run = (-2)/1 = -2. (A)
Using it's formula, it is found that the slope of line k is of -2, hence option A is correct.
Given two points (x,y) on a line, the slope is given by the change in y divided by change in x.
In this problem, two of the points are: (1,3) and (2,1).
Hence, applying the division:
[tex]m = \frac{1 - 3}{2 - 1} = -\frac{2}{1} = -2[/tex]
The slope of the line is of -2, hence option A is correct.
A similar problem, in which the objective is also finding the slope, is given at https://brainly.com/question/14829050
URGENT: A grocer has 150 kg of walnuts that sell for $6 per kg. She plans to add almonds that sell for $5.30 per kg to the walnuts to make a mixture that sells for $5.50 per kg. How many kg of almonds should she add? (MUST SHOW WORK)
Answers
Answer:
let c = cashew pounds, w = walnut pounds, m = mixed pounds
Here's what we know:
c + w = m
7c + 5.5w = 6.50m
m = 35
So we now have:
c + w = 35
7c + 5.5w = 227.5
We can use substitution or elimination here. Let's try substitution in this case:
c = 35 - w
7(35 - 7) + 5.5w = 227.5
245 - 7w + 5.5w = 227.5
245 - 1.5w = 227.5
-1.5w = -17.5
w = 11 2/3
Now to solve for cashews:
c = 35 - 11 2/3
c = 23 1/3
Check:
23 1/3 * 7 + 5.5 * 11 2/3 = 227.5
163 1/3 + 64 1/6 = 227.5
163 2/6 + 64 1/6 = 227.5
227 3/6 = 227.5
227.5 = 227.5
Step-by-step explanation:
i hope write answer
Factorise x² - x with explanation please?
Answers
Answer:
x(x + 1)
Step-by-step explanation: This is an important way of solving quadratic equations. The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1)
Find the value of x in 3x + 4y = 8 and 4x - 4y = 6.
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Answer:
x = 2
Step-by-step explanation:
by adding both equations ,
we get 7x = 14
that's why x = 2 .
mark me as Brainliest
The number 299 is divided into two parts in
the ratio 5:8. The product of the numbers
(A) 21140
(C) 21160
(B) 21294
(D) 31294
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please help me with this fast, because i don't understand it
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Answer:
3/4
Step-by-step explanation:
f(0) - f(3) / 0 - 3
f(0) = -4
f(3) = 9/4 - 16/4 = -7/4
f(0) - f(3) = [-4 - (-7/4)]
f(0) - f(3) = [-16/4 + 7/4]
f(0) - f(3) = -9/4
-9/4 ÷ -3 = -9/4 · -1/3 = 3/4
Section A has 80 marks Section B has 120 marks.
Riya scores
55% in Section A 70% in Section B.
To pass, Riya needs to score 65% of the total marks.
Does she pass? You must show your working.
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Answer:
Riya does not pass
Step-by-step explanation:
From the question:
Section A has 80 marks
Section B has 120 marks.
The total marks from both sections = 200 marks
To pass, Riya needs to score 65% of the total marks.
Hence: 65% of 200 marks
= 65/100 × 200
= 130 marks.
To pass Riya must score 130 marks.
Riya scores:
For section A
55% in Section A
Her marks in section A = 55% × 80
= 55/100 × 80
= 44 marks
For section B
70% in Section B.
Her marks in section A = 70% × 120
= 70/100 × 120
= 84 marks
Therefore , the total marks Riya scored in both sections =
44 marks + 84 marks
= 128 marks
Riya scored a total of 128 marks. SHE DOES NOT PASS. Because the pass mark is a total of 130 marks from Section A and Section B
need help again . i don’t understand this one either!
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Answer:
h = 10
Step-by-step explanation:
1. Find the equation of a line that is perpendicular to
y=-2/3+4 and goes through (0,5)
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since it’s perpendicular, flip the numerator and denominator of the slope and b=5 because it’s going through the y-axis at (0,5)
Answer:
Step-by-step explanation:
It says perpendicular, which means if you graphed the line given and the one you have to make, they would intersect at a right angle. I'm going to presume the x is after -2/3 since you didn't put one in, I hope that's correct.
The first part to solving problems like these is to invert the slope, which just means you have to switch the sign on it (negative to positive/positive to negative) and switch the numerator and denominator. This makes the new slope 3/2.
The next step is to find the y-intercept, which they thankfully gave you in this problem (when x=0 the y-value is always the y intercept), but you'll usually have to find it.
The equation is y=3/2x+5. You should double check this, I'm good at math but it's been a bit.
A student walks 1/4 miles from her home to the store on her way to a friends house. If the store is 1/3 of the way to her friends house, how far is her friends house from her home?
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Answer:
4/12 I think
Step-by-step explanation:
Answer:
3/4 of a mille.
Step-by-step explanation:
1/3 * 1/4
x=1/4*1/3
x=3/4
3/4 of a mile