Answers
y=4x²-1
#1
y=(2x)²-1²y=(2x+1)(2x-1)#2
Zeros are 1/2,-1/2
#3
Convert to vertex form y=a(x-h)²+k
y=(4x+0)²-1Vertex(h,k)=(0,-1)
#4
Graph attached
Answer:
i) [tex]y=(2x+1)(2x-1)[/tex]
ii) [tex]x=-\dfrac12, x=\dfrac12[/tex]
iii) (0, -1)
iv) see attached
Step-by-step explanation:
Given quadratic: [tex]y=4x^2-1[/tex]
Factored form
We can use the Difference of Two Squares to factor the given quadratic.
[tex]a^2-b^2=(a+b)(a-b)[/tex]
Therefore,
[tex]a^2=4x^2=(2x)^2\implies a=2x[/tex]
[tex]b^2=1=1^2 \implies b=1[/tex]
So the relation in factored form is:
[tex]y=(2x+1)(2x-1)[/tex]
Zeros
The zeros of the quadratic polynomial are the x-coordinates of the points where the graph intersects the x-axis, i.e. when y = 0
[tex]\implies y=0[/tex]
[tex]\implies (2x+1)(2x-1)=0[/tex]
[tex]\implies (2x+1)=0\implies x=-\dfrac12[/tex]
[tex]\implies (2x-1)=0\implies x=\dfrac12[/tex]
Therefore, the zeros are -1/2 and 1/2
Vertex
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\textsf{midpoint}=\dfrac{-\frac12+\frac12}{2}=0[/tex]
To find the y-coordinate of the vertex, substitute the found value of x into the given equation:
[tex]\implies y=4(0)^2-1=-1[/tex]
Therefore, the vertex is (0, -1)
Related Questions
MAX POINTS PLEASE HELP Will make Brainliest
What is the period and frequency of the function graphed and how would the equation be written??
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The required equation is :
[tex]\qquad \sf \dashrightarrow \:y =a \cos(bx) + k[/tex]
Now, let's find the required values :
period (p) = 6
[distance between any successive Crest or trough]
a = - 4 (flipped)
b = 2π/p = 2π/6 = π/3
k = -2
Distance of starting position from origin = k
Now, plug in the values ~
[tex]\qquad \sf \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]
There is not crest given so use distance between troughs
Period (T):-
Distance between two troughs|3-(-3)|6Frequency:-
[tex]\\ \rm\dashrightarrow \dfrac{1}{T}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{1}{6}[/tex]
[tex]\\ \rm\dashrightarrow 0.17Hz[/tex]
A triangle is graphed on the coordinate grid below.
What are the coordinates of the image of this triangle after a dilation, with a center of dilation at the origin and a scale factor of 2.
Explanation please!! Thank you
Answers
Answer:
The answer is D
Still stuck? Get 1-on-1 help from an expert tutor now.
Step-by-step explanation:
convert the following units to the units in bracket 12m (to cm)
Answers
We are converting 12 meters into centimeters.
A meter is a larger unit of messurment then centimeter. In fact, a meter is made up of many centimeters
How many centimeters are in a meter?
We can look at the word composition of the word centimeter to figure this out:
centimeter
centi = 100
There are 100 centimeters in 1 meter.
In this problem, we have 12 meters. That is twelve 100 cm or:
12 × 100 = 1,200
12 meters is the same as 1,200 centimeters
1 meter = 100 centimeter
So ,
12 m = 12 × 100 = 1,200 centimeter
x+y+z=-6
x-y+3z=-18
2x+2y+2z=-8
Answers
Answer:
Step-by-step explanation:
hello :
the system is : x+y+z=-6.....(1)
x-y+3z=-18.....(2)
2x+2y+2z=-8.....(3)
use (3): 2(x+y+z) = - 8 so : x+y+z = -4
use (1) : x+y +z = -6 -6=-4 false
no solutions
The perimeter of the rectangle below is 222 units find the length of side RS
Answers
Answer:
111
Step-by-step explanation:
divide 222 by 2 and you get your answer
Answer:
55.5
Step-by-step explanation:
since we don't know the length or width of any side, one length side will only be 1/4 of 222. And perimeter is all the sides added up. This rectangle will actually be a square.
222/4=55.5
could someone help me super duper fast with factoring trinomials
my previous questions are worth 50 each by the way
Answers
Answer:
(3a+3b+1)(2a+2b+3)
Step-by-step explanation:
This is the farthest they could be factored
#1
6(a+b)²+11(a+b)+3Let a+b=x
6x²+11x+36x²+2x+9x+32x(3x+1)+3(3x+1)(2x+3)(3x+1)Put value
(2(a+b)+3)(3(a+b)+1)#2
8(x+1)²-14(x+1)+3Let x+1=y
8y²-14y+38y²-2y-12y+32y(4y-1)-3(4y-1)(2y-3)(4y-1)Put value
(2(x+1)-3)(4(x+1)-3)Moderne Furniture Company had sales of $2,000,000 during its first year of operation. If the sales increased by $200,000/year thereafter, find Moderne's sales in the fifth year and its total sales over the first 5 years of operation.
Answers
Prove. An odd number cubed is an
odd number.
Answers
Answer:
If you're looking for the equation, it's:
[tex](2n+1)^3=8n^3+12n^2+6n+1=2(4n^3+6n^2+3n)+2=[/tex] an odd
I know because I got it right on acellus.
The cost of sending an overnight package from Kansas City to Miami is $23.50 for a package weighing up to but not
including 1 pound, and $3.80 for each additional pound or portion of a pound. A model for the total cost C in dollars) of
sending the package is C = 23.50 + 3.80Lx), x > 0, where x is the weight (in pounds).
What is the meaning of the coefficient 3.80 in the context of the problem?
O When the package weighs less than one pound, the price of the package is $3.80.
O For every pound that the package weight increases, the price of sending it increases by $3.80.
O For every pound that the package weight increases, the price of sending it increases by $23.50.
When the package weighs less than one pound, the price of the package is $23.50.
Answers
Answer:
For every pound that the package weight increases, the price of sending it increases by $3.80
Step-by-step explanation:
Overnight from KC to Miami = $23.50 for anything less than a pound + $3.80 per additional pound.
This means that for every pound that the package weight increases, the price of sending it increases by $3.80.
The graph of the relation H is shown below.
Give the domain and range of
H
Write your answered using set notation
Answers
Using the concepts of domain and range, it is found that:
The domain of the relation is {-1, 2, 3, 4}.The range of the relation is {-1, 0, 2, 4}.What are the domain and range of a relation?The domain of a function is the set that contains all possible input values. On a graph, it is given by the values of x.The range of a function is the set that contains all possible output values. On a graph, it is given by the values of y.In this graph, the points represented are given by: {-1, 2}, {2,0}, {3,-1} and {4,4}. Hence:
The domain of the relation is {-1, 2, 3, 4}.The range of the relation is {-1, 0, 2, 4}.More can be learned about the concepts of domain and range at https://brainly.com/question/10891721
Please look at the attachments I posted. Anyone help me please
Answers
Answer:
This will be option D
Replace the k with -1/2 and f(x) with x^2
this will look like -1/2*x^2
plug this into a graphing website such as Desmos
PLEASE HELP PLEASE HELP PLEASE
Answers
blue stars. let’s talk a bit about temperature. The color of a star is a function of its temperature. If a star looks red, that means its surface temperature is approximately 2,500 Kelvin. Just for comparison, our Sun, which actually looks white from space, measures about 6,000 Kelvin. The hotter the star, the further up the spectrum you go. The hottest stars are the blue stars. A star appears blue once its surface temperature gets above 10,000 Kelvin, or so, a star will appear blue to our eyes.
The segments shown below could form a triangle.
д
C
B
9
11
B
C
O A. True
B. False
Answers
Answer:
hi the answer is true
Step-by-step explanation:
hope it helps
The triangle can be formed using the given line segments. Therefore, the given statement is true.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Given that, line segments AC=9 units, BC=4 units and AB=11 units.
If a, b and c are the lengths of the sides of a triangle then
If a ≤ b ≤ c, then a + b > c.
9+4>11
13>11
Therefore, the given statement is true.
To learn more about the triangle inequality theorem visit:
https://brainly.com/question/1163433.
#SPJ7
Solve the system using the linear combination method:
x + 5y= -3
2x + 7y=3
Answers
Answer:
3x+12y=0
Step-by-step explanation:
x+2x=3x
5y+7y=12y
-3+3=0
Find the missing side.
Answers
It's 3ft
Step-by-step explanation:
Volume = lxwxh
252 = 7 x 12 x?
= 84 x?
÷84
3. =?
3x12x7=252
Hope this helps!
Find the surface area of the pyramid.
Answers
Answer:
i think the answer is 87.
Step-by-step explanation:
i think its 87.
Find the value of x
A. 4
B. 10
C. 17
D. 25
Answers
Answer:
X can be any of those numbers depending on which equation it is in
Step-by-step explanation:
Can someone help me?
Answers
Answer:
(i) [tex]y = 2x(x-5)[/tex]
(ii) zeros: x = 0 and x = 5
axis of symmetry: x = 2.5
(iii) vertex: (2.5, -12.5)
(iv) see attached
Step-by-step explanation:
Part (i)
Factor: [tex]y=2x^2-10x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies y=2x(x-5)[/tex]
Part (ii)
Zeros occur when [tex]y=0[/tex]
[tex]\implies 2x(x-5)=0[/tex]
Therefore:
[tex]\implies 2x=0 \implies x=0[/tex]
[tex]\implies (x-5)=0 \implies x=5[/tex]
So the zeros are x = 0 and x = 5
The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.
[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]
Therefore, the axis of symmetry is [tex]x=2.5[/tex]
Part (iii)
The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.
[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]
So the vertex is (2.5, -12.5)
Part (iv)
Plot the zeros and the vertex.
As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.
Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.
*see attached*
3+3x3+3
Whats the total
21
36
15
Answers
Answer:
c. 15
Hope it helpz~
please mark me as brainliest
Can someone help me please?
Answers
Answer:
the only answer that makes sense would be the length
A rectangle has a length of 15 cm and a width of 11 cm. What is its perimeter?
54 cm
52 cm
165 cm
26 cm
Answers
Answer:
52 cm
Step-by-step explanation:
perimeter = 2(length) + 2(width) for a rectangle.
2(15)+2(11)=52 cm
Answer:
52
Step-by-step explanation:
i got 100% on the quiz i got all the answers
there would you place -6?
Answers
Answer:
Integer
Step-by-step explanation:
Essentially Rational numbers are numbers that have decimals or fractions tied to them, negative or positive. EX: 3.66, 2 1/4.
Whole numbers are WHOLE numbers that are positive. They are to the right of zero always. EX: 1, 9, 100,258. There is no decimal or fraction tied to them. This also includes 0.
Integers are essentially a whole number that isn't a fraction. They contain all negative numbers too. EX: -1025, 56, -6.
Here is a better representation of that if you're a visual learner. Hope this helps!
Verify experimentally the sum of angle of triangle is 180°
Answers
Answer:
Draw line a through points A and B. Draw line b through point C and parallel to line a. Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'. It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees
Bethany is making a rectangular fenced-in area for her rabbit in her yard. The area measures 4 3/4 feet wide by 2 yards long. What is the total length of fencing, in feet, that Bethany will need?
Answers
Betty has some bottles.
4
7
of the bottles are big and
4
5
of the remaining bottles are small. The rest of the bottles are tiny.
What fraction of the bottles are tiny?
Answers
what is the slope of the line that passes through the points (-1,1) and (1,-15)
Answers
Answer:
[tex]\boxed{\text{The slope is -8.}}[/tex]Step-by-step explanation:
To find the slope of the line, you have to use a slope formula.
Slope formula:
[tex]\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]
⇒ y2=(-15)
⇒ y1=1
⇒ x2=1
⇒ x1=(-1)
Rewrite the whole problem down.
[tex]\Longrightarrow: \sf{\dfrac{-15-1}{1-\left(-1\right)}=\dfrac{-16}{2}=\boxed{\sf{-8}}[/tex]
So, the slope is -8, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
I need help with this please
Answers
Answer:
4 and 7
2 and 5
Step-by-step explanation:
4 and 7 are co interior angles
2 and 5 are co interior angles
sum of co interior angles are 180° hence they are Supplementary
Find an equation for the line that passes throughthe points (1,-1) and (-3,5)
Answers
y - 1 = 2(x-1)
y= 2x-2 +1
y = 2x-1
or
y-5 = 2(x-3)
y = 2x-6+5
y = 2x-1
y = -1.5(x) + 0.5
points: (1,-1) and (-3,5)
slope:
⇒ (y2-y1)/(x2-x1)
⇒ (5-(-1))/(-3-1)
⇒ 6/-4
⇒ -1.5
equation:
⇒ y -(-1) = -1.5(x-1)
⇒ y + 1 = -1.5(x) + 1.5
⇒ y = -1.5(x) + 0.5
Find the equation of the line that contains the point (4, - 2) and is perpendicular to the line y = - 2x + 5.
Answers
y=1/2x
Solution:The slopes of perpendicular lines are opposite reciprocals of each other.The simplest way to determine a number's reciprocal is to flip it over, like so:[tex]-2 ~ - > -\displaystyle\frac{1}{2}[/tex]Now, change the sign:[tex]\displaystyle\frac{1}{2}[/tex]So we have the slope of the line that's perpendicular to the given line.Now, let's find the line's equation.First, let's write it in Point-Slope Form:y-y1=m(x-x1)y-(-2)=1/2(x-4) y+2=1/2x-2 (Point slope)Now, convert to slope-intercept:y=1/2x+2-2y=1/2xHope it helps.
Do comment if you have any query.
Answer:
y=1/2x
Step-by-step explanation:
If 12% of a number is 30, find 4% of that number.
Answers
12%= 30
-> 100%= 30÷12×100
-> 100%= 250
4% of 250
-> 4%=250÷100×4
-> 4%= 10