Answers
Answer:
The graph is shown belowVertex = (2,1)Axis of symmetry is x = 2Domain = set of all real numbersRange = set of y values such that [tex]y \ge 1[/tex]=======================================================
Explanation:
Use your favorite graphing tool to graph the equation. If your teacher doesn't allow you to use graphing software, then you'll have to plug in various x values to find the paired y values. This gives the set of (x,y) points needed to be plotted to form the parabola. The more points you plot, the more accurate the curve.
The graph is shown below. I used GeoGebra to make the graph. It's free graphing software. Desmos is another tool that I recommend.
------------
The lowest point on the parabola is the vertex (h,k) = (2,1) which is shown in the graph below.
This is due to the equation being in vertex form y = a(x-h)^2 + k. We see that h = 2 and k = 1.
-------------
The axis of symmetry is the vertical line that passes through the vertex.
As such, the axis of symmetry equation is simply x = h. So that's how we get to x = 2.
In the graph below, the axis of symmetry is the red dashed line.
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There aren't any restrictions on x. We don't have to worry about dividing by zero or applying a square root to a negative number.
Therefore, any x value is allowed and the domain is the set of all real numbers.
-------------
The range however isn't the set of all real numbers. The lowest y can get is y = 1 due to the vertex point. We can have y = 1 or larger
Therefore, [tex]y \ge 1[/tex] is the range.
Related Questions
please help i don’t understand
Answers
Answer:
D
Step-by-step explanation:
First of, let's make a table for y = cos(x)
(x , y): (0 , 1) (π/2 , 0) (π , -1) (3π/2 , 0) (2π , 1)
Now, making a table for y = 2cos(x) is simple. We just have to multiply all the y-values from the previous table by 2.
(x , y): (0 , 2) (π/2 , 0) (π , -2) (3π/2 , 0) (2π , 2)
Graphing these coordinates, we find that the answer is D.
Find the area and perimeter of a rectangle.
the length is x+6 the width is x+2
Answers
Answer:
Area = x² + 8x + 12Perimeter = 4x + 16Step-by-step explanation:
The area of a rectangle is given by the formula:
Area=width×height
The perimeter of a rectangle is given by the formula
Perimeter=2(width+height)
Area
(x + 6) × (x+2) =
x² + 2x + 6x + 12
x² + 8x + 12
------------------
Perimeter
2 × (x + 6 + x + 2) =
2 × (2x + 8) =
4x + 16
PROBLEM SOLVING You deposit $300 into an investment account that earns 12% annual interest compounded quarterly. The graph shows the balance of a savings account over time. Write the functions that represent the balances of the accounts after t years. Round the growth factor to the nearest hundredth, if necessary.
Answers
Answer:
=25
Step-by-step explanation
:[tex]\sqrt{x}[/tex] 300 with 12 and you simply get 25
The function that represents the balance after t years is FV = $300( 4)^4t. The balance of the account after four years is; $914.92.
What is the function that represents the balance after t years?The formula for calculating future value:
FV = P (1 + r)^nm
Where: FV = Future value
P = Present value
R = interest rate = 12%/4 = 3%
m = number of compounding = 4
N = number of years
Thus FV = $300( 1+ 3)^4t
FV = $300( 4)^4t
Then the account balance after 4 years;
$300( 4)^(4 x 4)
= $914.92
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Which of the following is a factor of the expression 24x^2-30x-9?
Group of answer choices
12x+1
4x-3
2x+3
4x+1
Answers
Answer:
4x + 1
Step-by-step explanation:
24x² - 30x - 9 ( factor out 3 from each term )
= 3(8x² - 10x - 3) ← factor the quadratic
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 8 × - 3 = - 24 and sum = - 10
the factors are + 2 and - 12
use these factors to split the x- term
8x² + 2x - 12x - 3 ( factor the first/second and third/fourth terms )
= 2x(4x + 1) - 3(4x + 1) ← factor out (4x + 1) from each term
= (4x + 1)(2x - 3)
then
24x² - 30x - 9 = 3(4x + 1)(2x - 3) ← in factored form
so (4x + 1) is a factor of the expression
Cleo bought a computer for $1,495. What will it be worth after depreciating for 3 years at
a rate of 16% per year?
Answers
After 3 years of depreciation at a rate of 16% per year, the computer will be worth $886.93.
To determine the value of Cleo's computer after depreciating for 3 years at a rate of 16% per year, we need to calculate the depreciation amount for each year and subtract it from the original value.
First, let's calculate the depreciation for one year. The depreciation amount is obtained by multiplying the original value by the depreciation rate: $1,495 * 0.16 = $239.20.
After the first year, the value of the computer would be $1,495 - $239.20 = $1,255.80.
Now, we need to repeat this process for the next two years. For the second year, the depreciation amount would be $1,255.80 * 0.16 = $200.93. Subtracting this from the value after the first year gives us $1,055.87.
For the third year, the depreciation amount would be $1,055.87 * 0.16 = $168.94. Subtracting this from the value after the second year gives us $886.93.
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8x+4=4(2x+1)
Solve for X
Step by Step
Answers
Answer:
6x+5 that's the answer what I have
Nicholas has 28 more red peppers than green peppers. In all, he has 62 peppers. How many red peppers does Nicholas have?
Answers
Answer:Nicholas has 34 red peppers.
if A+B= 45° then prove that: tanA+ tanB+ tanA. tanB
Answers
Answer:
See Explanation
Step-by-step explanation:
[tex]A+B= 45 \degree \\ \\ assuming \: \tan \: on \: both \: sides \\ \\\implies \: \tan( A+B)= \tan 45 \degree \\ \\ \implies \: \tan( A+B)= 1 \: \: \\ ( \because \: \tan 45 \degree = 1) \\ \\ \implies \: \frac{\tan \: A +\tan \: B }{1 - \tan \: A .\tan \: B } = 1 \\ \\ \implies \: \tan \: A +\tan \: B = 1 - \tan \: A .\tan \: B \\ \\ \purple{ \implies }\: \orange{ \bold{\tan \: A +\tan \: B + \tan \: A .\tan \: B= 1 }} \\ \\ thus \: proved[/tex]
SIMPLIFY!!!!!!!! HELPPPPPP!!!!!
(10a^4b^6)(3a^5b^2) -7a^9b^8
Answers
Answer:
Step-by-step explanation:
then simplify
What is the slope of the line that passes through the points (-9, -2) and (-9,-6 )? Write in simplest form
Answers
Hello.
There are really 2 ways to think about the given problem.
First, we can use the slope formula:
[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex]
[tex]\displaystyle\frac{-6-(-2)}{-9-(-9)} =\frac{-6+2}{-9+9} =\frac{-4}{0} =[/tex]
Slope = undefined
The second way is to just take a look at the points.
You should notice that the x-coordinates are the same.'
If the x-coordinates are the same, then the slope is
[tex]\Large\boxed{Und.efined}}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
Answer:
undefined
Step-by-step explanation:
the x-coordinates are the same look
jonah bought 3 packs of hotdogs
Answers
Step-by-step explanation:
[tex] \sqrt{a {}^{2} } + 24 - 4 = a [/tex]
Find the ‘exact’ perimeter of each triangle
Answers
Answer:
The missing degree is 60, but the perimeter is 11 cm.
I hope this is correct, if it's incorrect, I'm sorry
Which value of "b" will make the trinomial 4x^2 + bx + 36 a perfect square trinomial? 0 24 O 6 O 12 O 4
Answers
Answer:
48
Step-by-step explanation:
Reverse solve for a perfect Square
(b/2a)^2=36
(b/2(4))^2=36
(b/8)^2=36
b/8=6
b=48
48 makes the trinomial a perfect square trinomial.
3) Find BC С B 51° 27 390 A 15.0 O 17.0 17.5 18.5
Answers
Answer:
your answer is
180-(51+39)=
180 - 90=90°
BC =90°
What is the domain and range written in inequalities?
I believe the domain is all real numbers but I need the range.
Answers
Answer:
Range => y ≤ -2
Domain => All real numbers
Step-by-step explanation:
As it extends horizontally either way, domain can be any possible value.
Whereas it only extends from -2 towards the bottom, therefore the range will be less than or equal to -2.
the original price of a dress is 350.00. it is sale on for 30% off. which of the following is the new price of dress? a.105 b.245 c.380 d.455 plss help
Answers
Answer:
The answer is 245
Step-by-step explanation:
you save 105$ but the total price will come out to 245$ 350 × 30/100
= 350 x 0.3
Answer:
b.245
Step-by-step explanation: [tex]350\times\left(1-30\right)[/tex]
Calculate
[tex]350\times\left(1-0.3\right)[/tex]
Calculate the sum or difference
[tex]350\times0.7[/tex]
Calculate the product or quotient
[tex]245\ YOUR\ ANSWER\ which\ can\ also\ be\ wrote\ out\ like\ 2.45\times{10}^2[/tex]
I hope this helps you
:)
Please help me I don't understand how to do it
Answers
Step-by-step explanation:
first, get a piece of tracing paper. then, place it on the grid and copy the shape and the point of rotation. then, place your pen on the point of rotation and rotate the paper 180°. then copy the shape to its new position on the grid. then move the shape 4 units left by counting 4 squares on each vertex and moving it. lastly, find the coordinates of point
Quadrilateral ABCD is inscribed in this circle,
What is the measure of
Enter your answer in the box.
Answers
Martin has a combination of 33 quarters and dimes worth a total of $6. which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, martin has? q d = 6 25q 10d = 33 q d = 6 0.25q 0.1d = 33 q d = 33 25q 10d = 6 q d = 33 0.25q 0.1d = 6
Answers
The linear equations which can be used to find the number of quarters, q, and the number of dimes, d will be [tex]q+d=33[/tex] & [tex]0.25q+0.1d=6[/tex]
What will be the Linear equation for the given data?It is given that
Martin has a combination of 33 quarters and dimes worth a total of $6.
Here
q = number of quarters
d = number of dimes
The linear equation can be represented as
[tex]0.1\ dollars =1 \ dime[/tex]
[tex]0.25\ dollars = \ 1 \ quarters[/tex]
now the equation will be
[tex]0.25q+0.1d=6[/tex]
The quarters and dimes in total 33. Therefore,
[tex]q+d=33[/tex]
Therefore, the combined equation will be as follows:
[tex]q+d=33[/tex]
[tex]0.25q+0.1d=6[/tex]
Thus linear equations will be [tex]q+d=33[/tex] & [tex]0.25q+0.1d=6[/tex]
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Determine if the sequence below is arithmetic or geometric and determine the common difference ratio in simplest form. 11,7,3
Answers
d = -4
A bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The tire pressure is currently 1,060 kilopascals. What will it be in 4 minutes?
If necessary, round your answer to the nearest tenth.
Answers
Answer:
4x10=40
It will lose 40% pressure after four minutes
It will lose 40% pressure after four minutes
What is exponential growth or decay function?Consider the function:
[tex]y = a(1\pm r)^m[/tex]
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
We have been given that a bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The tire pressure is currently 1,060 kilo-pascals. We are asked to find the tire pressure in 4 minutes.
We will use exponential decay formula to solve our given problem.
[tex]y = a(1\pm r)^m[/tex]
Let us convert 10% into decimal.
0.01
Initial value is 1,060 . Upon substituting our given values in above formula, we will get:
y = 1,060 (1 - 0.01)^4
Therefore, the tire pressure will be approximately 40% kilo-pascals in 4 minutes.
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A basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 30t – 16t2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker’s outstretched hands t seconds after he leaps is modeled by the equation h = 9 25t – 16t2. If the ball was on a path to reach the net 1. 7 seconds after the shooter launches it, does the leaping player block the shot? yes, exactly 0. 6 seconds after the shot is launched yes, between 0. 64 seconds and 0. 65 seconds after the shot is launched yes, between 0. 84 seconds and 0. 85 seconds after the shot is launched no, shot not blocked.
Answers
The shot was blocked between 0.84 and 0.85 seconds after the shot is launched.
what will be the time in which the blocker will block the ball?The given equation for ball height
[tex]=6+30t-16t^{2}[/tex]
The equation for the blocker's height will be
[tex]=9+25t-16t^{2}[/tex]
But, the shot is made before two-tenths of a second or 0.2 seconds therefore modified equation for ball height is
[tex]=6+30(t-0.2)-16(t-0.2)^{2}[/tex]
Now for the shot to be blocked, the height of the shot-blocker must be greater than the height of the ball which is shot before 0.2 seconds :
[tex]9+25t-16t^{2} \geq 6+30(t-0.2)-16(t-0.2)^{2}[/tex]
[tex]9+25t-16t^{2} \geq6+30t-6-16(t^{2} -0.4t+0.04)[/tex]
[tex]9+25t-16t^{2} \geq30t-16t^{2} -6.4t+0.64[/tex]
[tex]9+25t\geq36.4t-0.64[/tex]
[tex]9.64\geq11.4t[/tex]
[tex]t \leq \dfrac{9.64}{11.4}=0.846[/tex]
Thus the shot was blocked between 0.84 and 0.85 seconds after the shot is launched.
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Answer:
C
shot was blocked between 0.84 and 0.85 seconds after the shot is launched.
Step-by-step explanation:
On edge
X + 2 = 5, what is the value of x?
Answers
Answer:
X=3
Step-by-step explanation:
take 2 to right side 2 becomes negative subtract 5-2To get 3Answer:
answer is x = 3
Step-by-step explanation:
x + 2 = 5 , x = 5 - 2
x = 3
what is the mode of the following data: 52 bowls of spaghetti, 37 bowls of cereal, 14 sandwhiches, and 17 personal pizzas
Answers
The mode of the given data is equal to bowls of spaghetti.
Given the following data:
Bowls of spaghetti = 57.Bowls of cereal = 37.Quantity of sandwiches = 14.Personal pizzas = 17.What is mode?In Mathematics, a mode can be defined as a statistical terminology that is used to denote the value that appears most often or repeatedly occurring in a given data set.
This ultimately implies that, a mode represents the value (number) with the highest frequency. In this exercise, the bowls of spaghetti represents the mode of the given data.
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PLEASE HELP WHOEVER HELPS WILL GET A COOKIE
Answers
A: The plane is going 525 miles per hour.
B: In 13 hours the plane will travel 6,825 miles.
Answer:
(a) [tex]\sf 450 \ miles \ per \ hour[/tex]
(b) 675 miles in [tex]\sf 1\frac{1}{2} \ hours[/tex]
explanation:
(a)
given time: [tex]\sf 4\frac{2}{3}[/tex]distance: 2,100unit rate:
[tex]\sf \dfrac{total \ distance}{total \ time}[/tex]
[tex]\sf \dfrac{2100}{\sf 4\frac{2}{3}}[/tex]
[tex]\sf \dfrac{2100}{\sf \dfrac{14}{3}}[/tex]
[tex]\sf 450 \ miles \ per \ hour[/tex]
(b)
distance: speed * time
distance: [tex]\sf 450 \\[/tex] * [tex]\sf 1\frac{1}{2}[/tex]
distance: 675 miles
Find an expression which represents the sum of (6x-4)(6x−4) and (-2x+5)(−2x+5) in simplest terms
Answers
Answer:
40x^2-68x+41
Step-by-step explanation:
Multiply both expressions
(-2x+5)^2= 4x^2-20x+25
(6x-4)^2=36x^2-48x+16
Then add
Use multiplication table if you have difficulty with multiplying
Ex
-2x 5
-2x 4x^2 -10x
5 -10x 25
Then add them all to get the full expression
Who are two of the people credited with inventing calculus?.
Answers
Answer: Isaac Newton and Gottfried Leibniz.
Explanation: Today it is generally believed that calculus was discovered independently in the late 17th century by two great mathematiciansIsaac Newton and Gottfried Leibniz
Triangle has vertices D(1, 2), E(0, 4), and
F(1, –1). Find the coordinates of the triangle
after a dilation with a scale factor of 3.
Answers
Answer: D'(3, 6), E'(0, 12), F'(3, -3)
Step-by-step explanation:
Simplify each algebraic expression by combining like terms.
2x + 5y + 6x - 5x + 3y
x2 + 2x + 3x2 + 4x - 2x2 + x
Answers
Answer:
2x^2+7x and 8y+3x
Step-by-step explanation:
Okay for the first one when you combine like terms you are adding the ones with the same terms so the ones that have X in it you add, the one with Y you add so it would be
2x+6x=8x ----> 8x-5x=3x
5y+3y=8y so
8y+3x
same thing for the other one so the answer is:
2x^2+7x
4.55 is what percent of 6.5? Enter your answer in the box.
Answers
Answer: 70%
Step-by-step explanation:
Answer:
70%
Step-by-step explanation: