The function has the vertex value of (-1, -1)
How to calculate the vertex of the function?From the question, the definition of the functuion is given as
y = 2x² + 4x + 1
Start by differentiating the function
This is done as follows
y' = 4x + 4
Next, we set the differentiated equation to 0
So, we have the following equation
4x + 4 = 0
This gives
4x = -4
Divide by 4
x = -1
Next, we substitute x = -1 in the given equation y = 2x² + 4x + 1
So, we have the following equation
y = 2(-1)² + 4(-1) + 1
Evaluate
y = -1
Recall that
x = -1 and y = -1
So, we have
(-1, -1)
Hence, the vertex of the function is (-1, -1)
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The vertex of the given function y = 2x² + 4x+1 is (-1, -1) which is the correct answer would be an option (B).
The function is below given by,
y = 2x² + 4x + 1
Differentiate with respect to x to get the derivative of the above function,
y' = dy/dx = d/dx (2x² + 4x + 1)
y' = 4x + 4
Equating the derivative of the function to zero
y' = 0
4x + 4 = 0
4x = -4
Divide by 4 into both sides of the equation,
x = -1
Substitute x = -1 in the given function y = 2x² + 4x + 1
y = 2(-1)² + 4(-1) + 1
y = 2(1) - 4 + 1
y = -1
Therefore, the vertex of the given function is (-1, -1).
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1) Apples cost $16 for an 8 pound bag at the local price
club, but the club has a membership fee of $50.
Write and solve an equation to determine how many
pounds (p) of apples you can buy for $58.
Answer:
4 pounds with a membership
29 pounds without
i just added both because i didnt know if you meant 58 extra dollars after bbuying membership or not
Step-by-step explanation:
58 -50(membership fee)=8
16 divide by 8=2
16$=8 pounds
8$=4 pounds
---------------------------------------
without membership you could buy 29 pounds of apples
58 divide by 16=3.625
3.625 x 8=29
HELP!!! PLEASE!! I HAVE 10 MINUTES TO ANSWER THIS! I WILL GIVE 40 POINTS
Answer:
option number 3
Step-by-step explanation:
day 3 = 1000 sales
day 6 = 2000 sales
day 9 = 3000 sales
Which ordered pair would form a proportional relationship with the point graphed below?
-60-40-20 20 40 60 80 ×
x
*
O (-10, 30)
O (30, -15)
O (-30, 10)
10.0
40
30
20
10
20
30-
40-
(60,-20)
Answer: (-30, 10)
Step-by-step explanation:
A proportional relationship is of the form y=kx for some constant k.
From the point (60, -20), we know that k = -1/3.
So, we are looking for a point where the y coordinate is -1/3 of the x coordinate. This is satisfied by option 3.
If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}
When Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10) Q ∩ P = { 1, 9}
How to calculate the value?Set theory simply means the branch of mathematical logic that deals with sets, that can be described as collections of objects.
It should be noted that perfect squares are the numbers that can be divided to give same number.
Q = {all perfect squares less than 30}. This will be 1, 4, 9, 16, 25
P ={ all odd numbers from 1 to 10}. This will be 1, 3, 5, 7, and 9.
In this case, the common numbers to set of P and Q are 1 and 9.
Therefore, the numbers are 1 and 9 since they're common to both sides.
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If Q = {all perfect squares less than 30} and p={ all odd numbers from 1 to 10}. Find Q ∩ P.
a newsletter publisher believes that less than 68h% of their readers own a rolls royce. for marketing purposes, a potential advertiser wants to confirm this claim. after performing a test at the 0.050.05 level of significance, the advertiser failed to reject the null hypothesis. what is the conclusion regarding the publisher's claim?
A potential advertiser for marketing purpose, after performing a test at 0.05 level of significance fails to reject the null hypothesis leads to the conclusion that there is not sufficient evidence at the 0.05 level of significance to say that the percentage is less than 68%.
Hypothesis testing refers to a statistical inference approach used to determine if the available data sufficiently support a particular hypothesis. Hypothesis testing enable researchers to make probabilistic statements about population parameters. In the given case, the null and alternative hypothesis regarding the publisher’s claim state:
The null hypothesis stated that the 68% or more of the readers own a Rolls Royce. H0: p ≥ 0.68
The alternate hypothesis states that less than 68% of the readers own a Rolls Royce. H1: p < 0.68
As the advertiser failed to reject the null hypothesis, it was accepted and thus, 68% or more of the readers own a Rolls Royce. It is concluded that there is not sufficient evidence at the 0.05 level of significance to say that the percentage is less than 68%.
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Help Please!!
Unit 4 lesson 11 geometry Parallel and Perpendicular Lines Unit Test
I have been doing well in this test till this question... any help is appreciated!!
The values of x = 14 and y = 12
In the diagram given, there are two parallel lines and three angles formed by cutting the parallel lines.
So here, angles (2x+7)° and (3x-7)° are corresponding angles.
That is they occupy relatively same position, that is both are above each parallel line.
So they are equal angles.
i.e., 2x+7 = 3x-7
⇒ 3x-2x = 7 +7
⇒ x = 14
Now the angles 2x+7° and 12y+1° are supplementary angles.
Supplementary angles are formed on a straight line between a line cutting the straight line.
That is their sum = 180°
i.e., 2x+7° + 12y+1° = 180
⇒ 2 x 14 + 7 + 12y +1 = 180
⇒ 28 + 8 +12y = 180
⇒ 36 +12y = 180
⇒ 12y = 180 -36
⇒ 12y = 144
⇒ y = 12
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SOMEONE GO AND ANSWER MY QUESTIONS I ASKED 9 QUESTIONS AND THER SUPER EASY AND ITS MATH IM DOING MY HOMEWORK AND I NEED HELP MY MATH QUESTIONS ARE TOO EASY I PROMISE U ALL 6 QUESTIONS ARE SO SO SO SO EASY IF U ANSWER THEM ILLL MARK U AS BRAINLIST AND RATE U 5 STARTS ALL AND GIVE U A THANK YOU PLS IF YOU ANSWER 100 6 QUESTIONS BUT IF U DONT I WONT MARK U AS BRAINLIST PLS AND ALL QUESTIONS ARE EASY I GO TO K12 TRUST ME??!?!?!?!??!?!?!?!?!???!??!?!??!?!??
CMON I KNOW U WANT ME TO MAKR U BRAINLIST AND RATE U 5 STARTS AND GIVE U A THANK YOU?!? BUT U GOTTA ANSWER ALL SIX QUESTIONS I ASKED GO TO MY PROFILE AND SEE FOR URSELF
Answer:
I answered one of them so yeah
Write an equation in point-slope form of the line that passes through the given point and with the given slope m. A. (1, -8) m= -9
The point-slope form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing with point (1, -8) and m= -9, we get:
-8 = (-9)(1) + b
-8 = -9 + b
-8 + 9 = b
1 = b
Then, the equation is:
y = -9x + 1
1 What is the domain of the linear function
graphed below?
Answer:
Step-by-step explanation:
The domain of a function is the set of all possible inputs for the function - so all possible x values in some f(x) functions.
From the graph, you can see that the values on the x-axis below the graph are in the range -4 (exclusive) and 2 (inclusive) that's why the range is
-4 < x <=2, or simply (-4,2>
In Montyville, the value of homes has experienced an annual change of -2 percent. If the rate continues, what will be
the change over 10 years?
Answer:
I believe the answer would be -20 percent
A store sells 5 T-shirts for $48.60. What is the unit cost per T-shirt? A. $9.72 B. $8.10 C. $43.60 D. $0.10
Answer:$9.72
Step-by-step explanation: 48.60 DIVIDED BY 5 EQUALS 9.72
GIVE ME BRAINLEST PLSS
Homework #5
Question 9 of 12
AMORTIZATION Car loans are often spread into multiple regular payments over time. This process is called amortization. Each payment
reduces the remaining principal, and the interest accrued for the next payment is based on the reduced principal. The monthly payment is
fixed; so, with each subsequent payment, an increasing portion goes toward principal, and a decreasing portion goes toward interest. Lori
takes out a car loan of $15,000 for 3 years, with a 3% interest rate. When the loan is amortized into monthly payments, the total interest paid by
the end of the loan term will be $704.
Calculate the simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years.
$15
The simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years is $ 1,350.
It is given in the question that:-
Principal = $15,000
Time period = 3 years
Interest rate = 3 %
Total interest paid by Lori, if the loan was amortized = $ 704.
We have to find the simple interest Lori would pay if the loan was not amortized and the entire loan was paid at the end of 3 years.
We know that,
Simple interest = (Principal*Rate*Time)/100
Hence,
Simple interest = (15000*3*3)/100 = $ 1350.
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Ethan and Adrian are reading the same book. At the beginning of the month, Ethan was on page 18 and Adrian was on page 45. Ethan will read 12 pages per day and Adrian will read 9 pages per day. Let E represent the page of the book that Ethan is on at the end of t days into the month, and let A represent the page of the book that Adrian is on at the end of t days into the month. Write an equation for each situation, in terms of t, and determine whether Ethan or Adrian is farther along in the book after 4 days.
The equations are e = 18+12t and a = 45+9t
Adrian will be father along in the book after 4 days. She will be 15 pages ahead of Ethan
Ethan's page number at the beginning of the month = 18
Adrian's page number at the beginning of the month = 45
Pages read by Ethan each day = 12 pages
Pages read by Adrian each day = 9 pages
Let e represent the page of the book that Ethan is on at the end of t days into the month. Let a represent the page of the book that Adrian is on at the end of t days into the month.
Formulating the equation we get the following:
e = 18 + 12t
a = 45 + 9t
Finding the page number of both Ethan and Adrian after 4 days by substituting the values in the equations we get:
e = 18+12(4)
e = 66
a = 45 + 9(4)
a = 81
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Find the value of c that makes t^2 - 22t+ c a perfect square trinomial.
Write the expression as the square of a binomial.
The expression is
The expression is a perfect square trinomial if and only if c = 121.
How to get the value of c?
A perfect square trinomial is written as:
(a + b)^2 = a^2 + b^2 + 2ab
In this case, we have:
t^2 - 22t + c
We can rewrite this as:
t^2 - 2*11*t + c
Then we have:
a = t
b = -11
And we will have that:
c = b^2 = (-11)^2 = 121
Then we have:
t^2 - 2*11*t + 121
Which is a perfect square trinomial:
(t - 11)^2 = t^2 - 22t + 121
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MATH PLEASE DO THIS FOR BRAINLYIST
Answer: The percent of change in the perimeter is 100 percent and
the percent of change in the area is 300 percent .
Step-by-step explanation:
Rectangle is the closed shaped polygon with 4 sides. Opposite sides of the rectangle are equal. when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.
An angle measures 58° more than the measure of its supplementary angle. What is the measure of each angle?
Answer: 61° and 119°
Step-by-step explanation:
So for the smaller angle you have to do:
1. 180-58=122
2. 122/2=61
Then you just add 61+58=119 for the larger angle
You need a 30% alcohol solution. On hand, you have a 75 mL of a 10% alcohol mixture. You also have 55% alcohol mixture. How much of the 55% mixture will you need to add to obtain the desired solution?
60 ml of the 55% solution is required to get the desired solution.
A unique kind of homogenous mixture made up of two or more substances is called a solution.
A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture. Polarity effects of chemicals are engaged in the mixing of a solution at a scale that leads to interactions that are very specific to solvation. When the solvent makes up a significant large portion of the combination, as is frequently the case, the solution typically or normally has the condition of the solvent. The concentration of a solution, which measures how much solute is present in a given volume of solution or solvent, is one crucial parameter.Let x ml of 55% solution is taken.
therefore alcohol = 0.55x ml
water = 0.45x ml
Now it is added to 10% 75 ml solution.
Alcohol = 10% of 75 = 7.5ml
Water = 67.5 ml
New mixture = 75 + x
Alcohol = 30% of (75+x) = 22.5 + 0.3x
Therefore 22.5 + 0.3x = 7.5 + 0.55x
or, x = 60 ml
Therefore 60 ml of the 55% solution is required.
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find the two positive integers whose product is 24,999,999 and whose positive difference is as small as positive. Explain how you discovered them.
Two positive integers whose product is 24,999,999 are 4999 and 5001
Given
The product of two numbers should be 24,999,999.
The positive difference should be small
There are many ways to obtain those two numbers but an easiest way would be taking the square root of the given number and making decision by trial and error.
This may take few iterations but this is the optimal way to solve.
Square root of 24,999,999 is 4999.99
Hence try multiplying a number less than and a number equal to 4999.99.
Eventually we will reach to a conclusion 4999 x 5001 whose product is 24,999,999.
The difference of the numbers is 5001 - 4999 = 2
Hence the positive difference is small.
Hence the two numbers are 4999, 5001.
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My question is below but I only have 1/2 does anyone know how to get the last mark for 100%
Show that 155 can be expressed as the sum of a power of 2 and a cube number.
128 = 2^7 is a power of 2
27 = 3^3 is a perfect cube
=======================================================
Explanation:
This is something you'd find through trial and error.
The powers of 2 are
2, 4, 8, 16, 32, 64, 128, 256, ...
We double each value to get the next one.
The largest power of 2 that is smaller than 155 is 128
155-128 = 27 which is a cube number since x^3 = 3^3 = 27 as you've shown in the screenshot.
If the result of 155-128 wasn't a perfect cube number, then you'd have to try the next largest power of 2 (which is 64) and work your way down the list.
----------------------
Or you could work with the list of perfect cubes
1, 8, 27, 64, 125, 216, ...
Each value is of the form x^3 where x is a whole number.
Let's pick the largest perfect cube that is under 155, and subtract it
155-125 = 30 which isn't a power of 2 (refer to the list above)
Then try 155-64 = 91 which isn't a power of 2 either
Keep moving down the list until reaching 155-27 = 128 which is a power of 2 since 2^7 = 128
Help me with this i need to submit this assignment tyy
i think its ez but yk.. im lazy
Answer:
3x3x3x3=81
.......................
Consider the line y = - - X+4.4.***4.Find the equation of the line that is perpendicular to this line and passes through the point (-9, 6).Find the equation of the line that is parallel to this line and passes through the point (-9, 6).Note that the ALEKS graphing calculator may be helpful in checking your answer.Equation of perpendicular line: 0-Equation of parallel line:X0P
ANSWER:
[tex]\begin{gathered} \text{perpendicular} \\ y=\frac{4}{3}x+18 \\ \text{parallel} \\ y=-\frac{3}{4}x-\frac{3}{4} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation of a line in its slope and y-intercept form is the following:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]Now, when two equations are perpendicular, the slope of both are opposite, that is, the product between them is equal to -1, like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ -\frac{3}{4}\cdot m_2=-1 \\ m_2=\frac{4}{3} \end{gathered}[/tex]We replace the values of the point (-9, 6) and the slope to calculate the value of the y -intercept:
[tex]\begin{gathered} 6=-9\cdot\frac{4}{3}+b \\ b=12+6 \\ b=18 \end{gathered}[/tex]Therefore, the perpendicular equation that also passes through the point (-9,6) is:
[tex]y=\frac{4}{3}x+18[/tex]Now, when two lines are parallel, the slope is the same, therefore we calculate directly that it passes through the point (-9, 6)
[tex]\begin{gathered} 6=-9\cdot-\frac{3}{4}+b_{} \\ b=6+9\cdot-\frac{3}{4} \\ b=-\frac{3}{4} \end{gathered}[/tex]therefore, the equation of the line that is parallel to this line and passes through the point (-9, 6) is:
[tex]y=-\frac{3}{4}x-\frac{3}{4}[/tex]Describe how the graph of y= x2 can be transformed to the graph of the given equation. (2 points) y = (x-10)2+8 Shift the graph of y = x2 left 10 units and then down 8 units. Shift the graph of y = x2 up 10 units and then right 8 units. Shift the graph of y = x2 left 10 units and then up 8 units. Shift the graph of y = x2 right 10 units and then up 8 units.
Move the y = x2 graph 10 units to the right, then 8 units up.
There are y= x²——————> y = (x-10)²+8
The fact that
A point (x,y) in f(x) shifts up by d as a result of f(x)+d, a
and
f(x-e) ----> a point (x, y) in f(x) becomes a——————-> (x+e, y)——> shift right by in this issue
d=8
e=10
Therefore,
Shift the y = x2 graph.
8 up, 10 to the right
The law is
(x,y)———-> (x+10,y+8)
The vertex in the equation y=x2--------- (0,0)
The vertex in the equation y = (x-10)2+8 (10,8)
so
(10,8)------> (0,0)----------> (x+10,y+8)———> (10,8)------> (0+10,0+8)
As a result, shift the y = x2 graph 8 units up and then 10 units to the right.
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Find x of the triangle
Answer: The answer is 20°
Step-by-step explanation:
I think it’s 20° but I’m only in the 6th grade and I got my 180 ruler for this into the screen
Write an expression for the perimeter in terms of x. 2x and x+3
The perimeter of rectangle with the given dimensions is 6x+6.
Given that the dimensions of rectangle are 2x and x+3.
We need to find the perimeter of the given rectangle.
What is the perimeter of a rectangle?The overall length of the outline determines a shape's perimeter in two dimensions. We add the lengths of all four corners of a rectangle to find its perimeter. Rectangle perimeter is calculated using the formula perimeter of a rectangle = 2(l + w), where l is the rectangle's length and w is its width.
We know that, the perimeter of rectangle = 2(Length + Width)
Now, perimeter
=2(2x+x+3)
=2(3x+3) (Add like terms)
Using distributive property multiply 2 to 3x and 2 to 3
We get 6x+6
Therefore, the perimeter of rectangle with the given dimensions is 6x+6.
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10. Dan paid 20% down on 8 new car that cost
$16,584.00. He will pay the balance in
24 equal monthly installments.
He will pay S Drop-cown each month.
A. 1,105.60
B. 667.18
C. 552.80
D. 132.20
Answer:
552.8
Step-by-step explanation:
16584/8=2073
2073*0.8=1658.4
1658.4*8=13267.2
13267.2/24=552.8
What is the value of −5 + (−14) + 53?
Answer:
34
Step-by-step explanation:
The value would be 34
Arrange nine dots in such a way that
you have 8 rows with 3 dots in
each row.
Answer:
...
...
...
...
...
...
...
...
Using completing the square to solve
x^2-5x+3=0. Round to the nearest tenth as needed.
Simplify the following expression.
4√72
O A.
6√/24
OB.
144√6
O c.
24√6
O D. 24√2
Answer:
A = 34
B = 29.4
C = 58.8
D = 34
can you help with these two questions please