Answers
Answer:
no, the vertex of Function A is 6 units lower
Step-by-step explanation:
The vertex of Function A can be found several ways:
putting the equation in vertex formevaluating the function on the axis of symmetrygraphing the function__
Vertex FormTo put the equation in vertex form, we can consider separately the variabel terms and the constant. Once we have the variable terms separated, we can "complete the square" and then simplify the result to vertex form. The vertex form of a quadratic is ...
y = a(x -h)² +k . . . . for vertical scale factor 'a' and vertex (h, k)
We have ...
y = 2x² +12x +10
y = 2(x² +6x) +10
We complete the square by adding the square of half the x-coefficient inside parentheses. We subtract the same quantity outside parentheses, so we don't change the equation any.
y = 2(x² +6x +9) +10 -2(9)
y = 2(x +3)² -8 . . . . . . simplify to vertex form
The vertex of Function A is (-3, -8), which is (-2 -(-8)) = 6 units lower than the vertex of Function B in the graph. Bob is incorrect.
__
Axis of SymmetryThe axis of symmetry of quadratic expression ax² +bx +c is x=-b/(2a). For the given Function A, the axis of symmetry is ...
x = -12/(2(2)) = -3
The height of the vertex is the y-value for that x-value:
y = 2(-3)² +12(-3) +10 = 18 -36 +10 = -8
This is lower than the vertex of the graphed function, which is at y=-2. Bob is incorrect.
__
GraphingThe graph of Function A is the solid red curve in the attached. The graph of Function B is added as the dashed blue curve for reference. The graph clearly shows the vertex of Function A is lower than that of Function B. Bob is incorrect.
_____
Additional comment
Modern graphing calculators make the graphing option the quickest and easiest way to find the vertex of the function. The only "work" is to type the equation into the calculator.
Related Questions
Tina's teacher wrote 7/8 on the whiteboard. What percentage is equivalent to the fraction that Tina's teacher wrote on the whiteboard?
Answers
I think it's like 0.88, but I believe that's it rounded up.
Find the value of x.
(3x+9)
(4x + 3)
Answers
Answer:
For two different equations:
(3x+9)
x = -3
(4x+3)
x = -3/4
Finding x using both equations:
plug x = -3 into the other equation
4(-3) + 3 = -9
x = -9
plug x = -3/4 into the other equation
3(-4/3) + 9 = 27/4
x = 27/4
Set the equations equal to each other:
3x+9=4x+3
3x-4x = 3-9
-x = -3
x=3
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
A grocery store recently sold 20 cartons of yogurt, of which 5 were cherry. Based on past data, how many of the next 16 cartons of yogurt sold should you expect to be cherry?
Answers
Answer: 4
Step-by-step explanation:
If the half-life of that substance is 22 days, and only 1/4 of it remains, how many days have elapsed?
A- 11 days
B-22 days
C-44 days
D-88 days
Answers
Answer:
11
Step-by-step explanation:
if half of it is 22, then a whole life is 44 days. 1/4 of 44 days is 11 days so its A
Answer:
the answer is A (11 days)
Step-by-step explanation:
Hope this helps you!
This should be easy for me but I just can't get it right.
Please Help Me! ASAP! :) Thank you hope your day was alright.
Will try to mark Brainliest!
Answers
Answer:
1. 32
2. 47
3. See explanation for number 3 below
Step-by-step explanation:
All you have to do is simply add 17 to however old Titus is. So if he's 15 years old, you just simply have to do 15+17, which is 32. For number 3, I'm assuming that they just want an explanation for how you do this process, in which case, this explanation is the answer to number 3. If that's not what they're looking for in number 3, then I'm sorry. But I'm pretty sure that's what they want there.
It cost marci 33 cents to mail a postcard and 49 cents to mail a letter. she sent either a postcard or a letter to each of 28 people and spent $13.08. let x represent the number of postcards she wrote and write an algebraic expression for each item in parts a through c.
Answers
Answer:
24 Letters and 4 Postcards
Step-by-step explanation:
We have to set up a system of equations, since we have two unknown variables. Lets say postcards is the variable "x" and letters is the variable "y".
Our first equation will be the money spent: 0.33x + 0.49y = 13.08, this comes from knowing that it costs 0.33 dollars to mail a postcard and 0.49 dollars to send a letter.
The second equation is the total sent: x + y =28.
Now we need to solve for a single variable, let's do y (or letters). If we subtract y from both sides we get: x = 28 - y.
We can plug that into our first equatino to get: 0.33(28 - y) + 0.49y = 13.08.
If we multiply things out we get: 9.24 - 0.33y + 0.49y = 13.08, and now we have like terms. 9.24 + 0.16y = 13.08.
Subtract 9.24 from both sides to get: 0.16y = 3.84
Divide both sides by 0.16 to get: y = 24.
Now we can plug this into x + y = 28 to see that x= 4.
You could make sure this is correct by solving for x instead of y and do the same process.
Hope this helps.
The following stem-and-leaf plot represents the scores earned by Mr. Wood's class on their most recent science test.
How many of the students scored less than an 85?
10
12
11
9
Answers
Answer:
11
Step-by-step explanation:
If you count the total values
it equals 11
Here is an expression 3/5 divided by 1/4 Which situation matches this expression?
Which situation matches this expression?
A: An athlete runs 3/5 kilometers in 4 minutes. At that rate, how many kilometers does the athlete run in 1 minute?
B: A teacher fills an empty white pitcher with 3/5 gallons of water and an empty blue pitcher with 1/4 gallon of water. How many more gallons of water are now in the white pitcher than in the blue pitcher?
C: Mr. Smith has 3/5 pounds of beans. He uses 1/4 pound of beans each week. At the rate, for how many weeks will beans last?
D: A worker cuts pieces of string that are each 3/5 yards in length. How many pieces of string can the worker cut from a piece of string that is 1/4 yard in length?
Answers
Answer:
C
Step-by-step explanation:
To find A you have to divide 3/5 by 4 so that would not work.
To find B you have to subtract 1/4 from 3/5 and that doesn't match the problem.
To find C you do divide 3/5 by 1/4 which matches the problem.
And lastly for D you would divide 1/4 by 3/5 which is the opposite of what the question is asking for.
I know the measure of angle m is 100 degrees. I did this multiple times and J and L are not 80 degrees so what are the measures of angles L and J?
Answers
Answer:
[tex]m\angle L = 100^{\circ}[/tex].
[tex]m\angle J = 80^{\circ}[/tex].
[tex]m\angle M = 100^{\circ}[/tex].
Step-by-step explanation:
Since segment [tex]JM[/tex] is parallel to segment [tex]KL[/tex], quadrilateral [tex]JKLM[/tex] is a trapezoid.
Segment [tex]JK[/tex] and segment [tex]LM[/tex] (the two legs of this trapezoid) are equal in length. Hence, trapezoid [tex]JKLM[/tex] would be an isoscele trapezoid. By symmetry, [tex]m\angle L = m \angle K = 100^{\circ}[/tex].
Line [tex]JK[/tex] traverses line [tex]JM[/tex] and line [tex]KL[/tex]. [tex]\angle J[/tex] and [tex]\angle K[/tex] are a pair of consecutive interior angles as they are both between [tex]JM\![/tex] and [tex]KL\![/tex] and are on the same side of the traversal, [tex]JK\![/tex].
Since line [tex]JM[/tex] is parallel to line [tex]KL[/tex], any pair of consecutive interior angles between these two lines would add up to [tex]180^{\circ}[/tex] (supplementary angles.) Thus, [tex]\angle J[/tex] and [tex]\angle K[/tex] are supplementary angles; [tex]m\angle J + m\angle K = 180^{\circ}[/tex].
Since [tex]m\angle K = 100^{\circ}[/tex], [tex]m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}[/tex].
Find the measure of the missing angle
Answers
Answer:
g=118 degrees h=62 degrees
Step-by-step explanation:
So we can use some angle rules that I forget the name of to solve this.
Let's look at angle g first. We know that the opposite angle is 118 degrees. So that also means that g is going to be 118 degrees.
Since g is 118 degrees we can find h. The angle of a line is 180 degrees. This means that we can do 180-118 to find h. h=62 degrees.
We can do the same thing for k and m. Try doing what I did for g and h for those two. Comment if you need help.
Max made a journey of 700km partly by train and partly by bus.He started his journey at 8.00am. by train which travelled at 50km/hr. After alighting from the train, he took a lunch break of 30 minutes. He then continued his journey by bus which travelled at 75km/hr.The whole journey took 11.75hours. Determine the distance travelled by bus.
Answers
I really don't know I'm not big on school subjects
what is 6.7 x 192 ÷ 0.051 ?
Answers
Answer: Reduce the expression, if possible, by cancelling the common factors
25223.52941176
Hoped this helped :)
Please help ASAP!
The domain of this function is {-12, -6, 3, 15}.
y= 2/3x + 7
Complete the table based on the given domain.
Answers
16
21
Jade works as a decorator.
She is paid £22.80 per hour for the first 35 hours she works each week.
She is paid 15% more per hour for each extra hour she works.
One week, Jade was paid £981.54
In total, how many hours did she work that week?
You must show your working.
Answers
Let's assume that all hours she worked were the first 35 hours of the week.
She would've made £22.80 x 35 = £798
So, she would've made 981.54 - 798 = 183.54 less than the actual amount
She is paid 15% more per hour after the first 35 hours -> She will get £26.22 per hour.
So, she work for 183.54 : 26.22 = 7(hours) after the first 35 hours
So in total, she worked for 35 + 7 = 42(hours).
Answer:
42 hours
We know she works at least 35 hours, so 35x22.80=798. This is her base pay without any extra hours.
981.54-798 =183.54. This is the amount she earnt for working extra hours. if we divide this by the rate she earns for extra hours (22.80x1.15=26.22), 184.54/26.22=7, we know she worked an additional 7 hours.
and 35 plus 7 = 42 :)
(Pls Help ASAP) (If you don't know don't Answer)
Answers
Answer:
Step-by-step explanation:
4x + y = 8
x + 3y = 8
[tex]Here, \dfrac{a_{1}}{a_{2}}=\dfrac{4}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{1}{3}\\\\\\\dfrac{a_{1}}{a_{2}} \neq \dfrac{b_{1}}{b_{2}}[/tex]
So, this system of equations is consistent and independent.
-4x + 6y = -2
2x - 3y = 1
[tex]\dfrac{a_{1}}{a_2}}=\dfrac{-4}{2}=\dfrac{-2}{1}\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{6}{-3}=\dfrac{-2}{1}\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{-2}{1}\\\\\\\dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}}=\dfrac{c_{1}}{c_{2}}[/tex]
So, the system of linear equations are consistent and dependent.
5x -2y = 4
5x - 2y = 6
[tex]\dfrac{a_{1}}{a_{2}}=\dfrac{5}{5}=1\\\\\\\dfrac{b_{1}}{b_{2}}=\dfrac{-2}{-2}=1\\\\\\\dfrac{c_{1}}{c_{2}}=\dfrac{4}{6}=\dfrac{2}{3}\\\\\\ \dfrac{a_{1}}{a_{2}}=\dfrac{b_{1}}{b_{2}} \neq \dfrac{c_{1}}{c_{2}}[/tex]
This system of equations is inconsistent.
Given that the measure of 2x is 45°, and the measure of zy is 499, find the
measure of z
Answers
Answer:
86 degrees
Step-by-step explanation:
The angles of a triangle all add up to 180.
x is 45 degrees
y is 49 degrees
49 + 45 = 94
180 - 94 = 86
The last angle of the triangle is 86 degrees. Since z is on the opposite side of it, it is equal to 86
Write1 3/4 as a decimal and as a percent
Answers
Answer:
the decimal is 1.75 and The percentage is 175%
Step-by-step explanation:
Can someone please help me out with this question?
Answers
Use the slope formula and pick any two points to find the slope.
m= Y2- Y1/x2-x1
I picked the points (1,8) (3,14).
14-8/3-1= 6/2= 3
Hope this helps .
anyone know the answer to this
Answers
Answer: The bottom three: [tex]\frac{48}{-17}[/tex], [tex]\frac{-48}{17}[/tex], and -2 [tex]\frac{14}{17}[/tex]
Step-by-step explanation:
The first option is not because the numerator and denominator are flipped.
The second option is not because this one is positive while the one given is negative.
The third option is equivalent.
The fourth option is equivalent.
The fifth option is equivalent because - 48 / 17 = -2 [tex]\frac{14}{17}[/tex] when turned into a mixed number.
Answer:
[tex]\frac{48}{-17}, \frac{-48}{17}, -2\frac{14}{17}[/tex] (the last 3 options)
Step-by-step explanation:
As long as the negative is in either the numerator or the denominator (if it is in both then it is positive because the negatives cancel out), the entire fraction will be negative, so both [tex]\frac{48}{-17}[/tex] and [tex]\frac{-48}{17}[/tex] work as answers. The last option is just a simplified version of the fraction.
A lifeguard fills a pool with water at a constant rate. After 1/2 hour, 1/3 of the pool is filled.
At this rate, what fraction of the pool is filled per hour?
A. 1/6 of the pool
B. 1/3 of the pool
C. 1/2 of the pool
D. 2/3 of the pool
Answers
Answer:
D
Step-by-step explanation:
1/2 hour -> 1/3 pool
multiply this by 2
1 hour -> 2/3 pool
so D 2/3 pool
The fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
What is a Constant Rate?A constant rate can be described as a quantity that changes steadlity over time.
The rate that the pool gets filled is given as:
1/2 hr = 1/3 of the water that would be filled in the pool
1 hr would be: 1/3 × 2 = 2/3
Therefore, the fraction of the pool that would be filled per hour at the given rate is: D. 2/3 of the pool.
Learn more about rate on:
https://brainly.com/question/25184007
A rocket is shot off from a launcher. The accompanying table represents the height of
the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a
quadratic regression equation for this set of data, rounding all coefficients to the
nearest hundredth. Using this equation, find the height, to the nearest foot, at a time
of 14.7 seconds.
Time in Seconds (x) Height in Feet (v)
1.1
301
2
518
3.1
756
3.6
833
4.3
956
Copy Valoes for Calculator
Open Statistics Calculator
Regression Equation:
Final Answer:
Submit Answer
Answers
Answer:The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :y = - 15.57x² + 179.32x + 0.20height = yx = time Using the model obtained;The height, to the nearest foot, at a time, x = 6.4 seconds.y = - 15.57x² + 179.32x + 0.20y = - 15.57(6.4^2) + 179.32(6.4) + 0.20y = 510.1008y = 510
Step-by-step explanation:
A soccer stadium had a capacity of 25000 seats, but with the new area built this increased by 20%.
Calculate the number of people in the stadium if on a match only 65% of the seats are occupied.
Answers
Answer:
19,500 people
Step-by-step explanation:
20% of 25,000 is 5,000.
Add 5,000 to 25,000 - this will give you 30,000. That is a 20% increase.
65% of 30,000 is 19,500, thus there are 19,500 people in the stadium.
Is (1, 0) a solution to the equation y= –9x + 1?
Answers
Answer:
No
Step-by-step explanation:
→ Substitute the x value into the equation
-9 × 1 + 1
→ Simplify
-8
→ Compare to given y value
0 ≠ -8
Answer:
no
when you substite the values you don't get the same values
find x , y , sin alpha, tg beta and area of triangle
Answers
Answer:
Step-by-step explanation:
What is the simplified expression of (4-5r+8s)(5r-9)
Answers
Answer:
The simplified expression of (4-5r+8s)(5r-9) is
40r s-25r^2-72s+65r-36
(hope this helped)
The simplified expression of (4-5r+8s)(5r-9) is [tex]65r - 25r^2 + 9r + 40rs - 72s.[/tex]
The simplified expression of (4-5r+8s)(5r-9) step by step.
Understanding how to simplify expressions can be incredibly useful in algebra and will make solving equations much easier. By using the distributive property, we can multiply the terms inside the parentheses and then combine like terms to get the simplified expression.
To simplify the expression (4-5r+8s)(5r-9), we'll use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). This property allows us to multiply each term in the first parentheses by each term in the second parentheses.
1. First, we multiply the term "4" in the first parentheses by each term in the second parentheses:
4 * 5r = 20r
4 * (-9) = -36
2. Next, we move to the second term in the first parentheses, "-5r," and multiply it by each term in the second parentheses:
-5r * 5r = -25r²
-5r * (-9) = 45r
3. Lastly, we move to the third term in the first parentheses, "8s," and multiply it by each term in the second parentheses:
8s * 5r = 40rs
8s * (-9) = -72s
Now, we have all the resulting terms:
20r - 36 - 25r² + 45r + 40rs - 72s.
To simplify further, we combine like terms. Like terms have the same variable(s) raised to the same power:
20r + 45r = 65r
-36 + 45r = 9r
So, the simplified expression is:
65r - 25r² + 9r + 40rs - 72s.
In mathematical terms, we applied the distributive property to multiply each term in the first parentheses by each term in the second parentheses. Then, we combined like terms to obtain the final simplified expression, 65r - 25r² + 9r + 40rs - 72s.
To know more about Algebra here
https://brainly.com/question/29074939
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what is the diameter of a circular field whose area is 616cm^2
Answers
Answer:
28cmStep-by-step explanation:
[tex]d=2\sqrt{\frac{A}{\pi}} =2\sqrt{\frac{616}{\pi} }[/tex]≈[tex]28.00563cm[/tex]
rounding 28.00563 to 28.
So hence, your answer is 28cm
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Answer:
28
Step-by-step explanation:
area of a circle
[tex]\pi{r}^{2} [/tex]
616=3•142×r×r
616/3•142=r^2
196=r^2
r=√196
r=14
d=2r
d=2×14
d=28
Find the critical t-value that corresponds to % confidence. Assume degrees of freedom
Answers
Using a t-distribution, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.
How to find the critical value for a t-distribution confidence interval?It is found with the help of a calculator, having two inputs:
The confidence level.The number of degrees of freedom, which is one less than the sample size.Hence, using a calculator, with 20 degrees of freedom, the critical t-value that corresponds to 95% confidence is t = 2.0860.
More can be learned about the t-distribution at https://brainly.com/question/16162795
i
think of a number multiply it by seven then add 8 to it and the results is 29 find the number
Answers
Answer:
3
Step-by-step explanation:
29 - 8 = 21
21 / 7 = 3
Therefore, the answer is 3
Answer:
wouldnt it be 3? cause 3*7=21 then add 8 thats 29
Step-by-step explanation:
Compare using < , > , or =-1.75 and -1 3/4
Answers
Answer:
1.75 = 1 3/4
Step-by-step explanation:
1 3/4 = 1.75
Answer:
=
Step-by-step explanation:
-1.75 is the same as -1 3/4
The part of the clock that is shaded is_______________________.
A) one-half hour
B) one-quarter hour
C) three-quarters hour
D) one-third hour
Answers
Answer:
b) one quarter hour
Step-by-step explanation:
every section is worth 5 minutes, there are three sections, which equals 15 minutes, 15 minutes is a one-quarter hour. hope this helps :)
Answer:
B
Step-by-step explanation:
it Is one quarter of an hour because they are exactly 15 minutes