Answer:
1. what is the vertex of the parabola?
C : ( 1, -4 )
2. Which of the following has a graph that is wider than the graph of y=3x^2+2?
B : Y=0.5X^2+1
3. Which graph represents the unction y=-2x^2-5?
D : choose the graph that has the smaller curve and arrows facing down
4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
A : f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
Step-by-step explanation:
these are the correct answers for 2022
i finished the quick check UwU
Rewrite the following quadratic function in vertex form. Then, determine the axis of symmetry. y=5x^2+15x-2
Answer: The vertex form of the given function is [tex]y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}[/tex] and its axis of symmetry is [tex]x=-\dfrac{3}{2}.[/tex]
Step-by-step explanation: The given quadratic function is
[tex]y=5x^2+15x-2~~~~~~~~~~~~~~(i)[/tex]
We are to rewrite the above function in vertex form and to determine its axis of symmetry.
We have from equation (i),
[tex]y=5x^2+15x-2\\\\\Rightarrow y=5(x^2+3x)-2\\\\\Rightarrow y=5\left(x^2+2\times x\times \dfrac{3}{2}+\dfrac{9}{4}\right)-\dfrac{45}{4}-2\\\\\Rightarrow y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{45+8}{4}\\\\\Rightarrow y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}.[/tex]
So, the given function is a parabola with vertex at the point [tex]\left(-\dfrac{3}{2},-\dfrac{53}{4}\right).[/tex]
Therefore, the axis of symmetry is given by
[tex]x=-\dfrac{3}{2}.[/tex]
Thus, the vertex form of the given function is [tex]y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}[/tex] and its axis of symmetry is [tex]x=-\dfrac{3}{2}.[/tex]
To convert the quadratic function y = 5x² + 15x - 2 into vertex form, completing the square yields y = 5(x + 1.5)² - 13.25, with an axis of symmetry at x = -1.5.
To rewrite the quadratic function y = 5x² + 15x - 2 in vertex form and find the axis of symmetry, follow these steps:
Complete the square
Start with the given quadratic function:
y = 5x² + 15x - 2
To complete the square, first factor out the coefficient of x² (which is 5):
y = 5(x² + 3x) - 2
Now, focus on the expression inside the parentheses, x² + 3x.
To complete the square, need to add and subtract a constant term that will make it a perfect square trinomial.
add (3/2)² = 2.25 and subtract the same value inside the parentheses:
y = 5(x² + 3x + 2.25 - 2.25) - 2
Simplify the expression inside the parentheses
Now, simplify the expression inside the parentheses:
x² + 3x + 2.25 = (x + 1.5)²
So, the equation becomes:
y = 5[(x + 1.5)² - 2.25] - 2
Distribute the 5 and simplify further
y = 5(x + 1.5)² - 5(2.25) - 2
Rewrite in vertex form
y = 5(x + 1.5)² - 11.25 - 2
y = 5(x + 1.5)² - 13.25
Now, the quadratic function is in vertex form:
y = 5(x + 1.5)² - 13.25
Find the axis of symmetry
The axis of symmetry of a parabolic equation in the form y = a(x - h)² + k is given by x = h.
The axis of symmetry is x = -1.5 (opposite sign of the value inside the parentheses).
Therefore, the axis of symmetry for the quadratic function y = 5x² + 15x - 2 is x = -1.5.
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Help Please
Tamara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center each barrel is 7 ft deep and has a radius of 4 ft what is the volume of oil needed use 3.14 for the radius.
Answer:
1055.04 volume
Step-by-step explanation:
List the first five terms of each of the following geometric sequence.
A_1 = 10; r = 5
Use the data to create a scatter plot.
Stretch distance
(cm)
Weight
(Newtons)
2.0
1
3.5
2
4.0
2
4.5
3
5.5
5
6.0
6
7.5
8
9.0
9
Weight vs. Stretch Distance
Point
Move
Undo
Redo
Reset
Stretch distance (cm)
Weight (N)
To create a scatter plot for the given data, label the axes with 'Stretch distance (cm)' and 'Weight (Newtons)', plot the points, and observe the correlation. A positive trend is expected as weight increases with stretch distance.
Explanation:To create a scatter plot with the given data of stretch distance versus weight, you would typically use graphing software or graph paper. Here's a step-by-step explanation on how to plot the data:
Label the x-axis as 'Stretch distance (cm)' and the y-axis as 'Weight (Newtons)'.Mark even increments on both axes according to your data range. For stretch distance, you might use increments of 1 cm, and for weight, you could use increments of 1 Newton.Plot each pair of values from the table onto the graph. For example, you would place a point at (2.0 cm, 1 N), (3.5 cm, 2 N), and so on.Once all points are plotted, you may observe a pattern or trend which can be indicated by drawing a line of best fit if appropriate.
After plotting all the points, your scatter plot might show a positive correlation between stretch distance and weight, indicating that weight increases as the stretch distance increases.
How could you increase the mass of a wooden block?
Take it to Jupiter where there is more gravity.
Take it to the moon where there is less gravity.
Cutting it in half.
None of the above.,
1. Suppose that the amount of algae in a pond triples every 2 hours. If the pond initially contains 80 pounds of algae, how much algae will be in the pond after 8 hours? (1 point)
a) 720
b) 1,280
c) 6,480
d) 320
I need to know what 8(ii) because I don’t know the method
Which function increases at a faster rate on 0 to infinity, f(x)=x^2 or g(x)=2^x?Explain your reasoning.
Answer:
g(x) increase at a faster rate.
Step-by-step explanation:
Given : Two functions [tex]f(x)=x^2[/tex] or [tex]g(x)=2^x[/tex]
To find : Which function increase at a faster rate on 0 to infinity
Solution :
We put some value of x in the functions and note down the observation.
x → 0 1 2 3 4 5 6 7
[tex]f(x)=x^2[/tex] → 0 1 4 9 16 25 36 49
[tex]g(x)=2^x[/tex] → 1 2 4 8 16 32 64 128
Comparing the values of f(x) and g(x), we can see that that g(x) increases at a faster rate on 0 to infinity.
Reason - The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function f(x).
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Please give answer and explain how to solve.
What is 2 (log₃8+log₃z) - log₃(3⁴-7²) written as a single logarithm?
PLEASE HELP ASAAAAAPPPP
The histogram shows the number of hours volunteers worked one week.
What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?
Enter your answer in the box.
%
PLEASE HELP! An organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.
What does the margin of error imply?
A.It can be concluded, with 81% confidence, that between 93% and 97% of all employees will rate the vacation policy as "delightful."
B.It can be concluded, with 95% confidence, that at least 81% of all employees will rate the vacation policy as "delightful."
C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."
D.It can be concluded, with 81% confidence, that at least 95% of all employees will rate the vacation policy as "delightful."
Answer:
The answer is option C.
Step-by-step explanation:
Here, according to the given question, margin of error means that the number of people who rated the vacation as 'delightful' ranges between 81% (83-2) and 85% (83+2) of the population at a 95% confidence interval. The range is formed as 81% to 85% as its given that the margin of error is ±2% .
Therefore, only option C is having both the ranges, 81% and 85%. So, option C is the correct answer.
C.It can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."
Jenna is a professional typist.she can type 22,500 words in 5 hours of typing.in one hour how many words can she type?in one minute how many words can she types?
Extra points to the person who answer first
Mandana is ordering new tile for her kitchen floor. The area of the floor is 116.9 square feet, and she wants to order between 15% and 20% extra of the materials. Which of the following is a reasonable amount of tile for Mandana to order?
A. 131 square feet B. 138 square feet C. 133 square feet D. 141 square feet
In order to know what is the reasonable amount of tile for Mandana to order, you have to divide the choices with the area of the floor and deduct with 1 and multiply by 100. You have to assess if the answer you will get will fall between 15% and 20% which is the goal of Mandana.
a. 131/116.9 = (1.1206 – 1) x 100 = 12.06%, this does not fall between 15% and 20%
b. 138/116.9 = (1.1805 – 1) x 100 = 18.05%, this fall between 15% and 20%
c. 133/116.9 = (1.1377 – 1) x 100 = 13.77%, this does not fall between 15% and 20%
d. 141/116.9 = (1.2062 – 1) x 100 = 20.62%, this does not fall between 15% and 20%
Therefore, the reasonable amount of tile for Madana to order that is between 15% and 20% extra of the materials is 138 square feet.
**PLEASE HELP**
The area of a rectangle is 3x^2 + 14x + 8, and the length is x + 4. Which expression best describes the rectangle's width?
A.) 2x + 2
B.) 3x - 2
C.) 3x + 2
D.) 2x + 4
The histogram below shows the age distribution of Elizabeth’s grandchildren.
The box-and-whisker plot below shows the same data.
Which of the following best explains why one graph appears skewed and one graph appears symmetric?
A. The intervals on the x-adis of the histogram are too large
B. The interval on the y-axis of the histogram is too small
C. The interval on the x-axis of the histogram is inconsistent
D. The interval in the box-and-whisker plot is too small
Answer:
Option: C is the correct answer.
C. The interval on the x-axis of the histogram is inconsistent
Step-by-step explanation:
Clearly after looking at the histogram we see that the interval on the x-axis are inconsistent.
Since, the intervals given are:
0-4 ( length of interval is 4)
5-9 ( length of interval is 4)
10-14 ( length of interval is 4)
But the intervals:
(15-19) is missing in the given histogram.
And then a interval of length 4 is given i.e. (20-24)
Hence, option: C is the correct answer.
Jerry starts to save at age 35 for a vacation home that he wants to buy for his 50th birthday. He will contribute $300 each month to an account, which earns 1.7% interest, compounded annually. What is the future value of this investment, rounded to the nearest dollar, when Jerry is ready to purchase the vacation home? Answers: $61,960 $60,924 $5,077 $5,163 This is the only question I couldn't figure out , I just need help with it please. Thanks
how do you solve log base 3 (27) by hand
The log base 3 of 27 is equal to 3.
To solve log base 3 of 27 by hand, we need to determine the exponent to which the base 3 must be raised to obtain 27.
In this case, 3 raised to the power of what exponent equals 27?
By observing that [tex]3^3[/tex] equals 27, we can conclude that:
log base 3 of 27 = 3.
Therefore, the solution to log base 3 of 27 is 3.
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Mr.gleasons math class lasts 40 minutes . Math class starts at 9:55 a.m. At what time does math class end
Answer:
10:35
Step-by-step explanation:
Just add 9.55 and 40 mins:
9.55+40=10:35a.m
If dewayne answered 38 items correctly on a test, and received a score of 76%, How Many items were on the test?
Ursula and Andre competed against each other in a swimming race. Ursula swam at a rate of 60 meters per minute and Andre swam at a rate of 48 meters per minute. Ursula gave Andre a 1-minute head start.
Final answer:
Ursula, swimming at 60 meters per minute, and given Andre a 1-minute head start who swims at 48 meters per minute, will catch up to Andre 4 minutes after she starts.
Explanation:
Ursula and Andre competed against each other in a swimming race. Ursula swam at a rate of 60 meters per minute and Andre swam at a rate of 48 meters per minute. Ursula gave Andre a 1-minute head start. To determine who wins the race, we need to calculate the time it takes for Ursula to catch up to Andre, given the head start.
Let's denote the time it takes for Ursula to catch up to Andre as t (in minutes). Since Andre has a 1-minute head start, he would have swum 48 meters before Ursula starts. Therefore, the distance Andre swims in t+1 minutes is 48(t+1). Ursula's swimming distance in t minutes is 60t.
To find out when Ursula catches up to Andre, we set these distances equal to each other:
60t = 48(t+1)60t = 48t + 4860t - 48t = 4812t = 48t = 4Thus, Ursula will catch up to Andre 4 minutes after she starts swimming, which is 5 minutes after Andre starts.
please help asap!!! brainliest to best/right answer!!!!!!
1. Find the product of 2x4(2x2 + 3x + 4).
2x8 + 3x4 + 4x4
4x6 + 6x5 + 8x4
4x4 + 3x5 + 2x6
3x6 + 4x5 + 5x4
2. Find the product of (3x 4)(2x2 + 2x 1)
6x3 + 2x2 - 5x + 4
6x3 + 14x2 - 11x + 4
6x3 - 14x2 - 5x + 4
6x3 - 2x2 - 11x + 4
3. Find the product of (x2 + 4x 3)(2x2 + x + 6).
2x4 + 9x3 + 4x2 + 21x 18
2x4 + 9x3 + 10x2 + 21x 18
2x4 + 7x3 + 4x2 + 21x18
2x4 + 9x3 + 4x2 + 27x 18,
A cell phone plan charges $15$15 per month for 300300 text messages. The plan charges $0.08$0.08 for each additional text message. You use 6060 additional texts this month. What is your bill for the month?
The company charges 15 dollars per month for first 300 text messages and thereafter 0.08 dollars for any additional text message.
It says that we used additional 60 text messages (after fair usage of first 300 messages in the plan).
Our bill for this month would be sum of charges for 300 messages and charges for additional 60 messages.
Total bill = 15 dollars + 60x0.08 dollars = (15 + 4.80) dollars.
Total bill = 19.80 dollars.
Hence, our bill this month would be 19.80 dollars.
The options for number two is
31.5 m^2
63 m^2
84 m^2
126 m^2
Please help! I will give brainliest to the best explained answer.
Explain how to find the degree of a polynomial.
Answer:
The Degree of a Polynomial is the largest of the degrees of the individual terms. Add the degrees of the variables of each term to decide what is the Degree of the Polynomial. Degree of term 1 is 2 (1+1= 2), Degree of term 2 is 6 (2+4 = 6), Degree of term 3 is 7 (5+2 = 7) 7 is the Degree of the Polynomial.
Consider the function f (x) = (2x - a)(x - b)/5(x - b)(x - c). Determine where the following features of its graph
are located in terms of a, b, and/or c. Explain your reasoning for each situation.
a. the x-intercepts
b. the y-intercepts
c. any vertical asymptotes
d. any horizontal asymptotes
e. any “holes” in the graph
According to Okun's law, if the unemployment rate goes from 2% to 5%, what will be the effect on the GDP?
Answer: decreases by 3%
Step-by-step explanation:
A triangle with one obtuse angle must also have two acute angles.a. trueb. false