Next, the team wants to explore how it can change the steepness of the curved pit.
Identify how the graph of each equation compares with the graph of the parent quadratic equation, y = x2.
Drag the equations to the correct location on the chart. Not all equations will be used.
Answers
Given that the parent function, y = x², has a leading coefficient of 1, the
following are the comparisons of the equations with the parent functions;
[tex]\begin{array}{|c|cc|}Steeper \, than \, y = x^2&&Less \, Steep \ than \, y = x^2 \\y = 2 \cdot x^2&&y = \frac{1}{2} \cdot x^2 \\y = \left(2 \cdot x \right)^2&&y = \left(\frac{1}{2} \cdot x \right)^2 \end{array}\right][/tex]
How can the correct location of each equation be found?The parent function is y = x²
The leading coefficient of the parent function = 1
The steepness of a quadratic equation is given by the value of the
leading coefficient.
When the leading coefficient is larger than 1, we have;
The function is steeper than y = x²
When the leading coefficient is a fraction larger than 0 but lesser than 1, we have;
The function is less steep than y = x²
Which gives;
[tex]\begin{array}{|c|cc|}Steeper \, than \, y = x^2&&Less \, Steep \ than \, y = x^2 \\y = 2 \cdot x^2&&y = \frac{1}{2} \cdot x^2 \\y = \left(2 \cdot x \right)^2&&y = \left(\frac{1}{2} \cdot x \right)^2 \end{array}\right][/tex]
The function y = -x² is inverted has the same steepness as y = x², but will not be used.
Learn more about the properties of quadratic functions here:
https://brainly.com/question/10989920
Related Questions
Find P(C|Y) from the information in the table. A 5-column table has 4 rows. The first column has entries A, B, C, Total. The second column is labeled X with entries 32, 6, 18, 56. The third column is labeled Y with entries 10, 5, 15, 30. The fourth column is labeled Z with entries 28, 25, 7, 60. The fifth column is labeled Total with entries 70, 36, 40, 146. To the nearest tenth, what is the value of P(C|Y)? 0. 4 0. 5 0. 7 0. 8.
Answers
The probability is the ratio of the favorable event to the total number of events. The P(C|Y) is 0.5. Then the correct option is B.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
According to the problem, the table is made
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Then the probability of will be
[tex]\rm P(C|Y) = \dfrac{15}{30}\\\\P(C|Y) = 0.5[/tex]
The P(C|Y) is 0.5. Then the correct option is B.
More about the probability link is given below.
https://brainly.com/question/795909
I need help on this question in math
Answers
The rate of change or essentially the slope is a numerical value that describes the direction and the steepness of the line.
To find the slope, we just need any two points on the line
--> Let's pick (0,2) and (2,6)
The slope's equation = [tex]\frac{y2-y1}{x2-x1}[/tex]
Let's plug the known quantities into the equation
[tex]\frac{y2-y1}{x2-x1}=\frac{6-2}{2-0} =\frac{4}{2} =2[/tex]
Therefore the rate of change is 2 km/trip
Hope that helps!
The sum of twice a number and 5 is 21. What is the number?
Answers
Hello.
First, "twice a number" means we multiply 2 times that number.
Let the number be s.
Now, the sum of 2 times s and 5 is 21.
The product of 2 and s can be written like so:
[tex]\sf{2s[/tex]
Now, the sum of 2s and 5 is 21:
[tex]\sf{2s+5=21[/tex]
Subtract 5 from both sides:
[tex]\sf{2s=21-5[/tex]
[tex]\sf{2s=16}[/tex]
Now, divide both sides by 2:
[tex]\Large\boxed{\sf{s=8}}[/tex]
I hope it helps.
Have a nice day.
[tex]\boxed{imperturbability}[/tex]
x = 8
Step-by-step explanation:
Let the required number be x.
According to the given question,
=> 2x + 5 = 21
=> 2x = 21 - 5
=> 2x = 16
=> x = 16/2
=> x = 8
Hope it helps you!!London has a collection of 260 coins. How many coins represent 25% of her collection?
Answers
Answer:
65 coins
Step-by-step explanation:
Set this problem up with a porportion.
[tex]\frac{?}{260} \frac{25}{100}[/tex]
After that, cross multiple and divide.
25 times 260. Then divide by 100. That is then your answer.
Two numbers multiply together to give -30 and add together to give -1.
What are the two numbers?
Answers
a minus and a positive make a minus
Answer:
5, -6
Step-by-step explanation:
We just need to find out the factors of -30 and they are 1 x -30, 2 x -15, 3 x 10 and 5 x -6. We can try out every factor to add so it's either:
-29
-13
-7
-1
the last is the answer we're looking for so it's 5 x -6
The 2 numbers are 5 and -6
Factor perfect square binomial
9x^2+ 24x +16
Answers
Answer:
(3x + 4)(3x + 4)
Step-by-step explanation:
[tex]9x^2+ 24x +16 \\ \\ = 9x^2+ 12x + 12x +16 \\ \\ = 3x(3x + 4) + 4(3x + 4) \\ \\ = (3x + 4)(3x + 4)[/tex]
Math Questions about graph
Answers
Answer:
(i) gradient: 2/3
(ii) equation: y -1 = 2/3(x +1)
(iii) area: 10 square units
(iv) length: 4.12 units
Step-by-step explanation:
The gradient of a line is found by using the slope formula with two points on the line. The length between points is found using the distance formula, which is based on the Pythagorean theorem. The equation of a line can be written in several forms. One is the point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
__
(i)The points A and B can be used in the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (5 -1)/(5 -(-1)) = 4/6 = 2/3
The gradient of the line is 2/3.
__
(ii)Using the found slope in the point-slope equation with point A, we find the equation of the line to be ...
y -1 = 2/3(x +1)
__
(iii)The area of a triangle is found from the formula ...
A = 1/2bh . . . . . triangle with base b and height h
The base length will be the difference in x-coordinates of the horizontal segment AC: 4 -(-1) = 5.
The height will be the difference in y-coordinates from that horizontal segment and point B: 5 -1 = 4
Then the area of ABC is ...
A = 1/2(5)(4) = 10 . . . . square units
The area of ΔABC is 10 square units.
__
(iv)The length of BC is found from the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
d = √((5 -4)² +(5 -1)²) = √(1 +16) = √17
d ≈ 4.12 . . . . units
The length of BC is about 4.12 units.
How are solving equations and solving inequalities the same? How are they different?
Answers
Answer:
The only difference is: If you multiply or divide both sides of an equation by the same negative number, the equation remains the same, but If you multiply or divide both sides of an inequality by the same negative number, the inequality reverses. !!!!!
Step-by-step explanation:
PLEASE HELP!!!!50 POINTS
Answers
Answer:
i'm really not sure i'm sorry-
Step-by-step explanation:
ima get my smart friend to find the answer for you <3
Dana is building a wooden birdhouse for her mom. She finds a plank in the garage to use for the base. When she realizes it's too long, Dana cuts 3 inches off the plank. Now it's the correct length of 8. 25 inches.
Which equation can you use to find the length p of the plank before Dana cuts it?
1. P-3=8. 25
2. P/3=8. 25
3. P+3=8. 25
4. 3p=8. 25
Answers
Write a function rule for the table. (b is incorrect so please choose one of the other 3 answers.)
Answers
Answer: D
Step-by-step explanation: payment equals to money earned per hour (p=6.25h).
18. 9 decreased by twice a number is equal to 9. 9. What is the number?
Answers
Twice means two times
18.9 - 2x = 9.9
18.9 -18.9 -2x=9.9 - 18.9
-2x=9.9 - 18.9
(-2x= -9) divide both sides by negative two
-2x/-2 = -9/-2
x=4.5
600x + 200y = 500x solve for x
yes thats all i need.
Answers
Answer:
x = -2y
Step-by-step explanation:
Simplifying
600x + 200y = 500x
Solving
600x + 200y = 500x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-500x' to each side of the equation.
600x + -500x + 200y = 500x + -500x
Combine like terms: 600x + -500x = 100x
100x + 200y = 500x + -500x
Combine like terms: 500x + -500x = 0
100x + 200y = 0
Add '-200y' to each side of the equation.
100x + 200y + -200y = 0 + -200y
Combine like terms: 200y + -200y = 0
100x + 0 = 0 + -200y
100x = 0 + -200y
Remove the zero:
100x = -200y
Divide each side by '100'.
x = -2y
Simplifying
x = -2y
hope this helps!
ibrahim
Mrs. Katz is planning to create a flower
garden in the shape of a trapezoid.
She started by creating a blueprint.
What is the value of x?
Answers
The value of x can be found by using the formula for the area of a trapezoid. The value of [tex]$x$[/tex] is [tex]$4$[/tex] inches.
What is area?Area is a two-dimensional measurement that is used to measure the size of a shape or surface. It is measured in square units, such as square centimeters, square meters, square kilometers, and so on. The formula for the area of a trapezoid is: [tex](a+b)/2 *h[/tex], where a and b are the lengths of the parallel sides, and h is the height. Mrs. Katz needs to calculate the value of x by plugging in the lengths of the parallel sides and the height into the formula.
We know that the opposite sides of a trapezoid are parallel, so we have [tex]AB \parallel DC.[/tex]
Using the given information, we can set up an equation in terms of [tex]$x$[/tex] and solve for it. We know that the height of the trapezoid is [tex]$8$[/tex] inches, and we know that the bases are [tex]$x$[/tex] inches and [tex]$16$[/tex] inches.
Using the formula for the area of a trapezoid, we have:
[tex]\text{Area} = \frac{1}{2}(AB+DC)(\text{height})[/tex]
Plugging in the values we know, we get:
[tex]\text{Area} = \frac{1}{2}(x+16)(8)[/tex]
We are also given that the area of the trapezoid is [tex]$100$[/tex] square inches, so we can set up an equation:
[tex]100 = \frac{1}{2}(x+16)(8)[/tex]
Simplifying and solving for [tex]$x$[/tex], we get:
[tex]100 &= \frac{1}{2}(x+16)(8)\20 &= (x+16)\x &= 4[/tex]
Therefore, the value of [tex]$x$[/tex] is [tex]$4$[/tex] inches.
To know more about trapezoid, visit
brainly.com/question/13230099
#SPJ1
Sarah wants to swim across a 193 m river. Due to the current she is swept 67 m downriver from where she wanted to be. What is the length that she actually swam from start to where she ended? Round to the nearest tenth
Answers
Answer:
Step-by-step explanation:
Sarah swam the diagonal length of a right-angled triangle with sides of river width, 193m and how far she was swept downstream, 67m.
By Pythagorean Theorem, distance swam = sqrt(193^2+67^2)
= 204.3 m
Apply Pythagorean theorem
[tex]\\ \rm\rightarrowtail H^2=P^2+B^2[/tex]
[tex]\\ \rm\rightarrowtail H^2=193^2+67^2[/tex]
[tex]\\ \rm\rightarrowtail H^2=41738[/tex]
[tex]\\ \rm\rightarrowtail H=204ft[/tex](Approx)
please help
I put a photo
Answers
Answer:
[tex]\sf slope: \dfrac{5}{4}[/tex]
[tex]\sf y-intercept: 0[/tex]
explanation:
comparing with the formula: y = mx + b
Here the input equation: y = 5/4 x + 0
[tex]\hookrightarrow[/tex] m = 5/4 and b = 0
Find the product. (3b-2)(3b+2) *
Answers
Answer:
9b²-4
Step-by-step explanation:
(3b-2)(3b+2)
9b²+6b-6b-4
9b²+0-4
9b²-4
first to answer, pls brainliest.
Determine the area and perimeter and show your work please??
Answers
Dan pays £714. 73 a year on his car insurance. The insurance company reduces the price by 4. 1%. How much does the insurance cost now?Give your answer rounded to 2 DP
Answers
Answer:
[tex] \frac{4.1}{100} \times 714.73 = 29.30 \\ 714.73 - 29.30 = 685.43[/tex]
divide 4.1 with 100percent because per5 is always over 100 them multiply by the amount given
Step-by-step explanation:
subtract 29.30 from 714.30
subtract calculated amount from amount given
get yr final answer
What is the whole number for 15/4. If you have the answer please tell me.
Answers
Answer: 4
Step-by-step explanation:
Well 15/4 is 3.75 so to get the whole number you need to round up
.75 rounds up to .8 now round 3.8 well 3.8 rounded up is 4 there's your answer! :)
A tool that uses time-ordered values of a sample statistic to help detect the presence of correctable causes of variation in a process is a(n)
Answers
A Control Chart is a tool that uses time-ordered values of a sample statistic to help detect the presence of correctable causes of variation in a process.
What are the types of a Control charts?There are various kinds of control charts. They are:
The most commonly used control chart is the Individuals and Moving Range Chart.
Learn more about control chart at:
https://brainly.com/question/14285549
Student Guide (continued)
1) Using the regression calculator in your tool bar, create a scatterplot using your data set from step
1. Insert a screenshot of your scatterplot, or recreate it below.
The photo shows the 10 students I chose please Help!
Answers
so the scatterplot will more or less look like the one in the picture below.
Solve for x please!
No links or trolls.
Answers
Answer:
help me
Step-by-step explanation:
Drag each volume of a prism to match a rectangular prism on the left with the given dimensions.
Dimensions of Rectangular Prism | Volume of Rectangular Prism
4 in., 3 in., 6 in.
6 in., 3 in., 2 in.
4 in., 5 in., 4 in.
2 in., 9 in., 3 in.
Choices: 54 cu. in. 72 cu. in. 36 cu. in. 80 cu. in.
Answer for 20 points
Answers
The volume of the rectangular prisms is given by 72 in³, 36 in³, 80 in³ and 54 in³
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
The volume of a rectangular prism is given by:
Volume = length * width * height
a) Dimensions: 4 in., 3 in., 6 in.
Volume = 4 * 3 * 6 = 72 in³
b) Dimensions: 6 in., 3 in., 2 in.
Volume = 6 * 3 * 2 = 36 in³
c) Dimensions: 4 in., 5 in., 4 in.
Volume = 4 * 5 * 4 = 80 in³
d) Dimensions: 2 in., 9 in., 3 in.
Volume = 2 * 9 * 3 = 54 in³
The volume of the rectangular prisms is given by 72 in³, 36 in³, 80 in³ and 54 in³
Find out more on volume at: https://brainly.com/question/12410983
Find the mean absolute deviation (MAD) of your data. Show your work.
your data set: 23, 75, 79, 99, 105, 110, 110, 142, 149, 168, 168, 170, 183, 195, 202
mean: 131. 86667
Help! this is timed. I will give brainliest
Answers
The mean abosolute deviation of the given data set is: 42.9422.
What is the Mean Abosolute Deviation?The mean absolute deviation is the avergae of the distance of each data point from the mean of the data set.
Given:
23, 75, 79, 99, 105, 110, 110, 142, 149, 168, 168, 170, 183, 195, 202
Mean: (23 + 75 + 79 + 99 + 105 + 110 + 110 + 142 + 149 + 168 + 168 + 170 + 183 + 195 + 202)/15
Mean = 1978/15 = 131.8667
Mean aboslute deviation = [(23 - 131.8667) + ( 75 - 131.8667) + ( 79 - 131.8667) + ( 99 - 131.8667) + ( 105 - 131.8667) + ( 110 - 131.8667) + ( 110 - 131.8667) + ( 142 - 131.8667) + ( 149 - 131.8667) + ( 168 - 131.8667) + ( 168 - 131.8667) + ( 170 - 131.8667) + ( 183 - 131.8667) + ( 195 - 131.8667) + ( 202 - 131.8667)] / 15
Mean aboslute deviation = 644.1333/15 = 42.9422
Learn more about mean absolute deviation on:
https://brainly.com/question/447169
What is the value
of 9 2/3 - 4 1/5
Answers
9 2/3 = 29/3
4 1/5 = 21/5
29/3 - 21/5
145/15 - 63/15
82/15
5 7/15
Hope this helps!
Find the geometric mean between 20 and 5
Answers
Explanation 5/20
The answer is 10.
Step-by-step explanation:
I have the same question on some tests of mine
An isosceles right triangle has leg lengths of 4 centimeters. What is the length of the altitude drawn from the right angle to the hypotenuse?
2 cm
2 StartRoot 2 EndRoot cm
4 cm
4 StartRoot 2 EndRoot cm
Answers
Answer:
Step-by-step explanation:
(4sqrt2)/4 = 4/(projection)
sqrt2 = 4/(projection)
projection = 2sqrt2
So by the Pythagorean theorem, the altitude is also 2sqrt2.
Answer:
B
Step-by-step explanation:
Edge
Brenton packed 8 peanut bars in each box. If he had 398 peanut bars,
How many boxes were packed?
(ii)
How many bars remained?
Answers
Answer:
divide 8 and 398 and you will get ur answers
The sum of 4/5 and 1/10 is closer to 1/2 than to 1