Observe that
y = x² - 2kx = x (x - 2k)
has roots at x = 0 and x = 2k. Since the leading coefficient is 1 > 0, the parabola opens upward, and in particular this means the x-axis lies above the curve.
We can compute the area of R by integrating:
[tex]\displaystyle \int_0^{2k} |x^2-2kx| \, dx = - \int_0^{2k} (x^2-2kx) \, dx \\\\ = kx^2 -\frac{x^3}3 \bigg|_{0}^{2k} \\\\ = \frac{4k^3}3[/tex]
Solve for k :
[tex]\dfrac{4k^3}3 = 36 \implies k^3 = 27 \implies \boxed{k=3} ~~~~ (B)[/tex]
Suppose that in a random sample of 240 smartphone users, 160 used an iPhone. Conduct a hypothesis test at significance level 0.02 to test the claim that more than 58% of smartphone users use an iPhone.
State the null hypothesis, the alternative hypothesis, the test statistic, the (P-value or traditional method), and formulate your conclusion.
Null hypothesis: ____________________
Alternative hypothesis: __________________
Test Statistic:
p-value value: ________
Conclusion: __________________________________
Answer:
you will get the correct answer
Step-by-step explanation:
I need points ASAP!!
find the area of this triangle. round to the nearest tenth. 17 m, 15 m, and 35 degrees
area of triangle
= 1/2 b*h
=1/2 17*15
=8.5*15
=127.5m²
Subtract 8 from me. Then add 9. If you add 12 and then
subtract 4, you get 18. What number am I?
Answer:
9
Step-by-step explanation:
x - 8 + 9 + 12 - 4 = 18
x = 9
Point A is located at (1, 5), and point M is located at (−1, 6). If point M is the midpoint of segment AB, find the location of point B.
Question 6 options:
(−3, 7)
(0, 5.5)
(3, 4)
(0, 5)
The location of point B is (0,5.5).
What is section formula?The section formula tells us the coordinates of the point which divides a given line segment into two parts such that their lengths are in the ratio m : n.
Given: A(1,5), M(-1,6)
If M is the mid point of line AB, then
let the coordinates of B(a,b),
Using section formula,
a= 1*1+1*(-1)/(1+1)
a= 0/2
a=0
b= 1*6+1*5/2
b=11/2
b=5.5
Hence, the coordinated of B(0,5.5).
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Answer:
B. (0,5.5)
B's location is (0,5.5)
How would I make a dot plot with these requirements?:
1. It has at least 10 values.
2. It has at least 3 values that are different.
3. It has a mean and median of 12.
Answer:
2
Step-by-step explanation:
If the volume of sphere is 4574.9 cubic inches is the radius?
Answer:
10.3
Step-by-step explanation:
Volume of a sphere
V = 4/3 pi r^3
4574.9 = 4/3 (3.14) r^3
r= 10.3 in
writes 25 x 10 to the power of 6
[tex](25*10)^6[/tex]
Sure hope this helps you
And please mark me brianiest if this is correct
Suppose a 12 acre plot of land is being divided into 1/4 acre lots for a hosing development. How many lots will there be in the development.
Answer:
48 lots
Step-by-step explanation:
If:
JT = 22x +9,
CJ = 62 +4, and
CT = 37,
Find JT.
jt- 22x+9..
It clearly says JT=22X+9
try 22+9..?
How many solutions does this equation have?
–9d + 4 = –4 − 10d
Answer:
One Solution
Explanation:
–9d + 4 = –4 − 10dchange sides
–9d + 10d = -4 - 4one solution ↓
d = -8Answer:
One solution
Step-by-step explanation:
When solving for d, you get d = - 8
Sales $100 10 12 16 18 22 24 Temperature °C (a) How would you characterize the relationship between the money spent on calling fans to the temperature? Explain. (b) The function y=20x+0 is used to model this situation. What is the predicted amount of sales if the temperature is 21 degrees Celsius? Show your work. (c) What does the number 0 in the function mean in the context of this situation? Answers:
#1
As this is a scatter plot so we have to draw a suitable line then have to find the equation of line inorder to fulfill our requirements.
#2
y=20x+0Put temperature as 21(x)
y=20(21)y=420#3
0 is the y intercept or the initial amount of sales
It's denoting to the fact that there were initially 0 boxes
Help pls
In the figure below, the areas of rectangles A, B, and C are 11, 33, and 75,
respectively. Find the area of rectangle D.
If the areas of rectangles A, B, and C are 11, 33, and 75, respectively. Then the area of the rectangle D will be 25 square units.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
In the figure below, the areas of rectangles A, B, and C are 11, 33, and 75, respectively.
Then the area of the rectangle D will be
Let a be the length and b be the width of the rectangle D. Then we have
The ratio of the area of the rectangles will be
[tex]\rm \dfrac{A_A}{A_B} = \dfrac{A_D}{A_C}\\\\\\A_D = \dfrac{A_A \times A_C}{A_B}\\\\\\A_D = \dfrac{11 \times 75}{33}\\\\\\A_D = 25[/tex]
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Joe paid 14.00 for a board game this is 70 of the original price what was the original price
Answer:4.2
Step-by-step explanation:
14 times 70% subtracted from 4.2
The original price or cost price of a board game is 20.
What is cost price?The cost price is the price at which "goods are bought by merchant or retailer".
According to the question,
Joe paid 14.00 for a board game which is 70% of the original price or cost price.
In order to find cost price or original price. Let 'x' be the original price or cost price
70% = 14
100% = x
x = [tex]\frac{1400}{70}[/tex] [cross multiplication]
=20
Hence, the original price or cost price of a board game is 20.
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The volume of this rectangular prism is 122,264 cubic millimeters. What is the value of z? (will mark brainliest)
Answer:
z = 58 mm
Step-by-step explanation:
Volume of the rectangular prism :
Volume = length x breadth x heightSolving :
122,264 = 62 x z x 34122,264 = 2,108 x zz = 122,264/2,108z = 58 mmAnswer:
z = 58 mm
Step-by-step explanation:
Volume of a rectangular prism: length × width × height
V = L×W×H
v = 122,264 mm³l = 62 mmw = z mmh = 34 mmSubstitute the values above and solve for z:
122,264 = 62 × z × 34
122,264 = 2108z
122,264/2108 = 2108z/2108
58 = z
Final answer: 58 mm
Hope this helps!
Find the equation of the straight line passing through the point (3,5) which perpendicular y=3x +2 to the line
The equation of the straight line that passes through the point (3,5) which is perpendicular to the line y = 3x + 2 is x -3y -18=0
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
To find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y = 3x + 2, we will first find the slope(m).
To find the slope m of the perpendicular equation;
y = 3x + 2 --------------(1)
comparing the equation above with the standard equation of a circle
y=mx + c
m=3
The slope of the perpendicular equation;
= -1
3 = -1
Divide both-side of the equation by 3
= -1/3
so, the slope of our perpendicular equation is -1/3
Then, we go ahead to find our intercept
To find the intercept, we will plug in the points and the new slope into the formula y =mx + c
5 = -(3) + c
5 = -1 +c
Add one to both-side of the equation
5+1 = -1 + c + 1
6 =c
c=6
our intercept c is equal to 6
so we can now proceed to form our equation.
y = - x + 6
Multiply through by 3
-3y = -x + 18
We can rearrange the equation, hence;
x -3y -18=0
Therefore the equation of the straight line that passes through the point (3,5) which is perpendicular to the line y = 3x + 2 is x -3y -18=0
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what is 0.000285 expressed in scientific notation
Answer: the answer is 2.85 x 10^-4
Step-by-step explanation:
or u can just look up Mathway and that will give you the answer and a much quicker way too https
Please help me I will give brainliest I need help
Which data set is represented by the modified box plot?
Box and whisker plot on a number line from 90 to 160 in increments of 5. The whisker ranges from 114 to 152. The box ranges from 120 to 139 with the vertical bar inside the box at 128. One dot mark above ninety-one.
134, 142, 136, 128, 126, 152, 91, 114, 120, 139, 128
134, 142, 136, 128, 126, 168, 91, 114, 120, 139, 128
134, 142, 136, 120, 120, 152, 91, 114, 120, 139, 134
134, 142, 136, 128, 126, 152, 102, 114, 120, 139, 128
Answer:
I think it's B
Step-by-step explanation:
:)
Jacqueline is cleaning the barn and needs to give her horse freshwater.the water trough holds 70 gallons of water the hose she has to use as a flow rate of 6 gallons per minute. how long will it take to fill the water trough?
Reset Scarlet bought a coat originally priced at $120. She got a 15% discount. How much did she pay for the coat? $ $
Answer:
$102
Step-by-step explanation:
Reset Scarlet bought a coat originally priced at $120. She got a 15% discount. How much did she pay for the coat?
1. Convert the discount percentage to a decimal:
15/100 = 0.15
2. Multiply the original price by the decimal:
120*0.15 = $18
This is the discount they got.
3. Now, subtract the discounted value from the original price:
120 - 18 = $102
This means that they paid $102 for the coat.
Hope this helps!
Answer:
$102
Step-by-step explanation:
15% of 120
= 15/100×120
0.15×120=$18
therefore, 15% of 120 equal 18
discount= $18
Amount she paid= 120-18= $102
Use the inverse matrix to solve this system of equations:
An inverse matrix is drawn from the concept of reciprocity in which the product of a number and its reciprocal will sum up to one (1). Note that an identity matrix is equal to the product of a square matrix and its inverse.
What other kinds of matrixes are there?In mathematics you have the following types of matrices:
Column matrixNull MatrixSquare MatrixRow MatrixLower Triangular Matrix etc.It is to be noted that the information required to solve the equation is incomplete hence the general answer.
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What is the answer to this
Answer:
193 m²
Step-by-step explanation:
Let us separate the figure into three parts:
One right angled triangle, square and rectangle.
right angle triangle having height(h) = (10+5+3)m = 18m
base of right angled triangle(b) = 25-(8+4)m = 13m
length of square(l) = 8m
length of rectangle (a) = 4m
breadth of rectangle (w) = 3m
[tex]total \: area \: of figure = area \: of \: triangle + area \: of \: square + area \: of \: rectangle[/tex]
[tex] = \: ( \frac{1}{2} \times b \: \times h ) \: + ({l}^{2} )\: + (a \: \times w)[/tex]
[tex] = (\frac{1}{2} \times 13 \times 18) + {8}^{2} + (4 \times 3)[/tex]
[tex] = 193 \: {m}^{2} [/tex]
Which graph shows the solution to the system of linear inequalities?
2x – 3y <12
y < –3
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything above the line is shaded. The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything below the line is shaded.
The statement third is correct, which is the first dashed straight line is horizontal to the y-axis at y = -3. Everything below the line is shaded.
The second solid line has a positive slope and goes through (0, - 4) and (3, -2). Everything above the line is shaded.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have two inequality:
2x – 3y <12
y < –3
If we draw these two inequalities on the graph, we will see:
On a coordinate plane, 2 lines are shown. The first dashed straight line is horizontal to the y-axis at y = negative 3. Everything below the line is shaded.
The second solid line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything above the line is shaded.
Thus, the statement third is correct, which is the first dashed straight line is horizontal to the y-axis at y = -3. Everything below the line is shaded.
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PLEASE HELP!! I WILL MARK BRAINLEST!
Which of the following is the best buy?
4 lb. for $27.60
6 lb. for $41.28
7.5 lb. for $51.63
8 lb. for $55.12
Please help!! Giving Brainleist!
Answer: 30
Step-by-step explanation:
Bc all the numbers are near 30
CAN I PLEASE HAVE BRAINLIEST ✨
can i have help with this please if you do it you're a lifesaver
Answer:
1, 2, 5, and 10
Step-by-step explanation:
Factors of 30 :
1, 2, 3, 5, 6, 10, 15, 30
Factors of 20 :
1, 2, 4, 5, 10, 20
what is a venn diagram?a venn diagram is an illustration that uses circles to show the relationship between things or group of things. Circles that overlap share the same traits (in this case numbers) and those that do not overlap dont share the same traits.What numbers go in the shaded overlap?
1, 2, 5, and 10
Jesse needs to wrap the present shown below. How much wrapping paper would he need?
5 in
6 in
15 in
9 in
3 in
а
b
558 sq in
300 sq in
354 sq in
327 sq in
*ANSWER*
What is the value of x?
x =6
Answer;
10
Step-by-step explanation:
from the question we observed that the shape is a right angled triangle.
and according to Pythagoras theorem, In a right angled triangle the square of the hypothenus is equal to the square of the sum of the other two side
hypothenus = 10
10^2= 8^ + X^2
100= 64 +X^2
X^2 = 100-64
X^2 = 36
X = √36
X= 6
Select the correct answer from the drop-down menu. an automobile manufacturer wants to find out what types of product-related problems its customers are experiencing. the best method to gather the data is .
The correct answer from the drop-down menu is a survey, this is because the type of data you are interested in is more subjective and open-ended.
What is the survey method?To find out what types of product-related problems its customers are experiencing we need to investigate about the problems faced by customers by means of collecting data from a sample of population.
In this case, we have that a survey is a data collection of questions used to gather information about population.
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A rectangle has an area of 4y2 – 49 square
units. What are the dimensions of the
rectangle?
Answer:
D. (2y - 7) units by (2y + 7) units
Step-by-step explanation:
[tex]A(rectangle) =4y^2-49[/tex][tex]\implies A(rectangle) =(2y)^2-(7)^2[/tex][tex]\implies A(rectangle) =(2y-7)(2y+7)[/tex]-> D(rectangle) = (2y-7) units by (2y + 7) unitsI need help please I have a picture of the problem down below.
Answer:
Step 1: Create a net for the triangular prism by "cutting" two edges of the triangular faces and unfolding.
Step 2: Find the area of each triangle. Find the area of the rectangle.
Step 3: Add all areas from step 2 together. This is the surface area.
Step-by-step explanation: