Answers
y = (-3/2)x - 1
================================================
Explanation:
The general slope intercept form is y = mx+b
m = slopeb = y interceptThe slope of the original line in the graph is m = 2/3. Flip the fraction and flip the sign to get -3/2 as the perpendicular slope. The original slope and perpendicular slope multiply to -1.
Since the perpendicular slope is -3/2, this narrows the choices between B and D.
We'll plug this perpendicular slope as the new m value, along with the coordinates of the point (-2,2). Then we solve for the y intercept b value.
So,
y = mx+b
2 = (-3/2)*(-2) + b
2 = -1.5*(-2) + b
2 = 3 + b
2-3 = b
-1 = b
b = -1
With m = -3/2 and b = -1, we have the final answer y = (-3/2)x-1 which is choice B
Side notes:
Because -3/2 = -1.5, that equation in bold is the same as y = -1.5x-1The two perpendicular lines intersect at (0,-1). They both have the same y intercept. This won't always happen for any two random perpendicular lines.If you started at P(-2,2) and dropped down 3, and moved to the right 2, then you arrive at (0,-1).Related Questions
Write the following fractions in decreasing order: 4/7, 11/15, 2/3.
Answers
Answer:
11/15 4/7 2/3
Step-by-step explanation:
The diagram shows a triangle.
31° / 6x / x+16°
What is the value of x?
Answers
Step-by-step explanation:
31 + 6x + x + 16 = 180
7x + 47 = 180
7x = 180 - 47
x = 133/7
x = 19
Alex brought in 6 bottles of apple juice to share with himself and 3 friends at lunch. There are 3.5 liters of juice in each bottle.
If they combine all of the juice together, how much apple juice does each person get to drink?
If they share the apple juice equally among the 4 of them, how much apple juice does each person get to drink?
Answers
Answer:
5.25 litres.
Step-by-step explanation:
6 bottles * 3.5 litres = 21 litres of juice total.
21 / 4 = 5.25 litres per person.
PLEASE ANSWER UNDER 5 MIN!!!! ily!!!!
what is the period of the sinusoidal function? enter your answer in the box.
Answers
Answer:
Step-by-step explanation:
10
Ws
Sketch the graph of, 3x - 4y = 16.
Answers
Answer:
Step-by-step explanation:
√400=x² what is x? Thanks
Answers
Answer:
x=4.47213
I hope it's helps you
what is the value of x^2 - 6x + 9 when x = 2 + i?
Answers
The Expression x^2 - 6x + 9 when x = 2 + i is -2i
To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:
(2 + i)^2 - 6(2 + i) + 9
Simplifying the first term, we get:
(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2
Since i^2 = -1, we can substitute that in and simplify further:
(2 + i)^2 = 4 + 4i - 1 = 3 + 4i
Now we substitute this into the original expression:
(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9
Simplifying further, we get:
= 3 + 4i - 12 - 6i + 9
= 0 - 2i
= -2i
Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.
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on the 9th of february 2012, the heights of the water in the bristol channel in cardiff, uk were as follows. low tide was 1.2 m at 2:00 am and high tide was 12.4 m at 7:56 am. assuming sinusoid periodicity, estimate the height of the water at sunset (5:16 pm on that day). give your answer as a decimal (in metres) rounded to 1 decimal place.
Answers
It should be close to 7m at around 5pm. In fact, this is the time of day when the water rises the fastest, so perhaps 8m
What is the period of the sinusoidal signal?The interval between successive peaks in the sinusoidal signal graph, or period, is only the number of seconds needed for one cycle of the sinusoid.
Are all sinusoidal sequences periodic?Depending on the values of angular frequency (), discrete-time sinusoidal sequences may or may not be periodic. A discrete-time sinusoidal signal must have an angular frequency () that is a multiple of 2 to be considered periodic.
It takes roughly 6 hours from low tide to high tide, or 12 hours for the entire tide cycle. Since low tide was at 2 a.m., low tide will be at around 2 p.m. as well. Three hours later, or at around 5 p.m., the water should be at the average level, which should be at (12.4+1.2)/2=6.8 m. Therefore, it should be close to 7m around 5:45. Actually, this is when the water rises the fastest, so it's probably close to 8m. Your 5.5m is obviously too low, regardless of where it is.
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What is 5 divided by 1/8?
Answers
Answer: 50
Step-by-step explanation:
Its 40
Step-by-step explanation
For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
PLS HELP!!!
Solve.
2x-y+2z=-6
-3y+z=-2
2x-3z+4
Answers
The solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7
How to solve the system of equations?The system of equations is given as
2x - y + 2z = -6
-3y + z = -2
2x - 3z = -4
Subtract 2x - 3z = -4 from 2x - y + 2z = -6
This is represented as
(2x - y + 2z = -6) - (2x - 3z = -4)
This gives
- y + 5z = -2
Multiply - y + 5z = -2 by 3
-3y + 15z = -6
Subtract -3y + 15z = -6 from -3y + z = -2
This is represented as
(-3y + z = -2) - (-3y + 15z = -6)
This gives
-14z = 4
Divide by -14
z = -2/7
Substitute z = -2/7 in - y + 5z = -2
- y - 5 * 2/7 = -2
This gives
- y - 10/7 = -2
Rewrite as:
y = 2 - 10/7
Evaluate
y = 4/7
Substitute z = -2/7 in 2x - 3z = -4
2x - 3 * 4/7 = -4
This gives
2x - 12/7 = -4
So, we have:
2x = 12/7 - 4
Evaluate
2x = -16/7
Divide by 2
x = -8/7
Hence, the solution to the system of equations is x = -8/7, y = 4/7 and z = -2/7
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An art museum gift shop has rectangular posters that are similar to actual rectangular paintings. One poster that is 18 inches long is similar to a painting that is 45 inches long and 30 inches wide.(a) What is the scale factor used to reduce the size of the actual painting to the size of the poster? Express the scale factor as a fraction in simplest form. Show or explain how you got your answer.(b) What is the width, in inches, of the poster that is 18 inches long? Show or explain how you got your answer.(c) All the posters are sized using the same scale factor. A second poster is 16 inches long and 14 inches wide. What are the dimensions, in inches, of the actual painting? Show or explain how you got your answer.
Answers
A poster that is 18 inches long is similar to another that is 45 inches long (and 30 inches wide). The scale factor that is used to reduce the size of the painting is shown as;
(a) Scale factor = 18/45
Scale factor = 2/5
This is because the scale of reduction means multiplying the original size by a value that makes it reduce to a smaller size. Hence the scale factor calculated shows that the painting is reduced by a factor of 5 inches to 2 inches, hence its 2/5.
(b) The width of the poster is 18 inches long can be derived by multiplying the width of the painting by the scale factor and that is;
\(\begin{gathered} \text{Scale factor=}\frac{2}{5} \\ \frac{45}{30}=\frac{18}{x} \\ \text{Cross multiply;} \\ 45x=18(30) \\ x=\frac{18(30)}{45} \\ x=12 \end{gathered}\)The width of the poster that is 18 inches long is 12 inches wide
(c) All posters are sized using the same scale of 2/5.
A second poster is 16 inches long and 14 inches wide.
That means the dimensions of the actual painting are as follows;
\(\begin{gathered} \text{Length;} \\ \frac{16}{x}=\frac{2}{5} \\ 2x=5(16) \\ x=\frac{80}{2} \\ x=40 \\ \text{Width;} \\ \frac{14}{y}=\frac{2}{5} \\ 2y=5(14) \\ y=\frac{70}{2} \\ y=35 \end{gathered}\)Therefore, for another poster that is 16 inches long and 14 inches wide, the dimensions of the actual painting are
Length = 40 inches
Width = 35 inches
Write the equation of a line that is parallel to y = 2x + 5 and goes through the point (6,1)
Answers
slope of parallel line: 2
y = 2x + b
1 = 2(6) + b
1 = 12 + b
b = -11
equation of parallel line: y = 2x -11
Solution:
Since the original line is parallel to y = 2x + 5, the original line's slope must be 2.
Using point slope form:
y - y₁ = m(x - x₁)=> y - 1 = 2(x - 6)=> y - 1 = 2x - 12=> y = 2x - 11The equation of a line that is parallel to y = 2x + 5 and goes through the point (6, 1) is y = 2x - 11.
Question 14 (Essay Worth 12 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Sky View School
9, 7, 2,0
8, 7, 6, 5, 5, 5, 4, 3, 1, 0
0
1
South Lake School
5,8
0, 1, 2, 6, 6, 8
2
0 3
Key: 2|1|0 means 12 for Sky View and 10 for South Lake
5, 5, 6, 7, 8
0,6
Part A: Calculate the measures of center. Show all work. (5 points)
Part B: Calculate the measures of variability. Show all work. (5 points)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (2 points)
7
Answers
To find the measures of center, we need to determine the median for each school.
For Sky View School:
Arrange the data in order: 0, 0, 1, 2, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9
The median is the middle value, which is 5.
For South Lake School:
Arrange the data in order: 0, 0, 1, 2, 2, 5, 6, 6, 8
The median is the middle value, which is also 5.
Therefore, the median class size for both schools is 5.
Part B: Measures of variability
To find the measures of variability, we need to determine the range and interquartile range (IQR) for each school.
For Sky View School:
The smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 1 + 2 + 3 + 4)/5 = 2. The third quartile is the median of the upper half, which is (6 + 7 + 8 +9)/4 = 7.25 (rounded to two decimal places).
Therefore, the IQR is 7.25 - 2 = 5.25.
For South Lake School:
The smallest value is 0 and the largest value is 8, so the range is 8 - 0 = 8.
To find the IQR, we need to find the first and third quartiles. The median is 5, so the first quartile is the median of the lower half, which is (0 + 0 + 1 + 2)/4 = 0.75 (rounded to two decimal places). The third quartile is the median of the upper half, which is (6 + 6 + 8)/3 = 6.67 (rounded to two decimal places).
Therefore, the IQR is 6.67 - 0.75 = 5.92 (rounded to two decimal places).
Part C: Choosing a school based on class size
If you are interested in a smaller class size, South Lake School is the better choice. This is because the range and IQR for South Lake School are smaller than those for Sky View School, indicating that the class sizes at South Lake School are more consistent and less variable. Additionally, the largest class size at South Lake School is 8, while the largest class size at Sky View School is 9, further indicating that South Lake School may have smaller class sizes overall.
Measures of center for Sky View School:
Mean = (0+1+2+3+4+5+5+5+6+7+7+8+9)/13
Mean = 4.8
Median = 5
Measures of center for South Lake School:
Mean = (0+1+2+2+3+5+6+6+8+8)/10
Mean = 4.1
Median = 5
Part B:
Measures of variability for Sky View School:
Range = 9 - 0 = 9
Interquartile Range (IQR) = Q3 - Q1 = 7 - 2 = 5
Variance = [(0-4.8)^2 + (1-4.8)^2 + (2-4.8)^2 + (3-4.8)^2 + (4-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (5-4.8)^2 + (6-4.8)^2 + (7-4.8)^2 + (7-4.8)^2 + (8-4.8)^2 + (9-4.8)^2]/12
Variance = 7.6
Standard Deviation = √7.6
Standard Deviation = 2.76
Measures of variability for South Lake School:
Range = 8 - 0 = 8
Interquartile Range (IQR) = Q3 - Q1 = 6 - 1 = 5
Variance = [(0-4.1)^2 + (1-4.1)^2 + (2-4.1)^2 + (2-4.1)^2 + (3-4.1)^2 + (5-4.1)^2 + (6-4.1)^2 + (6-4.1)^2 + (8-4.1)^2 + (8-4.1)^2]/9
Variance = 6.45
Standard Deviation = √6.45
Standard Deviation = 2.54
Part C:
If you are interested in a smaller class size, South Lake School is a better choice for you. This is because the measures of center and variability for South Lake School are both smaller than those for Sky View School.
help me please........
Answers
Answer:
314x527Step-by-step explanation:
165,478 <-- Answer
Ryan has a checking account balance of -$25. Write an absolute value statement to show how much money Ryan owes the bank.
Answers
My best guess is x^2 + x - 25
I’m sorry if I’m wrong
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answers
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
You roll a die 2 times. What is the probability or rolling a 6 and then a 2?
Answers
Answer:
1 out of 6
Step-by-step explanation:
Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.
Imagine that the price per gallon of gas with a $7 car wash is $3.32 and the price without a car wash is $3.52 When is it worth it to buy the car wash? When is it worth it if the car wash cost $4
Answers
Answer: b and d
Step-by-step explanation:it IS
if e and f are mutually exclusive and p(e)>0 and p(f)>0, which one of the following statements is correct?
Answers
Neither statement "E and F are always independent" nor "E and F are always dependent" is correct for mutually exclusive events E and F with positive probabilities p(e)>0 and p(f)>0.
Events that are mutually exclusive cannot occur at the same time. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 2 on a fair die", These events cannot occur simultaneously since a 1 and a 2 cannot be rolled.
In probability theory, two events E and F are considered independent if the occurrence of one event has no effect on the probability of the other event occurring. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 6 on a fair die", these events are independent because the occurrence of one event (rolling a 1) does not affect the probability of the other event (rolling a 6) occurring.
In the case where events E and F are mutually exclusive, their occurrence does affect each other, as the occurrence of one event makes it impossible for the other event to occur. Therefore, the statement "E and F are always independent" is not correct. Similarly, the statement "E and F are always dependent" is also not correct because dependence is a different concept from mutual exclusiveness.
Therefore, "Neither of the above statements is correct" is the appropriate response.
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The complete question is:
Which of the following statements is correct if e and f are mutually exclusive and p(e)>0 and p(f)>0?
a) E and F are always independent
b) E and F are always dependent
c) Neither of the above statement is correct
What is the meaning of an absolute value
Answers
Answer:
"Absolute value" is the non-negative value of a number, disregarding whether or not it has a sign.
Step-by-step explanation:
"Absolute value" is the non-negative value of a number, disregarding whether or not it has a sign. It can be thought of as how far it is away from the number of 0, whether it's to the left or right. Absolute value of a number is written as |x|, where x = any number. Let's say x was -1. |-1| would be 1 because it's 1 away from 0. If x was just 1, then the number would stay the same.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
A group of 40 children attend a baseball game on a field trip. Each child received either a hot dog or a bag of popcorn. The hot dogs were $2.25 and the popcorn was $1.75. If the total bill was $83.50, how many of each were bought?
Answers
Answer:
26 hotdogs and 14 popcorn
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three statements that are true include the following:
A. The radius of the circle is 3 units.
B. The center of the circle lies on the x-axis.
D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r² .......equation 1.
Where:
h and k represents the coordinates at the center of a circle.
r represents the radius of a circle.
Based on the information provided, we have the following equation of a circle:
x² + y² – 2x – 8 = 0 ......equation 2.
In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:
x² – 2x + y² = 8 = 0
x² – 2x + (2/2)² + y² = 8 + (2/2)²
x² – 2x + 1 + y² = 8 + 1
(x – 1)² + (y - 0)² = 9 .......equation 3.
By comparing equation 1 and equation 3, we have the following:
Center (h, k) = (1, 0)
Radius (r) = 3
Additionally, this line and the center of the given circle lies on the x-axis (x-coordinate) because the y-value is equal to zero (0).
(x - 0)² + (y - 0)² = 3²
x² + y² = 9.
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What is the measure of angle AED?
Answers
Answer:
Step by step explanation:
well this is simble you just do it
Two lines are _______ if and only if they lie in the same plane and intersect at right angles.
Answers
Answer:
I believe your answer to go in the blank should be bisectors. I hope this helps you! :)
What is equivalent to 3;4
Answers
Answer:
6;8
3;4 that the lowest that it can go. the equivalent is 6;8 but if you want to change it into decimal form you can divide by two which is 1.5;2 but the answer is 6;8 because 3;4 is already in it's lowest form, or is already simplified to it's maximum extent.
Solve the inequality for w.
w+7<20
Simplify your answer as much as possible.
0
Answers
Answer:
w<13
Step-by-step explanation:
Works identically to a normal single-variable equation.
Subtract 7 on both sides in order to isolate w--->w+7-7<20-7
The answer (which cannot be simplified any further) is w<13.
Answer:
w < 1`3
Step-by-step explanation:
Isolate the variable w on one side of the inequality sign.
w+7<20
w<20 - 7
w<13.
Tammy rents a storage shed. The storage shed is in the shape of a rectangular prism with measurements as shown. A rectangular prism has a length of 10 feet, height of 9 feet and a width of 9 feet. Select the phrase and number from the drop-down menus to correctly complete each sentence. Tammy can find the volume of the storage unit by . To completely fill the storage shed, Tammy would need unit boxes that each measure 1 cubic foot.
Answers
Answer:
finding the product of 9,10,and 9
810
Step-by-step explanation:
Problem 3
Draw the pictures to compute 1 ÷ 11 in a base ten system, and show the answer is 0.09.
Answers
The result of 1/11 in the base 10 system is given as is 0.09.
How to solveTo visualize the long division of 1 ÷ 11 in a base ten system:
Set up the long division: 11 outside and 1.00 inside the division bracket.
Place the decimal point in the quotient above the dividend's decimal point.
Bring down the first digit (0) and divide 11 into 10; it goes 0 times.
Subtract the product (0) from 10, leaving 10.
Bring down the next digit (0) and divide 11 into 100; it goes 9 times.
Subtract 99 from 100, leaving a remainder of 1.
The result is 0.09.
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