I assume that we want to find the minimum distance between the point A(-1, 7) and the line y = 3x.
We will get that the distance is 3.22
So first, let's see how to get the distance between two points (x₁, y₁) and (x₂, y₂). We just use the general formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Now we want to find the distance between (-1, 7) and a point on the line y = 3*x, that can be written as (x, 3x)
That distance is:
[tex]d = \sqrt{(-1 - x)^2 + (7 - 3x)^2}[/tex]
Now we want to minimize this, which is equivalent to minimize d^2, then we can define:
D = d^2
and write:
[tex]D = (-1 - x)^2 + (7 - 3x)^2\\\\D = 1 - 2x + x^2 + 49 - 42x + 9x^2\\\\D = 10x^2 - 44x + 50[/tex]
Now we need to minimize this, which is a parabola, so the minimum will be at the vertex of the parabola (we know this because the leading coefficient is positive, thus the parabola opens upwards).
Remember that for a parabola like:
a*x^2 + b*x + c
The vertex is at:
x = -b/2a
Then for our parabola, the vertex will be at:
x = -(-44)/(2*10) = 44/20 = 2.2
Thus the minimum distance is given by:
[tex]d = \sqrt{(-1 - 2.2)^2 + (7 - 3*2.2)^2} = 3.22[/tex]
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it will be 12 degrees tonight. the weatherman predicts it will be 25 degrees warmer by noon tomorrow. what will the temperature be by noon tomorrow?
Henry drove 195 miles in 3 hours. How many miles per hour was he driving?
666-601=65
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it wont let me put it in without these words\
MATH HELP > WILL AWARD BRAINLIEST
The graph below shows the graphs of the linear function y=7x and the exponential function y=7^x
True or False: The growth rate of the exponential function exceeds the growth rate of the linear function for 1
Answer: True.
Step-by-step explanation:
Given: The graph below shows the graphs of the linear function y=7x and the exponential function [tex]y=7^x[/tex]
Both of the function have same value of rate =7
But in linear function y=7x , 7 is the constant of proportionality.
In exponential function [tex]y=7^x[/tex], 7 is the multiplicative rate of change.
For [tex]1\leq x\leq 3[/tex]
For y=7x ,
x y
1 7
2 14
3 21
For [tex]y=7^x[/tex]
x y
1 7
2 49
3 343
Thus, we can see the growth rate of the exponential function exceeds the growth rate of the linear function for [tex]1\leq x\leq 3[/tex].
Answer:
D
Step-by-step explanation:
Just took test on it
M and N are the acute angles of an isosceles right triangle.
Select the true statements.
cosM = sinM
cosM = cosN
cosM = tanN
sinN = cosM
tanM = tanN
Which property justifies the procedure used to eliminate fractions and decimals from equations?
Division Property of Equality
Identity Property of Multiplication
Multiplication Property of Equality
Addition Property of Equality
By multiplication property of equality, we can eliminate fractions and decimals from equations. Option C is correct.
Given that,
To determine which property justifies the procedure used to eliminate fractions and decimals from equations.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Suppose the equation
1 / 4 = 0.25
Now multiply both sides by 4
4 * 1/ 4 = 0.25 * 4
1 = 1
So, by multiplication property of equality, we can eliminate fractions and decimals from equations.
Thus, by multiplication property of equality, we can eliminate fractions and decimals from equations.
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7x-4y=3y-14 solve for y
Which linear function represents the line given by the point-slope equation y + 1 = –3(x – 5)?
f(x) = –3x – 6
f(x) = –3x – 4
f(x) = –3x + 16
f(x) = –3x + 14
answer asap
The linear function represents the line given by the point-slope equation y + 1 = –3(x – 5) is f(x) = -3x + 14.
What is point-slope equation?"In a Point-slope form it is likely to be y - y1 = m(x - x1). This form of a linear equation is derived from a equation for finding the slope of a line."
Given
The point-slope equation y + 1 = –3(x – 5)
By solving the above equation
y + 1 = -3x + 15
⇒ y = -3x + 15 - 1
⇒ y = -3x + 14
Replace y with f(x)
⇒ f(x) = -3x + 14
Hence, the linear function represents the line given by the point-slope equation y + 1 = –3(x – 5) is f(x) = -3x + 14.
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Explain why the t-distribution has less spread as the number of degrees of freedom increases
Solve for x. x + 5 = 2x
The solution to the equation x + 5 = 2x is x = 5.
We have,
To solve the equation x + 5 = 2x, we want to find the value of x that makes the equation true.
We start by isolating the variable x on one side of the equation.
In this case, we can do that by subtracting x from both sides of the equation.
By subtracting x from both sides, we have:
x + 5 - x = 2x - x
The x term on the left side cancels out, leaving us with:
5 = x
This means that x is equal to 5, and substituting x = 5 back into the original equation gives us:
5 + 5 = 2(5)
10 = 10
The equation is true, confirming that x = 5 is the correct solution.
Therefore,
The solution to the equation x + 5 = 2x is x = 5.
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use mental math to solve 4576 + 2842
which functons have graphs that are less steep than the graph of f(x)=2x^2
(select each correct answer)
h(x)= -2x^2
g(x)= -3x^2
m(x)= 3x^2
j(x)= -x^2
k(x)= x^2
Answer:
[tex]k(x) = x^{2} \\j(x) = -x^{2}[/tex]
Step-by-step explanation:
The slope has to be steep and the ones given above are all greater than 2 except for k(x) and j(x).
In which area did the French find the most success?
Shipbuilding
Fur trade
Lumber industry
Agriculture
If you start with an integer and , subtract -85 ,add -57 ,subtract 68, add -77,add 55 and subtract-73 the result is 0. Find the integer that you start with
Population has a mean of 180 and a standard deviation of 24. a sample of 64 observations will be taken. the probability that the mean from that sample will be between 183 and 186 is
The probability that the sample mean is between 183 and 186 would be 0.1359.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of a population
N = number of observations of population
X = mean
μ = population mean
It is given that the Population has a mean of 180 and a standard deviation of 24. a sample of 64 observations will be taken.
So, µ = 180, σ = 24 and n = 64.
By the Central Limit Theorem, the sample mean is normally distributed with a mean of 180 and a standard deviation of 24
Therefore, 24/√64
= 24/8 = 3.
Now let's convert the 183 and 186 into z -scores.
So, the z-score for 183 is (183–180)/3 = 1
The z-score for 186 is (186 –180)/3 = 2.
We can see that the area to the left of z = 1 is 0.8413
The area to the left of z = 2 is 0.9772.
The probability that the z is between 1 and 2 can be calculated as the difference between the area of z.
= 0.9772 – 0.8413
= 0.1359.
Thus, the probability that the sample mean is between 183 and 186 would be 0.1359.
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The _____ of a cone is the curved surface that connects the base of a cone to the apex of the cone.
The lateral surface of a cone is the curved surface that connects the base of a cone to the apex of the cone.
The lateral surface of a cone refers to the curved surface area that connects the base of the cone to its apex (the pointed top).
It forms the sloping sides of the cone.
In a cone shape, the base is a circle, and the lateral surface is the part that wraps around the sides to meet at the apex.
This surface does not include the base or the tip of the cone. It is only the curved part that connects the two.
The lateral surface area of a cone can be calculated using the formula A = πrl, where A represents the lateral surface area, r is the radius of the base of the cone, and l is the slant height, which is the distance from the apex to any point on the edge of the base.
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What is 1/4+1/2+x=−3/4?
1/4+2/4+x=−3/4
1/4+2/4+x-1/4=-3/4-1/4
2/4+x-2/4=-1-2/4
x=-1 1/2
Katy buys 3 dvds every two weeks. how many dvd's will she buy in 14 weeks?
Answer:
21 dvds
Step-by-step explanation:
Set up a proportion in terms of DVDs to weeks and solve.
3/2 = x/14
(2)(x) = (3)(14)
2x = 42
x = 21
Therefore, Katy will buy 21 DVDs in 14 weeks.
which expression shows how 6x45 can be rewritten using the distributive property
Write an inequality to model the situation. a number exceeds 9.
Answer:
n ≥ 9
Step-by-step explanation:
15b - 10c - 10b + 5=
List the steps to construct parallel lines using a compass and straightedge.
List the steps to construct parallel lines using a drawing program.
List the steps to construct perpendicular lines using a compass and straightedge. List the steps to construct perpendicular lines using a drawing program.
1. To construct parallel lines, first, you must start with a line segment AB that well copies. Mark another point called C. Set the compass to the point A and adjust the compass to the width of the original line. Then without moving the compass, put it on point C and mark the end and label it D. Use a straightedge to connect the points and now you’ve copied a line segment.
2. First, you click the line and make a line segment. Then make a separate point anywhere. Then you double-click perpendicular lines and click parallel lines. Click and drag the line segment onto the separate point.
3. First, you start with a point on a line. Then you put your compass on the point and mark an arc on each side of the line and put points on them. Then you put the compass on one of the points and make an arc above the original point. Do the same for the other side. You should end up with 2 X’s on top and bottom of the original point. Then mark points on the Xs. Finally, use a straight edge to connect the two X’s which will make a bisecting line through the original.
4. First, you make a line and click perpendicular lines and you will have a straight line cutting through the original.
Answer:
Step-by-step explanation:
q(a+y)=67y+93 Solve for y
The value of y is:
[tex]y=\dfrac{93-qa}{q-67}[/tex]
Step-by-step explanation:We are given a expression in terms of three unknowns q,a and y.
Now, we are asked to solve this expression for y.
i.e. we are asked to represent y in terms of other two unknowns.
We will first use the distributive property under multiplication in the left hand side of the equation.
i.e.
[tex]q\times a+q\times y=67y+93\\\\i.e.\\\\qa+qy=67y+93[/tex]
Now, we combine the terms of y at one side of the equation and the other terms to the other side.
i.e.
[tex]qy-67y=93-qa\\\\i.e.\\\\(q-67)y=93-qa\\\\i.e.\\\\y=\dfrac{93-qa}{q-67}[/tex]
Which two terms are often synonymous with or made possible with cidr?
CIDR, or Classless Inter-Domain Routing, is tied to IP address aggregation and subnetting, which help in efficient IP address allocation and network management.
Classless Inter-Domain Routing, commonly known as CIDR, is a method for allocating IP addresses and routing Internet Protocol packets.
Two terms often associated with CIDR are IP address aggregation and subnetting. IP address aggregation involves the grouping of multiple networks into a single, larger network, represented as a CIDR block.
Subnetting refers to dividing a larger network into smaller, more manageable sub-networks or subnets. This technique can help reduce the number of routing table entries needed in a network, which improves routing efficiency and conserves the limited supply of IP addresses.
Michelle jumps from a plane at an altitude of 1000 m. After 10 seconds her parachute opens. The graph shows the relationship between her altitude and time. How long does it take for her to be half way between the plane and the ground?
Answer: 1 minute
Step-by-step explanation: Michelle jumped from the plane at the altitude of 1000 m. To find the half way point, from the plane she jumped from and the ground; all you have to do is cut the altitude in half:
1000/2 = 500m which Is labeled at 1 minute
Meaning that it took 1 minute for her to be halfway from the ground
I have done this problem and taken the test, it is 100% correct
Good luck hope it helps! :D
Shen’s mother gave him $10 to go buy groceries. He picked up a gallon of milk for $3.49, three pounds of oranges that cost $1.14 per pound, and a box of cereal for $3.46. Shen used front-end estimation to determine whether he had enough money for the groceries. How much did he estimate the total cost would be?
Answer:
$9.
Step-by-step explanation:
We have been given that Shen’s mother gave him $10 to go buy groceries. He picked up a gallon of milk for $3.49, three pounds of oranges that cost $1.14 per pound, and a box of cereal for $3.46.
In front-end estimation, we round whatever number is in front instead of rounding each number to a given place value.
We can see that in $3.49, front number is and second number is less than 5, so we will round it down to $3.
Similarly, in $3.46, 1st number is 3 and second number is less than 5, so we will round it down to $3.
In $1.14, front or 1st number is 1 and second number is less than 5, so we will round down to $1. Cost of three orange boxes would be [tex]\$1*3=\$3[/tex].
[tex]\text{Total estimated cost}=\$3+\$3+\$3[/tex]
[tex]\text{Total estimated cost}=\$9[/tex]
Therefore, the total estimated cost of groceries is $9.
On scrap paper, determine if the triangle with the following vertices is a right triangle.
A(-3, 5), B(1, 4), and C(-1, 0).
in the box below, tell whether or not the triangle is a right triangle. Explain how you arrived at your answer.
Answer:
not a right triangle
Step-by-step explanation:
The slope of AB is -1/4; the slope of BC is 2. These are not negative reciprocals of one another.
Which equation is a point slope form equation for line AB?
A.y+1=3/2(x-1)
B.y+1=-3/2(x-1)
7x-y-17 = 0 Hope this helps!
The front of a tent is an equilateral triangle with the ratio of its base, b, to its height, h, given by b over h equal fraction numerator 2 over denominator square root of 3 end fraction. What equation can be used to find the tent's height?
I don't understand this :((
Express 5/14 as a decimal number rounded to the nearest thousandth.
0.357
2.8
0.3571
0.28
Rounded to the nearest thousandth, it's 0.357. So, the correct answer is: A) 0.357.
To express 5/14 as a decimal, divide 5 by 14 to get 0.357142857. Rounding to the nearest thousandth means considering the third digit after the decimal point. Since the fourth digit is 1, which is less than 5, it doesn't affect the rounding. Therefore, 5/14 as a decimal rounded to the nearest thousandth is 0.357. This approximation maintains three decimal places, with the third digit being 7.
[tex]\frac{5}{14}=0.357142857[/tex]
Complete Question:
Express 5/14 as a decimal number rounded to the nearest thousandth.
A) 0.357
B) 2.8
C) 0.3571
D) 0.28