It is proved that ca⇀ and cb⇀ are orthogonal .
Let AO = - u vector , OB = u vector and OC = α vector .
According to question ,
u * u = v * v = r ^ 2 and
AC vector = AO vector + OC vector = u + v
BC vector = BO vector + OC vector v - u ,
Applying dot - product ,
( AC vector ) . ( BC vector ) = ( v + u ) . ( v - u )
= ( v . v ) - ( u . u )
= ( r ^ 2 ) - ( r ^ 2 )
= 0
Hence , AC and BC are orthogonal .
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I cant find my answer please help!
Answer:
Domain: 1 ≤ x ≤ 6
Range 10 ≤ M(x) ≤ 60
Step-by-step explanation:
M(x) = 10x where x represents the number of tickets bought
Assume nobody goes with Victoria. In that case she will go alone, only 1 ticket is bought and total cost = $10
Maximum 5 friends means total of 6 tickets purchased so total cost is $60
Domain refers to the possible input values ie possible x values. Here the domain is 1 ≤ x ≤ 6 also written as [1, 6]
The range is the total possible set of output values. Here output of the function is cost and cost ranges between 10 and 60 inclusive
So Range = 10 ≤ M(x) ≤60 also written as [10, 60]
Given , find the average rate of change of f(x)=[tex]f(x)=\frac{1}{x+5}[/tex] on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp
The average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
Given,
The function = [tex]\frac{1}{x+5}[/tex]
We know the average rate of change of the function is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where a and b are the intervals
a= 1
b=1+h
f(a) =f(1)= [tex]\frac{1}{1+5}[/tex]
=[tex]\frac{1}{6}[/tex]
f(b)= f(1+h)
=[tex]\frac{1}{1+h+5}[/tex]
=[tex]\frac{1}{6+h}[/tex]
f(b)-f(a)= [tex]\frac{1}{6+h}-\frac{1}{6}[/tex]
[tex]=\frac{6-(6+h)}{6(6+h)} \\=\frac{6-6-h}{36+6h}\\ =-\frac{h}{36+6h}[/tex]
Then,
[tex]\frac{f(b)-f(a)}{b-a} =\frac{-\frac{h}{36+6h} }{1+h-1}[/tex]
[tex]=\frac{-\frac{h}{36+6h} }{h} \\=-\frac{1}{36+6h}[/tex]
Hence, the average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
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a password system uses four digits from 0 to 9. how many different four-digit passwords with no digit repeated are possible?
Total 5040 passwords can be generated when no digits are repeated
• Permutation in mathematics is an arrangement of objects in an definite order. The elements or sets or things are arranged in sequential order or linear order.
• Permutation is classified into four types :
1) where repetition is not allowed
2) where repetition is allowed
3) objects that are non distinct
4) circular permutation
• The formula for calculating permutation is n!/(n-r)!
As we are given that the password uses four digits from 0-9 and repetition is not allowed.
So, n = 10 and r = 4
Using the formula for permutation we get
= 10! / (10-4)!
= 10!/6!
= 10 * 9 * 8 * 7 * 6! / 6!
= 10 * 9 * 8 * 7
= 5040
Therefore, 5040 four digit passwords are possible when no digit is repeated.
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HELP ME PLEASE I need this rn!!!!! SOMEONE ANYONE PLEASEEEEE
question 4
Jeremy is 80 ft from a wall. Each time he moves toward the wall he reduces his distance from the wall by half. Which graph best models the situation?
the four photos are to this question
question 5
Which expressions describe the end behavior of the graph?
the 5 photo is to this one
Select EACH correct answer.
Using a geometric sequence, we have that:
Graph 1 models the situation.
The end behavior of the graph is given as follows:
As x decreases, y approaches the line y = 2.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q, hence the second term is the first multiplied by q, the third is the second multiplied by q, and so on.
For item 4, we have that:
The first term is of 80.The common ratio is of 0.5.Hence when x = 2, y = 40, when x = 3, y = 20, and so on.This means that the first graph is correct.
What is the end behavior of a function?The end behavior of a function is given by the limits of the function when x goes to infinity.
Hence, from the final graph, we have that:
As x decreases, y approaches the line y = 2. (lim x -> negative infinity = -2).As x increases, y decreases without bound. (lim x -> infinity = - infinity, not an option but just to explain).More can be learned about geometric sequences at https://brainly.com/question/24643676
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-4n algebraic expression
Answer: -1 x 2 x 2 x n
Step-by-step explanation:
-4n
factor
which leads to -1 x 2 x 2 x n
how many quarts of pure antifreeze must be added to 3 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution?
1.5 quarts of pure antifreeze must be added to 3 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
Given;
Percentage of 3 quarts of antifreeze solution = 40%
We have to find,
Quarts to obtain the antifreeze solution of 60%
Now,
The 3 quarts of 40% antifreeze solution contains 0.4 x 3 = 1.2 quarts of pure antifreeze solute
Let,
x is the number of quarts of pure antifreeze needed to make a 60% solution
The equation to solve becomes, where x is the amount of pure antifreeze to be added is
(1.2 + x )/(3 + x) =0.6
(1.2 + x ) = 0.6 * (3 + x)
(1.2 + x ) = 1.8 + 0.6x
x-0.6x = 1.8 - 1.2
0.4x = 0.6
x = 1.5
Therefore,
1.5 quarts of pure antifreeze to the current solution to make a 60% solution
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help please
just tell the answer get it right for brainliest!
Answer:
pretty sure its 2.9
Step-by-step explanation:
Answer:2.92 or just 3
Step-by-step explanation:
btw read your lesson and pay attentiom
what is 9/7 divided by 6
Ashley is constructing CD such that CD intersects AB at C and is the segment bisector of AB. Select the relationship that must be true.
A) Point C is equidistant from A and B.
B) Point D is equidistant from A and B.
C) Point A is equidistant from C and D.
D) Point B is equidistant from C and D
Answer:
Step-by-step explanation:
a,d
Answer:ad
Step-by-step explanation:
ad
Question 2 (1 point)
Given the following points, are lines CD and EF parallel, perpendicular, or neithe
A(1,2) B(3,4) C(5,2) D(8,3) E(3,8) F(-6,5)
a
b
C
parallel
perpendicular
neither?
Given lines CD and EF are parallel. Therefore answer is (a)
How to find slope of two lines and check whether they are parallel or perpendicular
Given are two points P (x₁, y₁) and Q ( x₂, y₂)
Then slope of the line PQ is given by (y₂-y₁)/(x₂-x₁)
If two lines have slopes m₁ and m₂ respectively
Then the lines are parallel when their slopes are equal i.e. m₁=m₂
and the lines are perpendicular when m₁*m₂= -1
Given C(5,2), D(8,3),E(3,8) F(-6,5)
Then,
Slope of CD = (3-2)/(8-5)= 1/3
Slope of EF = (5-8) / (-6-3) = 1/3
Slope of CD=Slope of EF
Therefore CD and EF are parallel
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A person who weighs 100 kilograms on Earth would weigh 16.5 kilograms on the moon. Determine how much a child who weighs 30.5 kilograms on Earth would weigh on the moon. Round to the nearest hundredth if necessary.
On Earth, a child weighing 30.5 kilograms would weigh 5 kilograms on the moon.
What is the basis of the difference between the weights on earth and the moon?Our weight on the Moon is 16.5% of what it would be on Earth. In other words, if we weighed 100 kilograms on Earth, we would only weigh 16.5 kilograms on the Moon. Assume we tipped the scales at 200 pounds for you imperial folks. On the Moon, our weight would be only 33 pounds. It's due to the Moon's lower gravity. Objects on the Moon's surface experience only 16.5% of the gravity that they would on Earth. Gravity is caused by mass. The more weight we have, the more gravity will pull on us.Given:
A person who weighs 100 kilograms on Earth would weigh 16.5 kilograms on the moon.Our weight on the Moon is 16.5% of what it would be on Earth.So, we have to take out 16.5% of 30.5 kilograms.
= 30.5/100 × 16.5= 0.305 × 16.5= 5.0325After rounding off, the weight becomes 5 kilograms.
Therefore, a child who weighs 30.5 kilograms on Earth would weigh 5 kilograms on the moon.
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jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 what is the range of the data jonathon collected?
The range of the data collected by Jonathon is [0.25,0.98]
Given that Jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 and asked to find the range of the data collected by Jonathon.
The minimum value of the data collected by Jonathon is 0.25 and the maximum value of the data collected by Jonathon is 0.98
The range of the given data:(minimum value,maximum value)
Here, The minimum value of the data collected by Jonathon is 0.25
The maximum value of the data collected by Jonathon is 0.98
Therefore,The range of the data collected by Jonathon is [0.25,0.98]
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Which transformation will preserve distance between points when applied to a figure
in the (x, y) -coordinate plane?
A . (x,y) → (x + 2,- 3y)
B . (x,y) → (-x+ 2, y + 7) C . (x,y) → (2x,- 3y)
D. (x,y) → (2x, y)
1 pts. PLEASE HELP FOR TEST
The transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)
How to determine the transformation will preserve distance between points when applied to a figure in the (x, y) -coordinate plane?Let the coordinate be represented as
(x, y)
For a transformation to preserve distance between points when applied to a figure in the (x, y)-coordinate plane, the transformation must be any of the following:
ReflectionRotationTranslationFrom the list of options, we have
B . (x,y) → (-x+ 2, y + 7)
This transformation is a translation
Hence, the transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)
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What is the value of the expression below when w=7?
w² +3w - 10
Answer:
The value of the expression is 60.
Find the area of the quarter circle with a radius of 10 in. Use
3.14 for , and round the answer to the nearest tenth, if
necessary.
10in
The area of the quarter-circle is_______in².
Answer:
314 in²
Step-by-step explanation:
A=3.14r^2
π·10^2≈314
The area of the quarter-circle is 314 in²
Altogether, tom and sarah have 32 baseball cards. if sarah has three times as many baseball cards as tom, how many does each of them have
tom has 8 cards and sarah has 24 cards .
Explain how many cards sarah and tom has?tom and sarah total baseball cards =32
sarah has three times as many baseball cards as tom
The 2 equations are
1. sarah + tom = 32
2. sarah = [tex]3 \times tom[/tex]
substitute equation 2 in 1.
[tex]3\times tom +tom= 32[/tex]
4 tom = 32
tom = 32/4
tom = 8 cards
sarah = [tex]3\times tom[/tex]
= [tex]3\times 8[/tex]
sarah = 24 cards
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a measurement that can be repeated is said to be and one that is close to the accepted or actual value is
A measurement that can be repeated is said to be precise and one that is close to the accepted or actual value is approximate.
Given that,
The incomplete statement is given we have to complete the statement.
All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.
Here,
A measurement that can be repeated is said to be precise values
A measurement that is close to the accepted or actual value is approximate.
Thus, the required words are precise and approximate.
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two accountants, lee and johnson, went to a business meeting together. lee drove to the meeting and johnson drove back from the meeting. if lee and johnson each drove 140 kilometers, what was the average speed, in kilometers per hour, at which lee drove? 1) the average speed at which johnson drove was 70 kilometers per hour 2) lee drove for exactly 2 hours
The average speed of Lee is 70 km/hr.
To clear up this trouble we want to understand the concept of average speed.
average speed is given while we divide the overall distance blanketed with the aid of the total time taken.
right here, it's miles given that Lee and Johnson each drove a hundred and forty Km. additionally, it's miles given that lee drove for two hours.
So, average speed of Lee = [tex]\frac{140}{2}[/tex]
= 70 km/hr
Here, the average speed at which Lee drove the car and went to business meeting is 70 km/hr.
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PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
Let f(x) be the integrand.
[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \implies \int^{4}_{-2} x^3 \text{ dx}=\approx \frac{1}{2}(2)[-8+64+2(0+8)] \\ \\ =\boxed{72}[/tex]
the perimeters of two squares are in the ratio 2 : 7. What is the ratio of the area of the smaller square to the area of the larger square
The ratio of the area of the smaller square to the area of the larger square = 4 : 49
Finding the area of a square from the perimeterLet the perimeter of the small square be [tex]P_1[/tex]
Lethe the perimeter of the large square be [tex]P_2[/tex]
Perimeter of a square = 4 Length
[tex]P_1=4L_1\\\\P_2=4L_2[/tex]
The ratio of the perimeters = 2:7
[tex]\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}[/tex]
The area of a square = L^2
[tex](\frac{L_1}{L_2} )^2=(\frac{2}{7} )^2\\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{2^2}{7^2} \\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{4}{49}[/tex]
Therefore, the ratio of the area of the smaller square to the area of the larger square = 4 : 49
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please solve u r the best thx
Answer:13
Step-by-step explanation:
Answer:
There are no values of f to make this equation true.
Hope this helps.
Step-by-step explanation:
In the second part of the equation, 6( 1/16f - 3 ), 6 * 1/16f is 3/8f. If both sides subtract a 3/8f and both sides add 18, you get 18.5 = 0 meaning there are no values of f to make this equation true.
can someone help me really quick
Shawn earn 11 per hour.
Hannah travel 25 miles in one gallon of gas.
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
given:
According to the graph the y- axis shows the earnings.
So, we have the coordinates are
(1, 11), (2, 22) and (3, 33)
So, Shawn earn = 22 - 11 / 2 -1 = 11 per hour.
Now, in second case
The coordinates are
(3, 75), (5, 125), (6, 150), (10, 250)
So, m= (125 - 75) / (5-3)
m= 50/2
m=25
So, Hannah travel 25 miles in one gallon of gas.
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The length of a rectangle is 4 inches more than 3 times its width. The perimeter of the rectangle is 48 inches. What are the length and width of the rectangle?
The length and width of the rectangle is found as 19 inches and 5 inches respectively.
What is defined as the perimeter of rectangle?To calculate the perimeter, or distance all around rectangle, add all four side lengths. This can be done quickly by adding the width and height and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = 2(length + width).Now, as per the given question;
Let width of a rectangle = w inches
Then, length of a rectangle = 3w + 4
Perimeter of a rectangle = 2(length + width)
Substitute the values in the formula of perimeter.
48 = 2(3w + 4 + w)
48/2 = 4w + 4
24 = 4w + 4
20 = 4w
w = 5
Thus, the width of the rectangle is 5 inches.
Put w = 5 inches in its length.
l = 3w + 4
l = 3×5 + 4
l = 15 + 4
l = 19 inches.
Therefore, the length of rectangle is found as 19 inches.
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Evaluate 15 − 6(7 + 5) ÷ 32.
Eva’s phone is 4 times the number of songs on Hank’s phone.
• The total number of songs on both phones is 600 songs.
How many songs (N) are on Hank’s phone?
Answer:
120 songs
Step-by-step explanation:
Eva=4u
Hank=1u
Eva+Hank=5u
5u=600
1u=600/5
=120
If 4 is subtracted from the numerator of a fraction, its value becomes 1/3. If 5 is added to the denominator of the original fraction its value becomes 1/2. What is the original fraction.
Answer:
79
Step-by-step explanation:
Let the numerator of the original fraction be 'x' and the denominator be 'y'. So, the original fraction becomes xy
According to the question,
Condition I,
If 4 is subtracted from the numerator of a fraction, its value becomes 1/3.
or,x−4y=13
or,3(x−4)=y
or,y=3x−12
Condition II,
If 5 is added to the denominator of the original fraction, the value becomes 1/2.
or,xy+5=12
or,2x=y+5
Put value of y from equation (i) in equation (ii), we get,
or,2x=(3x−12)+5
or,2x=3x−12+5
or,3x−2x−7=0
∴x=7
Put value of x in equation (i), we get,
or,y=3×7−12
or,y=21−12
∴y=9
So, (x,y) = (7,9)
Therefore, the required original fraction is 79.
can someone please anwser (5z+y)/7 (the number values of z and y are in the picture)
Answer:
2
Step-by-step explanation:
First substitute the values of z and y in the expression.
Use PEDMAS. We have to multiply 5 and 3, which gives 15. Subtract 1 from 15 and then divide the result by 7.
[tex]\sf \dfrac{5z + y}{7}= \dfrac{5*3 + (-1)}{7}\\\\[/tex]
[tex]\sf = \dfrac{15 - 1}{7}\\\\ = \dfrac{14}{7}\\\\= 2[/tex]
Simplify fully
4x^+ 4x/-2x^-2
Answer: -12x
Step-by-step explanation: 4x +4 −2 −2x
Calculate x to the power of 1 and get x.
4x+4×( −2 −2x )
Calculate 2 to the power of −2 and get 41.
4x+4×( − 41x)
Divide x by − 41
by multiplying x by the reciprocal of − 41 .
4x+4×( −1x×4)
Anything divided by -1 gives its opposite.
4x+4(−x×4)
Multiply 4 and −1 to get −4.
4x−4x×4
Multiply −4 and 4 to get −16.
4x−16x
Combine 4x and −16x to get −12x.
−12x
find the slope of the line that goes through the points (4,-6) and (3,7)
Answer:
m=-13
Step-by-step explanation:
the formula for getting the slope is[tex] = \frac{y 2- y1}{x2 - x1} \\ = \frac{7 - ( - 6)}{3 - 4} \\ = \frac{7 + 6}{ - 1} \\ = \frac{13}{ - 1} \\ = - 13[/tex]Hope this helpsWhat is the length of the shorter leg?
____________________________
What is the length of the longer leg?
____________________________
The shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.
How to get the length of the legs of the triangle?Here we know that we have a right triangle, and we know that:The hypotenuse measures √130 units.
The perimeter measures 14 + √130 units.
If we define:
x = shorter leg.
y = larger leg.
Then, using the Pythagorean theorem, we can write:x^2 + y^2 = √130^2 = 130
And for the perimeter equation we know that:
perimeter = x + y + √130 = 14 + √130
We can simplify this equation to:x + y = 14Then we have the system of equations:
x^2 + y^2 = 130
x + y = 14
Isolating one variable in the second equation we get.
x = 14 - y
Replacing that in the other equation we get:
(14 - y)^2 + y^2 = 130
Now we can solve this for y.
196 - 28y + y^2 + y^2 = 130
2y^2 - 28y + 196 - 130 = 0
2y^2 - 28y + 66 = 0
y^2 - 14y + 33 = 0
Using Bhaskara's formula we can get:
y = (14 ± √( 14^2 - 4*1*33))/2*1y = (14 ± 8)/2
Now, remember that y is the larger leg of the triangle, then:y = (14 + 8)/2 = 11For the value of x we use:
x = 14 - y = 14 - 11 = 3x = 3the shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.
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