A line has no thickness, but it does have direction and infinite length.
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
Given the variety of geometries in modern mathematics, the idea of a line is directly related to how the geometry is described. For instance, a line in the plane is frequently defined in analytic geometry as the collection of points whose coordinates satisfy a given linear equation, but in a more abstract context, such as incidence geometry, a line may be an independent object, distinct from the collection of points that lie on it.
In cartesian plane the general equation of a line is given by :
y=mx+c where the slope is denoted by m and the y-intercept by c.
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what value of x makes the equation 2(3 - 7x) = 4 - 6x true?
Linear equations are equations that has a leading degree of 1. The value of x that makes the equation true is 1/4
Solving linear equationsLinear equation are equations that has a linear degree of 1. The standard linear equation is y = mx + b
Given the expression below
2(3 - 7x) = 4 - 6x
Expand
6 - 14x = 4 - 6x
Collect the like terms
6 - 14x = 4 - 6x
-14x + 6x = 4 -6
-8x = -2
Divide both sides by -8
-8x/-8 = -2/-8
x = 1/4
Hence the value of x that makes the equation true is 1/4
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What do you get if you cross a chicken with a cow?
Yes, I know how these sound.
Answer:
roost beef
Step-by-step explanation:
5 less than one-fifth of c
Answer:
1/5 c - 5
Step-by-step explanation:
1/5 c - 5 = (c - 25)/5
Find the midpoint of FG given F(2, -6) and G(-8, 10)
the midpoint of FG given F(2, -6) and G(-8, 10) = (-3,2)
Solution :
The midpoint calculator will take two coordinates in the Cartesian coordinate system and find the point directly in-between both of them. This point is often useful in geometry.
1. Label the coordinates(x₁,y₁) and (x₂,y₂).
2. Input the values into the formula.
3. Add the values in the parentheses and divide each result by 2.
4. The new values form the new coordinates of the midpoint.
f we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x,y).
Given :
F(2, -6) and G(-8, 10)
FG= (-8+2)/2,(-6+10)/2
FG= (-6/2,4/2)
FG=(-3,2)
the midpoint of FG given F(2, -6) and G(-8, 10) = (-3,2)
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If they gave you $440 in quarters. how many coins would you receive?
Answer:
$110
Step-by-step explanation:
quarter is 1/4 of a thing
so $440 ÷ 4 = 110
hence we can conclude that if you get $440 in quarters you will get $110 each time
Hope it helps!!!
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Simplify completely:
(4x^3)^2
Answer:
16^6
Step-by-step explanation:
Use the diagram to the right to complete the statement.
Answer:
∠ GOF = 53°
Step-by-step explanation:
∠ LON and ∠ GOF are vertically opposite angles and are congruent, then
∠ GOF = 53°
is -4 rational or irrtaional
-4 is a rational number...
Please help with math question
Answer:
5b+35
Step-by-step explanation:
5*b=5b
5*7=35
please help my brother his having little problem here
Thank u so much
64°
Step-by-step explanation:
Let the missing angle be x.
Sum of angle of a triangle=180°
Therefore,
48°+68°+x=180°
x=180°-116°
x=64°
Find the values of a and b.
Answer:
Step-by-step explanation:
7a + 33° = 10a - 12° ( being vertically opposite angle )
33° - 12° = 10a - 7a
21° = 3a
a = 21/3
a = 7°
Now,
6b - 42 = 3b ( vertically opposite angle )
6b - 3b = 42°
3b = 42°
b = 42/3
b = 14
hence , the value of a is 7°and b is 14°...
☘☘☘....
(Precalc) NEED HELP 100PTS: (−2 ≤ x ≤ 2) f(x) = csc(x)
A. Find the intervals on which the graph of y = f(x) is increasing and the intervals on which the graph of y = f(x) is decreasing. Answer in interval notation.
Increasing: ___
Decreasing: ___
B. Find all relative extrema, if any, of the graph of y = f(x).
Relative min: ___
Relative max: ___
Thank youu!! <333
Answer:
Step-by-step explanation:
y=csc(x) x∈ [-2,2]
[tex]A.\\\displaystyle\\Increasing: \ [-2,-\frac{\pi }{2})U(\frac{\pi }{2},2]\\\\Decreasing:\ (-\frac{\pi }{2},0)U(0,\frac{\pi }{2} ) \\\\B.\\\\Relative\ min:\ 1\\\\Relative \ max:\ -1[/tex]
Watching the graph:
Answer:
[tex]\textsf{Increasing}:\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
[tex]\textsf{Decreasing}:\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Step-by-step explanation:
Part A
Given function:
[tex]f(x)=\csc (x), \quad -2\leq x\leq 2[/tex]
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
Therefore, the function f(x) is undefined when sin(x) = 0, leading to vertical asymptotes at the value of x where sin(x) = 0.
[tex]\sin(x) = 0 \textsf{ at }x = 0\pm 2 \pi n, \pi \pm 2 \pi n[/tex]
Therefore, f(x) has a vertical asymptotes at x = -2π, -π, 0, π, 2π etc.
Where the graph of the sine function increases, the graph of the cosecant function decreases.
Where the graph of the sine function decreases, the graph of the cosecant function increases.
The sine function increases on the intervals:
[tex]\left(-\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{\pi}{2}\pm 2 \pi n\right)[/tex]
and decreases on the intervals:
[tex]\left(\dfrac{\pi}{2}\pm 2 \pi n, \dfrac{3\pi}{2}\pm 2 \pi n\right)[/tex]
Therefore, for the interval -2 ≤ x ≤ 2, the cosecant function f(x):
Increases on the intervals:
[tex]\left[-2,-\dfrac{\pi}{2}\right) \textsf{ and }\left(\dfrac{\pi}{2},2\right][/tex]
Decreases on the intervals:
[tex]\left(-\dfrac{\pi}{2}, 0\right) \textsf{ and }\left(0, \dfrac{\pi}{2}\right)[/tex]
Part B
The relative minimums of the graph of the sine function are the relative maximums of the graph of the cosecant function.
The relative maximums of the graph of the sine function are the relative minimums of the graph of the cosecant function.
The sine function has a range of -1 ≤ sin(x) ≤ 1.
Therefore, its minimum points are when sin(x) = -1 and its maximum points are when sin(x) = 1.
[tex]\sin(x)=-1 \implies x=\dfrac{3\pi}{2}\pm 2 \pi n \implies \textsf{Minimum points}: \left(\dfrac{3\pi}{2}\pm 2 \pi n ,-1 \right)[/tex]
[tex]\sin(x)=1 \implies x=\dfrac{\pi}{2}\pm 2 \pi n \implies \textsf{Maximum points}: \left(\dfrac{\pi}{2}\pm 2 \pi n,1 \right)[/tex]
Therefore, the minimum and maximum points of the cosecant function in the given interval -2 ≤ x ≤ 2 are:
[tex]\textsf{Relative min}: \left(\dfrac{\pi}{2},1 \right)[/tex]
[tex]\textsf{Relative max}: \left(-\dfrac{\pi}{2},-1 \right)[/tex]
Note in the attached graph:
The given interval -2 ≤ x ≤ 2 is shown shaded in green.Vertical asymptotes are shown as red dashed lines.Function f(x) is the black curve.The sine function is the blue dashed curve.Relative min/max shown as black points.Arrange the students in order from shortest to tallest. kim 56.03 alexa 56.3 roy 56.14 tom 57.1
Arrangement of students from shortest to tallest is
Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.
As given in the question,
Number of students = 4
Height of the students
Kim = 56.03 units
Alexa = 56.3 units
Roy = 56.14 units
Tom = 57.1 units
Arrange the students from shortest to tallest
56.03 < 56.14 < 56.3 < 57.1
Kim < Roy < Alexa < Tom
Therefore, arrangement of students from shortest to tallest is
Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.
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He bought a pair of boots that cost 10 and spent the rest on hats that cost 8 each?
Answer:
what is the question?
Step-by-step explanation:
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Factorise C^2 - ( d + 2 )^2
Answer:
Step-by-step explanation:
[tex]\boxed{x^2-y^2=(x+y)(x-y)}[/tex]
[tex]c^2-(d+2)^2=\\(c+(d+2))(c-(d+2))=\\(c+d+2)(c-d-2)[/tex]
Q1: 1+2-3+4-5+6-…-99+100
Q2: 2+4-6+8-10+12-…-198+200
please help asap!!! Brainliest will be given if correct!!! Thanks <3
Answer:
Q1. 5050 Q2. 20100
Step-by-step explanation:
At a coffee shop, the first 100 customers'
orders were as follows.
Small Medium Large
Hot
5
48
22
Cold
8
12
5
If one of these customers has purchased a
large drink, what is the probability that it is
cold?
P( hot| Large ) = [?]
Round to the nearest hundredth.
Answer:
so there is a 5% change of or ordering a large cold drink
Step-by-step explanation:
first add the total of all drinks
5+48+22+8+12+5=100
the amount of large drinks that are cold are 5
so there is a 5% change of ordering a large cold drink
Solve the equation. Check your answer. 22 = 6x + 1 -3x what does x equal?
Answer:
7
Step-by-step explanation:
22=6x+1-3x
21=6x-3x
21=3x
7=x
Do u know how to do question 8
Answer:
a = -34 b = 141 c = 95 d = 74 e = -43 f = -15
Step-by-step explanation:
Subtract the payments from the balance and add the receipts.
Payment means money going out so your balance is decreasing.
Receipts means money coming in, so your balance increases
I will give brainliest to the person who give me a right answer with solution
Pls answer this ASAP ty
Answer:
∠ A = 42° , ∠ G = 85°
Step-by-step explanation:
the measure of an inscribed angle is half the measure of its intercepted arc.
(3)
∠ A is an inscribed angle , so
∠ A = [tex]\frac{1}{2}[/tex] BC = [tex]\frac{1}{2}[/tex] × 84° = 42°
(4)
∠ G is an inscribed angle but we require arc DF
the sum of the arcs in a circle = 360°
FG + GD + FD = 360°
70° + 120° + FD = 360°
190° + FD = 360° ( subtract 190° from both sides )
FD = 170°
Then
∠ G = [tex]\frac{1}{2}[/tex] DF = [tex]\frac{1}{2}[/tex] × 170° = 85°
ST
Problem number 26 of the Rhind Papyrus says:
Find a quantity such that when it is added to of itself
the result is a 15.
The modern day equation that models this problem is
x+x=15.
What is the solution to the equation?
O x = 10
x = 12
x = 15
x = 30
Step-by-step explanation:
please make sure that fractions are still in the problem text after scanning it.
because they are missing here, and I have to guess around.
Basically the problem is
x + 1/a × x = 15
that means
ax + x = 15a
(a+1)x = 15a
x = 15a/(a+1)
for a = 2 (so, 1/2 x is added to x), we get
x = 15×2/3 = 30/3 = 10
for a = 4 (1/4 of x is added to x), we get
x = 15×4/5 = 60/5 = 12
these are also the first 2 answer options. so, please pick the one that fits the complete problem definition.
the 3rd and 4th answer options are nonsense anyway, as when you add something greater than 0 to x and get 15, then the initial x cannot be already 15 or even bigger.
28. RS = 7a, ST= 12a, RT=76
Answer:
a=4
ST=48
As we know ,
RT=RS+ST=7a+12a=19a
And RT=76
That’s why RT=19a=76 => a = 76/19=4
ST=12a=12*4=48
then we find ,
a=4
ST=48
In geometry, variables often appear in problems related to perimeter, area and volume. Typical problems provide you with some precise measurements and ask you to find out an unknown measurement, or variable.
Determine which formula you need. For example, if you're working with the area of a triangle, you need to know that area equals one half the base times the height, or A=1/2bh.
Plug the known values into the formula. Using the area of the triangle example, assume you know that the area is 100 square inches and the base is 20 inches. When you plug these values into the formula, you get 100=1/2 (20h). The height of the triangle is the variable.
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The perimeter of a rectangle is 180 meters. If the length of the rectangle is 20 meters more than the width, what are the dimensions of the rectangle?
Divide.
(−16)÷(−56)
What is the quotient?
Answer:
Quotient = 0; Remainder = 16
Step-by-step explanation:
PLS EXPLAIN THIS ITS URGENT HOW DO YOU DO THISSSS
Answer:
It means you will have to match the name with the correct numbers on the right hand side.example:Animal bread
food dog
answeranimal— dog
food — bread
The real question answer:Zero slope — ( 16,3), (16,-80)Negative slope — (-5,-20), (-11,-20)undefined slope— (-1000,2500), (500,4000)Positive slope— (0,4,25), (1,25,1,75)Incase you aren't still convinced, you can try using the slope formula to solve it yourself .
slope = Y2 - Y1
————
X2 - X1
Hope this helpsGood luck ✅
In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16. what is the mean for this sample?
The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.
Then the data set will be given below.
10, 10, 10, 10, 10, 16
Then the mean of the data set will be
Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6
Mean = 66/6
Mean = 11
Thus, the mean of the sample will be 11.
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To pay for a home improvement project that totals $11,000, Genesis is choosing between taking out a simple interest bank loan at 6% for 3 years or paying with a credit card that compounds monthly at an annual rate of 16% for 6 years. Which plan would give Genesis the lowest monthly payment?
The monthly credit card payment would be $396.49, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.
The monthly credit card payment would be $354.44, which is lower than the monthly payment on the bank loan.
The monthly payment on a bank loan would be $323.89, which is lower than the monthly credit card payment.
The monthly payment on a bank loan would be $360.56, which is lower than the monthly credit card payment.
What is the monthly payment under simple interest?
The total interest on the simple interest basis can be determined as the cost of the home improvement multiplied by the annual simple interest rate and also multiplied by the number of years
I=PRT
I=interest for 3 years=unknown
P=principal=$11,000
R=simple interest rate=6%
T=number of years=3
I=$11000*6%*3
I=$1980
There are 12 months multiplied by 3 years
monthly payment=($11,000+$1,980)/(3*12)
monthly payment=$360.56
Monthly compounding option:
PV=PMT*(1-(1+r)^-N/r
PV=loan amount=$11,000
PMT=monthly payment=unknown
r=monthly interest rate=16%/12=0.0133333333333333
N=number of monthly payments in 6 years=12*6=72
$11,000=PMT*(1-(1+0.0133333333333333)^-72/0.0133333333333333
PMT=$238.61
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11. Pi (π) is the quotient of the circumference (C) and the diameter of a circle.
Type equation here.
The circle is a plane figure whose circumference is given by the formulae [tex]2\pi r[/tex]. Where r is the radius of the circle.
The area of the circle is given by the formulae [tex]\pi r^{2}[/tex] where again r is the radius of the circle and pie is the common factor in both the formulae
We also need to know that the radius of the circle is the half of the diameter of the circle and the diameter is twice the radius
From which we can derive the relation; d=2r where d is the diameter of the circle.
So, the formulae now in terms of diameter becomes [tex]\pi d[/tex] for circumference and [tex]\frac{\pi d^{2} }{4}[/tex] for area of the circle.
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Is 450 divisible by 2,3,4,5,6,8,9 or 10 explain why please
Help ASAP
Answer:
2,3,5,6,9 and 10
Step-by-step explanation:
450/2 = 225
450/3 = 150
450/4 = 112.5
450/5 = 90
450/6 = 75
450/8 = 56.25
450/9 = 50
450/10 = 45
To be divisiable, the answer should be an integer.
Thus: 2,3,5,6,9 and 10 are numbers which 450 is divisible by
Answer:
see below
Step-by-step explanation:
2×3×3×5×5 is it's prime factorization which has 2, 3, 4, 5, 6, 9, 10
The number of rabbits on a farm at the end of month n is Pn The number of rabbits at the end of the next month is given by Pn+1 = 1.2P - 50 At the end of March there are 200 rabbits on the farm. (a) Work out how many rabbits there will be on the farm at the end of June. (b) Considering your results in part (a), suggest what will happen to the number of rabbits on the farm after a long time.
We need to know how to solve the equations by substituting values for this problem. (a)The number of rabbits on the farm at the end of June is 164 and (b) after a long time the number of rabbits on the farm will become zero.
In the given question we know that the number of rabbits on a farm at the end of month n is [tex]P_{n}[/tex] and that the number of rabbits at the end of the next month is [tex]P_{n+1} =1.2P_{n} -50[/tex]. We know that the number of rabbits at the end of March is 200, so we can have [tex]P_{1}[/tex]=200, we need to find the number of rabbits at the end of June, which will be [tex]P_{4}[/tex], we can form an equation from here
[tex]P_{4} =1.2P_{3} -50[/tex]
Since we don't know what [tex]P_{3}[/tex] is we can replace it by [tex]P_{2}[/tex] and then replace that by [tex]P_{1}[/tex].
[tex]P_{4} =1.2P_{3} -50\\P_{4} =1.2(1.2P_{2} -50)-50\\P_{4} =1.2(1.2(1.2P_{1} -50)-50)-50 = 1.2(1.44P_{1} -60-50)-50=1.728P_{1} -72-60-50=1.728P_{1} -182[/tex]
We know that [tex]P_{1} =200[/tex]
So, [tex]P_{4}[/tex]=1.728x200-182=345.6-182≈164
Therefore the number of rabbits at the end of June is 164 and after a long time the number of rabbits on the farm might become zero since the number of rabbits is decreasing with every month.
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