(-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.
As, we know that the Tangent function is neither an One-One nor Onto function. So, the domain should be restricted to obtain the inverse function of the Tangent function.
Domain of the tangent function be, R - {(2n+1)π/2}
Range of the tangent function be, R
Now, to build the inverse tangent function we have to restrict the domain so that, the function will be one-one and onto both.
So, the restricted domain be (-π/2 , π/2).
In the domain (-π/2 , π/2), the tangent function is one-one and onto both and hence, we can build the inverse tangent function i.e. arctangent.
So, (-π/2 , π/2) is the restricted domain on the tangent function that allows us to build the arctangent (inverse tangent) function.
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Find the measurement of V.
Answer: 60 degrees
Step-by-step explanation: Because all sides are equilateral, and in an equilateral triangle all angles are 60 degrees, hope that helps.
Help me please ill add more points than usual!
Answer: how
Step-by-step explanation: love
PLEASE HELP!! I NEED SOMEONE TO HELP ME!
Use distributive property to remove parenthesis.
-9( -3w + 3u - 4)
The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)
Given,
In the question:
Use distributive property to remove parenthesis.
-9(-3w + 3u - 4)
Now, According to the question:
First, we know:
What does parentheses mean distributive property?
The distributive property allows us to multiply all terms in a parentheses by a number outside of it. a(b +c) = ab + ac.
We have:
-9(-3w + 3u - 4)
Solve by Distributive Property :
-9(-3w + 3u - 4)
Open the bracket:
27w - 27u +36
Hence, The answer is 27w - 27u +36 of the given -9( -3w + 3u - 4)
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Can anyone write the equation of this graph?
The translated absolute value function graphed is defined as follows:
y = |x - 3| + 5.
What is the absolute value function?The absolute value function, of vertex (h,k), is defined by the following piecewise rule, depending on the input of the function:
f(x) = |x - h| + k = x - h + k, x - h ≥ 0.f(x) = |x - h| + k = -x + h - k, x - h < 0.In this problem, the coordinates of the vertex are given as follows:
h = 3, as the x-coordinate of the vertex is of 3.k = 5, as the y-coordinate of the vertex is of 5.Hence the vertex is given by the following point:
(3,5).
Then the equation graphed is defined by the rule presented as follows:
y = |x - 3| + 5.
Which is a translation of 3 units right and 5 units up of the standard absolute value function.
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"14 more than twice a number" translate expression
Answer: 14=2x
Step-by-step explanation:
the answer is 14=2x7=14
lmn is straight line coordinates of L (-3,1) coordinates of M (4,9) LM:MN is 2:3 find coordinates of N
The coordinates of point N are (8.66, 21)
What is the general equation of a Straight line? What is Section Formula in 2 - D geometry?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
The coordinates of a point dividing a straight line joining two coordinates in the ratio m : n is given by -
x = [tex]$\frac{mx_2+nx_1}{m+n}[/tex]
y = [tex]$\frac{my_2+ny_1}{m+n}[/tex]
We have LMN as a straight line such that the coordinates of L are (-3,1) , coordinates of M are (4,9) and LM : MN is 2 : 3.
Assume the coordinates of point N are (a, b).
We can write -
9 = (2b + 3)/5
4 = (-6 + 3a)/5
2b + 3 = 45
b = 21
3a - 6 = 20
3a = 26
a = 8.66
Therefore, the coordinates of point N are (8.66, 21)
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five sevenths raised to the negative first power times eighteen hundredths raised to the second power.
Answer: 0.04536
Step-by-step explanation:
1. Calculate arithmetic mean from the following data. 50, 60, 70, 80, 65, 70, 90
Answer:
Here ,
sigma x=50+60+65+70+70+80+90=485
N=7
now,
Mean =sigma x÷N
=485÷7
=69.28
I need help that’s it
Answer:
x-intercept(s): (−5,0)
y-intercept(s): (0,−5)
Explanation:
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
Im also in K12 so Ez Good Luck
Hope this helped!
Find the highest common factor (HCF) of 72 and 90
Answer:
Step-by-step explanation:
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
The six frequent factors between 72 and 90 are 1, 2, 3, 6, 9, and 18.
Consequently, 18 is the number that links 72 and 90 most frequently.
Can somebody please explain what this question is asking, and how I solve it. I can not solve this, need help please.
Answer:
g(10)=-33, x=3
Step-by-step explanation:
g(x)=-4x+7. --------(1)
a) g(10)=?
since we know function x = -4x+7 to find function g(10) we will just place 10 whenever we see x
g(10)=-4(10)+7
g(10)=-40+7
g(10)= -33
b.)find x if g(x)=-5. ---------(ii)
g(x)=-4x+7. we will place (I) in (ii)
g(x)=-5
-4x+7=-5
-4x=-5-7
-4x=-12
cancel the minus(-) sign in both sides
4x=12
x=12/4
x=3
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A line passes through the points (-5,10) and (0,-10). What is its equation in slope-intercept form?
y=__x+___
Answer:
The equation for the slope-intercept form is y = 4x - 10
Hope this helps!
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex] Equation = y = mx + b
The two points given are ( -5, 10 ) and ( 0, -10 ).
Putting in the values gives you [tex]\frac{-10-10}{0-(-5)} = \frac{-20}{5} =-4[/tex].
y = 4x + b, to find b, insert one of the points:
-10 = 4(0) + b -> -10 = 0 + b, b = -10
Putting it all together gives you y = 4x - 10
Two cards are drawn without replacement from an ordinary deck. Find the probability that the second is not a red card, given that the first is not a red card.
What is the conditional probability?
Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.
What is the likelihood of receiving two red cards without being replaced?The probability of drawing a second red in the event that this red is not changed is 9/15,
hence the probability of A is 10/16 * 9/15, or 0.375.
The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier occurrence by the increased likelihood of the later, or conditional, event.Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.Is it possible to apply the conditional probability in its alternative form, P(R2|R1) is n(R1⋂R2) divided n(R1) Given that the product rule hasn't yet been taught, we have advocated this approach.To learn more about conditional probability refer to:
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Temperatures in °F can be converted in °C using the formula
5(F-32)
=
C=
Make F the subject of the formula.
aC + b
Give your answer in the form
C
Att
where a, b and c are all positive integers.
The given formula can be written as 5F = 9C + 160.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities. To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The conversion formula for °C into °F is 9C = 5(F - 32)
The given formula can be written in the form of cF = aC + b as,
9C = 5(F - 32)
⇒ 5F = 9C + 160
Hence, the given formula can be written by making F as the subject as 5F = 9C + 160.
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hree students are participating in a walkathon. The data for each student is shown.
Student A: The equation y = 13x represents the amount of money raised (y) for walking (x) miles.
Student B: $36 is raised after walking 3 miles.
Student C:
Miles Walked 4 5
Money Raised $52 $65
Determine which student raised the least amount of money after walking 7 miles.
Student A
Student B
Student C
All three students raised the same amount of money after walking 7 miles.
Student B has raised the least amount of money after walking for 7 miles.
What is unit rate?A unit rate means a rate for one of something.
Given that, three students are participating in a walkathon,
Student A's money is represented by the equation y = 13x, where y is money raised for walking x miles.
Student B raised $36 money for 3 miles and Student C has raised $52 and $65 money for 4 and 5 miles respectively.
Money raised by each of them for a mile =
Student A = $13
Student B = $12
Student C = $13
Money raised by them by walking 7 miles =
Student A = $13*7 = $91
Student B = $12*7 = $84
Student C = $13*7 = $91
Hence, Student B has raised the least amount of money after walking for 7 miles.
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Divide and answer in simplest form: 45 ÷ 2
Answer:22.5
Step-by-step explanation:
A railroad
car container can hold 42,000 pounds.
Mr. Evans wants to ship 90 ovens and
some freezers in the same container.
If each freezer weighs 600 pounds,
how many freezers could be shipped
in the container? Explain.
40 freezers could be shipped in the container.
What is a variable?
A variable is a quality that may be measured and take on several values.
We are given that
A railroad container can hold weight=42,000 pounds
Total number of ovens for ship=90
Weight of each oven=200 lbs
Weight of each freezer=600 pounds
We have to find the number of freezers that can be shipped in the container.
Let x be the number of freezers that can be shipped in the container.
According to the question,
42000=90(200)+600x
42000=18000+600x
600x=42000-18000=24000
x=24000/600=40
Hence, 40 freezers can be shipped in the container.
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IF T² = 4π² (h² + k²)
hg
Express k² in terms of T, g and h
The value of the expression in the form of k² will be (T²/4π²)-h²).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is T² = 4π² (h² + k²). The expression for the value of k² will be calculated as,
T² = 4π² (h² + k²)
(h² + k²) = T² / 4π²
k² = (T² / 4π²) - h²
Therefore, the value of the expression in the form of k² will be (T²/4π²)-h²).
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What is the equation of the line that passes through the point (8, 6) and has a slope
of o?
The equation of the line that passes through the point (8, 6) and has a slope of 0 is y = 8.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through the point (8, 6) and has a slope of 0.
Therefore,
m = 0
Hence, let's find the y-intercept using the (8, 6)
y = mx + b
6 = 0(8) + b
b = 8
Therefore, the equation is y = 8
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The temperature outside is 15°F. If the
temperature drops 20°, will the outside temperature be represented
by a positive or negative integer? Explain your reasoning.
please help what is the answer and how do you do it
Can write the equation of the graph?
7x=8x+12
How do I solve this
Answer:
x = -12
Step-by-step explanation:
Get X all on one side
7x - 8x = 8x - 8x + 12
-x = 12
x = -12
Answer:
x = -12
Step-by-step explanation:
To solve this, you will need to get all of the variables on one side, and the 12 on the other. You will subtract 8x from both sides to get the equation -x = 12. You can then divide both sides by -1 to get the x alone, and thus you get x = -12.
Jamal runs at a constant speed of 3.7 meters per second for
1/2
hour. Then he walks at a rate of 1.3 meters per seconds for 1/2 hour far did Jamal Uruk walk in 60 minutes
Answer:
9 km
Step-by-step explanation:
1/2 hr = 1800 seconds
3.7 m/s * 1800s + 1.3 m/s * 1800 s = 9000 m in 1 hr
( he walked AND ran this far)
Would the reaction rate on graph B of Model 2 ever reach a maximum level? Justify your answer.
By applying the concept of rate of a reaction, The graph B never saturates because the enzyme is always in excess.
What is the enzyme substrate reaction?
The enzyme is called a catalyst as it has an active site where the substrate can bind and convert into the product. Here in the graph the enzyme is amylase, and its substrate is starch. When there is an excess of enzymes in the solution, they can convert it into a product till substrates are available. If the substrate runs out, the reaction will come stop.
As per the concept of rate of a reaction, The graph B never saturates as the enzyme in the reaction is always in excess. These excess enzymes present will convert the starch into simple glucose molecules. Hence, there will be no upper limit, as both are in abundance.
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How do I do this can someone help me plss
Answer:
I think is 50m.
Step-by-step explanation:
how many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11? c) are divisible by both 7 and 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f ) are divisible by neither 7 nor 11? g) have distinct digits? h) have distinct digits and are even?
The set of positive integers less than 1000 that are:
a)Divisible by 7 are 142
b)Divisible by 7 but not by 11 are 130
c)Divisible by both 7 and 11 are 12
d)Divisible by either 7 or 11 are 220
e)Divisible by exactly one of 7 and 11 are 220
f)Divisible by neither 7 nor 11 are 780
g)Having distinct digits are 576
f)Having distinct digits and even are 337
What is a positive integer?A whole number that is greater than zero is known as positive integer
a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.
Total terms: 994, divided by 7, plus (n-1)
There are 142 total terms below 1000 that are divisible by 7.
b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.
The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.
c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.
There are 12 total integers below 1000 that can be divided by 77.
d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.
The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.
Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.
e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.
f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.
Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),
=> Unique digits from 1 to 100 equal 90.
=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),
=> Unique digits from 101 to 200 are: 100 to 28, 72.
=> Unique numbers between 201 and 1000 = 72 x 8 = 576.
h)Different digits and even values equal to 337
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determine whether the lines are parallel, intersect, coincide y = x-7, y = -x + 3
The given two equations are Perpendicular to each other .
What is intersection of lines ?
It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here the equation of line is y=mx+b .
Where m = slope . then,
=> y = x-7 where here slope m1= 1 and
=> y = -x+3 where here slope m2 = -1 .
Here the m1= -m2
Hence the given two equations are Perpendicular to each other .
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Convert the standard form equation into slope-intercept form. 6x-2y=-20
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A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
So we know that the perimeter of rectangle is
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
As we know the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.
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