The answer is expressed in terms of unit vectors x^ and y^ as B = B (cos θ x ^ + sin θ y ^)
For expressing the magnetic field B in terms of vectors we need to know the magnitude of the magnetic field and the angle between them.
the angle we have is with respect to the positive side of the x-axis, let's use trigonometry.
cos θ = Bₓ / B
sin θ = / B
Bx = B cosθ
By = B sinθ
hence the resulting vector is
B = Bₓ i ^ + [tex]B_{y}[/tex] j^
The unit vectors are
x ^ = i ^
y ^ = j ^
The answer is expressed in terms of unit vectors x^ and y^ as B = B (cos θ x ^ + sin θ y ^)
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How much is 12 out of 156 as a fraction in its simplest form?
Answer:
3/64
Step-by-step explanation:
12/156
DIvide both numbers by two
6/78
Divide both numbers by two
3/64
Answer: 1/13
Step-by-step explanation:
[tex]\displaystyle\\\frac{12}{156}=\\\\ \frac{3*4}{3*52}=\\\\ \frac{4}{52}=\\\\ \frac{4}{4*13}=\\\\ \frac{1}{13}[/tex]
5x+6y=-48 in slope intercept form
Answer:
y=-5/6x-8
Step-by-step explanation:
Slope intercept form: y=mx+b
5x+6y=-48
6y=-5x-48
y=-5/6x-8
luke measured a swimming pool and made a scale drawing. the scale he used was 7 centimeters : 3 meters. the pool is 105 centimeters long in the drawing. how long is the actual pool?
The actual length of the swimming pool be 15m if the scale used by Luke is 7cm : 3m.
Let the actual length of the pool be x m.
According to the given question.
Luke measured a swimming pool and made a scale drawing. The scale he used was 7 centimeters : 3 meters.
⇒ The scale is 7cm : 3m.
Also, the length of the pool in the drawing is 105cm.
Therefore, the actual length of the swimming pool is given by
7cm : 3m = 105cm : x (by proportion fromula)
⇒ 7x = 105
⇒ x = 15m
Hence, the actual length of the swimming pool be 15m if the scale used by Luke is 7cm : 3m.
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What are the points of intersection between the graphs of the functions
f(x) = (x+3)(x − 1) and g(x) = (x + 1)(x − 3)
Step-by-step explanation:
THE POINT OF INTERSECTION IS WHERE F(x) = G(x)
[tex](x + 3)(x - 1) = (x + 1)(x - 3) \\ {x}^{2} + 2x - 3 = {x}^{2} - 2x - 3 \\ \\ {x}^{2} - {x}^{2} + 2x + 2x - 3 + 3 = 0 \\ 4x = 0 \\ \frac{4x}{4} = \frac{0}{4} \\ x = 0[/tex]
find the y coordinate by plugging in the value of c in any of the function.You will get thw same value
[tex]g(0) = (0 + 1)(0 - 3) \\ g(0) = 1( - 3) \\ g(0) = y = - 3[/tex]
The point of intersection is (0,-3)
James, fay and sal share 160 apples. james got 1/4 of the apples. fay and sal shared the remainder in the ratio 3:2 respectively. 1) find how many oranges fay received 2) how many oranges did sal receive than james?
Using the ratio given in the question,
Apples received by Fay are 72.Apples received by James are 40.Apples received by Sal are 48.What is Ratio?The relation between the quantities of two or more objects—referred to as a ratio—indicates how much of one object is contained in the other. The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as, for any two quantities, let's assume a and b.
a:b = a/b
Given that James, Fay and Sal share 160 apples.
Total number of apples = 160
Hence, apples received by James = 1/4(160)
= 40 apples
Remaining apples = 160 - 40 = 120 apples
It is also given that the remainder is shared by Fay and Sal in the ratio 3:2.
Hence, the total share will be 3+2=5
So, we can write that Fay's share will be 3/5 of total apples and Sal's share will be 2/5 of the total apples.
Fay's share = 3/5(120)
=3(24)
=72 apples
Sal's share = 2/5(120)
=2(24)
=48 apples
Therefore, the number of apples with Fay is 72.
The number of apples with Sal is 48.
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Use your calculator to work out
a) (1.8 × 10⁹) + (6.2 × 107)
b) (6.4 x 10-¹¹) - (5.3 × 10-¹2)
Give your answers in standard form.
Answer:
a) 1800000663.4
b) 0.0000000000587
Step-by-step explanation:
Answer:
(a) (1.8×10^9)=1800000000
(6.2×107)=663.4
So therfore,
(1.8×10^9)+(6.2×107)=1800000663
Note: "^" means exponential (power)
Step-by-step explanation:
(b) (6.4×10^-11)=0.000000000064
(5.3×10^-12)=0.0000000000053
Therefore ,
Answer= 0.0000000000587
How to memorize multiplication tables in just one day?
Answer:
Skip counting
Step-by-step explanation:
Skip counting is when you count at intervals of any number you like. If I were to skip count by seven, I would count 7, 14, 21, and so on. You can easily accomplish single-digit multiplication with this method. For example, suppose your teacher asks you to multiply 4 x 7 =. Simply count sevens four times, 7, 14, 21, and 28. 4 x 7 = 28 is the answer.
Go over the skip-counting list until you get to the halfway mark (3, 6, 9, 12, 15, and 18). Allow yourself to speak it out loud while pointing to the answers one by one with a finger or a pen. This engages many senses at the same time.
Repeat the list from memory after they have gone over it a few times.
The mind is similar to muscles in that it requires exercise to grow stronger.
Memorize this list in both ascending and descending order.
Go through the remaining items on the list: 21, 24, 27, 30, 33, 36.
Finally, go over the entire list of answers. Repeat the list UP AND DOWN until it seems natural and effortless.
Step-by-step explanation:
First write it down by looking at a picture.
Then try writing it down without looking at a picture
Keep doing this.
Also study for 10 mins and then ask someone else to test you
PLEASE HELP MY DEADLINE IS TMR AND IVE BEEN TRYING TO DO THIS ALL DAY. I’ve tried using my notes it doesn’t make sense please help me answer all of the questions. THANK YOU!
13. 9,000 feet
14. 4,500 feet
15. descended 4,500 feet because 9000-4500=4500
16. base camp is 1,000 feet in elevation
17. during 3-4 pm he was descending the fastest because the slope between those two points is the greatest.
18. No because the graph is not linear.
Which transformation shows a reflection of δdef? 2 triangles have identical side lengths and angle measures. the second triangle has been rotated. 3 triangles have identical side lengths and angle measures. the second triangle is reflected. 2 triangles have identical side lengths and angle measures. the second triangle is slightly lower and to the right of the first triangle.
The transformation in reflection is that triangle may have identical aspect lengths and perspective measure.
The reflection concept must be nicely understood earlier than solving this problem.If a determine is reflected then it will have same lengths and same measures but the picture may be inverted.If we can see the meditated photo of an equilateral triangle then the image could be congruent to the object.If we are able to see the pondered image of a rectangular then it will likely be congruent to the figure.right here, the ideal choice is triangle may have identical facet lengths and perspective measure.To learn more about reflection visit the link:
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Answer:
b
Step-by-step explanation:
Which equations show a line that is parallel to the line y = -5/4x + 1?
select all that apply
1.
Steve drew line segments ABCD, EFG, BF, and C
as shown in the diagram below. Scalene ABFC i
formed.
Which statement will allow Steve to prove
ABCD||EFG?
1) LCFG = LFCB
2) LABF = LBFC
3) ZEFB=LCFB
4) ZCBF = LGFC
Answer:
Choice 1: ∠CFG = ∠FCB
Step-by-step explanation:
∠CFG and ∠FCB are interior alternate angles and equal only if ABCD||EFG
Help please. I cant figure this one out.
Answer:
x =52
Step-by-step explanation:
The angles shown are same side interior angles, and when the lines are parallel, same side interior angles add to 180 degrees
< 1 + <2 = 180
x+23 + x+53 = 180
Combine like terms
2x+ 76 = 180
Subtract 76 from each side
2x+76-76 = 180 -76
2x = 104
Divide by 2
2x/2 = 104/2
x =52
Answer:
x = 52
Step-by-step explanation:
Angle 1 and angle 2 are on the same side, and on the inside of the interior. This means that when added together they = 180
We can set up an equation
x+23+x+53 = 180
Simplify: 2x + 76 = 180
Subtract 76 from both sides
2x = 104
Now divide by 2
x = 52
1/2x+1/2x= x+1
Solution:
(The answer can be no solution and infinitely many solutions)
Answer:
No solution
Step-by-step explanation:
On the left side we have one half x plus one half x which equals x. On the right side we have x + 1. So the equation becomes x = x + 1. Subtracting x from both sides we get 0 = 1, which is false. Therefore there is no solution to this problem.
write the algebric expression two less than four times a number
PLEASE SHOW WORK
The expression two less than four times a number is represented as 4x - 2
Algebraic expressionsAn algebraic expression is an expression which is made up of variables and constants, along with algebraic operations such as the addition, subtraction, division and multiplication.
According to the question, we are to transform two less than four times a number into expression
Let the unknown number be x such that
four times a number = 4x
two less than four times a number = 4x - 2
Hence the expression two less than four times a number is represented as 4x - 2
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Kurt spent $96.39 over 414 months on movie streaming services. if he spent the same amount of money each month, how much money, in dollars, did kurt spend per month on movie streaming services?
Using proportions, it is found that Kurt spent $22.68 a month on movie streaming services.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, or operations such as multiplication and division.
These operations are used from the unit rates, as for example, when we have an amount over a period of time, the amount per unit of time is the total amount divided by the total time.
For this problem, we have that the important parameters are found as follows:
The total amount is of $96.39.The time is a mixed number, 4 and 1/4 months, hence it is of 4.25 months, as 4 + 1/4 = 4 + 0.25 = 4.25.Hence his monthly spending is given by the unit rate as follows:
96.39/4.25 = $22.68 a month.
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choose the equation that represents the line that passes through the point (6, −3) and has a slope of one half. (1 point)
The equation that represents the line that passes through the point (6, −3) and has a slope of one half is 2y - x = 13.
The equation of a line is represented as,
y = mx + c equation1
x and y are the coordinates of the point from where the line is passing and m is the slope of the line.
As per the question the line is passing from the point (6, -3). This means value of x = 6 and that of y = -3. The slope of line is (1/2), means m = (1/2).
The slope of the line through the point (-1,6) can also be written as (y - 6)/(x - (-1)) = (y-6)/(x+1).
i.e., m = (y-6)/(x+1)
On equating both the values of m, we will get
(y-6)/(x+1) = 1/2
On simplifying, we get
2y - 12 = x +1
or 2y - x = 13
The equation that represents the line that passes through the point (6, −3) and has a slope of one half is 2y - x = 13.
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Find the LCM of 34 ( use prime factorisation method
The LCM of 34 using prime factorisation method is 2 and 17
Which of the following expressions is NOT equal to the others?
ab + ac
(b + c)a
a(b + c)
ab + c
The expression that is NOT equal to the others is ab + c
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine which of the following expressions is NOT equal to the others?The expressions are given as
ab + ac
(b + c)a
a(b + c)
ab + c
Next, we evaluate the expressions as follows
So, we have
ab + ac = ab + ac
(b + c)a = ab + ac
a(b + c) = ab + ac
ab + c = ab + c
See that all but the last expression have a value of ab + ac
Hence, the expression that is NOT equal to the others is ab + c
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14. Salena says 38 ÷ 5 = 7. How do you respond to Salena? Explain
how to use patterns with multiplication and division facts to explain
your thinking.
Answer:
Salena is incorrect. I would advise her to try reversing the question to check her work. Please see below to check it.
Step-by-step explanation:
38 ÷ 5 = 7
Try reversing to check.
7*5=35
38 divided by 5 does not equal to 7.
Hope this helps!
Please mark as brainliest if correct!
drag each tile to the correct box. not all tiles will be used. one solution each is given for four quadratic equations. assuming that each quadratic equation has two solutions, what is the second solution for each equation? arrowright arrowright arrowright
for the equation is, x = -4 - 5i
The solution will be, x = -4 + 5i
for the equation is, x = 4 + 5i
The solution will be, x = 4 - 5i
for the equation is, x = 5 - 4i
The solution will be, x = 5 - 4i
Quadratic equation defind as:Any equation in algebra that can be written in proper format as where x stands for an unknown, where a, b, and c stand for known numbers, and where a 0
According to the given information:If (a + bi) is a complex number and a quadratic equation has one solution,
The second solution to the equation will be the conjugate of the first.
Consequently, the alternative solution will take the form of (a - bi).
for the equation is, x = -4 - 5i
The solution will be, x = -4 + 5i
for the equation is, x = 4 + 5i
The solution will be, x = 4 - 5i
for the equation is, x = 5 - 4i
The solution will be, x = 5 - 4i
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a pedometer treats walking 2,000 steps as walking 1 mile. it assumes that one step is a bit over 18 inches (1 mile
The required code for the pedometer is illustrated below:
steps_per_mile=2000
def steps_to_miles(steps, inches_per_step):
distance = steps * inches_per_step
miles = distance / (steps_per_mile * inches_per_step)
return miles
if __name__ == '__main__':
steps = int(input())
inches_per_step=float(input())
miles_in_pedometer = steps_to_miles(steps,inches_per_step)
print(f"You walked {steps} steps which are about {miles_in_pedometer:.2f} miles.")
what is a pedometer?
which will matter steps and decide the gap traveled, pedometers are made to apprehend vertical hip motionthey're not able to offer data at the multivariate framework of regular workout or the period of time spent carrying out numerous activities of various intensities.The required code for the pedometer is illustrated below:
steps_per_mile=2000
def steps_to_miles(steps, inches_per_step):
distance = steps * inches_per_step
miles = distance / (steps_per_mile * inches_per_step)
return miles
if __name__ == '__main__':
steps = int(input())
inches_per_step=float(input())
miles_in_pedometer = steps_to_miles(steps,inches_per_step)
print(f"You walked {steps} steps which are about {miles_in_pedometer:.2f} miles.")
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What is the measure of XYZ?
V
33
Y
O D. 54°
N
X
75⁰
O A. 33°
OB. 75°
O C. 108°
What’s the next number in the pattern, and what is the formula to find the next number in the pattern?
7, 28, 63, 112..
Answer:
7, 28, 63, 112, 175, 252, 343, ...
Step-by-step explanation:
Step-by-step explanation:
7, 28, 63, 112, 175
7*1, 7*4, 7*9, 7*16, 7*25, ...
7*1², 7*2², 7*3^2, 7*4², 7*5²
Hence, 7n², n=1, 2, 3, 4, ...
7*6²=
7*6*6=
252
7*7²=
7*7*7=
343
Thus,
7, 28, 63, 112, 175, 252, 343, ...
f(x)=-x-4 solve when f(x)=6
Answer: Pretty sure the answer is -10
Step-by-step explanation: If you replace f(x) with 6, you can figure out the answer more quicker.
6 = -x-4
10 = -x
x=-10
Answer:
2
Step-by-step explanation:
Since f(x) is 6, we can plug that into the equation:
6-4,
which gives us 2
Simplify the fraction 24/56 until it is in simplest form.
explain
Answer: 3/7
Step-by-step explanation:
You would divide this by the number 8.
8*3 = 24
8*7 = 56
Therefore the answer is 3/7
Hey there!
24/56
= 24 ÷ 8 / 56 ÷ 8
= 3/7
Therefore, your answer should be:
3/7
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Bella has a bag that contains pineapple chews, lemon chews, and watermelon chews. She performs an experiment. Bella randomly removes a chew from the bag, records the result, and returns the chew to the bag. Bella performs the experiment 58 times. The results are shown below:
A pineapple chew was selected 53 times.
A lemon chew was selected 2 times.
A watermelon chew was selected 3 times.
the probability is pinapple 53/58
lemon 2/58
watermelon 3/58
The given values are
A pineapple chew was selected 53 Times
A lemon chew was selected 2 times
A watermelon chew was selected 3 times
The probability that you Bella remove from the bag is pineapple chew.
Probability is which we can't predict actual it is usually about the prediction
As we know
Probability - expected outcome/total outcome
The question Bela perform experiment 58 times then the total outcome will be 58 if you pineapple was selected 53 times the probability of the chew Bella pick of pineapple is 53/58
The probability of Bella pick chew of lemon -2/58
The probability of Bella pick watermelon is - 3/58
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for the given functions f and g,find the composition please help
Answer:
[tex](f \cdot g)(x)=18x^3+15x^2[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=6x^2+5x \\ g(x)=3x\end{cases}[/tex]
Function composition is an operation that takes two functions and produces a third function.
The composite function (f · g)(x) means to multiply function f(x) by function g(x):
[tex]\begin{aligned}\implies(f \cdot g)(x) & = f(x) \cdot g(x)\\& = (6x^2+5x)(3x)\\& = 6x^2 \cdot 3x+5x\cdot 3x\\& = 18x^3+15x^2\end{aligned}[/tex]
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question which angles are a pair of alternate exterior angles? angle 3 and angle 6 angle 3 and angle 6 angle 4 and angle 6 angle 4 and angle 6 angle 2 and angle 8 angle 2 and angle 8 angle 1 and angle 5 angle 1 and angle 5
The pair of angles from the given options that are a pair of alternate exterior angles is:
C. ∠2 and ∠8
What are Alternate Exterior Angles?
Alternate exterior angles are pairs of exterior angles that lie alternate to each other along a transversal that cuts across two parallel lines.
Thus, in the image given, we have the following alternate exterior angles:
∠2 and ∠8
∠1 and ∠7
Therefore, the pair of angles from the given options that are a pair of alternate exterior angles is:
C. ∠2 and ∠8
the complete question is
Which angle are a pair of alternate exterior angles
A. Angle 4 and angle 6
B. Angle 3 and angle 6
C. Angle 2 and angle 8
D. Angle 1 and angle 5
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Write an equation for a line that passes through the points (1, 2) and (11, 22). The form is your choice
Its too confusing pls help!
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A small plane flies for 3 hours to an airport 450 kilometers away against a strong headwind. the plane then returns to its starting location flying with the wind, taking 2 hours. the wind speed remains constant for the round-trip flight.
The speed of the plane and wind in km/hr is 187.5 and 37.5 respectively.
What is a linear equation ?A linear equation has highest degree of 1.
According to the given question a small plane flies for 3 hours to an airport 450 kilo meters away against a strong headwind. the plane then returns to its starting location flying with the wind, taking 2 hours.
Form these we can form two linear equations in two variables.
Assuming speed of the plane to be x km/hr and speed of wind to be y km/hr.
We know Distance = speed × time.
3( x - y) = 450. and 2( x + y) = 450.
3x - 3y = 450...(i) and 2x + 2y = 450...(ii)
multiplying eqn (i) by 2 and eqn (ii) by 3 and solving we get
x = 187.5 km/hr and y = 37.5 km/hr.
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