Given u = (-1, 3), v = ( 2, 4) , and w = (2, -5), by applying scalar multiplication of vectors, ³/₂ v = (3, 6)
In the 2D coordinate system, vectors can be split into x-component and y-component.
We can write, for example, a vector s = (4,–1), which means:
x-component = 4
y-component = –1
Some vector operations:
Addition / subtraction of vectors: Just add or subtract the corresponding components.In the given problem:
u = (-1, 3), v = ( 2, 4) , and w = (2, -5)
Then,
³/₂ v = ³/₂ . (2, 4)
= ( ³/₂ . 2, ³/₂ . 4)
=(3, 6)
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1¼ x 3.14 x ¾ to the second power
2 133/640 or 2.2078125
Find the gcf of 18a and 20ab
Answer:
the gfc is 1 because of the unknowns which are a and b
Sphere A has radius 2 cm. Sphere B has radius 4 cm. a) Calculate the volume of each sphere.
Given the radius of each sphere, the volume of sphere A and B are 33.49cm³ and 267.95cm³ respectively.
What are the volumes of sphere a and b?A sphere is simply a geometrical object with a three-dimensional analogue to a two-dimensional circle.
The volume of a sphere is expressed as;
V = (4/3) × π × r³
Where r is radius and π is constant pi ( π = 3.14 ).
Given the data in the question;
Radius of Sphere A = rA = 2cmRadius of Sphere B = rB = 4cmVolume of each sphere = ?First, we determine the volume of sphere A.
V = (4/3) × π × r³
V = (4/3) × 3.14 × (2cm)³
V = (4/3) × 3.14 × 8cm³
V = 33.49cm³
Hence, the volume of sphere A is approximately 33.49cm³.
Next, we determine the volume of sphere B.
V = (4/3) × π × r³
V = (4/3) × 3.14 × (4cm)³
V = (4/3) × 3.14 × 64cm³
V = 267.95cm³
Hence, the volume of sphere Bis approximately 267.95cm³.
Given the radius of each sphere, the volume of sphere A and B are 33.49cm³ and 267.95cm³ respectively.
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Solve. Check for extraneous solutions. (2 x)¹/₂=(x+5)¹/₂
x = 5 is not an extraneous solution of the equation.
[tex](2x)^{1/2} = (x+5)^{1/2}[/tex]
Taking square on both the side of the equation, we get
[tex]((2x)^{1/2})^{2}[/tex] = [tex]((x+5)^{1/2})^{2}[/tex]
2x = x + 5
Subtracting x on both the sides of the equations, we get
2x - x = 5
x = 5
Check for Extraneous Solution by putting x = 5 in the original equation, we get
[tex](2(5))^{1/2} = (5+5)^{1/2}[/tex]
[tex]10^{1/2}[/tex] = [tex]10^{1/2}[/tex]
⇒ LHS = RHS
∴ x = 5 is not an extraneous solution of the equation.
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Suzy's kitchen measures 17 feet by 4 feet She would like to add a small tile border around the entire room. How much should she expect to pay
if the tile strip costs $0.95 per foot
Total Cost = $
Preview My Answers Submit A
Room DimensionsLiving Room:·Room: 12 feet x 19 feet·Wall Height: 8 feet 4 walls painted
Step-by-step explanation:
Una elevación de 10 pies está más cerca o más lejos de la superficie del océano que una elevación de -8 pies?
Answer:
farther
Step-by-step explanation:
2 feet farther from the surface of ocean than elevation of -8feet
Write an equation of the line that passes through (-7,9), (-5,3)
Answer:
y = - 3x - 12
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, 9 ) and (x₂, y₂ ) = (- 5, 3 )
m = [tex]\frac{3-9}{-5-(-7)}[/tex] = [tex]\frac{-6}{-5+7}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3 , then
y = - 3x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 5, 3 )
3 = 15 + c ⇒ c = - 3 - 15 = - 12
y = - 3x - 12 ← equation of line
PLEASE HELP WILL GIVE 150 POINTS IF HELPED
what is the anwer
What is an era
a a time period consisting of distinct historical events
b the effect of a historical event
c a visual representation of historical events
d the cause of a historical event
Answer:
Its A
Step-by-step explanation:
I will answer so you can give the other person brainliest :)
help me please
show your solution
Hello,
[tex]1) \: - 24[/tex]
[tex] 2) \frac{ - 24}{2} = - 12[/tex]
[tex] 3)\frac{ - 12}{2} = - 6[/tex]
[tex]4) \frac{ - 6}{2} = - 3[/tex]
[tex]5) \frac{ - 3}{2} = - 1.5[/tex]
Answer → -1,5
A/b= 3/5 and b/c= 4/5
The answer of the following fraction which involves ABC is said to be 12:20:25
The transformation of a ratio into a fraction is known as the simple fraction form. In order to convey the relative size of two or more variables, the ratio is utilized. The fraction similarly identifies the components of the total. A:B or a/B are two ways to represent the ratio. As an illustration, the ratio is 12: 15.
Express the ratio in terms of a
a/b = 3/5 (cross-multiply)
3b = 5a (Divide the total both sides by 3)
b= 5/3 a
b/c = 4/5 (cross-multiply)
4c = 5b (divide the total both sides by 4)
c= 5/4 b=5/4×5/3 a=25/12a
then
a:b:c
=a:5/3 a:25/12 a (multiply each part by 12 to clear the fractions)
=12a:20a:25a (divide each part by a)
=12:20:25
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swer.
At the beginning of the month, Sarah had $600 in her bank account. Within the month she
made two deposits of $40 and $25. She also made three withdrawals of $100, $50, and $20.
How much was in her account at the end of the month?
Sarah have $495 in her account at the end of the month.
Given,
The amount Sarah had in her bank account at the beginning of the month = $600
The deposits she made within the month = $40 and $25
The withdrawals she made = $100, $50 , $20
We have to find the balance amount in Sarah's account after all these transactions made:
The deposits Sarah had = 600 + 40 + 25 = 665
Sarah had $665 in her account in a month.
Withdrawals made by Sarah = 100 + 50 + 20 = 170
Sarah made a total withdrawal of $170 in the month.
Now, we have to find the account balance of Sarah:
Account balance = Total deposits - Total withdrawals
Account balance = 665 - 170 = 495
That is, Sarah have $495 in her account at the end of the month.
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What is the midpoint of (3,5) and (6,0)
The midpoint of (3,5) and (6,0) is (9/2, 5/2)
How to calculate the midpoint of (3,5) and (6,0)?The points are given as
(3,5) and (6,0)
The midpoint of the points is calculated using
Midpoint = 1/2 * (x1 + x2, y1 + y2)
So, we have
Midpoint = 1/2 * (3 + 6, 5 + 0)
Evaluate the sum
So, we have
Midpoint = 1/2 * (9, 5)
Evaluate the product
So, we have
Midpoint = (9/2, 5/2)
Hence, the midpoint of (3,5) and (6,0) is (9/2, 5/2)
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What is the employee yearly contribution to the
U.S. Medicare tax on a salary of 40,000 $/year?
A. $2480
C. $1160
FICA Taxes
Social Security
12.4%
employer exployee
6.2%
6.2%
Medicare
2.9%
employer employee
1.45% 1.45%
B. $4960
D. $580
The employee yearly contribution to the
U.S. Medicare tax on a salary of 40,000 $/year is $580.
Medicare is a federal employment tax that helps pay the Medicare insurance program.
The Medicare duty, occasionally known as the" sanitarium insurance duty," is a civil employment duty that contributes to the Medicare insurance program. Medicare duty, like Social Security duty, is taken from an hand's payment or paid as a tone- employment duty.
Part A of the Medicare program, which covers sanitarium insurance for grown-ups 65 and aged, as well as persons with certain impairments or medical conditions, is funded by the Medicare duty. Medicare sanitarium insurance includes hospitalization, lodge care, nursing home care, and certain home healthcare.
Anyone working in the United States is obliged to pay Medicare levies.
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I thought of a number, subtracted
7/18
from it, added 1 5/6 and got 3 2/3.
What was my number?
Answer:
[tex]\dfrac{20}{9}[/tex]
Step-by-step explanation:
Convert mixed fractions to improper fractionsAnswer
[tex]x = \dfrac{20}{9}[/tex]. So the original number = [tex]\dfrac{20}{9}[/tex]
The original number is 20/9.
What is mean by Fraction?
A number expressed as a quotient in which a numerator is divided by denominator is called a fraction.
Given that;
The numbers are 1 5/6 and 3 2/3.
Now, Let us assume original number 'x'.
Change mixed fraction into improper fraction,
1 5/6 = 11/6
3 2/3 = 11/3
Then by the given condition,
Subtracting 7/18 from x and add 11/6, we get;
x - 7/18 + 11/6
And this is equal to = 11/3
So, we get;
x - 7/18 + 11/6 = 11/3
Add 7/18 both side,
x - 7/18 + 11/6 + 7/18 = 11/3 + 7/18
x + 11/6 = 11/3 + 7/18
Subtract 11/6 both side,
x + 11/6 - 11/6 = 11/3 + 7/18 - 11/6
x = 11/3 + 7/18 - 11/6
x = 66/18 + 7/18 - 33/18
x = 40/18
x = 20/9
Thus, The original number is 20/9.
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We know 2×6=12.
So, which of the following statements are also true?
Choose 2 answers:
A, 12 is a multiple of 2
B, 12is a multiple of 6
C, 6 is a factor of 6
fyi kinda bad at factors a multiples...
Answer:
A and C is true statements
hope this helps :)
Step-by-step explanation:
Answer:
C and A
Step-by-step explanation:
6(x - 4y) how to I answer this question
Answer:6x-24y
Step-by-step explanation:You basically distribute the 6 with the x and the you do the same with the 4y. and thats how u get ur answer
Answer:
6x - 24y
Step-by-step explanation:
I'm guessing that they want you to distribute the 6 to each term inside the parentheses...
Please help me need help
Answer:
81 100 121 144 169 196 225 256
17 19 21 23 25 27 29 31
Step-by-step explanation:
the formula is to square the number then subtract the preceding number in the box
Find the real and imaginary solutions of each equation.
125 x³-1=0
A solution that is real in its nature is called the real solution of that equation.
X + 5 = 0
We can solve the above equation as,
X + 5 = 0
X = -5
Now, if we plug the value of X into the equation,
X + 5 = 0
-5 + 5 = 0
0 = 0
The solution is real and is true for this equation.
While the solution of an algebraic expression solution is imaginary if it is the square root of a negative number. It involves the imaginary unit iota.
The complete solution of the expression is given below in the picture.
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Solve each equation. If necessary, round to the nearest ten-thousandth. 12⁴⁻x=20
The solution of the given equation by rounding off it to the nearest ten-thousandth is 20716.0000.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: 12⁴ - x = 20
We are given that 12⁴ - x = 20 —- 1
We know that 12⁴ = 20736
So, equation 1 becomes,
20736 - x = 20
x = 20736 - 20
= 20716
Hence, the solution of the given equation to the nearest ten-thousandth is 20716.0000.
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Nathaniel is an insurance underwriter. He earns $31.45 per hour, is paid weekly, and works 40 hours per week. His current federal withholding per week is
$106. Nathaniel lives in a state with a flat-rate income tax of 5.3%. He will receive a 5.25% raise and his new federal withholding will be $117. Determine
the following after taxes:
Answer:
Step-by-step explanation:
yyyyyyyyyyyyyyyyyyyyyyyyyyyy
During spring break, Ian studied 3 hours
on the first day, 6 hours on the second
day, and 4 hours on the third day. How
many hours must he study on the fourth
day if he wants to spend an average
(arithmetic mean) of 5 hours each day
studying?
A. 6
B. 7
C. 8
D. 9
4=q+13. Solve the equation using addition or subtraction A. q=4. B.q=17 C.q= -9 D. q= -2
Answer:
C. q= -9
Step-by-step explanation:
4=q+13
-13 -13 (4-13= -9)
q=-9
hope this helps :)
The solution of the given equation 4=q+13 is -9. Thus option C is correct.
The equation is defined as an expression consisting of an equality sign.
let us consider an example :
[tex]2x - 5 = 13.[/tex]
The given equation is:
[tex]4 = q + 13 \rightarrow 1[/tex]
For part A when q = 4 (given)
on substituting the value in equation 1 we get,
On transposing 13 to opposite side we get,
[tex]4 -13 = q[/tex]
[tex]-9 = q[/tex]
rewrite the equation as,
[tex]q =9[/tex]
The solution of the given equation [tex]4=q+13[/tex] is -9.
Thus option C is correct.
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Using a letter to represent the unknown number, select the equation that matches the problem.
A stick is 5 m long. A rope is 4 times as long as the stick. If the rope is divided into 2 pieces, how many meters long is each piece of rope?
The length of each piece of rope is 10m.
What is the length of each peace of rope?The first step is to determine the length of the rope before it was cut. In order to determine the length of the rope, multiply the length of the stick by the number of times the rope is as long as the stick.
Multiplication is the process that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.
Length of the rope = length of the stick x 4
4 x 5 = 20m
lf the length of the rope is divided into two prices, divide the length of the rope by 2. Division is the mathematical operation that is used to determine the quotient of two or more numbers. It entails grouping a number into equal groups using another number.
Length of each piece = Length of the rope / 2
20m / 2 = 10m
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If p and q are positive integers such that pxq = 37, find the value of p + q. Show your working clearly and explain your answer. Please explain ty
The perimeter of a rectangle is 102 feet. Find the length and width if the length is an integer and the width is 3 times the next consecutive integer.
Length = [_] feet
Width = [_] feet
The length of the rectangle is 12feet and the width is 26feet.
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed according to the equation below:
Perimeter = 2(length + width)
If the width is 3 times the next consecutive integer, then;
w = 3(x+1)
l = x
Substitute
102 = 2(x + 3x + 3)
102 = 2(4x + 3)
102/2 = 4x+ 3
51 = 4x + 3
4x = 48
x = 12 = length
For the width
width = 2(x+1)
width = 2(12+1)
width - 26 feet
Hence the length and the width of the rectangle are 12 feet and 26 feet respectively
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Can someone help me please? This is imporant
The solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622. (Correct choice: B)
How to solve graphically a system of equations
In this question we find a system formed by one nonlinear equation and one linear equation, which can be resolved by using a graphic approach. g(x) = f(x) represents the point of intersection of the two curves. First, we plot the graphs of the two curves and, second, the point of intersection is marked on the Cartesian plane.
According to the result given by the graphing tool, there are two solutions for the system of equations: x₁ ≈ - 3.967, x₂ ≈ - 0.622.
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Write the equations for the lines parallel and
perpendicular to the given line j that passes
through Q. . y = −4x + 1; Q(6, −1)
Answer:
Parallel: y = -4x + 23
Perpendicular: y = (1/4)x - (5/2)
Step-by-step explanation:
Parallel Line:
y = -4x + 1; (6, -1)
(x₁, y₁)
y - y₁ = m (x - x₁)
y - (-1) = -4 (x - 6)
y + 1 = -4 (x - 6)
y + 1 = -4x + 24
y = -4x + 23
----------------------------------------------------------------------------------------------------------
Perpendicular:
y = (1/4)x + 1
y - y₁ = m (x - x₁)
y - (-1) = (1/4) (x - 6)
y + 1 = (1/4) (x - 6)
y + 1 = (1/4)x - (6/4)
-1 -1
y = (1/4)x - (5/2)
I hope this helps!
Does this graph represent a function? Why or why not?
Check the picture below.
well, according to the line vertical test, if a vertical line anywhere on the graph hits the graph only once, then yeap, it's a function.
What is the decimal equivalent of 1/7 and how can you do the order and how it goes?
Answer:
Answer: 1/7 as a decimal is 0.143
Step-by-step explanation:
Let us understand the division method to write 1/7 as a decimal. Explanation: To convert any fraction to its decimal form, we just need to divide the numerator by the denominator. Irrespective of the methods used, the answer to 1/7 as a decimal will always remain the same
At a large university it is known that 30% of the students eat at dinning halls on campus. The director of student life is going to take a random sample of 300 students. What is the probability that less than a quarter of the sampled students eat at dinning halls on campus?.