Let [tex]\vec K,\vec L,\vec M,\vec N[/tex] be vectors pointing the vertices K, L, M, and N, respectively.
The side KL is parallel to and has the same length as the vector
[tex]\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k[/tex]
Similarly, the side KN is parallel and as long as
[tex]\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath[/tex]
These vectors have magnitudes
[tex]\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5[/tex]
[tex]\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}[/tex]
and their dot product is
[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6[/tex]
The parallelogram spanned by the vectors [tex]\vec L-\vec K[/tex] and [tex]\vec N-\vec K[/tex] has area equal to the magnitude of their cross product, for which we have the identity
[tex]\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)[/tex]
where [tex]\theta[/tex] is the angle between the sides KL and KN.
From the dot product identity, we have
[tex](\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)[/tex]
Then
[tex]\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}[/tex]
Simplify by combining like terms. Write the answer with the variables in alphabetical order and any constant term last.
a+ ab^3 + ab^3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. a+ ab^3 + ab^3 simplifies to [ ]
O B. The expression cannot be simplified.
a+ ab³ + ab³ simplifies to 2ab³+a.
For simplifying the terms first we have to add Like Terms.
Like Terms: Terms that have identical variable parts (same variable(s) and same exponent(s)). When simplifying using addition and subtraction, you combine “like terms” by keeping the "like term" and adding or subtracting the numerical coefficients.
In Algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers. The order of the variables does not matter unless there is a power.
So hence we will add ab³ + ab³= 2ab³
For any given term, we almost always list the variables in alphabetical order and any constant terms last — this is helpful in identifying common terms, a topic discussed in the next section. So, for example, it is simply not cool to write 15yx, 15 y x , we want to stay alphabetical and write 15xy. Exponents play no role in this decision.
Therefore a+ ab³ + ab³ simplifies to 2ab³+a.
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What is the value of 5 x 3 + 4 y 3 when x=4 and y=3?
Answer:
96
Step-by-step explanation:
HELP!!!! WILL MARK BRAINLIEST!!!!
18x+3=21
Solve for x.
Answer:
x=1
Step-by-step explanation:
18x+3=21
-3 = -3
18x= 18
18x/18 = 18/18
x= 1
Answer:
x = 1
Step-by-step explanation:
[tex]18x + 3 = 21\\18x = 21 - 3\\18x = 18\\18x/18 = 18/18\\x= 1[/tex]
BD bisects
Find m
ABC= 25x+34
CBD = 11x+23
The measure of angles are
i) Angle ABD = 67°
ii) Angle CBD = 67°
iii) Angle ABC = 134°
We have been given that ray BD bisects angle ABC and also
Angle ABC = (25x+34)°
Angle CBD = (11x + 23)°
Note that angle ABC = angle ABD + angle CBD (1)
And angle ABD = angle CBD = (11x + 23)° as it is bisected into two equal half.
Therefore putting the required values of angle in equation (1) we get
(25x+34)° = 2(11x+23)°
25x+34 = 22x+46
25x – 22x = 46 – 34
3x = 12
x = 4
Hence, angle ABD = (11*4 + 23) ° = 44+23 = 67°
Angle CBD = (11*4 + 23) ° = 44+23 = 67°
angle ABC = (25*4 + 34)° = 100+34 = 134°
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f) (a² - a + b)(a + b − 2)
Answer:
Step-by-step explanation:
Rewrite the equation below so that it does not have fractions.
2/3x+4=2/5
do not use decimals in your answer.
The rewritten form of the equation as given in the task content such that it has no fraction is; 10x + 60 = 6.
In order words, when the equation " 2/3x+4=2/5" is rewritten such that it does not have fractions, it is rewritten as 10x + 60 = 6.
What is the rewritten form of the equation such that it has no fractions?It follows from the task content that the equation given be rewritten such that it has no fraction.
Given:
(2/3)x + 4 = 2/5
Hence, we multiply all terms in the equation by the lowest common multiple of 3 and 5.
Multiply both sides by 15 so that we have;
10x + 60 = 6.
Ultimately, the rewritten form is as indicated above.
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I have a series of questions. The faster I get the answer the more point I give.
We have
28 = 2²•7
48 = 2⁴•3
and GCD(28, 42) = 2² = 4.
33. In this code puzzle each letter has a different numerical value. The totals for each word are reached by adding together individual values. What is the total value of the word ENTREE?
tea = 30
neat = 50
tan = 40
ten = 35
tear = 55
Answer:
tear 35 is ans
pla mark me brainliest ans
Answer:
Hello,
Answer 80
Step-by-step explanation:
[tex]\left\{\begin{array}{cccc}t+e+a&=&30&(1)\\n+t+e+a&=&50&(2)\\t+a+n&=&40&(3)\\t+e+n&=&35&(4)\\t+e+a+r&=&55&(5)\end{array} \right.\\\\\\\left\{\begin{array}{cccc}n&=&20&(2)-(1)=(6)\\t+a&=&20&(7)\\t+e&=&15&(8)\\r&=&25&(5)-(1)=(9)\\t+e+a&=&30&(1)\end{array} \right.\\\\\\\left\{\begin{array}{cccc}n&=&20&(6)\\t&=&5&(7)+(8)-(1)=(10)\\a&=&15&(7)\ and \ (10)\\e&=&10&(8)\ and \ (10)\\r&=&25&(9)\\\end{array} \right.\\[/tex]
[tex]\\\\\boxed{ENTREE=3*e+n+t+r=3*10+20+5+25=80}\\[/tex]
Points on the coordinate plane
Point N is graphed on the coordinate plane.
-5-2
is
OF
Write the coordinates of point N.
If we reflect the point (-5,2) (five, -two) over the x-axis (line of symmetry) the reflected point is (-5,-2). If we reflect the point (-5,2) (five, - two) over the y-axis (line of symmetry) the reflected point is (5,2).
What are the x-axis, and y-axis?
The vertical axis is generally called the x-axis. The perpendicular axis is generally called the y- axis. The point where the x- and y- axis intersect is called the origin. The x-axis is generally the vertical axis, while the y- axis is the perpendicular axis. They're represented by two number lines that cross perpendicularly at the origin, located at( 0, 0). The x-axis is also called the abscissa and the y- axis is called the ordinate.
The point (-5,2) is plotted as red in the picture attached.
To reflect a point over the x(ax)-axis, the x(ax) value must be the same and the y value must be the opposite.
To reflect a point over the x(ax)-axis, the y(y) value must be the same and the x(ax) value must be the opposite.
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Find the volume of the solid.
Answer:
Mushroom is a friends as as well as a foe give reason for the value of a and shss sag ni khana banaun lako I think it is a friends as as well as a foe give reason for the value of a and the value for money and the value of a and the value for money and the value for money and the value for money and the value.
Step-by-step explanation:
Mushroom is a friends as as well as a result in Nepal and bhailo essay writing about deusi and the value of x of a and the value of x of the following figure of a mushroom the value of a and the value of x of the following figure of a mushroom the value of x of the following a foe give reason for the value of x of the following figure out of the following figure of x of the value of a and the value for money and the value of a and the value of a and the value for money and the value for money and the value of a and the value for money and the value for money and the value for money to start a and the value of a and the value for money to start a and the value for money and the value for money and the value.K garde Khana khani I think. Um tani twvarkhar kam garxu bye badar vanar karako ni khana ko captain America and the value for money and the value for money and
Aliya hikes up a mountain for 2 hours. During this time, she hikes a
distance of 1 miles. Which expression shows Aliya's rate in miles per
1
hour?
The expression shows Aliya's rate in miles per hour will be 1/2.
How to compute the expression?From the information, Aliya hikes up a mountain for 2 hours and during this time, she hikes a distance of 1 miles.
Therefore, the rate will be:
= Distance / Time
= 1 / 2
Therefore, the expression shows Aliya's rate in miles per hour will be 1/2.
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A power company calculates a person's monthly bill from the number of
kilowatt-hours (kwh), x, used.
the function b(x)
The bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
The given functions are
b(x) = 0.15x; x ≤ 360
b(x) = 0.10(x - 360) + 54; x > 360
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
For a person who uses 560 kWh, it means that:
x > 360
So, we use the following function to determine the bill
b(x) = 0.10(x - 360) + 54
Substitute 560 for x
b(560) = 0.10(560 - 360) + 54
⇒b(560) = 74
Hence, the bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
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Your question is incomplete, probably the complete question/missing part is:
A power company calculates a person's monthly bill from the number of kilowatt-hours ( Nh), x, used. The function b(x)= 0.15x, and x≤360. 0.10(x-360)+54, and x>360 determines the bill. How much is the bill for a person who uses 560 kWh in a month? A. $84 B. $54. $64 D. $74.
help. Solve for x and show work
Answer: i belive x=1
27-28=1
2x-x
x
Step-by-step explanation: hope this helps
2173 rounded to neatest hundred
Answer:
2200
Step-by-step explanation:
that is the answer jf
Evaluate the expression for the given values of the variables.
-k²-(4k - 7n) + 3n; k= -2 and n=-5
For k = -2 and n=-5, -k²-(4k-7n) + 3n=
(Simplify your answer.)
the answer for given expression is 54
How do you define expression in math?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.
the given expression is
[tex]-k^2 - (4k-7n)+3n\\-k^2 -4k +7n+3n\\put k = -2 and n=5\\-( -2)^2 - 4(-2) + 10 *5\\-4 +8+50\\54the answer for given expression is 54[/tex]
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Jasmine is 20 years old. Her brother Zac is 6 years more than half her age. Which of the following is the correct expression for Zac's age?
(20 ÷ 2) + 6
(20 ÷ 2) − 6
10 x 2 + 4
10 − (2 x 4)
Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)
The mass of the wire is found to be 40π√2 units.
How to find the mass?To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass = [tex]\int_a^b \delta\left|r^{\prime}(t)\right| d t[/tex]
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
[tex]\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}[/tex]
Further simplifying;
[tex]\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}[/tex]
Now, use integration to find the mass of the wire;
[tex]\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}[/tex]
Therefore, the mass of the wire is estimated as 40π√2 units.
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5
An ordinary deck of 52 cards is shuffled. what is the probability that the top four cards have (a) different denominations? (b) different suits?
The different denomination is 0.6761
The different suits are 0.1055
What are deck of cards consist of?A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.
Given:
Deck of cards= 52
Now,
There are 4 denomination in each cards
and there are 4 suits in deck of cards
a) different denominations
=52*48*44*40/(52*51*50*49)
= 0.6761
b) different suits
=52*39*26*13/ /(52*51*50*49)
= 0.1055
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please help quick im so confused
Answer:
(-5/2,-4)
Step-by-step explanation:
the answer is (x, y) = (-5/2, -4)
If I spend $35 every 2 weeks, how much do I spend in a year?
HELP PLS EXPLAIN THISSSS
(image included)
Answer:
The slope is [tex]-\frac{3}{4}[/tex]
Step-by-step explanation:
To find the slope, you take 2 points and use rise/run. I used (0,1) and (4,-2) because they look like they are being touched by the line. So by looking at the graph, I have to look at how I can get from (0,1) to (4,-2). So from (0,1), I go down 3 units which makes my number -3, over the run which is 4 units to the right, which makes it positive. so I went down 3 and then went right 4, making this [tex]-\frac{3}{4}[/tex]. You could also use point-slope which means [tex]\frac{y2-y1}{x2-x1}[/tex] or [tex]\frac{-2-1}{4-0}[/tex] which equals the same thing
A loaf of bread 9 in. long is cut into slices 3/8 in. thick.
Answer:
32
Step-by-step explanation:
There is nothing this but the answer is 32.
What is the midpoint of line segment AB? if a is -1,3 and b 5.-7
The midpoint of line segment AB is (2, 5)
What is the midpoint of line segment AB?The coordinates are given as:
A= (-1,3)
B = (5.-7)
The midpoint of line segment AB is calculated as
Midpoint = 0.5 * (x1 + x2, y1 + y2)
So, we have:
Midpoint = 0.5 * (-1 + 5, 3 + 7)
Evaluate
Midpoint = (2, 5)
Hence, the midpoint of line segment AB is (2, 5)
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After his first month he had more than he expected to have due to interest the bank provided. this let rob come up with a better expression. where w is the number of weeks. how much will he have in 1 year?
He will earn 2603.16 dollar in one year.
What is expression?An expression is a collection of terms that have been joined together using the operations +, -, or x, such as 4 x 3 or x 2 - x y + 17.
Two expressions are said to be equal in value by an equation, such as 4 b 2 = 6.
Given:
A copy of the entire query is provided below:
45w+ 155
He will therefore save
=45*6+155
=270+155 =425 dollars
so, w=6.
Knowing that a year equals 52 weeks
Also,
w=52 and
w²/25+45w+155
Thus,
=52*52/25+45*52+155
=108.1602340+155
= $263.16
Hence, he will make $2603.16 in a year.
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22 17 25 41 39 4
Work out the difference between the two prime numbers in the list above.
The difference between the two prime numbers 17 and 39 is 22.
What are referred as the prime numbers?Prime numbers are those who have only two factors: 1 and the number on its own.
A prime number is a number greater than one with precisely two factors, i.e., 1 as well as the number itself. For example, the number 7 has only two factors: 1 and 7. As a result, it is a prime number. However, the number 6 has four factors: 1, 2, 3, and 6. It is a composite numbers.A prime number is one that is the whole number larger than one.It has only two factors: 1 and the number it's own.There's only the one even prime number: 2.Such a two prime numbers always are co-prime numbers.Every number can be represented as a prime number product.For the number given:
22 17 25 41 39 4
The two primes numbers are 17 and 39.
The difference is 39 - 17 = 22.
Thus, the difference between the two prime numbers is 22.
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Which of the following is equivalent to the expression x² - 64?
A) (x-8)²
B) (x-64)²
C)(x-8)(x-8)
D) (x+8) (x-8)
Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards
long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
11 inches : ? yards
The scale used by Wyatt is; 11 inches : 4 yards.
What is defined by the term scale factor?The Scale Factor is utilised to scale forms in various dimensions. The scale factor is a measurement for figures with similar appearances but distinct scales or measures. Assume two circles appear similar but have different radii.The scale factor specifies how much larger or smaller a figure is than the earlier figure.Now, for the given values in question.
For the area of picnic is 84 yards.= long.
The length in the drawing is 31 inches.
Let the scale for yards is 'x'.
Then;
231 inches: 84 yards = 11 inches: x yards
Write in the fraction form,
231/84= 11/x
Cross multiplying;
x = (11×84)/231
x = 4
Thus, scale becomes; 11 inches : 4 yards.
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HURRY PLS!!
A company orders 22 boxed lunches from a deli for $273.90. If each boxed lunch costs the same amount, how much do 16 boxed lunches cost?
Answer:
Step-by-step explanation:
1 box costs x amount
18 boxes cos 223.20
Cross multiply
223.20 * 1 = 18 x
Divide by 18
223.20 / 18 = 18x / 18
x = 12.40
Cost of 1 box is 12.40
Answer:
It should be 199.20 for 16 boxes
Step-by-step explanation:
I divided 273.90 by 22 which came out to 12.45
so then i multiplied 12.45 by 16 and it gave me 199.20
Write a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.
Float rate_of_pay a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.
What is float rate_of_pay?
In contrast to fixed (or unchangeable) interest rates, floating interest rates change on a regular basis. Companies that offer credit cards and mortgages frequently use floating rates. Floating rates follow the market, a benchmark interest rate, an index, or both.Is a fixed or floating rate preferable?
In a rising rate environment, banks offer fixed rate loans at a higher rate than variable rate loans in order to profit more from the latter when rates rise. Fixed rate loans may have interest rates that are 300–350 basis points higher than floating rate loans.float rate_of_pay
rate_of_pay = 11.50, 12.75;
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Simplify the expression -6y - 7y
Answer:
-13y
Step-by-step explanation:
Since this expression has the same coefficient, all you have to do is solve -6-7. Just follow the keep change change rule when subtracting negative numbers so -6 + -7 = -13. Therefore, your answer will be -13y.
Let me know if you do not understand or need more explanation.