Answers
Answer:
[tex]-\frac{1}{2} \vec {c}[/tex]
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because [tex]\frac{4}{4}=1=\frac{-2}{-2}[/tex]
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that [tex]k \vec{c} = \vec {d}[/tex], or equivalently, [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex].
If [tex]kc_x=d_x[/tex] and [tex]kc_y=d_y[/tex], we just need to substitute known values and solve for k:
[tex]kc_x=d_x\\k(4)=(-2)\\k=\dfrac{-2}{4}\\k=-\frac{1}{2}[/tex]
Double checking that k works for the y-coordinates as well:
[tex]kc_y=d_y[/tex]
[tex](-\frac{1}{2}) (4)[/tex] ? [tex](-2)[/tex]
[tex]-2=-2 \text{ } \checkmark[/tex]
So, [tex]-\frac{1}{2} \vec {c} = \vec {d}[/tex]
Answer:
Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that , or equivalently, and .
If and , we just need to substitute known values and solve for k:
Double checking that k works for the y-coordinates as well:
?
So,
Related Questions
Graph g(x)=|x−4|+3.\
Answers
I insert an image graphing the function.
Function:[tex] \boxed{ \boxed{g(x) \: = \: |x \: - \: 4| \: + \: 3}}[/tex]
MissSpanishGEOMETRY! 50 POINTS
Please explain as best as you can for the second part of the question, I dont understand how to do it.
Answers
The geometry is that the number of sides for a 15- gon is 15 sides and the angles are 156° each.
How to calculate the angle?The total angles in a 15 gon will be calculated as:
= (n - 2) × 180
= (15 - 2) × 180
= 2340
The value of each angle will be:
= 2340/15
= 156°
The total angles in a 16 gon will be calculated as:
= (n - 2) × 180
= (16 - 2) × 180
= 2520
The value of each angle will be:
= 2520/16
= 157.5°
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What is the difference between normal definition of set and contors definition of set
Answers
Step-by-step explanation:
The collection of well defined object is called set
The height of a cone is twice the radius of its base. a cone has a height of 2 x and a radius of x. what expression represents the volume of the cone, in cubic units?
Answers
Answer:
Step-by-step explanation:
The volume of a cone is V = 1/3 [tex]\pi[/tex] * h * r^2
The height of the cone = the diameter of its circle.
Here is the expression:
Volume = 1/3 π * 2x * x^2
[tex]\frac{\pi *x^{2} *2x}{3}[/tex]
Hope I helped!
Exit A bag contains 4 blue balls, 7 yellow balls and 4 white balls. Event A is defined as drawing a blue ball on the first draw and event B is defined as drawing a white ball on the second draw. If two balls are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 2/7
B. 3/14
C. 4/15
D. 4/11
please hurry
Answers
P(B|A) expressed in simplest form is 4/15. Option C is correct answer.
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of event A = 4/15
probability of event B = 4/15
P(B|A) = P(A ∩ B)/P(B)
P(A ∩ B) = P(A) X P(B)
= (4/15)(4/15)
= 16/225
Now, conditional probability;
P(B|A) = (16/225) / (4/15)
= (16/225)(15/4)
= (16 X 15) / (225 X 4)
= 4/15
Thus, P(B|A) expressed in simplest form is 4/15. Option C is correct answer.
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How to determine whether square root equation is always, sometimes , never, or true?
Answers
Answer:
While identity is true for all values of x, an equation may be true only for some values of x, or for no values of x. Examples: 2x + 6 = 4 is true when x = -1, but not when x = 0. The equation x + 5 = x is never true because a number is never equal to five more than itself.
Step-by-step explanation:
I hope this helps
NEED HELP ON THIS ASAP!!!!!!
Answers
Answer: Choice B (If you need to do questions like this in the future i recommend using the desmos graphing calculator online, inputting the equations and comparing them)
help asap!!!!
Select the correct answer.
Which equation could represent the data in the table?
Answers
Answer:
A. y = 3x + 1
Explanation:
Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Take two points: (0, 1), (1, 4)
[tex]\sf \rightarrow slope \ (m) : \dfrac{4-1}{1- 0 } = 3[/tex]
Equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 1 = 3(x - 0)[/tex]
[tex]\sf y = 3x + 1[/tex]
Which triangles in the diagram are congruent?
70°
triangle 1
70°
triangle 3
OA triangle 1 and triangle 2
OB. triangle 1, triangle 2, and triangle 3
OC. triangle 1 and triangle 3
OD. triangle 1, triangle 3, and triangle 4
70°
triangle 2
#
triangle 4
Submit Test
Rea
Answers
Answer:
its e
Step-by-step explanation:
because e is is referring to savvy
A rectangular prism has a base that is 4 m by 6 m and a height of 10 m. If all dimensions are doubled, what happens to the volume? Explain why he steps that you take to arrive your answer.
Answers
If we double the dimension the volume will be increased by 8 times, and the volume will be 1920 cubic m.
What is the Volume of a rectangular prism?The Volume of rectangular prism = l×b×h
The volume of a prism,
V = L x B x H
V = 4 x 6 x 10
V = 240
When all the dimensions are doubled, the new volume will become
V1 =2L x 2B x 2H
V1 = 8(4 x 6 x 10)
V1 = 8(240)
V1 = 1920 cubic m
If we double the dimension the volume will be increased by 8 times, and the volume will be 1920 cubic m.
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Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.
Answers
Answer:
1.2x = 22x = 55/3 ≈ 18.3322 AUD = 18.33 USDStep-by-step explanation:
1 USD - 1.2 AUD
x USD - 22 AUD
cross multiply
1.2 · x = 1 · 22
1.2x = 22multiply both sides by 10
12x = 220
divide both sides by 12
x=55/3 ≈ 18.33USD - United States dollar
AUD - Australian dollar
Suppose we want to choose 6 letters without replacement from 10 distnict letters. how many ways can this be done if the order of the choices is relavant
Answers
The number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.
What are permutation and combination?A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
We have:
Suppose we want to choose 6 letters without replacement from 10 distinct letters.
Number of letters = 10
Number of letters need to select = 6
Order is important.
A number of ways:
C(10, 6) = 10!/(10-6)!
= 10!/(4)!
= 151200
Thus, the number of ways this can be done is 151200 if they choose 6 letters without replacement from 10 distinct letters.
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7. Miguel draws a square on a coordinate plane. One vertex is located at (5, 4). The
length of each side is 3 units. Circle the letter by all the ordered pairs that could be
another vertex.
A. (5, 1)
B. (5, 7)
C. (7, 8)
D. (2, 6)
E. (2, 1)
Answers
Answer:
A, B and E
Step-by-step explanation:
Answer: A,B and E i did the test
Step-by-step explanation:
There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
Answers
Answer:
11:12
Step-by-step explanation:
You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio
Mark's Digital Place has a compact digital camera at a price of $425, a 8 inch tablet for $540 and a
game console for $610. If you want to get an additional three years warranty, then you need to pay
15% extra on the original price and $50.
Daphne wants to buy a digital camera and a tablet to start a photography course. When she went into
the store, she found that the store id offering a discount of 5% on the camera and 80 on the tablet.
Daphne also want the additional three years warranty. How müch money does Daphne need to pay to
buy both the items with a three years additional warranty on each item?
Answers
Answer:
jjxfzhfxjgjhzjjjtxjxjxktxjtxjtxtxh
How do u solve 3/8+1/8-2/7+1/4
Answers
Answer:
13/28
Step-by-step explanation:
using pemdas we can determine that the equation is directly solves from left to right
so
first
we have
3/8 + 1/8
which is 4/8
you can simplify this to 1/2
then you have 1/2 - 2/7
you must make them have the same numerator
you can multiple 1/2 by 7/7 and 2/7 by 2/2
7/14 - 4/14 = 3/14
now you must add 3/14 and 1/4
but you to make them have the same numerator
so you multiply 3/14 by 2/2 and 1/4 by 7/7
6/28 + 7/28 = 13/28
that is your final answer
cotpheta•sin2pheta=
1+cos2pheta
1+cospheta
1+sin2pheta
Answers
Answer:
Step-by-step explanation:
Did you mean.
[tex] = \cot( \theta) . \sin(2 \theta) [/tex]
[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]
[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]
[tex] = 2 \cos {}^{2} ( \theta) [/tex]
[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]
[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]
No option Solution.
What is the equation of the line that passes through the point (8,4) and has an undefined slope?
Answers
Answer:
x = 8
Step-by-step explanation:
An undefined slope indicates that the line is vertical and parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (8, 4 ) with x- coordinate 8 , then
x = 8 ← equation of line
4
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3% simple annual interest paid on $250
A 2-column table with 4 rows. Column 1 is labeled Year with entries 1, 2, 3, 4. Column 2 is labeled Total Interest Paid with entries question mark, 15 dollars, 22 dollars and 50 cents, question mark.
The simple interest earned in year 1 is calculated as
.
The simple interest earned in year 1 is
.
The total interest earned at the end of year 4 is
.
Answers
The simple interest earned in year 1 is 7.5. The simple interest earned in year 1 is $7.50. The total interest earned at the end of year 4 is $30.00
How to calculate a simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, it is left for T years for that simple interest.
3% simple annual interest paid on $250
A 2-column table with 4 rows.
Column 1 is labeled Year with entries 1, 2, 3, 4.
Column 2 is labeled Total Interest Paid with an entries question mark, 15 dollars, 22 dollars, and 50 cents,
The simple interest earned in year 1 is calculated as
The first one is (0.03)(250) = 7.5
The simple interest earned in year 1 is
The second one is $7.50
The total interest earned at the end of year 4 is
The third one is $30.00
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A biologist is studying the effects of using a type of bacteria to clear drain pipes. She creates a simulation of a typical kitchen drain system and
uses it regularly for three days before introducing the bacteria. She then carries out her simulation for another 15 days.
The population of bacteria can be approximated using function b, where dis the number of days since she started the experiment and (d) is the
bacteria population in hundreds.
b(d) = √5.2d-15.6 +2
Use this information to complete the statement.
The domain over which the bacteria population Increases is
Answers
The domain over which the bacteria population Increases is [tex]d \ge 3[/tex]
How to determine the domain?The function is given as;
[tex]d = \sqrt{5.2d - 15.6} + 2[/tex]
Set the radicand greater than or equal to 0
[tex]5.2d - 15.6 \ge 0[/tex]
Add 15.6 to both sides
[tex]5.2d \ge 15.6[/tex]
Divide both sides by 5.2
[tex]d \ge 3[/tex]
Hence, the domain over which the bacteria population Increases is [tex]d \ge 3[/tex]
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express 80 as a product of its prime factors, write the prime numbers in accending order
Answers
Answer:
80 as a product of prime numbers can be expressed as 2×2×2×2×5
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answers
Answer:
-9
Step-by-step explanation:
-9
Reece and Sarah share some money in the ratio 9 : 16.
Reece says that Sarah gets more than 60% of this money. Show that Reece is correct.
Answers
Answer:
64% > 60%
Step-by-step explanation:
Total Units = 9 + 16 = 25 units.
Sarah Receives 16 units out of 25.
Percentage = 16/25 * 100
= 64%
Therefore Sarah received more than 60% of this money and therefore Reece is correct.
PLEASE HELP. FUNCTIONS AND RELATIONS. PROVIDE ANSWER OPTION A,B,C OR D? THANKS!!
Answers
Step-by-step explanation:
please mark me as brainlest
What is the remainder of the quantity 5 x cubed plus 7 x plus 5 end quantity divided by the quantity x plus 2 end quantity? Show all necessary steps.
Answers
The remainder of the polynomial equation is -49
What is a remainder of a polynomial equation?The remainder of a quantity in an algebraic expression of a polynomial equation is the remaining amount of the quantity left and can not be divisible by the divisor.
From the given information, we are to find the remainder of the given algebraic equation:
[tex]\mathbf{= \dfrac{5x^3+7x+5}{x+2} }[/tex]
Using the long division method, we have:
[tex]\mathbf{= \dfrac{5x^3+7x+5}{x+2} } \implies \mathbf{5x^2 + \dfrac{-10x^2+7x+5}{x+2}}[/tex]
Divide by [tex]\mathbf{ \dfrac{-10x^2+7x+5}{x+2}}[/tex], we have:
[tex]\mathbf{= 5x^2- 10x+ \dfrac{27x+5}{x+2}}[/tex]
Divide by [tex]\mathbf{\dfrac{27x+5}{x+2}}[/tex], we have:
[tex]\mathbf{= 5x^2- 10x+ 27 +\dfrac{-49}{x+2}}[/tex]
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evaluate the following expression when x=-4 and y=4
x³-x /4y[tex]\frac{x}{y}[/tex]
Answers
Answer: - 60
Step-by-step explanation:
[tex]\frac{(-4)^3 - (-4)}{4(4)^-4/4} \\\\= -60[/tex]
40 points, please help lol
Answers
The simplified expression of [tex]x^{-2/3} . x^{6/7}[/tex] is [tex]x^{4/21}[/tex]
How to simplify an expression?The expression [tex]x^{-2/3} . x^{6/7}[/tex] can be simplified as follows:
using law of indices,
xⁿ . xᵇ = xⁿ⁺ᵇ
Therefore,
[tex]x^{-2/3} . x^{6/7}[/tex] = [tex]x^{-2/3 + 6/7}[/tex]
[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21}[/tex]
[tex]x^{-2/3 + 6/7} = x^{ -14+18/ 21} = x^{4/21}[/tex]
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Preform the indicated operation.
(2x+y)(3 x² + y)
Answers
Answer:
[tex]6x^3+3x^2y+2xy+y^2[/tex]
Step-by-step explanations:
[tex](2x+y)(3x^2+y)\\2x*3x^2+2xy+3x^2y+y*y - Distribute\\6x^3+3x^2y+2xy+y^2 - Simplify[/tex]
Answer:
6x^3 + 2xy + 3x^ 2y + y^2
Step-by-step explanation:
Apply the distributive property of multiplication. First multiply (3x^2 + y) by 2, obtaining 6x^3 + 2xy, and then multiply (3x^2 + y) by y, obtaining
3x^2y + y^2. Finally, combine like terms (if any) in these two results:
6x^3 + 2xy + 3x^ 2y + y^2
Find the y-intercept of the rational function.
A (0, -10)
B (-10, 0)
C (0 , -2)
D (-2, 0)
Answers
Answer:
C
Step-by-step explanation:
The y intercept is when the graph passes the y axis. This occurs at (0,-2)
A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.
Each rectangle contains a shaded rhombus. The left angle is 50 degrees and the top angle is (2 x + 20) degrees.
What is the value of x?
50
55
125
145
Answers
According to the computations, this rhombus's value of x is equal to 55°.
How can we calculate x's value?The total of all the angles in a rhombus should be 360 ° because the opposing angles in a rhombus are always identical.
We may infer the preceding information from the rhombus's picture:
Neighboring angles= 2x+ 20 & 50°
Opposite angles=2x+ 20 & 50°
Combining the angles results in:
2x+20+50+2x+20+50=360
⇒4x+140= 360
⇒4x=360-140
⇒4x=220
⇒x=220/4
⇒x=55°
Hence, it is concluded that the value of x is (b) 55°.
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