PLATO: Type the correct answer in each box. The vector is first dilated by a factor of 2.5 and then rotated by pi/2 radians. If the resulting vector is [a / b], then a = __ and b = __
Answers
Answer:
a = -1, b = -2.5
Step-by-step explanation:
Rule for the dilation of a vector [tex]\binom{x}{y}[/tex] by a scale factor of k is,
(x, y) → (kx, ky)
BY using this rule for a vector [tex]\binom{-1}{4}[/tex] by a scale factor of 2.5
[tex]\binom{-1}{4}[/tex] → [tex]\binom{-2.5}{1}[/tex]
Followed by the rotation by 90° Or [tex]\frac{\pi }{2}[/tex] radians,
Rule for rotation of a vector by 90° is,
(x, y) → (-y, x)
By this rule vector [tex]\binom{-2.5}{1}[/tex] will become,
[tex]\binom{-2.5}{1}[/tex] → [tex]\binom{-1}{-2.5}[/tex]
If we represent this vector by [tex]\binom{a}{b}[/tex],
Then a = -1 and b = -2.5 will be the answer.
Answer:
a= -10 b= -2.5
Step-by-step explanation:
Related Questions
Aiyanna wrote the ratio 3:5 to compare the number of pairs of shorts that she owns to the number of pairs of jeans that she owns. Which is equivalent to Aiyanna's ratio?
Answers
Answer:
3/5
3:5 and 3/5 and 0.6 are the same thing just in different forms
You can convert by putting it into a fraction and dividing the fraction
3:5 becomes 3/5 and 3 divided by 5 = 0.6
Hope this helps
Step-by-step explanation:
On a piece of paper, graph y = 2x - 4. Then determine which answer matches
the graph you drew.
Answers
Answer:
Step-by-step explanation:
The graph which matches the equation y = - 2x - 4 is the graph drawn in the option B.
The equation is written in slope - intercept form such that :
The slope = - 2 The intercept = - 4This means that the slope of the graph is negative and the trend line crosses the y - axis at - 4.
Only the graph in option B has a negative slope and its intercept at negative 4
Therefore, the appropriate option is the graph B.
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What value or values of x satisfy 2x + 5.31 = 4.2?
ESBE
x can only equal -3.2.
x can only equal 7.4.
O x can equal -3.2 or -7.4.
O x can equal -3.2 or 7.4.
Answers
Answer: x can equal -3.2 or -7.4.
Step-by-step explanation:
The correct expression is:
2|x+5.3|=4.2
So, we have an absolute value equation, where it can be positive or negative:
Positive2 (x+5.3)=4.2
2x+10.6 =4.2
2x=4.2-10.6
2x = -6.4
x= -6.4/2
x = -3.2
Negative2[-(x+5.3)]=4.2
-2x-10.6 =4.2
-2x= 4.2+10.6
-2x= 14.8
x= 14.8/-2
x= -7.4
x can equal -3.2 or -7.4.
Feel free to ask for more if needed or if you did not understand something.
Answer:
(C)
Step-by-step explanation:
x can equal –3.2 or –7.4.
It Was Correct On Edge
A real friend is one who walks in when the rest of the world walks out
HAVE A GREAT DAY :)
helpp i got -4 am i correct?
Answers
Answer:
-4
Step-by-step explanation:
Slope is rise over run:
[tex]m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}[/tex]
The table is a linear function, so any two points from the table would have a consistent slope.
Pick two points and apply them to the formula:
(-4,-2) and (-2, -10)
[tex]m=\frac{-10+2}{-2+4}=\frac{-8}{2}=\boxed{-4}[/tex]
The slope is -4. Yes, your answer should be correct.
SOMEONE PLEASE HELP ME ASAP PLEASE!!
Answers
Answer:
hope its helpful to uh..
What is the 7th term in the sequence of square numbers?
Answers
Answer:
49
Step-by-step explanation:
The n th term of square numbers is calculated using
[tex]a_{n}[/tex] = n²
Thus for the 7 th term, let n = 7 , that is
a₇ = 7² = 49
Lines m and n are parallel. Lines m and n are parallel. Lines s and t intersect lines m and n to form a triangle. The top angle of the triangle is (2 x) degrees. At the intersection of lines s and n, the top left angle is 100 degrees. At the intersection of lines n and 7, the bottom left angle is 70 degrees. What is the value of x? 10 15 30 35
Answers
Answer:
B: 15
Step-by-step explanation:
I got it right on Edge
The value of 'x' in the top angle is 5 degrees.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Given, The angle formed at the top of the triangle is 2x° and the angle formed at the intersection of s and n is 70° and at t and n is 100°.
We know the sum of all the interior angles in a triangle is 180°.
Therefor, 2x + 100° + 70° = 180°.
2x = 10°.
x = 5°.
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PLEASE I NEED AWANSER NOW The Stem-and-Leaf Plot and the Box-and-Whisker Plot here display the number of shoes sold daily in a 12-day sale held in a shoe-store at the local supermarket. What is the range of this data set? A.(20 B.(29 C.(24 D.(26
Answers
Answer:
c
Step-by-step explanation:
Answer:
(d) makes sense to me!!
Step-by-step explanation:
which of the following represents a term from 3x^2+8x-10
Answers
Answer:
3x^2 or 8x
Step-by-step explanation:
Task: E = mc2
E = mc2 is one of the most recognizable equations in the world. Published by Albert Einstein in 1905, the
equation describes a fundamental relationship between energy, E, and matter (or mass), m. But what exactly
is the relationship? What does it mean? In this task, you will parse, or analyze the parts.of the equation in
order to understand it better. Let's start with what the variables represent: E stands for energy, m stands for
mass, and c stands for the speed of light. Use these definitions to complete the exercises below.
4. [10 points] Rewrite the equation to solve for the speed of light, c. Use rational exponents instead of
roots (radicals).
Answers
Answer:
[tex]$c=\left(\frac{E}{m} \right)^{\frac{1}{2} }$[/tex]
Step-by-step explanation:
[tex]E = mc^2[/tex]
[tex]$c^2=\frac{E}{m} $[/tex]
[tex]$c=\sqrt{\frac{E}{m} } $[/tex]
or
[tex]$c=\left(\frac{E}{m} \right)^{\frac{1}{2} }$[/tex]
The equation will be , C= (E/3)^1/2
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division.
Algebraic ExpressionsAn algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). An example of an algebraic expression is 5x + 6. Here 5 and 6 are fixed numbers and x is a variable.
Given:
E = mc^2
c² = E/m
c= √ (E/m)
or,
C= (E/m) ^1/2
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ABCD is a parallelogram. Find the measure of angle , (Give reason)
Answers
Answer:
D=100(opposites angles are equal)
A=C=80 (adj angles are supplementry)
Step-by-step explanation:
Answer:
x = 80
y = 100
z = 80
Step-by-step explanation:
In a parallelogram, opposite angles are congruent. Thus, angle y = 100 degrees. In a parallelogram adjacent angles are supplementary so angle x and z are 80 degrees.
Hope it helps <3
The following quadrilateral is a parallelogram.
W
V
12
?
T
11.5
Side WT is
units long
Answers
Answer:
12
Step-by-step explanation:
By definition, opposite sides of a parallelogram are congruent.
We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilateral is shown below. Seven distinct points are chosen on a circle. We draw all $\binom{7}{2} = 21$ chords that connect two of these points. Four of these $21$ chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?
Answers
Four chosen chords form a bow-tie quadrilateral 2210 .
What is a quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices. The word 'quadrilateral' is derived from the Latin words 'quadri,' which means four, and 'latus', which means side. The above image is an example of a quadrilateral.The bowtie, or crossed rectangle, is a nonconvex semi-uniform quadrilateral with the same vertices as a rectangle but with two of the original sides removed and with the original's diagonals in place instead.Given,
We are aware that a quadrilateral requires four vertices (or points on the circle). The cross can always be connected in one of two ways: horizontally or vertically. My understanding of combinations is inadequate, but we can deduce that picking four points from a possible seven equals 21. Four points can be used to create 21*2 = 42 "bow-tie quadrilaterals" on the circle by multiplying the two methods to join those lines (again, horizontally and vertically). Since there are 2210 possible combinations of four chords out of a possible 21 chords, the probability is 42/2210, and we just need to reduce that fraction.Therefore, Four chosen chords form a bow-tie quadrilateral 2210 .
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The probability that the four chosen chords form a bow-tie quadrilateral is: 60%.
First, let's calculate the total number of ways to choose four chords out of the 21 available chords.
= 21!/ 4! (21-4)!
= 21! / 4! 17!
= 5985
The number of ways to choose two intersecting chords can be represented as [tex]\binom{7}{2}.[/tex]
= 7! / (7-2)!
= 7!/ 5! 2!
= 7 x 6/ 2
= 21
However, we also need to account for the fact that we are choosing four chords in total.
So we need to choose two more chords from the remaining 19 chords.
C(19, 2)= 19!/{2!(19-2)!
= 19! / 2! 17!
= 19 x 18 /2
= 171
Now, the number of ways to choose four chords that form a bow-tie quadrilateral
= 21x 17
= 3591
Therefore, the probability that the four chosen chords form a bow-tie quadrilateral is:
= [tex]$\frac{\text{Number of ways to choose four chords forming a bow-tie quadrilateral}}{\text{Total number of ways to choose four chords}}[/tex]
= 3591/5985
= 0.600
So, the probability is 0.600, or 60%.
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y = x^2 + 2x - 8 Solve with zeros
Answers
Answer:
x=-4 x=2
Step-by-step explanation:
y = x^2 + 2x - 8
Set equal to zero
0 = x^2 + 2x - 8
Factor
What two numbers multiply to -8 and add to 2
4 * -2 = -8
4+-2 = 2
0=(x+4) ( x-2)
Using the zero product property
x+4 =0 x-2 =0
x=-4 x=2
Express 3*(4*5) as a common fraction given a*b= (ab)/(a+b) .
Answers
Sorry, not sure I understand. (ab)/(a+b) is NOT equal to a*b, as a*b is the same thing as ab.
14. An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, how many dogs are there?
A. 45
B. 90
C. 15
D. 20
Answers
Answer:
your answer would be 45 I hope this was helpful
Step-by-step explanation:
Answer:
The answer is A, 45.
Step-by-step explanation:
The graph below shows the daily high temperature and bottled water sales for a street vendor. Daily High Temperatures and Bottled Water Sales A graph has temperature (degrees Fahrenheit) on the x-axis and number of bottles sold on the y-axis. Points are scattered all over the graph. What relationship exists between the daily high temperature and bottled water sales? no correlation a positive correlation a negative correlation a weak correlation
Answers
Answer:
No correlation
Step-by-step explanation:
You said that Points are scattered all over the graph so The two quantities on x-axis and y-axis have no correlation. No correlation is when the points are scattered all over the graph and have no connection between them. No correlation means they have no relation between them.
Answer:
No correlation
Step-by-step explanation:
The crridnents are placed randomly about so they do not form a trend line therefor making it no correlation.
2 A garden hose supplies 36 gallons of water in 3 minutes. Use a table or eq
ratios to show the garden hose's water flow in gallons per minute and minutes
per gallon.
Answers
Answer ↣ 12 gallons per minute
Step-by-step explanation ↣ Ok I'm gonna use ratios because I can't draw a graph here.
Ok so if the garden hose supplies 36 gallons of water in 3 minutes, then the ratio is 36:3 because every 3 minutes the garden hose "sprays" 36 gallons.
To simplify this ratio, you need find the amount of water the garden hose supplies in 1 minute.
Well to get from 3 to 1, you have to divide by 3.
Do the same thing to 36. 36/3 equals 12.
So the final ratio is 12:1
This is the unit rate. The unit rate is when one variable is 1 unit (most of the time it is speed).
You can multiply 1 by any number and multiply 12 by the same number.
Here are some ratios...
m=minutes
g=gallons
1m:12g
2m:24g
3m:36g
4m:48g
5m:60g
Hope this helped!
BTW why do I sound like this I'm not a aesthetic person-
Let (3, -2) be a point on the terminal side of 0.
Find the exact values of sin , seco, and tan 0.
Answers
Answer:
sinθ = -0.554
tanθ = -0.667
secθ = 1.203
Step-by-step explanation:
Consider the point (3, -2)
The value of x is positive and the value of y is negative.
It means the the terminal sides of angle lies in 4rth quadrant, such that:
Base = 3
Perpendicular = 2
Hypotenuse² = 2² + 3²
Hypotenuse = 3.61
sinθ = Perpendicular /Hypotenuse
sinθ = 2/3.61
As sine is negative in 4rth quadrant
sinθ = - (2/3.61)
sinθ = -0.554
tanθ = Perpendicular/ Base
tanθ = 2/3
tanθ = 0.667
As tan is negative in 4rth quadrant
tanθ = -0.667
secθ = Hypotenuse/Base
secθ = 3.61/3
secθ = 1.203
secant is positive in 4rth quadrant
Please help! Will mark brainliest!
Answers
Sorry, misunderstood question, answer beneath me much better.
Answer:
a = 1/2b
b = 2a
Step-by-step explanation:
-3a + 6b = a + 4b
Add -a and -6b on both sides.
-3a - a = 4b - 6b
-4a = -2b
Divide both sides by -4.
a = -2/-4b
a = 1/2b
To find b, multiply both sides by 2.
2a = b
What is the difference between profit and revenue?
Revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production costs.
Revenue is the total amount producers earn after subtracting the production costs. Profit is the total amount producers receive after selling a good.
Revenue is the total amount producers pay to manufacture a good. Profit is the total amount producers earn after subtracting the production costs.
Revenue is the total amount producers pay to manufacture a good. Profit is the total amount producers receive after selling a good.
Answers
Answer:
Revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production costs.
Step-by-step explanation:
Profit, or net gain, is the amount of money made after subtracting production costs.
Revenue is the total amount of money earned, or gross weight, before anything is subtracted for production costs.
Answer:
The revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production cost.
Step-by-step explanation:
To answer the question, let us picture that you have a business, and you sell bread.
If you sell bread for $5 per loaf, and you sell 2 loaves, your revenue will be 2 * 5 = $10.
Let's say that in order to bake the bread, you have to rent your neighbor's oven for $0.25 per hour, the flour costs $1 per loaf, and the yeast costs $1 (these are all made-up numbers). If each loaf takes one hour to bake, two loaves will cost 0.5 + 2 + 2 = $4.50 to make. Your profit will then be your revenue minus your cost, or 10 - 4.5 = $5.50.
From this scenario, we can see that the revenue is the total amount producers receive after selling a good. Profit is the total amount producers earn after subtracting the production cost.
Hope this helps!
Triangle M' is the image of triangle M under a dilation.
What is the center of the dilation?
A
B
C
D
Answers
Answer:
B
Step-by-step explanation:
trust me
The center of dilation of the figure M' is B thus option (B) is correct.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.
If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).
As per the give M and M'.
If we draw a line of the same corner points of M' and M then it goes from point B.
So it is clear that M is dilated with respect to point B.
Hence "The center of dilation of the figure M' is B".
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IF YOU ANSWER THE QUESTIONS ALL CORRECT I WILL MARK YOU BRAINIEST!
1. What is the interquartile range of the data set shown? {3,4,4,5,7,10,11,12,15}
2. What is the upper quartile of this data set? {66,66,67,69,70,72,72,73,75}
3. What is the lower quartile of the following data set? {23,23,24,27,31,33,34,38,40}
Answers
Answer:
IQR = 7.5
UQ = 72
LQ = 24
Answer:
1. 7.8888888888889
2. 70
3.23,23,24,27,31,33,34,38,40
simplify the following
Answers
Answer:
5
Step-by-step explanation:
Simplify
(5 1/3)^3=?
Solution:
Using Identity
(x^a)^b=x ^(a*b)
So in the given expression
x=5
a=1/3
b=3
Therefore,
(5 1/3)^3= 5 (1/3*3)= 5^1=5
Therefore,
(5 1/3)^3=5
Answer:
5
Step-by-step explanation:
5 to the power of (1/3) = ∛5
(∛5) cubed would be 5 because the cube is essentially undoing the cube root.
The sum of three consecutive integers is greater than 66. What is the smallest possible product of the largest and smallest of these integers?
Please help me on this
Answers
Answer:
528
Step-by-step explanation:
So naturally at first sight for this question we would think -->
Oh 3 consecutive integers = 66 --> 66/3 = 22 (n-1), (n+1) so --> 21, 22, and 23.
But no. At second look it is the sum of 3 consecutive integers is greater than 66. So we find the next possible pair since it says smallest possible product.
We get the set (22, 23, 24). => Multiply the least and greatest integers together respectively 22 and 24 which amounts to => 528
And thus, we have out answer of 528
Hope this helps!
A person can do a job in 6 days. Another can do the same job in 4 days. If they work together, how long do they need to finish the job?
Answers
Answer:
2.4 days
Step-by-step explanation:
Time working together,t ,is
1/t = 1/a+ 1/b where a and b is the times working alone
1/t = 1/4 + 1/6
Multiply each side by 12t to clear the fractions
12t( 1/t )= 12t(1/4 + 1/6)
12 = 3t+2t
12 = 5t
Divide by 5
12/5 = 5t/5
2 2/5 =t
2.4 days
Answer:
2.4 days
Step-by-step explanation:
i just took a test and got a 100%
last one , somebody help me please .
Answers
Answer:
4x -2 = -2x +6
Step-by-step explanation:
The red is negative
4x -2 = -2x +6
Answer:
B
Step-by-step explanation:
A
B
a
If c = 16 and B = 67, find a.
a. 4.5
b. 5.6
C. 6.3
d. 7.4
Please select the best answer from the choices provided
СА
ОВ
Answers
Answer:
a
Step-by-step explanation:
The measure of side a is 6.3 unit.
What is Sine law?The ratios of the length of a side to the sine of the angle opposite the side must all be the same if A, B, and C are the measurements of the angles of an oblique triangle and a, b, and c are the lengths of the corresponding sides.
Given:
c= 16 and B= 67 degree
<C= 90 degree
Using sine law
b / sin B = c / sin C
b / sin 67 = 16 / sin 90
b/ sin 67 = 16 / 1
b = 16 sin 67
b = 16 x 0.9205
b = 14. 728
Using sine law
c / sin C = a / sin A
16 / sin 90 = a / sin 23
16 = a / sin 23
a = 6.25
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250 people went to a "couples only" party at 9pm.70 people left at 11pm, how many couples stayed at the party?
Answers
Answer:
90
Step-by-step explanation:
Total People = 250
Left the party at 11 pm = 70
Stayed = 250-70
=> 180
Couples that stayed = 180/2
=> 90
Answer:
90 Couples
Step-by-step explanation:
There were 250 total people at the beginning at the party. 70 people left at 11pm.
Subtract 70 from 250:
[tex]250-70=180[/tex]
There were 180 people that stayed.
A couple consists of two people. The question asks how many couples stayed at the party, not people.
Divide 180 by 2:
[tex]\frac{180}{2}= 90[/tex]
There would be 90 couples that stayed at the party.
what connection do you notice between the likelihood and the probability of an event? Use numbers in your explanation
Answers
Meaning of probability: the extent to which something is probable; the likelihood of something happening or being the case.
Meaning of likelihood: the state or fact of something's being likely; probability.
These are similar and are literally the same. Probability is the chance of something happening. Likelihood is the change of something happening too.
Probability is a number or ratio and likelihood is a statement.
Probability: the probability of the dice rolling on (one dot) is 1/6.
Likelihood: the likelihood of the dice rolling on (one dot) is equal to the likelihood of the dice rolling on all the different numbers
Answer: The results from this activity indicate that events that are unlikely to occur have a probability close to 0, events that are neither likely nor unlikely to occur have a probability close to 1/2, or 0.5, and events that are likely to occur have a probability close to 1.
Step-by-step explanation: Edmentum answer