The inverse of the given matrix, if it exists, is (1/(a^2 + b^2)) times the matrix [a b; -b a].
To find the inverse of a 2x2 matrix [a -b; b a], we can use the formula for the inverse of a 2x2 matrix. The formula states that if the determinant of the matrix is non-zero, then the inverse exists, and it can be obtained by taking the reciprocal of the determinant and multiplying it by the adjugate of the matrix.
In this case, the determinant of the given matrix is a^2 + b^2. Since the determinant is non-zero for any non-zero values of a and b, the inverse exists.
The adjugate of the matrix [a -b; b a] is [a b; -b a].
Therefore, the inverse of the given matrix is (1/(a^2 + b^2)) times the matrix [a b; -b a].
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16. If x= y² + 12, what is the value of y in terms of (A)x+12 (B) x-12 (C) √√x+12 (D) √√x-12
Answer:
D. y = √(x - 12)
Step-by-step explanation:
x = y² + 12
y² = x - 12
y = √(x - 12)
Q.2. If the line y=x is reflected over the x - axis and made flatter(less steep) by a factor of ½ then write the equation of the new line
Using translation concepts, the equation of the new line is:
[tex]y = -\frac{1}{2}x[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem:
The function is reflected over the x-axis, hence it is multiplied by -1.It is made flatter by a factor of 0.5, that is, it is multiplied by 1/2.Hence the equation of the new line is:
[tex]y = -1 \times \frac{1}{2} \times x = -\frac{1}{2}x[/tex]
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solve for the balloon volume using the equation below
The volume of the balloon is 1441.64cm³.
How to calculate the volume?The radius of the balloon is given as 7cm. Also, the equation to calculate the volume is given as c³/6π²
The circumference c will be:
= 2πr = 2 × 22/7 × 7
= 44
The volume will be:
= c³/6π²
= 44³/(6 × 3.14²)
= 85284/(59.1576)
= 1441.64
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Draw a graph of Lin’s distance as a function of time for this situation:
Lin walked a half-mile to school at a constant rate. Five minutes after arriving at school, Lin realized that she had left her permission slip at home. Lin began sprinting home, but when she was halfway there she got tired and walked the rest of the way.
The graph of Lin's distance as a function of time cannot be a straight line graph because of decrease in speed.
Given that Lin walks half a mile at a constant rate i.e. Lin velocity is constant.
If the speed is low then the time will be high. If speed is high then the time will be low because of the following rule:
Speed=Distance/ time.
For the first five minutes the graph will be upward sloping because he was sprinting and his speed was high so he will cover much more distance.
But after five minutes the graph will be downward sloping as the speed becomes low and he willcover less distance.
Hence the graph of Line's distance will not look like linear curve.
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Read each question carefully and show work. Put your answer in the provided space.
what is the range of the function of graph?
a.) all real numbers
b.) all real numbers greater than or equal to 0
c.) all real numbers greater than or equal to 1
d.) all real numbers greater than or equal to 2
The correct answer is "all real numbers greater than or equal to 2".
i’ll give brainliest
Answer:
5
Step-by-step explanation:
-2x - y = -3
y = -3x + 2
-2x - (-3x + 2) = -3
-2x + 3x - 2 = -3
x = -1
y = -3*-1 + 2 = 5
After a robbery, a thief jumps into a taxi and disappears. An eyewitness on the crime scene is telling the police that the cab is yellow. In order to make sure that this testimony is worth something, the assistant district attorney makes a Bayesian analysis of the situation. After some research, he comes up with the following information: (1) In that particular city, 80% of taxis are black and 20% of taxis are yellow; and (2) Eyewitnesses are not always reliable and from past experience, it is expected that an eyewitness is 80% accurate. In other words, he will identify the color of a taxi accurately (yellow or black) eight out of ten times. What is the probability that the cab was really yellow, given that it was reported as being yellow
The probability that the cab was really yellow given that it was reported as being yellow is 0.32.
Given that there are 80% black taxis and 20% yellow taxis, witness is 80% accurate.
Probability is the chance of happening an event among all the events possible. It lies between 0 and 1. The value of probability can be calculated through the following formula:
Probability=Number of items/ total items.
Black taxis=80%
Yellow taxs=20%
Eyewitness is accurate=80%
Probability that the cab was really yellow=
P(X=Yellow)P(Witness is correct)+P(X=Black)P(Witness is incorrect)
Probability that car is black=0.8
Probability that car is yellow=0.2
Probability that witness is correct=0.8
Probability that witness is incorrect=1-0.8
=0.2
We have to just put the values in the formula given above.
Required probability=0.2*0.8+0.8*0.2
=0.16+0.16
=0.32
Hence the probability that the cab is really yellow is 0.32.
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Find the mixed number halfway between 6.4 and 6½. Give
your answer in its simplest form.
Answer:
6.45
Step-by-step explanation:
I am not staring at zero. I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.
6.4 + 1/2(6.5-6.4) Combine in the parentheses
6.4 + 1/2(.5) Take half of .5
6.4 + .05 add
6.45
Which represents the inverse of the function f(x) = 4x?
O h(x) = x + 4
• h(x) = x-4
O h(x) = =x
• h(x) = =x
Answer: [tex]f^{-1}(x)=\frac{x}{4}[/tex]
Step-by-step explanation:
Let [tex]f(y)=x[/tex].
[tex]x=4y\\\\y=\frac{x}{4}\\\\\therefore f^{-1}(x)=\frac{x}{4}[/tex]
[please answer quickly] it takes 8 hours to paint a room. how long will it take to paint 2/3 of the room?
Answer:
5 hours 20 minutes.
Step-by-step explanation:
8 * 2/3
= 16/3
= 5 1/3
= 5 hours 20 minutes.
HALP PLS
what is x?
x =x=x, equals
^\circ
∘
degrees
Answer:
x = 90°
Step-by-step explanation:
The line that contains angle x and the 90° angle is a straight line.
A straight line measures as 180°.
So, subtracting the given 90° from the 180° line that the two angles share, we would get the measure of x.
[tex]180-90 =x[/tex]
Which means, [tex]x=90[/tex].
So the value of x is 90°.
Rule 1: Multiply by 2 then add 1 starting from 1.
Rule 2: Divide by 2 then add 4 starting from 40.
please help me make a sequence :)
PLEASE DONT DELETE MY QUESTION :(
Rule 1: Multiply by 2 then add 1 starting
( n x 2 +1) => 2n + 1
n is the position of our terms, so I substitute 1 because you're told to start from 1 which becomes our first term
2n + 1
2 x 1 + 1 =3
2 x 2 + 1 = 5
2 x 3 + 1 = 7
2 x 4 + 1 = 9
3,5,7,9....
(you can clearly see the sequence increasing by 2 each time, not following Multiply by 2 then add 1)
However, if we were to do add one each time, you'll add one to your pervious answer. So, this time I'll substitute the pervious answer
2 x 1 + 1 =3
2 x 3 + 1 = 7
2 x 7 + 1 = 15
2 x 15 + 1 = 31
3,7,15,31....
(from 3 to 7, you clearly see its multiplied by 2, then +1 & that's our sequence, this method apply to the second rule too of using previous)
Rule 2: Divide by 2 then add 4
(n ÷ 2 + 4) => n/2 + 4
n/2 + 4
(starting from 40.)
40/2 + 4 = 24
24/2 + 4 = 16
16/2 + 4 = 12
12/2 + 4 = 10
24,16,12,10.....
Answer: (started off with the number it asked of)
R 1 -
1,3,7,15,31....
(1 x 2 +1 does give 3)
R 2 -
40, 24,16,12,10.....
(40÷2 = 20, then + 4, gives 24)
Hope this helps!
Find the sum of the arithmetic series 19 + 25 +31 +37 +… where n=9
The sum of the arithmetic series 19 + 25 + 31 + 37 + … at n = 9 exists 387.
An arithmetic series exists given, 19 + 25 + 31 + 37 + … sum of this series exists to be defined at n = 9.
What is arithmetic progression?Arithmetic progression exists the series of numbers that contain a common difference between adjacent values.
The sum of an arithmetic series exists given as
[tex]$S_n = \frac{n}{2}[2a+(n - 1)d][/tex]
Where n be the total terms =9
a be the first term = 19
d be the common difference = 6
Substitute the values in the above equation, we get
[tex]$S_9 = \frac{9}{2}\left[2\cdot 19+\left(9\:-\:1\right)6\right][/tex]
[tex]$ = \frac{9}{2}\left[86\right][/tex]
= 387
Therefore, the sum of the arithmetic series 19 + 25 + 31 + 37 + … at
n = 9 exists 387.
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Solve the following for x, x∈W
a) 76 x 75 x 74 x ... x 6 = P(76, x)
The required value is 70. Using the permutations formula the required value is calculated. I.e., P(76, x) = P(76, 70).
How to calculate permutations?The formula for permutations is
nPr = P(n, r) = n!/(n - r)!
Where P -number of permutations,
n - number of objects in the given set
r - number of choosing objects
Calculation:The given series is
76 × 75 × 74 × ... × 6 = P(76, x)
We know that,
76! = 76 × 75 × 74 × ... × 1 ...(i)
But to get the required series,
Divide the equation (i) by 6! = (76 - 70)!
Then,
76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6
So, x = 70.
That is,
n!/(n - r)! = P(n, r)
⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108
Hence the required x value is 70.
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Select the correct answer.
If vector u = <-3.5, -1.5> and vector v = <-1.25, 2.25>, which graph shows the resulting vector for 2v - u?
The graph that aligns with the information is graph D.
How to illustrate the graph?We know that vector addition is scalar addition.
Given vectors are u = <-3.5, -1.5> and v = <-1.25, 2.25>
2v = < -2.5, 4.5>
2v - u = < -2.5, 4.5> - <-3.5, -1.5> = < -2.5 - (-3.5) , 4.5 -(-1.5) >
2v-u = < 1 , 6 >
This vector is basically i + 6j which is drawn in option D
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Examine the inequality and its graph. Which values are part of the solution set? Check all that apply. x = 3 x = –5 x = negative one-half x = –4.5 x = –4
The value "x = 3" and "x = -1/2" are part of the solution set.
What can be represented on linear inequality?We can represent any linear inequality using any of the following forms:
x > bx < bx ≥ bx ≤ bNow, if the sign is pointing towards x, it means that x is greater than b., so, the line under the greater sign means that x can also equal b.
The options given are:
3: is greater than -4-5: is not greater than -4-1/2: is greater than -4-4.5: is not greater than -4-4: is not greater than -4.Hence, the value "x = 3" and "x = -1/2" are part of the solution set.
Therefore, the Option A and C is correct.
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PlllZZZZZZZZ HELPPPPP
Answer:
x = 1.4
Step-by-step explanation:
Visualize the figure as a rectangle with width 4 and height 1 combined with a triangle with base 1 and height 1.
Next, use the Pythagorean Theorem, a^2 + b^2 = c^2. Variables a and b represent the lengths of the legs, in this case 1 and 1, and variable c represents the length of the hypotenuse, in this case x.
1^2 + 1^2 = x^2
2 = x^2
x = 1.41421356237
Step-by-step explanation:
imagine that this shape is the combination of 2 shapes :
1. a rectangle 4×1
it goes from the top down the side of 4 until the tilted line x begins.
2. a right-angled triangle
x being the Hypotenuse (the baseline opposite of the 90° angle). and the legs are the invisible line of 1 (going from the top right of x in parallel to the 1 line all the way to the 5 line) and the part of the 5 line below the 4 line : 5-4 = 1.
so, x can be solved by using Pythagoras
c² = a² + b²
c being the Hypotenuse, a and b are the legs.
x² = 1² + 1² = 2
x = sqrt(2) = 1.414213562... ≈ 1.4
There are 52 people in a room. What is the largest value of n such that the statement ""at least n people in this room have birthdays falling in the same month"" is always true?
The largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5
How to determine the value
From the given information, we have 52 people in the room
Note that there are 12 months in a year
Let's divide the number by people by the months of the year
⇒ [tex]\frac{52}{12}[/tex]
⇒ 4 remaining 4
If 48 people are evenly distributed over twelve months, then there will be four people born in each month.
The remaining four people can be placed each in any of the twelve different months.
Hence, if 52 people are evenly distributed as possible, there will be eight months with four people and four months with five people.
Thus, the largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5
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To get 14 liters of antifreeze solution, how much do i need to add to x liters of the solution?
To get 14 liters of antifreeze solution, add 14 - x liters of the solution
Calculating volumeFrom the question, we are to determine how many liters should be added to the solution
From the given information,
We are to get 14 liters of antifreeze solution,
and
we already have x liters of the solution
To get 14 liters of antifreeze solution, we will add 14 - x liters of the solution
Hence, to get 14 liters of antifreeze solution, add 14 - x liters of the solution
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Look at sample problem 23.2. How many unpaired electrons are in (enter a number such as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) 1. Ag 2. Mn3 3. Cr3
To find the unpaired electrons:
Ag+ represents the d10 system. Because there are no unpaired electrons, the system is diamagnetic.Mn3+ has the electronic structure [Ar]3d44s0. In 3d, there are four unpaired electrons.Because of the loss of three electrons, the chromium ion Cr3+ has 24e3e=21e.Therefore, unpaired electrons are:
Ag+ = No unpaired electronMn3+ = 4 unpaired electronCr3+ = 3 unpaired electronKnow more about unpaired electrons here:
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A paper bag contains a mixture of 3 types of candy. there are 10 packs of fuzzy peaches, 7 packs of sour keys, and 3 packs of nerds. suppose a game is played in which a candy is randomly taken from the bag, replaced, and then a second candy is drawn from the bag. if you are allowed to keep the second candy only if it was the same type a the one that was drawn the first time, calculate the probability of each of the following: a) you will keep a pack of fuzzy peaches b) you will be able to keep any of the candy c) you will not be able to keep any of the candy
The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.
How to calculate the probability?a. Based on the information given, the probability that the person will be able to keep a pack of fuzzy peaches will be:
= 10/(10 + 7 + 3) × 10/(10 + 7 + 3)
= 10/20 × 10/20
= 1/4
= 0.25
The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.
b. The probability to be able to keep any of the candy will be:
= (10/20 × 10/20) + (7/20 × 7/20) + (3/20 × 3/20)
= 100/400 + 49/400 + 9/400
= 158/400
= 0.395
The probability to be able to keep any of the candy will be 0.395.
c. The probability that you will not be able to keep any of the candy will be:
= (10/20 × 10/20) + (7/20 × 13/20) + (3/20 × 17/20)
= 100/400 + 91/400 + 51/400
= 242/400
= 0.605
The probability that you will not be able to keep any of the candy will be 0.605.
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Determine the unknown value in the table using the constant of proportionality.
Time (seconds) 12 18 40
Number of Pencils Produced 42 63
The unknown value in the table using the constant of proportionality is; 96
How to find the constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
We are given the coordinates;
(12, 42), (18, 63), (40, y)
where x-values represents time in seconds and y-values represents number of pencils that were produced.
To find the constant of proportionality is as good as finding the slope between two consecutive points as;
m = (63 - 18)/(42 - 12)
m = (45/30)
m = 1.5
Thus to find the unknown value y, we will use the formula;
(y - y1)/x - x1) = m
So we will use the coordinates; (18, 63), (40, y)
Plugging them into the formula above will result in;
(y - 63)/(40 - 18) = 1.5
y - 63 = 1.5 * 22
y - 63 = 33
y = 33 + 63
y = 96
Thus, we can conclude that using the constant of proportionality, the number of pencils that were produced after a time of 40 seconds is 96 pencils.
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Jonh is paid $26 for 8 hours work how much should he be paid for working 37 hours at the same wage
Answer:
$120.25
Step-by-step explanation:
Divide 37 by 8. You get 4.625. Multiply 4.625 by 26. You get 120.25.
I hope this helps!
Gavin collects a certain type of seashell. He has 160 seashells. The seashells' weights are distributed normally with a mean of 120 grams and a
standard deviation of 26 grams.
How many of the seashells weigh at least 68 grams?
A 109
B. 156
C. 134
D. 152
Answer:
Answer: B.156
Step-by-step explanation:
Given: Total seashells = 160
mean = 120
population standard deviation = 26 grams
The probability that the seashells weigh at least 68 grams :-'
Total seashells weigh at least 68 grams = 0.9772 x 160 = 156.352≈ 156
Hence, the correct option is B.156
please mark brainiestWhich of the following is a proper way to enter an answer of 1.666 on the SAT SPR answer grid?
A
1/66
B
1.67
C
1.66
D
1.666
The correct answer is Option B) 1.67 after rounding off.
What is rounding off a decimal number?Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. Rounding decimals refer to the rounding of decimal numbers to a certain degree of accuracy.
Given here, the number with decimal 1.666 , thus rounding off we get the answer a 1.67
Hence, the correct answer is Option B)
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if 4200 men have sufficient food for 32 days at the rate of 12 hectogram per person , how many men may leave so that the same food is sufficient for 42 days at the rate of 16 hectogram per person
Using proportions, it is found that 66 men can leave so there will still be enough food.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the situation described, the rule of three is given as follows:
4200 men - 32 days - 12 hectogram per person.
x men - 42 days - 16 hectogram per person.
Considering that the amount per person and the number of people is inverse proportional, we have that:
[tex]\frac{4200}{x} = \frac{32}{42} \times \frac{16}{12}[/tex]
[tex]\frac{4200}{x} = \frac{512}{504}[/tex]
Applying cross multiplication:
512x = 504 x 4200
x = 504 x 4200/512
x = 4134.
The amount of men that can leave is:
4200 - 4134 = 66.
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make x the subject! urgent help
Answer:
[tex]x = \frac{n}{b - {t}^{2} } [/tex]
Step-by-step explanation:
I supposed that is a "n".
Steps as below:
[tex] {t}^{2} = b - \frac{n}{x} \\ b - \frac{n}{x} = {t}^{2} \\ - \frac{n}{x} = {t}^{2} - b \\ \frac{n}{x} = - ( {t}^{2} - b) \\ \frac{n}{x} = b - {t}^{2} \\ n = x(b - {t}^{2} ) \\ x(b - {t}^{2} ) = n \\ x = \frac{n}{b - {t}^{2} } [/tex]
Answer:
[tex]x = \frac{h}{b-t^2}[/tex]
Step-by-step explanation:
[tex]t^2 = b - \frac{h}{x}[/tex]
• First add [tex]\frac{h}{x}[/tex] to both sides:
⇒ [tex]\frac{h}{x} + t^2 = b[/tex]
• Now subtract [tex]t^2[/tex] from both sides:
⇒ [tex]\frac{h}{x} = b - t^2[/tex]
• Now multiply both sides by [tex]x[/tex] :
⇒ [tex]h = x(b - t^2)[/tex]
• Next divide both sides by [tex](b - t^2)[/tex] :
⇒ [tex]\frac{h}{b-t^2} = x[/tex]
∴ [tex]\boxed{x = \frac{h}{b-t^2}}[/tex]
Which of the following is 25 9/16 equal to?
Answer:
Step-by-step explanation:
25.5625
Answer:
25.5625
Step-by-step explanation:
The solution is in the image
If there are 24 blue blocks and six of them are red what percentage of the blocks are red
Answer:
20 % are red
Step-by-step explanation:
I THINK this is what you mean:
24 blue + 6 red = 30 blocks total
6 red / 30 total = 6/30 = .2 = 20 %