Answer:
Many mathematical operations are reversible, meaning you can go not just from A to B, but by the same reason go from B back to A.
Example x + 4 = 7. Subtract 4 from each side to get x = 7 - 4 = 3. But you could, if you wished, go from x = 3 to x + 4 = 7 by simply doing the opposite, adding 4.
Now consider an operation that is NOT reversible.
Example: Given sqrt(x) = x - 2. Square each side to get x = (x - 2)^2 =x^2 - 4x + 4, or
x^2 - 5x + 4 = 0. Factoring gives (x - 1) (x - 4) = 0. So, IF the original equation holds for a real number x, then the only possibilities are x = 1, x = 4.
If you plug x = 4 back into original equation, you get sqrt(4) = 4 - 2, which is true. But, if you plug in x = 1, you get sqrt(1) = 1 - 2, which is NOT true, as sqrt(1) = 1, not -1. The logic of the derivation was that, IF original equation were true, then x could possibly be only 1 and/or 4. In effect, it was really telling you what x is NOT, namely any number besides 1 and 4. Once you test the two “candidates” you see that one works and the other doesn’t.
Why does this happen? It has to do with the fact that square root is only a principal branch. Just as sqrt(16) is only 4 and not -4, so we are dealing with a limited possibility with which to start. Squaring glosses over this, and when you solve a quadratic equation, it generally gives two solutions (not nec. real). Because sqrt(x) started out to be nonnegative, that created the problem at end.
Which steps should be used to find perimeter? Check all that apply
Multiply the perimeter of the original figure by the scale factor
A rectangle has perimeter 88 cm and length 36 cm. What is its width?
Performance task trigonometric identities
x = 0
Simplify — x/ 2
x ((((cs•(c2))•x)-2c3sx2ot)+((co•(t2))•x))-((ta•(n2))•—) = 0 2
xtan2 ((((cs•(c2))•x)-2c3sx2ot)+((co•(t2))•x))
Equivalent Fraction:
Rewrite the whole as a fraction using 2 as the denominator :
-2c3sx2ot + c3sx + cxot2 (-2c3sx2ot + c3sx + cxot2) • 2 -2c3sx2ot + c3sx + cxot2 = 0
The equations are solved below using trigonometric identities.
What are trigonometric identities?Trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
[tex]\frac{sin(x)}{1-cos(x)} -cot(x) = cosec(x) \\\\LHS= \\\\=\frac{sin(x)}{1-cos(x)} -cot(x) \\\\=\frac{sin(x)}{1-cos(x)} -\frac{cos(x)}{sin(x)}\\ \\\frac{sin^{2}(x) - (1-cos(x))cos(x) }{sin(x)(1-cos(x))}\\\\=\frac{sin^{2}(x)-cos(x) +cos^{2}(x) }{sin(x)(1-cos(x))}\\\\=\frac{1-cos(x)}{sin(x)(1-cos(x))}\\ \\=\frac{1}{sin(x)} \\\\=cosec(x)\\\\RHS=\\\\=cosec(x)[/tex]
[tex]cosec(x)^{2} - 2cosec(x)cot(x) + cot(x)^{2} = tan^{2}(\frac{x}{2})\\\\LHS= \\\\= cosec(x)^{2} - 2cosec(x)cot(x) + cot(x)^{2} \\\\=( cosec(x) - cot(x) )^{2} \\\\=(\frac{1-cos(x)}{sin(x)}) ^{2}\\\\=(\frac{(1-cos(x))(1+cos(x))}{sin(x)(1+cos(x))}) ^{2}\\\\=(\frac{sin(x)^{2} }{sin(x)(1+cos(x))}) ^{2}\\\\=(\frac{sin(x) }{1+cos(x)}) ^{2}\\\\=(\frac{2sin(x/2)cos(x/2) }{1+2cos^{2}(x/2)-1}) ^{2}\\\\= (\frac{sin(x/2)cos(x/2) }{cos^{2}(x/2)}) ^{2}\\\\= tan^{2}\frac{x}{2}\\\\RHS = \\\\=tan^{2}\frac{x}{2}[/tex]
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You start at (-2, -1). You move up 6 units. Where do you end?
Answer:
(-2,5)
Step-by-step explanation:
Since you're only moving up on the graph then only the Y axis will change and -1+6 is 5.
Answer:
(-2,4)
Step-by-step explanation:
When you move UP it changes the Y axis so you just add whatever number to there. But when you move down it subtracts the number of units your moving.
The graph of the linear parent function, f(x), is shown. Which function, g(x), would representa vertical stretch of 2 and a shift to the left of 3?
A. g(x) = 2 (2+3)
B. g(2) = 2 (2-3)
C.g(2) = 21 +3
D.g(z) = 21 - 3
P.S. Please do not post answer in a file.
Answer:
C.g(2) = 21+3
Step-by-step explanation:
Explain e everything
Using measures of center and variability to compare data- quiz answers?
herehopes it helps can i pleaseget brainliest
Answer is YES.
Steps for Comparing a Data Set by Measures of Center & Variation:
Measure of center: a value that describes the center of a set of data. Measures of center include the mean, median, and mode.
Measure of variability: a value that describes how spread out numbers in a data set is. Measures of variability include the range and mean absolute deviation.
Step 1: Calculate the measure of center/variation for each set of data.
Step 2: Compare the two measures of center/variation based on the problem.
Here, we can use both to compare data - quiz answers.
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HZC ~ PEF. If CH = 20, find FP
If it can be determined with is FP
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
According to given expression, we can say that the Triangles HZC and PEF are congruent, Therefore their corresponding sides will be equal.
that is :
CH = FPand value of CH = 20 units
So, FP = CH = 20 units
hence, value of FP can be determined .
What is the equation in point-slope form of the line that passes through the points (7, 5) and (-4, -1)
Answer:
y - 5 = (-6/11)(x - 7)
Step-by-step explanation:
Looking at the points (7, 5) and (-4, -1), we see that x decreases by 11 (from 7 to -4) and y decreases by 6 (from 5 to -1). Therefore, the slope of this line is m = rise / run = -6 / 11.
Start with the point-slope form y - k = m(x - h). Substitute the x- and y-coordinates of one of the given points for h and k in the above form:
y - k = (-6/11)(x - h) => y - 5 = (-6/11)(x - 7)
This is the equation of the line in question, in point-slope form.
4) Solve each pair of simultaneous equations.
a. x+y=1 y=2x-8
b. x+y= 19 y=5x+1
c. x+y=-2 y=x-10
5) Solve these simultaneous equations.
3x=y x=y-16
Given are the points A(0,1) and B(4,-7). Find an equation (the point-slope form is perfectly acceptable) of the perpendicular bisector of line segment AB
Answer:
y + 3 = 1/2(x - 2)Step-by-step explanation:
Find the slope of the given line using the coordinates of A and B.
The slope:
m = (-7 - 1)/4 = -2Find the midpoint of segment AB:
x = (0 + 4)/2 = 2y = (1 - 7)/2 = -3The perpendicular line has a slope of 1/2 ( opposite-reciprocal of -2) and passes through the point (2, -3).
The equation of this line is:
y - (-3) - 1/2(x - 2)y + 3 = 1/2(x - 2)Slope-intercept form:
y = 1/2x - 4Abigail's math teacher finds that there's roughly a linear relationship between the
amount of time students spend on their homework and their weekly quiz scores. This
relationship can be represented by the equation y = 6.2 + 69, where y represents
the expected quiz score and I represents hours spent on homework that week. What
is the meaning of the s-value when y = 91?
The time taken by the student to complete the weekly quiz if she had 91 is 3.55 hours
Given the linear relationship between the amount of time students spends on their homework and their weekly quiz scores expressed as:
y = 6.2s + 69
If the value of y is 91, we need to get the value of "s"
Substitute s = 91 into the function to have:
91 = 6.2s + 69
6.2s = 91 - 69
6.2s = 22
s = 22/6.2
s = 3.55
Hence the value of s when y is 91 is 3.55
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A. 0.15
B. an equal sign
C. a multiplication sign
D. a percent sign
Answer:
C.
Step-by-step explanation:
If 4.2 cups equals 1 liter, how many liters equals 21 cups?
Nine times a number more than 8 equals 12.
What is the number?
Pls Help!
Answer:
21
Step-by-step explanation:
Plz helpp it’s due tonight and I don’t hunderstand it!!
Answer:
What is the question? I don't see it... Hmmm
Step-by-step explanation:
Consider the following data set:
0, 10, 12, 3, 13, 7, 2, 5
Find the upper quartile.
Answer:
11
Step-by-step explanation:
The upper quartile Q3 is the median of the upper half of the data.
can someone help me with this I'm stuck
Answer:
you got to subtract 4 from 1
_A triangle has height 15 in. and area 120 in... What is
the length of its base?
3240000 boooooooooooooooom
Answer:
16 inches
Step-by-step explanation:
The function y=5x+10 represents the total cost y of a group of x members to go paintballing.
What do the independent and dependent variables represent?
Answer:
The independent variable (x) represents the members to go paintballing.
The dependent variable (y) represents the total cost.
Step-by-step explanation:
The y is always dependent on the x. The number of people attending affects the total cost of the trip. The more people attend, the more it costs.
PLEASE HELP I WILL GIVE BRAINLIEST
Questions: The temperature at 9am was 46.5 degrees below zero. By 1pm the temperature was 32.5 degrees. What was the change in temperature?
Ms. Price has $ 50.00 deducted from her checking account for her Disney plus subscription every month. How much money will be debited from Ms. Price’s account after five and a half years?
Omar is sitting on a rock 22..2 feet above the surface of a pond.
He drops a stone that falls 778 feet to the bottom of the pond. What is the stone's final position, relative to the surface of the pond?
The temperature at 9am was 32.7 degrees below zero. By 1pm the temperature was 45.6 degrees. What was the change in temperature?
Drake has $ 75.00 deducted from her checking account for his gym membership every month. How much money will be debited from Drake’s account after three and a half years?
Daniella is sitting on a rock 90.3 feet above the surface of a pond.
He drops a stone that falls 556 feet to the bottom of the pond. What is the stone's final position, relative to the surface of the pond?
Ms. Jackson initially has $ - 450 in her checking account. She withdrawals $ 1,250.80. Then, she purchases a pair of vapor max for $ 220.00. Ms. Jackson is unhappy with her purchase and gets a credit for the sneakers. Lastly, she deposits $ 550.00 in her account. How much money does Ms. Jackson after these transactions?
I will give Brainliest For whoever explained !!
Answer:
Question 1)
-14 degrees.
Question 2)
$3,300
Question 3)
755.8 feet
Question 4)
$3150
Question 5)
465.7 feet
Question 6)
-$2250.80 (Are you sure you wrote this out correctly? She has minus 450, then withdraws 1,250.80, then pays 550? So she starts off in debt, and continues to go in debt? They're all subtractions.
Step-by-step explanation:
Q1)
46.5 - 32.5 = 14
Q2)
There are 66 months in 5 and half years. So:
66 * 50 = 3,300.
Q3)
The rock travels 778 feet, from Omar to the bottom. Omar is sitting 22.2 feet from the surface of the pond. So the distance from the surface to the bottom of the pond is:
778 - 22.2 = 755.8 feet
Q4)
There are 42 months in 3 and half years. So
42 * 75 = $3,150
Q5)
The rock travels 556 feet, from Daniella to the bottom. Daniella is sitting 90.3 feet from the surface of the pond. So the distance from the surface to the bottom of the pond is:
465.7 feet
Q6).
She starts out with (-$450). She withdraws (I'm assuming she has a decent overdraft or something) another $1,250.80. Then buys (with money she doesn't have, further going into her overdraft) a pair of vapormax for $550. So you're just start at (-$450) and subtracting the other two values.
(-$450) - $1,250.80 - $550 = -$2250.80
I hope you typed that last question correctly.
what is the y-intercept
Answer: y-intercept=0
Step-by-step explanation: it meets at the origin, so its 0
PLZ HELP!!!!!!!
Identify two angles that are marked congruent to each other on the diagram below. plz answer quickly!!!!!
Lennon has a checking account at Bank of America.
Tuesday he withdrew $130 from an ATM.
Wednesday he deposited $240.
Friday he wrote a check for $56.
more detail pleaseAnswer:
Step-by-step explanation:
henry is 7 years older than his brother,ted.the sum of their ages is 23 years how old is each
Answer:
The answer is Henry is 15 and Ted is 8.
Step-by-step explanation:
Step 1: Take 7 away from 23. You will then get 16.
Step 2: Divide 16 by 2. Your answer will then be 8.
8 will end up being Ted's age.
Step 3: Add 7 to 8. Once you do this, you will get Henry's age.
Jocelyn has 400 pounds of chemical A that she must react with 200 pounds of chemical B to create chemical C for use in an industrial manufacturing process. How many pounds of chemical C will Jocelyn have after the reaction is complete?
Answer This chemical reaction should follow the Law of Conservation of Mass where mass cannot be created nor destroyed. That is, what goes in a system should be equal with what goes out the system. For this problem, the mass of C that is produced assuming there are no by-products should be 600 pounds.
Step-by-step explanation:
Jocelyn will have 600 pounds of the chemical (C) after the reaction is complete
these follows ''law of conservation of mass''
Jocelyn has 400 pounds of the chemical (A) that she must react with the 200 pounds of the chemical (B) to create chemical (C) for use in an industrial manufacturing process. 600 pounds of chemical (C) will Jocelyn have after the reaction are complete.
What is Law of conservation of mass ?By the law of conservation of ''mass states that in the chemical reaction mass is neither created or destroyed.
The chemical reaction in the given case can follow the Law of Conservation of Mass where mass can't be created and destroyed.
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21 p?=u² + 2as
u= 12 a = -3
s= 18
(a) Work out a value of v.
Answer:
6 or -6
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
[tex]v^2 = 12^2 + 2(-3)(18)[/tex] [tex]v^2 = 144 + (-6)(18)[/tex] [tex]v^2 = 144- 108[/tex] [tex]v^2 = 36[/tex]Step 2: Take square root of both sides.
[tex]\sqrt{v^2} =[/tex] ± [tex]\sqrt{36}[/tex] [tex]v =[/tex] ± [tex]\sqrt{36}[/tex] [tex]v = 6[/tex] or [tex]-6[/tex]Therefore, the answer is 6 or -6.
for an infinite queuing situation, if the arrival rate for loading trucks is 5 trucks per hour, what is the mean time between arrivals?
Using proportions, it is found that the mean time between arrivals is of 12 minutes.
This question is solved by proportions, using a rule of three.In one hour(60 minutes), 5 trucks arrive, thus what is the time necessary for 1 truck to arrive?The rule of three is:
5 trucks - 60 minutes
1 truck - x minutes
Applying cross multiplication:
[tex]5x = 60[/tex]
[tex]x = \frac{60}{5}[/tex]
[tex]x = 12[/tex]
The mean time between arrivals is of 12 minutes.
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Simplify the problem plss.
Answer:
it is c
Step-by-step explanation:
what i the answer to
25(15-0.05)
Answer:
[tex]373.75[/tex]
Step-by-step explanation:
[tex]25\left(15-0.05\right)[/tex]
Subtract:- 15- 0.05= 14.95
Multiply:-
[tex]25\times \:14.95[/tex]
[tex]373.75[/tex]
What is the image of the point (0,-2) after a rotation of 90∘
counterclockwise about the origin?
Answer:
-2, 0
Step-by-step explanation:
Answer:
(2,0)
Step-by-step explanation:
yes it is