Answers
Answer:
[tex]d=-18[/tex]
Step-by-step explanation:
The only way we can achieve an extraneous solution is by squaring both sides. Example:
[tex]\sqrt{-1}=x, \\\sqrt{-1}^2=x^2,\\1=x^2,\\x=1\text{ [extraneous]}[/tex]
Square both sides of the equation:
[tex]\sqrt{\frac{1}{2}y-1}^2=(\frac{3}{4}y+d)^2[/tex]
Substitute [tex]y=20[/tex]:
[tex]9=(15+d)^2[/tex]
Expand the right side using [tex](a+b)^2=a^2+2ab+b^2[/tex]:
[tex]9=15^2+2(15)(x)+x^2,\\x^2+30x+225=9[/tex]
Subtract 9 from both sides:
[tex]x^2+30x+216=0[/tex]
Factor:
[tex](x+12)(x+18)=0,\\\begin{cases}x+12=0, x=\boxed{-12},\\x+18=0,x=\boxed{-18}\end{cases}[/tex]
Substitute both solutions to see which work:
[tex]\sqrt{\frac{1}{2}(20)-1}=(\frac{3}{4}(20)+d), \\\\d=-12\checkmark\\d=-18\times[/tex]
The solution [tex]d=-18[/tex] yields [tex]3=-3[/tex] which does not work and therefore is extraneous.
Related Questions
3. A rectangular sheet of paper is 121/2 cm long and 102/3 cm wide. Find its perimeter .
Answers
Answer:189 cm
Step-by-step explanation:
the area of a perimeter is 2L+2w while l is length and w is width
in this case, 121/2 is the length and 102/3 is the width.
using the formula it should be
121/2 x 2 +102/3 x
= 121 + 68
=189 cm
i hope this helps.
An experiment consists of 400 observations and four mutually exclusive groups. If the probability of a randomly selected item being classified into any of the four groups is equal, then the expected number of items that will be classified into group 1 is ________.
Answers
Answer:
The expected number of items that will be classified into group 1 is 100.
Step-by-step explanation:
For each observation, there are only two possible outcomes. Either it will be classified into group 1, or it will not. The probability of an observation being classified into group 1 is independent of any other observation, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
400 observations
This means that [tex]n = 400[/tex]
Four mutually exclusive groups. The probability of a randomly selected item being classified into any of the four groups is equal.
This means that [tex]p = 0.25[/tex]
Then the expected number of items that will be classified into group 1 is
[tex]E(X) = np = 400*0.25 = 100[/tex]
100 is the answer.
Which expression is equivalent to 3√x10
Answers
Explanation
sqrt(x^10) is x^5 since the power of x is 10 and the square root is of degree 2, so 10/2 = 5 and x^5 will be the new power of x after the square root. Hence, 3x^5.
Hope this helps :)
Answer:
Hes correct ^
Step-by-step explanation:
Use Taylor series to evaluate
limx→0(tan x − x)/x^3
Answers
Recall that
tan(x) = sin(x)/cos(x)
and
sin(x) = x - x ³/6 + x ⁵/120 - x ⁷/5040 + …
cos(x) = 1 - x ²/2 + x ⁴/24 - x ⁶/720 + …
Truncate the series to three terms. Then
[tex]\displaystyle \lim_{x\to0}\frac{\tan(x)-x}{x^3} = \lim_{x\to0}\frac{\frac{x-x^3/6+x^5/120}{1-x^2/2+x^4/24}-x}{x^3} \\\\ = \lim_{x\to0}\left(\frac{x-x^3/6+x^5/120}{x^3-x^5/2+x^7/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2-x^4/2+x^6/24}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac1{x^2}\right) \\\\ = \lim_{x\to0}\left(\frac{1-x^2/6+x^4/120}{x^2\left(1-x^2/2+x^4/24\right)}-\frac{1-x^2/2+x^4/24}{x^2\left(1-x^2/2+x^4/24\right)}\right) \\\\ = \lim_{x\to0}\frac{x^2/3-x^4/30}{x^2\left(1-x^2/2+x^4/24\right)} \\\\ = \lim_{x\to0}\frac{1/3-x^2/30}{1-x^2/2+x^4/24} = \boxed{\frac13}[/tex]
find the derivative of y=(x³-5)⁴(x⁴+3)⁵
Answers
Answer:
[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]
Step-by-step explanation:
Help me
Thank you
(Make you the brainliest☺️)
Answers
Answer:
55°
Step-by-step explanation:
sin(x°) = [tex]\frac{opposite}{hypotenuse}[/tex]
x° = [tex]sin^-1(\frac{9}{11} )=54.90319877[/tex]
Rounded to the nearest degree, the answer is 55°
If 6 pounds of fruit is 96 cents how much is one pound
Answers
Answer:
16 cents per pound
Step-by-step explanation:
Take the cost and divide by the number of pounds
96 cents / 6 lbs
16 cents per pound
Which equation represents an exponential function that passes through the point (2, 36)?
O f(x) = 4(3)
O fx) = 4(x)
O f(x) = 6(3)
O f(x) = 6(x)
Answers
Answer: It would be the first equation because:
Step-by-step explanation:
In order to be an exponential function, the X
variable has to be in the exponent, that eliminates
the second and fourth answers
f(X) = 4(3)X
using the point (2,36)
f(2) = 4 (3)2
= 4 (9 )
= 36
The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Let the point on the graph be P ( 2 , 36 )
So , when x = 2 , the value of y = 36
f ( x ) = 4 ( 3 )ˣ be equation (1)
when x = 2
f ( 2 ) = 4 ( 3 )²
f ( 2 ) = 4 x 9
f ( 2 ) = 36
Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ
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the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
Answers
9514 1404 393
Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
urgent !!!!!!!!!!!!!!! 10 points
Answers
Answer:
136 cm²
Step-by-step explanation:
Surface area = 2(lw+wh+hl)
l = 7
w = 2
h = 6
so,
2(7×2+2×6+7×6)
= 136 cm²
Answer:
136 cm^2
Step-by-step explanation:
L 7cm
W 6cm
D 2cm
7 x 6 + 6 x 2 + 2 x 7 (x 2) = 68 x 2 = 136cm^2
Someone help please
Answers
9514 1404 393
Answer:
B.
Step-by-step explanation:
The relation between a function f(x) and its inverse g(x) is ...
f(g(x)) = g(f(x)) = x
On can compute these functions of functions, or take an easier route and do the computation with a couple of numbers. It is often easiest to use x=0 or x=1. If we find g(f(x)) ≠ x, then we know the functions are not inverses. If we find g(f(x)) = x for one particular value of x, then we need to try at least one more to verify the relation.
__
If we call the two given functions f and g, then we have ...
A. f(0) = -2/3, g(-2/3) ≠ 0 . . . . not inverses
__
B. f(0) = -3/2, g(-3/2) = 0 . . . . possible inverses
f(1) = 4/2 = 2, g(2) = 7/7 = 1 . . . . probable inverses
__
C. f(0) = -2, g(-2) = 0 . . . . possible inverses
f(1) = 1/2, g(1/2) = -5/3 . . . . not inverses
__
D. f(0) = 5, g(5) = 27 . . . . not inverses
_____
Additional comment
Our assessment above is sufficiently convincing to let us choose an answer. If we want to verify the functions are inverses, we need to graph them or compute f(g(x)). The graph in the second attachment shows each appears to be the reflection of the other in the line y=x, as required of function inverses.
Find the coordinates of the vertices of the figure after the given transformation: T<0,7>
A. X′(1,−1),L′(0,2),W′(2,1)
B. X′(−4,2),L′(−5,5),W′(−3,4)
C. X′(3,2),L′(2,5),W′(4,4)
D. X′(0,−3),L′(−1,0),W′(1,−1)
Answers
Answer: B
Step-by-step explanation:
Why did historians choose to study this topic?
I need help answering this ASAP
Answers
Answer:
A the input x=3 goes to two different output values
Step-by-step explanation:
This is not a function
x = 3 goes to two different y values
x = 3 goes to t = 10 and y = 5
The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. Point A is on ordered pair negative 4, 5, and the point B is on ordered pair 5, 5.
If the area of the rectangle to be drawn is 90 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?
C(4, −5), D(−3, −5)
C(5, −4), D(−4, −4)
C(5, −5), D(−4, −5)
C(−5, 5), D(−5, −4)
Answers
Answer:
C(5, −5), D(−4, −5)
Step-by-step explanation:
9 across
A(-4, 5) ————————— B(5, 5)
| |
| 90 square units | 10 down
| |
D(-4, -5) ————————— C(5, -5)
please help me solve this question
Answers
someone help me pls i need to pass summer school
Answers
Answer:
A
Step-by-step explanation:
The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain
14 → 4
12 →5
10 →6
8 →7
–20 ÷ 5 =
I need help
Answers
-20 divided by 5 ^
pls help! I need the answer fast!
Answers
Answer:
B is the answer
Step-by-step explanation:
hope it helps
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
Answers
9514 1404 393
Answer:
b. y = f(x -3)
Step-by-step explanation:
The translation right h and up k units is ...
y -k = f(x -h)
Here, the red graph is translated right 3 and up 0, so the translated function is ...
y = f(x -3)
_____
Additional comment
You can check this if you like by listing a couple of corresponding points:
y = f(x)
1 = f(-3) . . . . left-most point on black graph.
The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...
1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)
identify an equation in point slope form for the line perpendicular to the y=-1/2x+11 that passes through (4,-8). a. y+8=1/2(x-4) b. y-4=2(x+8) c. y-8=1/2(x+4) d. y+8=2(x-4)
Answers
Answer:
d. y+8=2(x-4)
Step-by-step explanation:
There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.
Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].
Please see the attached picture
Answers
Answer:
C.I = (0.259,1.175) -> Fail to Reject H0
Step-by-step explanation:
In this problem, assume that the probability that a person is born on a given day is 1/365. (For simplicity, ignore Feb 29.) In a group of 100, what is the expected number of pairs of people who have the same birthday
Answers
Answer:
the expected number of pairs of people who have the same birthday is 14
Step-by-step explanation:
The computation of the expected number of pairs of people who have the same birthday is as follows:
= 100 (100 - 1) ÷ 2 × 365
= 100 × 99 ÷ 730
= 9900 ÷ 730
= 13.5616
= 14
Therefore, the expected number of pairs of people who have the same birthday is 14
Help Please
2(-1+-4)-d^2
Answers
Hope this helps !
Explain why the equation x=x+1 is a contradiction
Answers
Answer:
It results in no solution.
Step-by-step explanation:
If you subtract x on both sides, this will leave you with 0 ≠ 3. The result is no solution. This is why it is contradictory.
Stella and Michael are helping their friend Austin move. Stella can move one box for every four boxes that Michael can move. If Stella moves ten boxes, how many boxes can Michael move?
Answers
Explanation:
Stella can move 1 box for every 4 boxes Michael moves.
She moves 10 boxes, so that must mean Michael moved 40 boxes (since 4*10 = 40).
Put another way, the ratio 1:4 bumps up to the equivalent form 10:40 after multiplying both parts by 10. The first value of each ratio is the amount of boxes Stella moves, and the second part is what Michael moves.
You could also solve it like this
1/4 = 10/x
1*x = 4*10
x = 40
In the second step, I used cross multiplication.
Algebra II Part 1
Choose the expression or equation that correctly represents this information
Rose works eight hours a day for five days a week. How many hours will she work in sa
weeks?
hours = 40 = 6
hours = 40.6
hours = 6 = 40
Answers
Answer:
240 i.e 40*6
Step-by-step explanation:
if rose works 8hrs per day then she works 40 hrs per week (5 days) therefore 40 hrs per 6 weeks =40*6=240
Answer:
40
Step-by-step explanation:
3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}
A.657
B.2433
C. -843
Answers
Answer:
657
Step-by-step explanation:
pemdas
The value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.
Hence option A is correct.
Given is an expression, 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}, we need to simplify it,
Let's break down the expression step by step:
First, let's simplify the expression inside the innermost parentheses:
8 - 2 x 3 = 8 - 6 = 2
Next, let's simplify the expression inside the brackets:
3 x 23 - 2 = 69 - 2 = 67
Now, let's substitute the simplified expression inside the brackets back into the original expression:
(300 - 70 ÷ 5) - 67
Next, let's simplify the expression inside the remaining parentheses:
70 ÷ 5 = 14
Now, let's substitute the simplified expression inside the parentheses back into the expression:
(300 - 14) - 67
Next, let's simplify the expression inside the remaining parentheses:
300 - 14 = 286
Now, let's substitute the simplified expression inside the parentheses back into the expression:
286 - 67
Finally, let's perform the subtraction:
286 - 67 = 219
Now, let's multiply the result by 3:
3 x 219 = 657
Therefore, the value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.
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NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. Find each measurement. Round your answers to the nearest tenth. Part 2dd
Answers
Answer:
see explanation
Step-by-step explanation:
Using the Sine rule in all 3 questions
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]
(2)
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values
[tex]\frac{45}{sin133}[/tex] = [tex]\frac{c}{sin26}[/tex] ( cross- multiply )
c × sin133° = 45 × sin26° ( divide both sides by sin133° )
c = [tex]\frac{45sin26}{sin133}[/tex] ≈ 27.0 ( to the nearest tenth )
(4)
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values
[tex]\frac{19}{sinB}[/tex] = [tex]\frac{30}{sin97}[/tex] ( cross- multiply )
30 sinB = 19 sin97° ( divide both sides by 30 )
sinB = [tex]\frac{19sin97}{30}[/tex] , then
∠ B = [tex]sin^{-1}[/tex] ( [tex]\frac{19sin37}{30}[/tex] ) ≈ 38.9° ( to the nearest tenth )
(6)
[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex], substitute values
[tex]\frac{18}{sin102}[/tex] = [tex]\frac{xAB}{sin45}[/tex] ( cross- multiply )
AB sin102° = 18 sin45° ( divide both sides by sin102° )
AB = [tex]\frac{18sin45}{sin102}[/tex] ≈ 13.0 ( to the nearest tenth )
Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d
Answers
Answer:
10/21 of the distance
Step-by-step explanation:
2/7 distance
------------------
3/8 tank
The rest of the tank is 8/8 - 3/8 = 5/8
2/7 distance x
------------------ = ----------------------
3/8 tank 5/8 tank
Using cross products
2/7 * 5/8 = 3/8x
10/56 = 3/8x
Multiply each side by 8/3
10/56 * 8/3 = 3/8x * 8/3
10/3 * 8/56=x
10/3 * 1/7 =x
10/21 =x
10/21 of the distance
Mutiplying intergers.
Right answer only! Help!! Lots of points and free brainlist! Wrong and scam answers wiLl be reported and dealed with.
(-1) x 1=
Answers
Answer:
Step-by-step explanation:
(-1) × 1 = -1
Answer:
-1
Step-by-step explanation:
anything times 1 =1. except 0.
