Answer:
14+p= sister's current age
Step-by-step explanation:
If you are 14 years younger, then you add 14 to your current age to find her current age.
Suppose the graph of f(x)=x^2 is translated 3 units eight and 1 unit down. If the resulting graph represents g(x), what is the value of g(2.7)?
Answer:
The value of g(2.7) is 31.49.
Step-by-step explanation:
Translations of a function:
Suppose that we have a function f(x).
The translation of f(x) a units to the left is given by g(x) = f(x+a).
The translation of f(x) a units to the right is given by g(x) = f(x-a).
The translation of f(x) a units up is given by g(x) = f(x) + a.
The translation of f(x) a units down is given by g(x) = f(x) - a.
Suppose the graph of f(x)=x^2 is translated 3 units right and 1 unit down.
Three units right:
[tex]g(x) = f(x+3) = (x+3)^2[/tex]
One unit down:
[tex]g(x) = f(x+3) - 1 = (x+3)^2 - 1[/tex]
What is the value of g(2.7)?
This is g when [tex]x = 2.7[/tex]. So
[tex]g(2.7) = (2.7+3)^2 - 1 = (5.7)^2 - 1 = 31.49[/tex]
The value of g(2.7) is 31.49.
Reduce the following differential equation to first-order and solve it.
Given that y₁(x) = x is a solution to the given second-order ODE, assume a second solution of the form
y₂(x) = y₁(x) v(x) = x v(x)
Take the first two derivatives and substitute this solution into the ODE:
y₂ = x v
y₂' = x v' + v
y₂'' = (x v'' + v' ) + v' = x v'' + 2 v'
→ (1 - x ²) y₂'' - 2 x y₂' + 2 y₂ = 0
→ (1 - x ²) (x v'' + 2 v' ) - 2 x (x v' + v) + 2 x v = 0
→ (x - x ³) v'' + (2 - 4 x ²) v' = 0
Next, reduce the order by substituting w(x) = v'(x) and w'(x) = v''(x) :
→ (x - x ³) w' + (2 - 4 x ²) w = 0
and now you have a linear equation in w. Solve for w(x) however you like; I'll just separate variables.
Write w'(x) = dw/dx, then separate variables as
(x - x ³) dw/dx + (2 - 4 x ²) w = 0
(x - x ³) dw/dx = (4x ² - 2) w
dw/w = (4x ² - 2) / (x - x ³) dx
Integrate both sides:
∫ dw/w = (4x ² - 2) / (x - x ³) dx
ln|w| = ∫ (4x ² - 2) / (x - x ³) dx
For the remaining integral, expand the integrand into partial fractions.
x - x ³ = x (1 - x ²) = x (1 - x) (1 + x)
→ (4x ² - 2) / (x - x ³) = a /x + b / (1 - x) + c / (1 + x)
→ 4x ² - 2 = a (1 - x ²) + b x (1 + x) + c x (1 - x)
→ 4x ² - 2 = (-a + b - c) x ² + (b + c) x + a
→ -a + b - c = 4, b + c = 0, a = -2
→ a = -2, b = 1, c = -1
→ (4x ² - 2) / (x - x ³) = -2/x + 1 / (1 - x) - 1 / (1 + x)
Then
ln|w| = ∫ (-2/x + 1 / (1 - x) - 1 / (1 + x)) dx
ln|w| = -2 ln|x| - ln|1 - x| - ln|1 + x| + C
ln|w| = -ln|x ² (1 - x ²)| + C
exp(ln|w|) = exp(-ln|x ² (1 - x ²)| + C )
w = C / (x ² (1 - x ²))
v' = C / (x ² (1 - x ²))
Solve for v(x) by integrating both sides, expanding the right side into partial fractions again:
x ² (1 - x ²) = x ² (1 - x) (1 + x)
→ 1 / (x ² (1 - x ²)) = a / x + b / x ² + c / (1 - x) + d / (1 + x)
→ 1 = a x (1 - x ²) + b (1 - x ²) + c x ² (1 + x) + d x ² (1 - x)
→ 1 = (-a + c - d) x ³ + (-b + c + d) x ² + a x + b
→ -a + c - d = 0, -b + c + d = 0, a = 0, b = 1
→ a = 0, b = 1, c = 1/2, d = 1/2
→ 1 / (x ² (1 - x ²)) = 1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))
dv/dx = C (1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x)))
dv = C (1/x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))) dx
Integrate both sides:
∫ dv = ∫ C (1 / x ² + 1/2 (1 / (1 - x) + 1 / (1 + x))) dx
v = C₁ (-1/x - 1/2 ln|1 - x| + 1/2 ln|1 + x|) + C₂
v = C₁ (1/2 ln|(1 + x) / (1 - x)| - 1/x) + C₂
Solve for y₂(x) by multiplying both sides by x :
y₂ = C₁ (1/2 x ln|(1 + x) / (1 - x)| - 1) + C₂ x
Now, y₁(x) = x, so we can omit the last term from the second solution, giving us
y₂(x) = C (1/2 x ln|(1 + x) / (1 - x)| - 1)
Joaquin gets paid every Friday. His paychecks for the past 8 fridays were $324, $245.25, $245.25, $245.25, $324,$324,$245.25 and $402.75 find the median
Answer:
284.625
Step-by-step explanation:
Arrange the numbers highest to lowest.
Find the middle value in the arrangement.
An auditorium contains 224 occupied seats and was 7/11 filled. How many empty seats were there?
Answer:
128 seats
Step-by-step explanation:
7/11 = 224 seats
11/11 = ?
(11/11 × 224) ÷ 7/11
224 ÷ 7/11 =
224 × 11/7 = 352 seats(total number of seats)
352 - 224 = 128 seats
What is the value of this expression?
5+6×(5−2)+9
77
62
42
32
Answer:
32
Step-by-step explanation:
5 + 6 * (5 - 2) + 9
5 + 6 * 3 + 9
5 + 18 + 9
23 + 9
32
Find the value of "x" in each angle
Answer:
x = 45°
Step-by-step explanation:
x = 90° - 45° = 45°
Writing ratios as a percentage
In the past year Heather watched 16 movies that she thought were very good. She watched 50 movies over the whole year. Of the movies she watched, what percentage did she rate as very good?
She rated 32% percent of the movies very good
Pls help me on this question
Answer:
C
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
If probablikty is 5/12 then, not picking is 7/12
4x + 3 2x+9 solve for x
Answer:
The value of x is 28°
Step-by-step explanation:
Here, In a given figure
4x + 3° ...(1)
2x + 9° ...(2)
Now, we know that the sum of all angle is 180° on a straight line
So,
4x + 3° + 2x + 9° = 180°
6x + 12° = 180°
6x = 180° - 12°
6x = 168°
x = 168° ÷ 6
x = 28°
Thus, The value of x is 28°
FOR VERIFICATION ONLY:-4x + 3° + 2x + 9° = 180°
4(28) + 3° + 2(28) + 9° = 180°
112° + 3° + 56° + 9° = 180°
180° = 180°
Hence, L.H.S = R.H.S
-TheUnknownScientist
Yolanda brought a CD to listen to on the bus the CD is 78 minutes long The bus ride was 2 1/2 hours long How many minutes longer was the bus ride than thr CD?
Answer:
2.5 times 60 equals 150. 150-78 equals 72. So the answer is 72.
Step-by-step explanation:
Hope this helps.
Harvey is placing a microwave oven on his kitchen counter. What information does Harvey need?
A. the volume of the microwave oven and the volume of the kitchen counter
B. the area required for the microwave oven and the area of the kitchen counter
C. the perimeter of the microwave oven and the perimeter of the kitchen counter
Answer:
b the area
Step-by-step explanation:
you will need to see if you have enough area for the microwave to fit
What are the slope and y-intercept of the graph of the equation?
Answer:
Slope= -1/2
y-intercept= 2/3
Use the distance that these 9 students skimmer cars traveled in inches to calculate the MIDDLE 50%
468, 376, 540, 198, 230, 531, 281, 426, 346
a. 458 - 353.3
b. 255.5 - 499.5
c. 281 - 468
d. 230 - 531
9514 1404 393
Answer:
b. 255.5 to 499.5
Step-by-step explanation:
The middle 50% is the range between the first and third quartiles. In this group of 9 numbers, the first quartile is the average of numbers 2 and 3 when the numbers are listed from smallest to largest.
first quartile = (230 +281)/2 = 255.5 . . . . . . matches answer choice B
The third quartile is the average of numbers 7 and 8:
third quartile = (468 +531)/2 = 499.5 . . . . . also matches answer choice B
The middle 50% is 255.5 to 499.5.
_____
When I put the numbers in order, I get ...
198 230 ^ 281 246 376 426 468 ^ 531 540
^ indicates that the quartile here is the average of the adjacent numbers
bold indicates the median (2nd quartile)
If y = 8(2. 4)* represents the number of bacteria in a culture at time t, how
many will there be at time t =9 ?
Answer:
21134 bacteria
Step-by-step explanation:
The given parametrs can be interpreted as:
[tex]y = 8(2.4)^t[/tex]
Required
Find y when t = 9
Substitute [tex]t = 9[/tex]
So:
[tex]y = 8(2.4)^9[/tex]
[tex]y = 8 * 2.4^9[/tex]
[tex]y = 8 * 2641.81[/tex]
[tex]y = 21134.48[/tex]
[tex]y = 21134[/tex] --- approximated
Hence, there are 21134 bacteria
How many eggs does a rooster lay a day???
Answer:
a rooster can't lay eggs
Step-by-step explanation:
a rooster is a male-
Answer:
0, A rooster is a male, it does not lay eggs. Hens lay eggs
Step-by-step explanation:
Solve the following polynomial function. y=x^4−21x^2−100
Answer:
y= x⁴ -21x²-100
combine x's I think
x⁴= 1x? cuz if it's 1x⁴ that's 1x*1x*1x*1x = 1x
1x * -21x²
-21x * -21x = 441x
+1x = 442x
y= 442x -100
I'm not sure if I did that right
Solve this for me (geometry)
Given:
A figure of a circle. [tex]KJ=6,KL=x-2,ML=4[/tex].
To find:
The length of KJ.
Solution:
From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.
Therefore, the length of KJ is 6 units.
Note: In the given question we need to find KL instead of KJ because KJ is already given.
According to the tangent secant theorem:
[tex]a^2=bc[/tex]
Where,
a is the length of the tangent.b is the length of the external segment of the secant.c is the measure of the secant.Using the tangent secant theorem, we get
[tex]ML^2=KL\times JL[/tex]
[tex](4)^2=(x-2)\times (6+x-2)[/tex]
[tex]16=(x-2)\times (4+x)[/tex]
[tex]16=4x+x^2-8-2x[/tex]
On further simplification, we get
[tex]16=x^2+2x-8[/tex]
[tex]0=x^2+2x-8-16[/tex]
[tex]0=x^2+2x-24[/tex]
Splitting the middle term, we get
[tex]x^2+6x-4x-24=0[/tex]
[tex]x(x+6)-4(x+6)=0[/tex]
[tex](x+6)(x-4)=0[/tex]
[tex]x=-6,4[/tex]
For [tex]x=-6[/tex],
[tex]KJ=-6-2[/tex]
[tex]KJ=-8[/tex], which is not possible because side cannot be negative.
For [tex]x=4[/tex],
[tex]KJ=4-2[/tex]
[tex]KJ=2[/tex]
Therefore, the measure of KL is 2 units.
Can you solve for x and type the correct code? Please remember to type in ALL CAPS with no spaces.
Answer:
Hypotenuse = 85 cm
Hypotenuse = 89 cm
Hypotenuse = 103.08 cm (Approx.)
Hypotenuse = 54.71 cm (Approx.)
Step-by-step explanation:
Shape 1
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √36² + 77²
Hypotenuse = √1,296 + 5,929
Hypotenuse = √7,225
Hypotenuse = 85 cm
Shape 2
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √39² + 80²
Hypotenuse = √1,521 + 6,400
Hypotenuse = √7,921
Hypotenuse = 89 cm
Shape 3
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √25² + 100²
Hypotenuse = √625 + 10,000
Hypotenuse = √10,625
Hypotenuse = 103.08 cm (Approx.)
Shape 4
Hypotenuse = √Perpendicular² + Base²
Hypotenuse = √17² + 52²
Hypotenuse = √289 + 2,704
Hypotenuse = √2,993
Hypotenuse = 54.71 cm (Approx.)
Help please I need to complete this before 12
Answer:
Look at the answers bolded below
Step-by-step explanation:
To get the reference angle, just subtract 115° from 180°
180 - 115 = 65
So the reference angle is 65°
I'm not sure how many coterminal angles you need, but to get them you could just add or subtract 360°.
For example, a positive coterminal angle could be:
115 + 360 = 475°
a negative coterminal angle could be:
115 - 360 = -245°
Hope this helped :)
Draw the image of the rotation of quadrilateral SORT by 270° about the origin
Answer:
70
Step-by-step explanation:
Find x to the nearest tenth. Click on the pic i really need help
Answer:
140 degrees i think
Step-by-step explanation:
I need help with this question can someone help plz
Answer:
The height is 13.3 in
Step-by-step explanation:
Pythagorean Theorem
23.5²+b²=27²
552.25+b²=729
b²=729-552.25
b²=176.75
b=√176.75
13.2947
Snow fell at a rate of
of an inch/hour. How much
snow fell in a period of 6
hours?
Answer:
Step-by-step explanation:
that implies a simple multiplication:
snow = (3/4)(6) = 4.5 inch
and note the units elimination in the operation as well:
= [inch/hour][hour] = inch
My fault if im wrong :(
If you work 7 miles from your home and work 5 days a week, how many miles do you travel for work each week?
Select all equations that have at least one integer solution.
Answer:
b and d
Step-by-step explanation:
The equations have at least one integer solution are equation B: √(3x) = 75 and equation D:√x = x - 12.
What is the solution to the given equations?The value of x is known as the solution.
A. √(4x) = 5
On squaring, we have
4x = 25
x = 6.25
The value is not an integer.
B. √(3x) = 75
On squaring, we have
3x = 5625
x = 1875
The value is an integer.
C. 8√x = √16
On squaring, we have
64x = 16
x = 0.25
The value is not an integer.
D. √x = x - 12
On squaring, we have
(x - 12)² = x
x² - 24x + 144 = x
x² - 25x + 144 = 0
(x - 16)(x - 9) = 0
x = 9, 16
The value is an integer.
E. √(10 - x) = x - 2
On squaring, we have
(x - 2)² = 10 - x
x² - 4x + 4 = 10 - x
x² - 3x - 6 = 0
(x - 4.37)(x + 1.37) = 0
x = -1.37, 4.37
The value is not an integer.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
Solve for x. round to the nearest tenth
Answer:
41.81
Step-by-step explanation:
∠B = arcsin(b·sin(A)a)
= 0.72973 rad = 41.81° = 41°48'37"
∠C = 180° - A - B = 0.84107 rad = 48.19° = 48°11'23"
c = a·sin(C)sin(A)=4.47214 = 2√5
Solve for angle X in the diagram
NO LINKS PLEASE
Answer:
it would be 145
Step-by-step explanation:
the two angles make a straight line, 180-35 is 145
Answer: 145
Step-by-step explanation:
supplementary angle rule: on a straight line, all angles add up to 180
180 = 35 + x
180 - 35 = x
145 = x
Melissa, Dan, and Henry have $87 in their wallets. Dan has 3 times what Henry has. Melissa has $8 less than Henry. How much does each have?
Answer:
Henry has $19, Dan has $57, and Melissa has $11
Step-by-step explanation:
Let x represent how much money Henry has
Since Dan has 3 times what Henry has, his amount is 3x
Since Melissa has $8 less than Henry, her amount is x - 8
Create an equation that sets these 3 values equal to 87, then solve for x
(x) + (3x) + (x - 8) = 87
5x - 8 = 87
5x = 95
x = 19
So, Henry has $19
Find how much Dan has by multiplying 19 by 3
19(3)
= 57
Find how much Melissa has by subtracting 8 from 19
19 - 8
= 11
So, Henry has $19, Dan has $57, and Melissa has $11
Answer:
Dan has $261 and Melissa has $79
find the missing length
Answer: 14
Step-by-step explanation:
VW corresponds to BA. VW is twice the length of BA, so VU must be twice the length of BC
30 is to 150, like ___ is to 45 A)9 B)400 C)5 D)15
Answer:
D.
Step-by-step explanation:
divide 45 by 3
