Answer:
The answer is 1/42 as you take reciprocal of 6=(1/6) and reciprocal of 7=(1/7) and multiply.
Answer:
[tex]\boxed {\frac{1}{42}}[/tex]
Step-by-step explanation:
Reciprocal of 6 : 1/6
Reciprocal of 7 : 1/7
Their product :
1/6 × 1/71/42Find the inverse of the function.
y=x+9
Answer: [tex]y=x-9[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=y+9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]y+9=x[/tex]
Step 2: Subtract 9 from both sides.
[tex]y+9-9=x-9\\y=x-9[/tex]
if A={4,7,10,13,17} and B={3,5,7,9}, then which of the following statements is true
A U B= {7}
B c A
B c B
Answer:
good questing it is something
Step-by-step explanation:
1-1-2- --3--1234-3
3-4
Q-
-4
-24
-4
-
q 43-
43-
3 4-3
4-
4-4
- answer is 2def not cap i need 5 poinnts i gues
Patrisse and Makayla began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Patrisse took a test in English and earned a 81.4, and Makayla took a test in Art History and earned a 60.6. Use the fact that all the students' test grades in the English class had a mean of 72.8 and a standard deviation of 11.8, and all the students' test grades in Art History had a mean of 67 and a standard deviation of 8.6 to answer the following questions. a) Calculate the z-score for Patrisse's test grade. z = [Round your answer to two decimal places.] b) Calculate the z-score for Makayla's test grade. z = [Round your answer to two decimal places.] c) Which person did relatively better? Patrisse Makayla They did equally well.
a) Z-score for Patrisse test grade is 0.7288
b) z-score for Makayla test grade is -0.7441
c) Patrisse did better.
What is z- score?
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
Z-score for Patrisse test grade.
X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 81.4 - 72.8/ 11.8
Z= 0.7288
Now, z-score for Makayla test grade.
X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 60.6 - 67/ 8.6
Z= -0.7441
Hence, Patrisse did better as she had better z- score.
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I walked 280m of the road from the park to the station. This is equivalent to 9/10 of the total distance. How many meters is the total distance from the park to the station?
Answer:
311 1/9 or 311.11 mStep-by-step explanation:
Let the total distance be x.
We have:
9/10 of x is 280 m.Set this as equation and solve for x:
(9/10)x = 280x = 280 ÷ 9/10x = 280 × 10/9x = 2800/9 = 311 1/9 or 311.11 mTotal distance from the park to the station is approximately 311 m.
Let that be d
9/10 of d=2809/10d=280d=280(10/9)d=311.1mMaximiza a: z=5x+2y
Sujeta a: x+2y≤12
x+y≥4
x,y ≥0
Answer:
hi
Step-by-step explanation:
no
ON ECRIT SUR LES DUN DE EQUILIBRE CHACUNE DES LETTRES AMURES
Answer:
oh.
Step-by-step explanation:
Camp pine cone has 20 campers for every 6 counselors if there are 60 campers how many counselors are needed
Answer:
18
Step-by-step explanation:
20*3=60 so do 6*3 to get your answer
Factor the following expression. x² - 10x +9 2 Factor the following expression . x² - 10x +9 2
Answer:
x² - 10x + 9 = (x-9)(x-1)
the factored expression would be (x-9)(x-1)
Find the equation of the line parallel to y = 2x - 4 that runs through the point (-2, 4).
y = 1/2x + 4
y = 2x + 8
y = 2x + 4
y = -1/2x + 8
Answer:
y = 2x + 8
Explanation:
Equation: y = 2x - 4
Comparing it with slope intercept form "y = mx + b" where 'm' is slope and 'b' is y-intercept. This function has slope: 2 and y intercept of -4
Parallel lines has same slope.
Passes through (-2, 4)
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 4 = 2(x - (-2))[/tex]
[tex]\sf y - 4 = 2(x + 2)[/tex]
[tex]\sf y = 2x + 4 + 4[/tex]
[tex]\sf y = 2x + 8[/tex]
Answer: y = 2x + 8
Step-by-step explanation:
This is a fairly simple problem. I hope this helps!
So, to find a line parallel, it's simple, and it only requires that for the other line to have the same slope and a different y-intercept (or same "m" and different "b" in the equation y = mx + b).
To find a line parallel to a point is slightly harder, but don't worry, I'll teach you how.
To do this, we have to recognize the point. The point given is (-2, 4) where -2 is the x-value and 4 is the y-value. Remember, points always go by (x, y).
So, we set y to 4, and we set x to -2.
When testing out lines that are parallel to a point, you must always be careful that you end up with the same value. Such as 4 = 4 or 8 = 8, etcetera.
We get:
4 = 2 × (-2) + 8
Simplifying, we get:
4 = -4 + 8
Adding -4 to 8, we get 4:
4 = 4
Thus, y = 2x + 8 is parallel to the point (-2, 4)
Need some help ASAP and work shown. Ps; If you answer I’ll mark you brainliest.
Answer:
h ≈ 37 ft
Step-by-step explanation:
let x be the height of the tree from the viewers eye level
using the tangent ratio, then
tan24° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{72}[/tex] ( multiply both sides by 72 )
72 × tan24° = x
then
height of tree = x + 5 = 72tan24° + 5 ≈ 37 ft ( to the nearest foot )
Answer:
37ft
Step-by-step explanation:
It can be considered as a right angle triangle. The height of the tree is equal to the product of tan(24°) and the distance between the man and tree+5 Therefore
⇒h=tan(24°)*72+5⇒h≈32ft+5⇒h≈37In conclusion
The height of the tree is 37ft
Find the interval in which the function f(x) = |x + 4| is increasing.
[tex]f { }^{ - } (x) = \frac{2(x + 4)}{2 |x + 4| {}^{} } = \frac{x + 4}{ |x + 4| } [/tex]
[tex] |x + 4| \: is \: always \: positive[/tex]
[tex]solve \: x + 4 > 0[/tex]
[tex]x > - 4[/tex]
[tex]f(x) \: is \: incresing \: from \\[/tex]
]-4,∞[A 400 second song is divided into three parts the beginning the middle and the end the beginning is one sixth as long as the end
The beginning, middle and end part of the song is 40, 120 and 240 seconds respectively
How to find equation of the unknownlet
x = end partBeginning = 1/6xMiddle = 1/2xTotal = 400 secondsx + 1/6x + 1/2x = 400
(6x+x+3x) / 6 = 400
10/6x = 400
x = 400 ÷ 10/6
x = 400 × 6/ 10
= 2400 / 10
= 240 seconds
Therefore,
End part = x
= 240 seconds
Beginning = 1/6x
= 1/6 × 240
= 40 seconds
Middle = 1/2x
= 1/2 × 240
= 120 seconds
Complete question:
The beginning is one sixth as long as the end. The middle is one half as long as the end. Find the length of each part
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Which expression is equivalent to the given expression? 4lh x + lh 3 - lh x
(7 + 7i)(2 − 2i)
(a) Write the trigonometric forms of the complex numbers. (Let
0 ≤ < 2.)
(7 + 7i) =
(2 − 2i) =
(b) Perform the indicated operation using the trigonometric forms. (Let
0 ≤ < 2.)
(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).
The complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
We have a complex number shown in the picture:
-7i(3 + 3i)
= -7i
In trigonometric form:
z = 7 (cos (90) + sin (90) i)
= 3 + 3i
z = 4.2426 (cos (45) + sin (45) i)
[tex]\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)[/tex]
[tex]\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)[/tex]
[tex]\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}[/tex]
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
=21-21i
After converting into the exponential form:
[tex]\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}[/tex]
From part (b) and part (c) both results are the same.
Thus, the complex number -7i into trigonometric form is 7 (cos (90) + sin (90) i) and 3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)
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Hello all! Please help me out with this.
I want to find a certain number which I will call Y. It is four times as great as another number which is two less than twenty. What is Y?
Answer:
Y=72
Step-by-step explanation:
First we set up the equation which is (20-2) times 4=Y
Then we solve, 20 minus 2 is risk since it is in the parentheses. 20 minus 2 is 18.
After that 18 times 4 is 72
Y=72
3. Measure the length of each leg and
the hypotenuse of this triangle:
AD =
units
AE=
units
DE=
units
Correct!
Check
The length of each leg and the hypotenuse of this triangle will be:
AD = 2 units.
AE = 2 units.
DE = 2.8 units
How to compute the hypotenuse?From the information given and the attached diagram, the value or AD and AE are 2 units respectively.
The value of DE will be calculated as the square root of 2² + 2². This will be:
= 2² + 2² = 8
= ✓8 = 2.8
Therefore, the correct options are 2, 2, and 2.8 units.
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Drag the tiles to the correct boxes to complete the pairs. Match each function to its domain and range.f(x)=5x-3
f(x) is a linear function, so both the domain and the range are the set of real numbers.
Considering only the values of β for which (1+cosβ)(1−cosβ)sinβ is defined, which of the following expressions is equivalent to (1+cosβ)(1−cosβ)sinβ?
Select the correct answer below:
sinβ
sin3β
secβ
1
sec2β
The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β
What are Trigonometric Ratios ?In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.
The trigonometric expression given in the question is
(1+cosβ)(1−cosβ)sinβ
(a+b)(a-b) = a² - b²
( 1 - cos²β)sinβ
By the trigonometric Identity
1-cos²β = sin² β
sin² β x sin β
sin³β
Therefore Option B is the correct answer.
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Rationalize the Denominator
2i/i-2
Answer:
2-4i/5
Step-by-step explanation:
[tex]\frac{2i}{i-2} *\frac{i+2}{i+2}\\=\frac{2i(i+2)}{i^2-4}\\= \frac{2i(i+2)}{-1-4}\\ =\frac{2i(i+2)}{-5} \\ = \frac{-2 + 4i}{-5}\\ =( 2 - 4i )/ 5[/tex]
Answer:
[tex]\frac{2i}{i-2}=\frac{2-4i}{5}[/tex]
Step-by-step explanation:
[tex]\frac{2i}{i-2}[/tex] (Given)[tex]=\frac{2i}{i-2}\times \frac{i+2}{i+2}[/tex] [Multiply numerator and denominator both by (i + 2)][tex]=\frac{2i(i+2)}{(i-2)(i+2)}[/tex][tex]=\frac{2i^2+4i)}{i^2-2^2}[/tex][tex]=\frac{2(-1)+4i)}{-1-4}[/tex][tex]=\frac{-2+4i)}{-5}[/tex][tex]=\frac{2-4i)}{5}[/tex][tex]\implies \frac{2i}{i-2}=\frac{2-4i}{5}[/tex]Analyze the diagram below and complete the instructions. Find the value of x and the value of y
The value of the variable x and y will be 15 and 5√3. Then the correct option is D.
The complete question is attached below.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The right triangle is shown.
Then the value of x will be
x = 10√3 × sin 60°
x = 15
Then the value of y will be
y = 10√3 × cos 60°
y = 5√3
Then the correct option is D.
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Can someone please solve
Answer: [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]3^2 + b^2 = 4^2\\\\9+b^2 = 16\\\\b^2 = 7\\\\b=\boxed{\sqrt{7}}[/tex]
The graph shows the function f(x) = 2x.
What is the value of x when f(x) = 8?
[tex]\large\orange\implies \rm \large \:f(x) \: = \: 2x[/tex]
We have to find x when f(x) is 8
[tex]\large\orange\implies \rm \large \:8 = \: 2x[/tex]
[tex]\large\orange\implies \rm \large \: \cancel\frac{8}{2} \: = \: x \\ [/tex]
[tex]\large\orange\implies \rm \large \: \: 4 \: = \: x[/tex]
The value of x is 4 when f(x) is 8[tex]f(x) \: = \: 2x[/tex]
We have to find x when f(x) is 8
[tex]8 = \: 2x[/tex]
[tex]x = \frac{8}{2} \\ \\ x = 1.[/tex]
The value of x is 4 when f(x) is 8 .
A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula
represents the volume of the pyramid?
A. V = 1/12 s ^3
B. V=1/6 s ^3
C. V=1/3s ^3
D. V=3s³
E. V=6s³
Answer:
V = (s^3)/6 (Answer B )
Step-by-step explanation:
If the length of a side of the base is s, then the height of the pyramid is half that, or s/2.
The volume of a pyramid with a square base and base side length S and height H is V = (1/3)(S^2)(H).
In this case, the formula is V = (1/3)(s^2)(s/2), or V = (s^3)/6 (Answer B)
A community center has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool?
The total volume of the pool is 1040 cubic ft. The correct answer is option B.
The complete question is given below:-
The community centre has an L-shaped swimming pool that is 10 feet deep. What is the volume of the pool
1200
1040
640
880
What is volume?Volume is defined as the space covered by any solid body in the three-dimensional plane.
We know that the total volume of the pool is the sum of the volume of two rectangular prisms.
One is a rectangular prism with dimensions 20ft.×10ft.×4ft.
and the other rectangular prism has dimensions: 6ft.×4ft.×10ft.
Hence, the volume of a first rectangular prism is:
20×10×4=800 cubic ft.
The volume of a second rectangular prism is:
6×4×10=240 cubic ft.
Hence, the total volume of the pool is:
800+240=1040 cubic ft.
Therefore the total volume of the pool is 1040 cubic ft. The correct answer is option B.
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A researcher believes that singing to plants causes them to grow an extra 0.5 inches on average per month. She tests this with 20 of her own plants by bringing 10 to work and leaving 10 at home. The ones at home she sings to each day, and she does not sing to the ones at her work.
The control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.
How to depict the control variable?According to the information, the researcher wants to seek whether singing to plants causes them to grow taller.
The explanatory variable is singing. Therefore, the researcher can control some of the variables to determine the explanatory variable on the growth of the plant.
Hence, the control variable that can be used in the research experiment is to ensure that the two set of plants will receive the same amount of water and light.
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find the value of x. round to the nearest tenth
Answer:
*79.40*
Step-by-step explanation:
using sine rule..
a/sinA = b/sinB
42/sin19= x/sin142
x= sin142*42/sin19
= 79.42356..
to the nearest tenth = 79.40.
Answer:
Step-by-step explanation:
a/sinA = b/sinB
(42/sin19) = (x/sin142)
x = (sin142 *42 / sin19)
Round to the nearest tenth -> 79.4
A student has a test scores of 87, 89, 94 points. What must he score on the fourth exam to have an average of at least 92 points?
Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.
Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.
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 values that are part of the solution are x = -5 and x = -4.5
Number linesNumber lines are lines that are used to represent the solution to inequalities.
From the given number line with he solution x > -4, this shows that all the solutions must be values that are greater than -4.
The values that are part of the solution are x = -5 and x = -4.5
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Determine the values of x and y.
Answer: x = 23, y = 40
Step-by-step explanation:
By the same-side interior angles theorem, y+30 and 110 are supplementary.
110 + y + 30 = 180 [supplementary angles add to 180 degrees]y + 140 = 180 [combine like terms]y = 40 [subtract 140 from both sides]We know that the 3x + 1 angle and y + 30 are also congruent, so:
3x + 1 = y + 30 [congruent angles have equal measure]3x + 1 = 40 + 30 [substitute y = 40]3x + 1 = 70 [combine like terms]3x = 69 [subtract 1 from both sides]x = 23 [divide both sides by 3]A scientist studying insects start with a population of 10. the population triples every hour. how many insects wil there be after 20 minutes
The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:
After 1 hour, the population is 3*10
After 2 hours, the population is 3*3*10
After 3 hours, the population is 3*3*3*10
.....
This can be generalised as a function of t, the time in hours:
f(t) = (3^t) * 10
Since the function determines the population at a given time, it is more prudent to replace f(t) with P, the population after time t:
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.4224957031 ≈ 14
Therefore the population after 20 minutes is 14.
