We want to find one-half of the reciprocal of 7/sqrt(98). Let's write down an expression for this:
[tex]\dfrac{1}{2} \times \dfrac{\sqrt{98}}{7}[/tex]
We can rewrite 98 into [tex]2 \times 49[/tex]
[tex]\dfrac{1}{2} \times \dfrac{\sqrt{2 \times 49}}{7}[/tex]
[tex]=\dfrac{1}{2} \times \dfrac{\sqrt{2} \times \sqrt{49}}{7}[/tex]
The square root of 49 is 7
[tex]=\dfrac{1}{2} \times \dfrac{\sqrt{2} \times 7}{7}[/tex]
[tex]=\dfrac{1}{2} \times\sqrt{2}[/tex]
[tex]=\dfrac{\sqrt{2}}{2}[/tex]
This should be your answer. Let me know if you need any clarifications, thanks!
The required answer in the form of √a/b is √2 / 2.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
The given term is,
7 / √98
The one half of the reciprocal of the term 7 / √98 = 1/2 x √98/ 7
Solve the expression 1/2 x √98/ 7,
= 1/2 x (7 √2 / 7)
= 1/2 x (√2)
= √2 / 2.
The simplest of the given expression is √2 / 2.
To know more about Simplification on :
https://brainly.com/question/2804192
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4. Which regions contain more than 3 million males?
Answer:
The Eastern region has more than 3 million males.
helppppp Help me out :O What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side length.
Answer:
1/9 cubic feet
Step-by-step explanation:
The volume of one cube would be (1/3)³ = 1/27, therefore the volume of three cubes would be triple that amount, which is 1/27 * 3 = 1/9 ft³.
If m∠1 = 3x, m∠3 = 2x + 20 and m∠5 = 30, what is the value of x?
10
20
26
50
Answer:
50 degrees
Step-by-step explanation:
The diagram is attached below.
Theorem: The Exterior angle of a triangle is equal to the sum of two opposite interior angles.
By the theorem stated above:
m∠3+m∠5=m∠1
2x+20+30=3x
3x-2x=50
x=50
The value of x is 50 degrees.
Answer:
50
Step-by-step explanation:
NEED IT ASAP What is the value of x in the diagram below? A.18/ ROOT 3 B.18 ROOT 2/ROOT 3 C.18 ROOT 3/ ROOT 2 D. 18 ROOT 2
Answer:
x = B. 18 ROOT 2/ROOT 3
Step-by-step explanation:
There are two Triangles in the diagram above.
Step 1
We would solve for Triangle A First
Using Trigonometric function Cosine
cos θ = adjacent /hypotenuse
θ = 30°
Adjacent = 9 units
Hypotenuse = unknown
cos 30= 9/ Hypothenuse
Cross Multiply
cos 30 × Hypotenuse = 9
Hypotenuse = 9 / cos 30
cos 30 in surd form = √3/2
Hypotenuse = 9/√3/2
Hypotenuse = 9 × 2/√3
= 18/√3 units
Step 2
We would solve for the upper triangle = Triangle B
We are looking for x
θ = 45°
For Triangle B, the Hypotenuse we solved for in Triangle A is equivalent to the adjacent in Triangle B
Therefore ,
Hypotenuse for Triangle A = Adjacent side for Triangle B
θ = 45°
Adjacent = 18/√3 units
Hypotenuse = x = unknown
We would solve for this using Trigonometric function cosine
cos 45 = 18/√3 units / Hypothenuse
Cross Multiply
cos 45 × Hypotenuse = 18/√3 units
Hypotenuse = 18/√3 units / cos 45
cos 45 in surd form = 1/√2
Subtituting, we have
Hypotenuse (x) = 18/√3 units / 1/√2
Hypotenuse (x) = 18/√3 units ×√2/1
= 18× √2/ √3 units
= 18 √2/√3 units
Therefore x = Option B. 18 ROOT 2/ROOT 3
Answer:
18sqrt2/sqrt3
or B on Edg
Step-by-step explanation:
A tree 10 meters high casts a 17.3 meter shadow.
Find the angle of elevation of the sun.
Round your answer to the nearest degree.
means having the
metry helps us to find
10 m
sa function the inve
e use the symbols to
17.3 m
to find side lengths, y
is cos(x).
Answer:
the angle of elevation of the sun is [tex]\approx 30^o[/tex]
Step-by-step explanation:
Let's make a diagram of the tree, ground and inclination of the rays of the sun, so we understand what right angle triangle we have. Please see the attached image.
Notice that our unknown is the angle [tex]\theta[/tex], and that we know the size of the side opposite to it, and of the side adjacent to it. Therefore the most convenient trigonometric formula to use is the tangent of the angle because:
[tex]tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{10}{17.3}\\\theta=arctan(\frac{10}{17.3})\\\theta\approx 30^o[/tex]
7. Write the slope-intercept form of the equation that passes through the point (2, 3) and is perpendicular to the line y = 5/8x - 4 y = 5/8x + 17/4 y = -5/8x + 7/4 y = -8/5x + 31/5 y = -8/5x - 31/5
Answer:
y = -8/5 x + 31/5
Step-by-step explanation:
Write the slope-intercept form of the equation that passes through the point (2, 3) and is perpendicular to the line y = 5/8x - 4 y = 5/8x + 17/4 y = -5/8x + 7/4 y = -8/5x + 31/5 y = -8/5x - 31/5
The slopes of perpendicular lines are negative reciprocals.
Slope of given line: 5/8
Slope of perpendicular line: -8/5
Point on perpendicular line: (2, 3)
Slope-intercept form of the equation of a line:
y = mx + b
We know the slope of the perpendicular is -8/5, so now we have
y = -8/5 x + b
We need to find b.
We use the given point for x and y and solve for b.
y = -8/5 x + b
3 = -8/5 * 2 + b
15 = -8 * 2 + 5b
15 = -16 + 5b
5b = 31
b = 31/5
Now that we know that b = 5, we can write the equation of the perpendicular line:
y = -8/5 x + 31/5
a particular dam contains approximately 1,900,000,000,000 cubic feet of water. for a week long spike flood, the dam released at a rate of 24,600 cubic feet per second. how much water was released during the flood?
what percentage of the dam was released during the flood?
Answer:
a) How much water was released during the flood?
14878080000 cubic feet or 14,878,080,000ft³
b) What percentage of the dam was released during the flood?
0.78%
Step-by-step explanation:
a) How much water was released during the flood?
The first step would be to find out how many seconds are in a week
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
Hence, the number of seconds in a week =
1 week × (7 days/1 week)× (24 hours/1 day )×( 60 minutes/1 hour) ×( 60 seconds/1 minute)
= 604800 seconds
Therefore, the quantity of water released per week =
604800 seconds × 24,600 cubic feet per second
= 14,878,080,000 cubic feet or 14,878,080,000ft³
b) What percentage of the dam was released during the flood?
This is calculated as quantity released during the week ÷ Quantity of water in the dam × 100%
Quantity of water released during the flood in a week = 14,878,080,000 cubic feet
Quantity of water in the dam= 1,900,000,000,000 cubic feet of water
Percentage of the dam released during the flood =
14,878,080,000 cubic feet ÷ 1,900,000,000,000 × 100
= 0.7830568421%
Approximately = 0.78%
Find the value of the following expression: (3^8 x 2^-5 x 9^0)^-2 x (2^-2/3^3)^4 x 3^28
sorry if this is overwhelming!!! Trying to put this out there for this Awful end exam
Answer:
4
Step-by-step explanation:
(3^8 x 2^-5 x 9^0)^-2 x (2^-2/3^3)^4 x 3^28 =
= 3^-16 x 2^10 x 1 x 2^-8 x 3^-12 x 3^28
= 3^0 x 2^2
= 4
Help me out :O What is the volume of three cubes, each with a side length of fraction 1 over 3 foot? V = s3, where s is the side length.
Answer:
3. 1/9 feet^3
Step-by-step explanation:
First, find the volume of one cube.
The volume of a cube can be found using the following formula:
V=s^3
We know that s, the side length is 1/3 feet. Therefore, we can substitute 1/3 ft in for s.
V= (1/3 ft)^3
Evaluate the exponent.
1/3 ft^3
=1/3 ft * 1/3 ft* 1/3 ft
=1/9 ft^2*1/3 ft
= 1/27 ft^3
V= 1/27 ft^3
Now find the volume of 3 cubes. We know the volume of one cube is 1/27 ft^3, therefore we can multiply 1/27 ft^3 by 3.
1/27 ft^3 * 3
Multiply 1/27 and 3.
1/27 * 3/1
=(1*3)/(27*1)
=3/27
=1/9
V= 1/9 ft^3
The volume of 3 cubes is 1/9 cubic feet, and choice 3 is correct.
Answer:
1/9; C
Step-by-step explanation:
V=s*s*s
Side Length: 1/3
V=1/3*1/3*1/3
V=1/27
1/27*3= 3/27
3/27 simplified eqauls 1/9
If A=(0,0) and B=(6,3), what is the length of AB?
Answer:
3√5 unitssolution,
A(0,0)---->(X1,y1)
B(6,3)---->(x2,y2)
Now,
[tex]ab = \sqrt{ {(x2 - x1)}^{2} + (y2 - y1) ^{2} } \\ \: \: \: = \sqrt{ {(6 - 0)}^{2} + {(3 - 0)}^{2} } \\ \: \: \: = \sqrt{ {(6)}^{2} + {(3)}^{2} } \\ \: \: \: \: = \sqrt{36 + 9} \\ \: \: \: \: = \sqrt{45} \\ \: \: \: = 3 \sqrt{5 } \: units[/tex]
Hope this helps...
Good luck on your assignment..
P and Q are reflections of (2, – 3) across the x-axis and the y-axis, respectively. Find the length of PQ in simplest radical form.
Answer:
(-2,3)
Step-by-step explanation:
When you reflect a point over the x axis, the y value is changed to the opposite value (positive)
So (2,-3) reflected across the x axis is (2,3)
Next, we need to reflect this across the y axis
When you reflect a point over the y axis, the x value is changed to the opposite value (negative)
(2,3) reflected across the y axis is (-2,3)
George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request. He asked 500 students at his school the following questions: "Are you in the Art Club?" and "Did you get the art class you requested?" The results are shown below:
Art class and in art club: 100
Art class and not in art club: 265
Total in art class: 365
Not in art class and in art club: 65
Not in art class and not in art club: 70
Total not in art class: 135
Total in art club: 165
Total not in art club: 335
Total students: 500
Help George determine if all students at his school have an equal opportunity to get into the art class they requested. Show your work, and explain your process for determining the fairness of the class assignment process.
Answer:
If you're not an art club member and you want to request the art class, you have a greater chance of getting into our class. There isn't an equal opportunity for all students to get into the art class they requested, therefore the class assignment is unfair.
As a non-art club member, you have a 79% chance of being assigned to the art class they request.
As an art club member, you have a 61% chance of being assigned to the art class they request.
Step-by-step explanation:
265, divided 335, that's 79%. So this means that if you are not in the art club and you wish to enroll in an art class, you have 79% of percent of being admitted in your request in art class.
Total not in art club 335/ Total students 500= 0.791= 0.79%
Art class and in art club 100/ Total in art club 165= 0.606 = 0.61%
Non art club requested 79% against art club requested 61%.
4)
If the first three Fibonacci numbers are x, = 1, .x = 1, x3 = 2,
what is the value of n for which .x. +x... + x = 68?
Answer:
The value of n for which xₙ₋₂ + xₙ₋₁ + xₙ = 68 is n = 9
Step-by-step explanation:
The nth term of Fibonacci number is given by the following relation;
[tex]F_n = \dfrac{(1 + \sqrt{5} )^n - (1 - \sqrt{5} )^n }{2^n\sqrt{5} }[/tex]
Given that we have ;
[tex]\Sigma x_n = \dfrac{(1 + \sqrt{5} )^{n-2} - (1 - \sqrt{5} )^{n-2} }{2^{n-2}\sqrt{5} } + \dfrac{(1 + \sqrt{5} )^{n-1} - (1 - \sqrt{5} )^{n-1} }{2^{n-1}\sqrt{5} }+\dfrac{(1 + \sqrt{5} )^{n} - (1 - \sqrt{5} )^{n} }{2^{n}\sqrt{5} }[/tex]When n = 3, we have;
∑xₙ = 4
When n = 4 we have
∑xₙ = 4
When n = 6 we have
∑xₙ = 16
When n = 9 we have
∑xₙ = 68
Therefore, we have the value of n for which xₙ₋₂ + xₙ₋₁ + xₙ = 68 is n = 9.
Which is the graph of the system x+3y>-3 and y<1/2x+1?
Answer:
The y-intercept of the first inequality is -1.
The y-intercept of the second inequality is +1.
The fourth graph has these correct.
The volume of a cuboidal box is 21952 cubic cm. Find the length of each side of the box.
Answer:
28 cm
Step-by-step explanation:
V=a³
a= ∛V= ∛21952 cm³ = 28 cm
Answer:
28 is the answer because you have to find the cube root of the volume.Step-by-step explanation:
28 is the answer because you have to find the cube root of the volume. This is because a cube has equal sides so it means that the sides have to be equal. When you find volume, you have to multiply the length, width, and height. So you have to find the cube root of 21952. The cube root is 28.
Hope this helped,
Kavitha
Inez rides a bike with 24 inch (2 feet) wheels. What is the distance he can travel in 1500 revolutions?
Answer:
9420 ft
Step-by-step explanation:
1500 revolutions = 1500 full rotations or 360 degrees
Circumference = 6.28 ft ( 3.14 x 2 )
Then we take rotations by the circumference
1500 x 6.28 = 9420
MARK AS BRAINLIEST
Answer:
9420 ft or 2.88 km
Step-by-step explanation:
d= 2 ft
1500 revs
C= πd= 3.14*2= 6.28 ft
distance= 1500*6.28= 9420 ft ≈ 2.88 km
Ashley is doing some math exercises on a website called Khon Academy. In Khon Academy, you have to get at least 70% of the problems in an exercise right in order to gain proficiency. So far, Ashley has answered correctly 3 out of 7 times. Suppose she answers all of the following q questions correctly and gains proficiency in the exercise. Write an inequality in terms of q that models the situation.
The inequality in terms of q that models the situation is [tex]3+\frac{q}{7}+q \geq 0.7[/tex]
Given that,
There is 70% of the problems for gaining the proficiency. Also, the 3 answered are correct out of 7 times.Q represents the questions.Based on the above information, the inequality in terms of q should be [tex]3+\frac{q}{7}+q \geq 0.7[/tex]
Therefore we can conclude that The inequality in terms of q that models the situation is [tex]3+\frac{q}{7}+q \geq 0.7[/tex]
Learn more: brainly.com/question/15137133
Answer:
3+q/7+q is greater than or equal to 0.7
Step-by-step explanation: Khan
3+q/7+q is a fraction You`re welcome :)
Please help with this
Answer: x = 10
Step-by-step explanation:
Hi, to answer this question we have to apply proportions, since the sides are equivalent.
15/25
6/x
So, for equal ratios:
15/25 = 6/x
Solving for the missing side x:
x = 6 / (15/25)
x = 10
In conclusion, the correct option is D) 10
Feel free to ask for more if needed or if you did not understand something.
right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.
"sqrt" stands for "square root"
=======================================================
Explanation:
Angle C is 60 degrees because adding the angles gets A+B+C = 180. Put another way, C = 180-A-B. Therefore, C = 180-30-90 = 60.
We have a 30-60-90 triangle with
BC as the short leg (since it is opposite the smallest angle A = 30)AB as the long leg (because it is opposite the medium angle C = 60)AC as the hypotenuse (it is opposite the largest angle, so AC is the longest side)Check out the diagram below.
----------
From here, we use the 30-60-90 triangle template. The short leg is x, the hypotenuse is 2x and the long leg is x*sqrt(3). The area of this template triangle is
area = 0.5*base*height
area = 0.5*(short leg)*(long leg)
area = 0.5*x*(x*sqrt(3))
area = 0.5*x^2*sqrt(3)
set this equal to 32*sqrt(3) and you should find that 0.5x^2*sqrt(3) = 32*sqrt(3) solves to x = 8
----------
Therefore we can say,
BC = short leg = x = 8AB = long leg = x*sqrt(3) = 8*sqrt(3)AC = hypotenuse = 2x = 16Find the product. Write your answer in
exponential form.
2^-7•2^9•2^6
Answer:
exponential form = 2 ^8 = 4^ 4 = 16^ 2 = 256^ 1
Step-by-step explanation:
256
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= 2 ^8 = 4^ 4 = 16^ 2 = 256^ 1
Answer:
4^4Step-by-step explanation:
[tex]2^{-7} \times2^9\times2^6\\\frac{1}{2^{7} } \times2^9\times2^6\\\frac{1}{128} \times 512 \times 64\\= 32768/128\\ = 256\\= 16^2 or\\ 4^4[/tex]
If you were asked to describe how you would solve for an unknown value in an
equation, how would you explain that process? Give it a try here, using the equation
given as a step by step example to go along with your explanation. Be as detailed as
possible for each step of the solution.
3(x - 2) = 5x – 14
Answer:
4
Step-by-step explanation:
3(x - 2) = 5x - 14 (given)
3x -6 = 5x -14 (Distribute the "3" to "x" and "2")
-2x -6 = -14 (subtract "5x" from both sides)
-2x = -8 (Subtract "-6" from both sides)
x = 4 (divide both sides with "-2")
Guys, what does this r stand for in math?
Answer:
All real numbers
Step-by-step explanation:
This denotes all real numbers in any case. Instead of writing out "all real numbers" you can use this
Answer:
real numbers
Step-by-step explanation:
This is the representation for the real numbers
Triangle ABC is transformed to triangle A′ B′ C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 3, 4, B at ordered pair negative 4, 2, C at ordered pair negative 1, 1. A triangle A prime B prime C prime has A prime at ordered pair 3, 4, B prime at ordered pair 4, 2, C prime at ordered pair 1, 1.
Which equation shows the correct relationship between the measures of the angles of the two triangles?
The measure of angle ABC = The measure of angle A prime B prime C prime
The measure of angle ABC = The measure of angle B prime C prime A
The measure of angle BCA = The measure of angle A prime B prime C prime
The measure of angle BCA = The measure of angle C prime A prime B prime
Answer:
The measure of angle ABC = The measure of Angle A' B' C'
Step-by-step explanation:
Because
<A = <A'
<B = <B'
<C = <C'
The answer above is right.
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.
x y
0 -6
1 -9
2 -12
3 -15
4 -18
A. quadratic; y = -x^2 - 2x
B. exponential; y = -6 • 1.5x
C. linear; y = -3x - 6
D. quadratic; y = -x^2 + 2x - 6
Answer: The correct answer is c
Step-by-step explanation: you would have to plot your graph and the put the answer in slop intercept for y=mx+b or y=-3x-6
Answer:
exponential; y = –6 • 1.5x
Step-by-step explanation:
1.5 x 1 = 1.5
1.5x-6= -9
Solve the following system of equations by elimination. What is the value of x?
Answer:
Answer is x = 3
Step-by-step explanation:
x = 2+ 1/2 * 2
x = 3
Answer:
x= 3 and y = 2 is the answer..
6.5+(-8.3)-(-1.6)+0.7-9.9
Answer:
-12.6
Step-by-step explanation:
OK so I might have done something wrong but just remember when you're adding a negative and and a positive number you're technically just subtracting
A is the set of integers greater than -9 and less than -3
Answer: -8, -7, -6, -5, -4
Step-by-step explanation:
Answer:
A = {-8, -7, -6, -5, -4}
Step-by-step explanation:
The integers greater than -9 and less than -3 are -8, -7, -6, -5, -4.
-9 < x < - 3
x = -8, x = -7, x = -6, x = -5, x = -4
Est. Length: 2:00:00
x
Wyatt Stewart: Attempt 1
(06.01 MC)
What is the value of the expression shown below?
(2) 12 point)
4 + 16 +2244
O 1) 20
O 2 16
0 3 2
O 4) 5
Answer:
Step-by-step explanation:
B
WILL MARK BRAINLIEST FOR QUICK AND CORRECT ANSWER Determine the sum of the given probabilities. Are the events complementary? P(A) = 4/7 ; P(B) = 1/7 ; The events are complementary. ; The events are not complementary. ; The events are complementary. ; The events are not complementary.
Step-by-step explanation:
The numical sum of probabilities P(A) and P(B) = 4/7+1/7 = 5/7
Events A and B cannot be complementary because complementary events have their probabilities add up to exactly one.
Since P(A)+P(B)=5/7, A and B cannot be complementary.
help will give brainliest
Answer:
c. quadrant 111
Step-by-step explanation:
Answer: Quadrant IV
or 4
Step-by-step explanation:
Because quadrant 4 has both positive and negative, x is positive, y is negative, 7 is positive and -5 is negative.