Help please. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
A.5√2 /2
B.5√3
C.5√2
D.5√3 /2
Answers
Answer: The value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
Step-by-step explanation: We are given to find the value of the variable 'x' in the figure.
We can see that the figure is a right-angled triangle with the length of the hypotenuse as follows:
h = 5 units.
Now, with respect to the angle of measure 45°, the length of the perpendicular is x units.
That is, p = x units.
From relations between trigonometric ratios, we have
[tex]\sin 45^\circ=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{p}{h}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{x}{5}\\\\\\\Rightarrow x=\dfrac{5}{\sqrt2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{(\sqrt2)^2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{2}.[/tex]
Thus, the value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
Related Questions
What set of transformations is performed on LMNO to form L'M'N'O
Answers
100 POINTS!!!! Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table for at least four values for the function. Remember to include the two points of intersection in your table. Can you just give me the X and Y values?
Answers
If you use these two points to create a line we get the equation:
[tex]y - 6 = \frac{34 - 6}{-2 - 5}(x - 5)[/tex] (I just used point slope form)
This can be simplified to:
[tex]y = \frac{40}{-7}x + \frac{242}{7}[/tex]
Now we just need to create a table of points on this line. We already have the points you gave and we can also use the y-intercept: [tex](0, \frac{242}{7})[/tex] and the x-intercept: [tex](\frac{121}{20}, 0)[/tex].
So our table of value can be:
x | y
______|________
-2 | 34
0 | 242 / 7
5 | 6
121/20 | 0
explain why the diagram displqyed on the right cannot represents a real object
Answers
f f(x)=2(x)^2+5 sqrt (+2) complete the following statement: The domain for f(x) is all real numbers greater than or equal to _____.
Answers
Then since the minimum of x^2 is 0, so f(x) must be greater or equal to 5sqrt(2)
The domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
In interval notation, we can express this as:
Domain: x ∈ [-2, ∞)
Given is a function f(x) = 2x² + 5√2, we need to determine the domain of the function,
To complete the statement, we need to determine the domain for the function f(x) = 2x² + 5√(x + 2).
The domain of a function represents all the possible values of x for which the function is defined.
In this case, we need to consider two factors that can restrict the domain:
For a real number to be a valid input for the square root (√), the expression inside the square root (x + 2) must be greater than or equal to 0.
Otherwise, we would encounter the issue of taking the square root of a negative number, which is not defined in the real number system.
There are no other restrictions in the function that would cause it to be undefined for certain values of x.
Since x² is defined for all real numbers, there are no issues there.
Let's solve the inequality for the square root expression:
x + 2 ≥ 0
Subtract 2 from both sides:
x ≥ -2
So, the domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
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which of the following correctly describes the end behavior of the polynomial function, f(x)=3x^4+2x^2-x
Answers
Answer:
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty[/tex]
Step-by-step explanation:
Given polynomial function is,
[tex]f(x)=3x^4+2x^2-x[/tex]
Since, the end behavior of a polynomial is same as the end behavior of leading term,
Here, the leading term = [tex]3x^4[/tex]
[tex]\text{As }x\rightarrow -\infty[/tex]
The leading term is positive,
[tex]\text{While, as }x\rightarrow +\infty[/tex]
The leading term is positive,
Hence, the end behavior of the given polynomial is,
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty[/tex]
⇒ In the graph of f(x), both ends will go upward.
Answer:both ends go down !
Step-by-step explanation:
Find x and RS if S is between R and T
RS=6x,ST=12,and RT=72
Answers
RST
so RS+ST=RT
6x+12=72
minus 12 both sides
6x=60
divide both sides by 6
x=10
x=10
The value of x is 10 and RS is 60 units.
It is required to find the value of x and RS.
What is length ?Length is defined as the measurement or extent of something from end to end. It is the larger of the two or the highest of three dimensions of geometrical shapes or objects.
Given:
S is between R and T
RS=6x, ST=12, RT=72
We know that ,
RS + ST = RT
6x + 12 = 72
Substract 12 on both sides we have,
6x + 12 - 12= 72 - 12
6x = 60
x = 10 units.
Put the value of x in RS we have,
RS = 6x
RS = 6(10)
RS = 60 units.
Therefore, the value of x is 10 and RS is 60 units.
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Help on this please show my work ?
Answers
x^2+3x-10
(x+5)(x-2)
(x-2)/((x+5)(x-2))
The x-2 in the numerator and denominator cancel out.
Final answer: x+5
A=1/2(a+b)h solve for h
Answers
Cross multiplication:→2A = (a+b).h.
Divide both sides by (a+b):
2A/(a+b) =h
A cab ride from your home to the airport cost $23.47. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?
$0.24
$1
$3
$8
Answers
Answer:
Step-by-step explanation:
For all Plato users.
Use the information about the bakery to explain how a manager can use a system of equations to plan employee time. Include a demonstration of how to solve the system of equations given in the problem and an explanation of how a restaurant manager would schedule oven and employee time.
Answers
20c + 10b = 800
10c + 30b = 900
Multiply the second equation by -2.
20c + 10b = 800
-20c - 60b = -1800
Now it is only to add the two equations.
0 - 50b = -1000
b = -1000/-50
b = 20
Now that we have discovered the 'b' we will substitue in the equation.
10c + 30 . 20 = 900
10c + 600 = 900
10c = 300
c = 300/10
c = 30
b=20 c=30
ok? thanks, i hope i have helped.
Implify the expression. write your answer using decimals. 22.5 + 7(n−3.4
Answers
22.5 + 7(n−3.4)
22.5 + 7n - 23.8
7n - 1.3
The simplified expression would be written as 7n - 1.3.
Five members of the soccer team and five members of the track team ran the 100-meter dash. Their times are listed in the table below: Soccer Track 12.3 12.3 13.2 11.2 12.5 11.7 11.3 12.2 14.4 13.7 What is the difference of the means for the two groups? 0.52 12.22 12.74 24.96
Answers
track : (12.3 + 11.2 + 11.7 + 12.2 + 13.7) / 5 = 61.1 / 5 = 12.22
difference is : 12.74 - 12.22 = 0.52 <=
Answer:
Hence, the difference in Mean of two teams is:
0.52
Step-by-step explanation:
Five members of the soccer team and five members of the track team ran the 100-meter dash.
Their time is listed as:
Soccer Track
12.3 12.3
13.2 11.2
12.5 11.7
11.3 12.2
14.4 13.7
The mean of the soccer team is given by:
[tex]Mean_1=\dfrac{12.3+13.2+12.5+11.3+14.4}{5}\\\\Mean_1=12.74[/tex]
The mean of track team is given by:
[tex]Mean_2=\dfrac{12.3+11.2+11.7+12.2+13.7}{5}\\\\Mean_2=\dfrac{61.1}{5}\\\\Mean_2=12.22[/tex]
Hence, the Difference in Mean is:
[tex]Mean_1-Mean_2\\\\=12.74-12.22\\\\=0.52[/tex]
Hence, the difference in Mean of two teams is:
0.52
When students have a perfect math test score, the teacher gives them 5 fake dollars to spend in the class store. If one student already has 25 fake dollars and 4 perfect math test scores, how many total fake dollars does the student have to spend?
Answers
Answer:
45 Fake Dollars
Step-by-step explanation:
4x5=20
d=20+25
d=45 Fake Dollars
Answer:
45
Step-by-step explanation:
Pablo plans to both run and swim. let r be the number of laps he runs and let s be the number of laps he swims. each lap he runs takes him 5 minutes, and each lap he swims takes him 2 minutes. he wants to exercise for at least 45 minutes today write an inequality
Answers
2s=time he swims
total must be at least 45
5r+2s≥45
Given the ordered pairs (-1,1), (0,3), (1,5), (2,7), what is the equation of the line
Answers
and y intercept is y = 3 ( because of the point (0.,3) being on the line
the equation in slope intercept form is
y = mx + c where m =2 and c = 3
answer is:-
y = 2x + 3
The equation of the line with the given ordered pairs is y = 4x + 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The ordered pairs:
(-1,1), (0,3), (1,5), and (2,7)
The equation of the line is y = mx + c.
Pick any two ordered pairs.
(-1, -1) and (0, 3)
m = (3 - (-1)) / (0 - (-1)) = (3 + 1)/1 = 4/1 = 4
Now,
(0, 3) = (x, y)
3 = 4 x 0 + c
c = 3
Thus,
The equation of the line is y = 4x + 3
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A traffic light is needed at each intersection. How many traffic lights are needed if there are 6 streets in the town.
Answers
To calculate the number of traffic lights needed for a town with 6 streets intersecting each other, you can use the formula Number of traffic lights = Number of intersections. In this case, 15 traffic lights are needed.
Explanation:A traffic light is needed at each intersection. How many traffic lights are needed if there are 6 streets in the town?
To determine the number of traffic lights needed for 6 streets, we use the formula: Number of traffic lights = Number of intersections. In a town with 6 streets, each street intersects with every other street, resulting in 15 intersections. Therefore, 15 traffic lights are needed for the 6 streets.
59:26 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple? 22 29 41 42
Answers
a²+b²=c²
so
if the legs are 20 and 21 and the hypotnuse is x then
20²+21²=x²
400+441=x²
841=x²
29=x
Answer: the correct option is (B) 29.
Step-by-step explanation: We are given to find the length of the hypotenuse x, if (20, 21, x) is a Pythagorean triple.
We know that
in a right-angled triangle, the lengths of the sides (hypotenuse, perpendicular, base) is a Pythagorean triple, where
[tex]Hypotenuse^2=Perpendicular^2+base^2.[/tex]
So, for the given Pythagorean triple, we have
[tex]x^2=20^2+21^2\\\\\Rightarrow x^2=400+441\\\\\Rightarrow x^2=841\\\\\Rightarrow x=\sqrt{841}~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm29.[/tex]
Since the length of the hypotenuse cannot be negative, so x = 29.
Thus, the length of the hypotenuse, x = 29.
Option (B) is CORRECT.
The following set of coordinates most specifically represents which figure?
(−5, 6), (−1, 8), (3, 6), (−1, 4)
Answers
All 4 sides are = sqrt20
Looks like a rhombus
The correct answer is C: Rhombus. This is how you find your answer: desmos.com because you just plant in the ordered pair into the program and it plots out the shape for you. The only thing you need to know is your shapes and you should be set.
The box plot shows the number of years during which 24 colleges have participated in a local college fair
At least how many schools have participated for 2 years or fewer?
A.2 kids
B.4 kids
C.6 kids
D.7 kid
Answers
Minimum = 0
First quartile = 2
Median = 4
Third quartile = 7
Maximum = 9
The sum is 2+4+7+9 = 22
The unaccounted for participants is 24 - 22 = 2 (outliers).
Those who participated for 2 years or less is 2.
Answer: A. 2 kids
How many permutations are possible for 11 objects taken 7 at a time?
Answers
-------- = ------------------------------------ = 1,663,200
(11-7)! 4*3*2*1
Find s10 for a geometric series with first term 10 and a common ratio 4
Answers
[tex]S_{n}=\frac{a_1(1-r^n)}{1-r}[/tex]
so
given first term of 10 and common ratio 4 and n=10
[tex]S_{10}=\frac{10(1-4^{10})}{1-4}[/tex]
[tex]S_{10}=\frac{10(1-1048576)}{-3}[/tex]
[tex]S_{10}=\frac{10(-1048575)}{-3}[/tex]
[tex]S_{10}=\frac{-10485750}{-3}[/tex]
[tex]S_{10}=3495250[/tex]
In spherical geometry, which indicates the possible number of right angles a triangle may have?
1
2
3
All of the above
Answers
So, if a triangle has one 90° angle, there are still excess angles to make up for a maximum of 540°. The same is true for two 90° angles. You would exceed 180° but that is just the lower limit so that is still acceptable. If you have three 90° angles, you form a spherical triangle with a total of 270°, which is within the given range. Thus, the answer is all of the above.
Find the possible value or values of n in the quadratic equation 2n^2-7n+6=0
Answers
n = [-b +- sq root (b^2 -4*a*c)] / 2a
n = [--7 +- sq root (49 -4*2*6)] / 4
n = [--7 +- sq root (49 -48)] / 4
n = [--7 +- sq root (1)] / 4
n1 = (7 + 1) / 4
n1 = 2
n2 = (7 -1) / 4
n2 = 1.5
If the resistance of one component of a series circuit is 3+j5 ohms, and the resistance of the second component of the circuit is 5−j8 ohms, and the resistance of the third component of the circuit is 6+j4 ohms, what is the total resistance in the circuit?
Answers
Final answer:
The total resistance in a series circuit is found by summing the resistances of individual components. For the given resistors of 3+j5 ohms, 5-j8 ohms, and 6+j4 ohms, the total resistance is 14+j1 ohms.
Explanation:
In a series circuit, the total resistance (Rtotal) is the sum of the individual resistances. We have three resistors with complex resistance values: R1 = 3 + j5 ohms, R2 = 5 - j8 ohms, and R3 = 6 + j4 ohms. Adding these together will give us:
Rtotal = R1 + R2 + R3
Calculate the real parts of each resistor and the imaginary parts separately:
Real part = 3 + 5 + 6 = 14 ohms,
Imaginary part = j5 - j8 + j4 = j1 ohm.
Thus, the total resistance in the circuit is Rtotal = 14 + j1 ohms.
determine whether a relation shown represents a function and justify your answer. domain 6, 10, 12 and range 7, 32
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At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?
Answers
x= child
2x = adult
6.20x +9.80(2x) =593.40
6.20x +19.6x=593.40
25.80x =593.40
x=593.40/25.80 = 23
23 childrens tickets were sold
Two angles are supplementary and one of the angles is 8 times the other. find the measure of the larger angle.
Answers
supplementary angles add up to 180 degrees
angle 1 = x
angle 2 = 8x
x +8x = 180
9x = 180
x = 180/9 = 20 degrees
larger angle = 8*20 = 160 degrees
To find the measure of the larger angle, set up an equation. Solve the equation to find the value of the smaller angle. Multiply the smaller angle by 8 to find the measure of the larger angle.
Explanation:To find the measure of the larger angle, we need to set up an equation based on the given information. Let's say the smaller angle is x degrees. The larger angle is then 8 times the smaller angle, which means it is 8x degrees. We know that two angles are supplementary, meaning they add up to 180 degrees. So we can set up the equation x + 8x = 180. Simplifying this equation gives us 9x = 180. Dividing both sides by 9, we find that x = 20 degrees. Therefore, the larger angle is 8x = 8 * 20 = 160 degrees.
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A gardener wants to enclose a circular garden with a square fence. If the circumference of the circular garden is about 99 feet, about how many feet of fencing would be needed? Use 3.14 to approximate for\pi π . Round your answer to the nearest tenth.
Answers
C=πd
d=C/π
p=4d so
p=4C/π feet, since C≈99 ft and π≈3.14
p≈4(99)/(3.14)
p≈126.1 ft (to nearest tenth of a foot)
The function g(x) is defined as g(x) = 6x2 + 23x – 4. When does g(x) = 0?
A.) x = –6 or x = 1/4
B.) x = –4 or x = 1/6
C.) x = -1/4 or x = 6
D.) x = -1/6 or x = 4
*The answer is B, but if there's anyone looking to earn Brainliest, please answer with a full explanation.*
Answers
6x^2 + 23x - 4 = 0
Factoring
(6x - 1)(x + 4) = 0
6x - 1 = 0 or x+ 4 = 0
X = 1/6 or x = -4
Answer:
B.) x = –4 or x = 1/6 .
Step-by-step explanation:
Given : g(x) = 6x² + 23x – 4.
To find : Solve.
Solution : We have given that
g(x) = 6x² + 23x – 4.
If g(x) = 0
6x² + 23x – 4 = 0 .
On factoring
6x² + 24x - 1x – 4 = 0
Taking common 6x from first two terms and -1 from last two terms.
6x ( x + 4 ) -1 (x + 4) = 0.
On grouping
(6x -1) ( x +4) = 0
For 6x -1 = 0
6x = 1
on dividing by 6
x = 1/6.
For x +4 = 0
On subtracting 4 from both sides
x = -4.
Therefore, B.) x = –4 or x = 1/6 .
Which features describe the graph of y^2/96^2 - x^2/40^2 =1? Check all that apply.
a focus at (104, 0)
a focus at (0,−96)
a vertex at (−40, 0)
a vertex at (0, 96)
the center at (0, 0)
Answers
[tex] \frac{y^{2}}{96^{2}} - \frac{x^{2}}{40^{2}} =1[/tex]
From the given equation,
a = 40
b = 96
(h,k) = (0,0), the center
The vertices are at (0,96) and at (0, -96).
The curves open upward and downward.
c² = a² + b² = 40² + 96² = 10816
c = 104
Therefore the foci are at (0, -104) and (0, 104).
Check the given answers:
1. a focus at (104, 0) is INCORRECT
2. a focus at (0, -96) is INCORRECT
3. a vertex at (-40, 0) is INCORRECT
4. a vertex at (0, 96) is CORRECT
5. the center at (0, 0) is CORRECT