A 100-foot ramp is tilted at a 45° angle. How high is the top of the ramp from the ground?
Answers
now, let's rationalize the denominator.
[tex]\bf \cfrac{100}{\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{100\sqrt{2}}{\sqrt{2^2}}\implies \cfrac{100\sqrt{2}}{2}\implies 50\sqrt{2}[/tex]
Related Questions
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 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 .
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.
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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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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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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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
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:
How many permutations are possible for 11 objects taken 7 at a time?
Answers
-------- = ------------------------------------ = 1,663,200
(11-7)! 4*3*2*1
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
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)
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.
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
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]
What is the solution to the system that is created by the equation y=-x+6 and the graph shown below?
Answers
so
y=1/2x and y=-x+6
y=y so
1/2x=-x+6
times 2 both sides
x=-2x+12
add 2x both sides
3x=12
x=4
sub back
y=1/2x
y=1/2(4)
y=2
(4,2) is the solution
To find the solution of y₁ = 1/2 x and y= -x + 6, let's y=y₁
-x + 6 = 1/2 x ↔ -2x +12 = x ↔ -3x= -12 and x = 4. For x = 4 , y =2.
And the solution is the intersection point between y and y₁ which is nothing but the solution or te coordinate of this point that is (4,2)
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.
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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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
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
(08.06)The following data show the height, in inches, of 11 different garden gnomes:
2 9 1 23 3 7 10 2 10 9 7
After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a garden gnome varies 3.2 inches from the mean of 7 inches.
On average, the height of a garden gnome varies 3.6 inches from the mean of 6 inches.
On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
On average, the height of a garden gnome varies 3.6 inches from the mean of 7 inches.
Answers
Answer:
The correct statement is:
On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
Step-by-step explanation:
We are given a data of 11 gardens as:
2 9 1 23 3 7 10 2 10 9 7
Now on removing the outlier i.e. 23 (since it is the very large value as compared to other data points) the entries are as follows:
x |x-x'|
2 4
9 3
1 5
3 3
7 1
10 4
2 4
10 4
9 3
7 1
Now mean of the data is denoted by x' and is calculated as:
[tex]x'=\dfrac{2+9+1+3+7+10+2+10+9+7}{10}\\\\x'=\dfrac{60}{10}\\\\x'=6[/tex]
Hence, Mean(x')=6
Now,
∑ |x-x'|=32
Now mean of the absolute deviation is:
[tex]\dfrac{32}{10}=3.2[/tex]
This means that , On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
Credits to him ♥️
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
determine whether a relation shown represents a function and justify your answer. domain 6, 10, 12 and range 7, 32
Answers
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:
if you roll a normal dice 120 times. How many odd numbers would you expect to get
Answers
This means there's a 50% chance of an odd number, so 120/2 = 60
Answer:
60 odd numbers
Step-by-step explanation:
A normal dice has 6 different sides numbered from 1 to 6, each side has the same probability of appearing when you roll the dice, i.e., in the long run each number will appear 1/6 of the times. We have three different odd numbers in a normal dice each will appear 1/6 of the times in the long run. Therefore, in the long run we hope to get 3/6 = 1/2 of the times an odd number and rolling the dice 120 times will produce about 120(1/2) = 60 odd numbers.
explain why the diagram displqyed on the right cannot represents a real object
Answers
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
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.
What set of transformations is performed on LMNO to form L'M'N'O
Answers
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.
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.