How you know when there is only one solution triangle possible from a side-side-angle?
Answers
Answer:
There will be only on solution if either of these conditions is met:
the given angle is opposite the longest sidethe triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)Step-by-step explanation:
Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.
There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):
the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.
Related Questions
A ramp 24 ft long rises to a platform that is 20 ft off the ground. find x , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.
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Final answer:
To determine the angle of elevation x, we use the sine function with the opposite side (20 ft) and the hypotenuse (24 ft) to get sin(x) = 20/24, and by taking the arcsin of the result, we find that x ≈ 56.4° when rounded to the nearest tenth of a degree.
Explanation:
To find x, the angle of elevation of the ramp, we can use trigonometric functions. Since we have the length of the ramp (hypotenuse) and the height of the platform (opposite side) in a right-angled triangle, we can use the sine function, which is defined as the ratio of the opposite side to the hypotenuse.
Using the sine function: sin(x) = opposite/hypotenuse = 20/24.
We first calculate the ratio: sin(x) = 20/24 = 0.8333.
To find the angle x, we take the inverse sine (also known as arcsine) of the ratio: x = arcsin(0.8333).
Using a calculator set to degree mode, we find that x ≈ 56.4° when we round to the nearest tenth of a degree.
At the Atkins County Fair, the crowd for a concert by The Cooper Band cannot exceed a certain number. The limit for the number of people who can attend the concert is 0.04 people per square foot of space in the arena. If the arena is shaped as a rectangle with sides 220 feet by 200 feet, how many people can attend the concert?
Answers
220*200= 44000
the area is [tex]44000ft^{2} [/tex]
next you would do:
44000/.4 to find how many people can fit
this equals 11000
11,000 people can attend the concert
The mapping diagram shows a relation.
What is the domain of the relation?
{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 11, 3}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 11, 3}.
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Answer:B. {x| x = –7, –6, 2, 11, 3}.
If a sphere has a radius of 2 cm what is the approximate surface area of the sphere
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If your radius is 2, then filling in that formula looks like this:
[tex]SA=4 \pi ( 2^{2} )[/tex] or [tex]16 \pi [/tex]. If you leave your answer in terms of pi, which is the exact answer, you're done. But if you multiply pi in, your surface area is SA = 50.264 square cm.
A ladder is leaning up against a 17 foot Wall at an angle of elevation of 37°. How far is the foot of the latter from the wall? Round your answer to the nearest 10th of a foot
Answers
tan theta=[opposite]/[adjacent]
opposite=17 ft
adjacent=x ft
theta=37°
thus
tan 37=17/x
x=17/tan 37
x=22.56 ft
=22.6 ft (to the nearest 10th of a foot)
A building manager installs sensors to see how often people turn off the lights when they leave a room. After a month, the manager has a sample size of 400, a sample mean of 47%, and a sample standard deviation of 4%. What is the confidence level for a confidence interval of 46.6% to 47.4%?
A. 68%
B. 85%
C. 99.7%
D. 95%
Answers
The answer is C.
The figures in your problem are inconsistent with
the data.
The sample std deviation is not and cannot be .04 (4%).
the sample std dev is sqrt[(.47)(1-.47)/400]=.02495.
The margin of error from your CI is .474 -.47= .004 (very
small).
This would represent .02495/.004= 6.24 std dev. from
expected, which would have a very
high level of confidence (99.97.. %). Something is likely
wrong with the figures in your problem.
Answer: 95%
Step-by-step explanation:
What is the distance, in radians, between 0 and 0=pie , sin0=0
Answers
The value of pi in degrees is 180 degrees. In radians, its value is 3.1415. So from 0 to pi, the distance is simple 3.1415 rad. Since sin 0 is equal to 0, then its distance from 0 is also 0.
Answer:
What is the distance, in radians, between 0 and the value you identified in part A? (PLATO QUESTION) pi (PLATO ANSWER)
Step-by-step explanation:
pi is the answer for plato users
A board is 27 inches long. How long is the board in centimeters? Use the following conversion: 1 inch is 2.54 centimeters.
Answers
1 inch = 2.54 cm
so multiply 27 by 2.54
27 x 2.54 = 68.58 cm long
To convert 27 inches to centimeters, multiply 27 by the conversion factor of 2.54 cm per inch, resulting in 68.58 centimeters.
The student has asked how long a board that is 27 inches long is in centimeters, given the conversion factor that 1 inch is equal to 2.54 centimeters. To convert inches to centimeters, you multiply the length in inches by the conversion factor. In this case, you would multiply 27 inches by 2.54 to find the length in centimeters.
Here is the calculation:
27 inches x 2.54 cm/inch = 68.58 centimeters.
Therefore, a board that is 27 inches long is 68.58 centimeters long.
To which subset of real numbers does -18 not belong?
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So, it doesn't belong in the sets of irrational numbers, whole numbers, and the natural numbers.
We have that the -18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.
Rational number & Integer
Real numbersGenerally
The subsets of the actual numbers are as follows
Irrational numbersRational numbersWhole numbersNatural numbers etc-18 is a rational quantity due to the fact it can be expressed as a fraction of two integers. It's additionally an integer.
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Create a set of numbers where the mode is equal to 10 the median is equal to 12 and the average is 12.
Please I really need help!
Answers
MEDIAN: 12
MODE: 10
MEAN: 12
mean 12 because it's the average so you have to add the data set all up and divided by the numbers that are in the data set like 84 divided 7 which is 12, your answer.
1) 8k-(6k-4)=10 show work please
2) -12x+8+5x=36 show work please
3) -2y+4=8y-6
Answers
1) 8k - (6k - 4) = 10
[tex]\mathsf{8k-6k+4=10}\\\\ \mathsf{2k=10-4}\\\\ \mathsf{2k=6}\\\\ \underline\mathsf{k=\dfrac{6}{2}=3}}[/tex]
2) -12x + 8 + 5x = 36
[tex]\mathsf{-12x+8+5x=36}\\\\ \mathsf{-12x+5x=36-8}\\\\ \mathsf{-7x=28}\\\\ \mathsf{x={28}{-7}}\\\\ \underline{\mathsf{x=-4}}[/tex]
3) -2y + 4 = 8y - 6
[tex]\mathsf{-2y+4=8y-6}\\\\ \mathsf{-2y-8y=-6-4}\\\\ \mathsf{-10y=-10}\\\\ \mathsf{y=\dfrac{-10}{-10}}\\\\ \underline{\mathsf{y=1}}[/tex]
what is the simplified form of (6^2+4)-15
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1). At what point does line A intersect line B?
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slope = (-1 - 5)/(3+1) = -6/4 = -3/2
y = mx + b
5 = -3/2(-1) + b
b = 5 - 3/2
b = 7/2
equation of line A: y = -3/2x + 7/2
Line B
slope = (-1 - 2)/(6-7) = -3/-1 = 3
y = mx + b
2 = 3(7) + b
b = 2- 21
b = - 19
equation of line B: y = 3x -19
line A intersect line B when -3/2x + 7/2 = 3x -19
so
-3/2x + 7/2 = 3x -19
3x + 3/2x = 19 + 7/2
9/2x = 45/2
x = (45/2) * (2/9)
x = 5
y = 3x - 19 = 3(5) -19 = 15 -19 = -4
(5 , -4)
answer
line A intersect line B at (5, -4)
Complete the statement f(3) is
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The corresponding output for an input value of 3 is -1. Hence f(3) is -1
from the mapping function given, the domain values are the input values of the function while the range is the output.
To get the value of f(3), we need to check the corresponding output when the input variable is 3.
From the given one-on-one mapping, we can see that the corresponding output for an input value of 3 is -1. Hence f(3) is -1
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2x-3y=8 solve for (y)?
Answers
Subtract 2x from both sides
-3y=-2x+8
Divide both sides by -3
y=2/3x-8/3
so
2x-3y=8
minus 2x both sides
-3y=-2x+8
divide both sides by -3
y=(-2/-3)x+(8/-3)
y=2/3 x-8/3
Identify the terms and coefficients for4p+5-3g
Answers
Terms:
4p
5
-3g
Coefficients are numbers multiplied by variables.
Coefficients:
4
-3
Is the data set “heights of the women in the U.S. Congress” quantitative or qualitative? If it is quantitative, is it discrete or continuous?
Answers
It is continuous because there are more than integer values of heights.
Answer with explanation:
The “heights of the women in the U.S. Congress” is Quantitative,because height of person does not represent Quality, it shows "Quantity".It means it has Magnitude.
We can find mean , median and mode of women in Congress.
So, Height of women in US congress is Quantitative.
As, different Women have different Heights, that is any rational number , so The Height of different women will be a discrete data set.For, example, height of different women can be={167 cm, 187.6, 176.6,165.5,.....}
The perimeter of a rectangle is 120 feet. The ratio of the width to the length is 2:3. Find the length and width.
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Multiply this by 2 (P = 2L + 2W) = 10 parts.
120/10 = 12
Each part = 12
W:L
12*2:12*3 = 24:36
CHECK
2(24) + 2(36) ??=?? 120
48 + 72 ??=?? 120
120 = 120 checks
Length = 36 ft
Width = 24 ft
what is the last line of proof
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hope this helps:)
What is the graph of the function?
f(x) = 2x 2
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Check the coordinate of y when x=0 ⇒ f(0)=0
Check the coordinate of x when y=0 ⇒ x=0
We have two pairs of coordinate, (0, 0) and (0, 0)
The first two graphs have these coordinates so we need to do further checking
take x=1 ⇒ f(1) = 2(1)² = 2
take x=2 ⇒ f(2) = 2(2)² = 8
we have two pairs of coordinates; (1, 2) and (2, 8)
The correct answer is OPTION A
Answer:
For f(x)=2x² graph, the answer is A.
Step-by-step explanation:
For x = -2; y = 8For x = -1; y = 2For x = 0; y = 0For x = 1; y = 2For x = 2; y = 8what is 67912 to the nearest 10
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A vehicle travels on a highway at a rate of 65 mi/h. How long does it take the vehicle to travel 25 mi?
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The function H(t) = −16t2 + 80t + 112 shows the height H(t), in feet, of a cannon ball after t seconds. A second cannon ball moves in the air along a path represented by g(t) = 20 + 5.2t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 3 through 6 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answers
are both functions which give the heights of cannonballs thrown from 2 different cannons.
A.
[tex]H(3)= -16(3)^{2}+80(3)+112=208 [/tex]
[tex]H(4)= -16(4)^{2}+80(4)+112=176 [/tex]
[tex]H(5)= -16(5)^{2}+80(5)+112=112 [/tex]
[tex]H(6)= -16(6)^{2}+80(6)+112=16 [/tex]
g(3)=5.2(3)+20=31.6
g(4)=5.2(4)+20=40.8
g(5)=5.2(5)+20=46
g(6)=5.2(6)+20=51.2
up to the 5th second, the ball from H is higher than the one from g,
then from the 6th second the ball from H is lower than the ball from g,
this means that the solution of H(t)=g(t), is between the 5th and 6th seconds.
B. The solution of part A means that during the 3rd, until it falls, the ball from H is falling to the ground, but it is still higher than the ball g which is rising, until a point between the 5th and 6 th seconds, where the balls are at the same height for just one instant, then the ball H continues falling, while g rises up for a few more second.
All right triangles with the same acute angle θ are
Answers
What part of a aday is 4 hours and 20 mintes?
Answers
A day has 24*60 = 1440 minutes
4 hours and 20 minutes is 4*60+20 = 260 minutes
The fraction 260/1440 simplifies to 13/72 part of a day.
In two supplemantary angles, the measure of one angles is 6 more than the twice the measure of the other.the measure of these two angles are
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________________________________________________________
The measurements of the 2 (TWO) supplementary angles are:
________________________________________________________
58° and 122° .
________________________________________________________
Explanation:
_________________________________________________
Two supplementary angles:
_________________________________________________
Angle 1: "x:
_________________________________________________
Angle 2: "(6 + 2x)"
_________________________________________________
All supplementary angles, by definition, add up to 180 degrees, so given that the 2 (two) angles are supplementary:
(x) + (6 + 2x) = 180 ; Find "x" and "(6 + 2x)" .
__________________________________________________
x + 6 + 2x = 180 ;
3x + 6 = 180 ;
Subtract "6" from each side of the equation ;
___________________________________________________
3x + 6 − 6 = 180 − 6 ;
3x = 174 ;
___________________________________________________
Divide each side of the equation by "3" ;
to isolate "x" on one side of the equation ; and to solve for "x" ;
3x / 3 = 172 / 3 ;
x = 58 ;
________________________________________________
So:
________________________________________________
Angle 1: "x" : x = 58 .
________________________________________________
Angle 2: "(6 + 2x)" = " 6 + 2(58) = 122 .
________________________________________________
122 + 58 =? 180 ? Yes!
________________________________________________
So, the measurements of the 2 (TWO) supplementary angles are:
58° and 122° .
________________________________________________
How did Greek mathematician Pythagoras come up with the Pythagorean Theorem. Explain
Answers
I'm having a bit of trouble, could you help?
Answers
-5-(3^2+2)=-16,
2^2-3*6=-14,
-2+4*3^2-6=28
5+4^2/2(3)=29
Evaluate: 12-6+(14-8)^2=42
-5-(3^2 + 2)
= -5 - 9 -2
= -16
= D
2^2 - 3 × 6
= 4- (3 × 6) <==== principle of BODMAS
= -14
= C
-2 + (4×3^2) -6
= -2 + 36 - 6
= 28
= A
so the next answer is obviously B
Question 2.
12-6+(14-8)^2
= 6 + 6^2
= 6 + 36
= 42
It takes Brian 15 hours longer to build a model car than it takes John. If they work together, they can build the model car in 4 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Brian to build the car on his own
Answers
It would take Brian 20 hours to build the model car on his own.
To determine the time it would take Brian to build the model car on his own, we can follow these steps:
1. Let's denote the time it takes John to build the model car as J hours.
2. Since it takes Brian 15 hours longer than John, we can express the time it takes Brian as J +15 hours.
3. If they work together, they can build the model car in 4 hours. This means that in 1 hour, they complete [tex]\(\frac{1}{4}\)[/tex] of the job together.
4. In 1 hour, John completes [tex]\(\frac{1}{J}\)[/tex] of the job, and Brian completes [tex]\(\frac{1}{J + 15}\)[/tex] of the job.
5. So, the equation representing the rate at which they work together is:
[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]
6. Now, we solve this equation to find J, the time it takes John to build the model car on his own.
7. Once we find J, we can find J+15 which represents the time it takes Brian to build the model car on his own.
So, the equation representing the rate at which they work together is:
[tex]\[ \frac{1}{J} + \frac{1}{J + 15} = \frac{1}{4} \][/tex]
To solve this equation, we can multiply both sides by the least common denominator, which is [tex]\( 4J(J + 15) \)[/tex], to clear the fractions:
[tex]\[ 4(J + 15) + 4J = J(J + 15) \][/tex]
Expanding and simplifying:
[tex]\[ 4J + 60 + 4J = J^2 + 15J \]\[ 8J + 60 = J^2 + 15J \]\[ J^2 + 15J - 8J - 60 = 0 \]\[ J^2 + 7J - 60 = 0 \][/tex]
Now, we have a quadratic equation. We can solve this equation using factoring, completing the square, or the quadratic formula. Let's use factoring:
[tex]\[ (J - 5)(J + 12) = 0 \][/tex]
Setting each factor equal to zero:
[tex]\[ J - 5 = 0 \] or \( J + 12 = 0 \)[/tex]
Solving each equation:
[tex]For \( J - 5 = 0 \), we get \( J = 5 \).For \( J + 12 = 0 \), we get \( J = -12 \).[/tex]
Since time cannot be negative, we discard the negative solution.
Now that we have found J=5 hours, which represents the time it takes John to build the model car on his own, we can find [tex]\( J + 15 = 5 + 15 = 20 \)[/tex] hours.
The solutions to the inequalities 0≤x≤2,0≤y≤1, and y≤−12x+32 form a polygonal region in the plane. How many sides does this polygon have?
Answers
y≤−12x+32
0 ≤ -12(0)+32
0 ≤ 32
This is true. Thus, the shaded region must include (0,0) which is located to the left of line (blue-shaded region). Next, use the two remaining boundaries. The inequality 0≤x≤2 is denoted as the black horizontal line from x=0 to x=2. Moreover, the inequality 0≤y≤1 is denotes as the black vertical line. The resulting figure is a rectangle. Therefore, the polygon has 4 sides.