Using the Pythagorean theorem, it is determined that the paths between the three cities, given their distances of 200 km, 300 km, and 400 km, do not form a right triangle because the sum of the squares of the shorter distances does not equal the square of the longest distance.
Explanation:To determine if the paths between the three cities form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The equation is a² + b² = c².
According to the provided distances, one city is 200 kilometers (a) from a third city, and the other city is 300 kilometers (b) from the third city.
The two original cities are 400 kilometers (c) apart.
Plugging these numbers into the Pythagorean theorem:
Since a² + b² does not equal c² (130000 ≠ 160000), the paths do not form a right triangle.
Jeremy will roll a number cube, numbered 1-6, twice. What is the probability of rolling an even number, then the number 3?
For the even number it would be I think a 6/6 chance for the three a 2/6 chance.
Answer:
1/12
Step-by-step explanation:
a chance of an even number is 1/2 and the chance of getting a three is 1/6 when you multiply these it’s 1/12
Please help fast!!!!!!!
Answer:
A
Step-by-step explanation:
because 1/9^2 is also 9^-2 because when it is a negative exponent it turns into a fraction. it does this because it is negative and the negative is equal to the number of one with the exponent positive
What is the slope of the line that passes through the points (0,-7) and (-4,3)
Answer:
Step-by-step explanation:
To find slope you have to take y2-y1 over x2-x1
y2=your second y poiny
y1=first y point
x2=second x point
x1=first x point
Since it is minus a negative you get to change it to a plus sign, because they cancel each other out.
3 + 7
____
-4-0
10/-4
This isn't quite simplified, so you find a common factor for the numerator (top number) and the denominator (bottom number). You should note the number has to go into both numbers, not just one. The largest common factor would be 2 in this case.
10/2=5
-4/2=-2
Now your simplified answer would be 5/2
The slope of the line will be "[tex]-\frac{5}{2}[/tex]".
The given points are:
[tex](x_1, y_1) = (0,-7)[/tex][tex](x_2, y_2)= (-4,3)[/tex]The slope (m) will be:
= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the given values, we get
= [tex]\frac{3-(-7)}{-4-0}[/tex]
= [tex]\frac{3+7}{-4}[/tex]
= [tex]-\frac{10}{4}[/tex]
= [tex]-\frac{5}{2}[/tex]
Thus the above slope is right.
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The pilot of a glider plane wants to estimate his altitude. He picks a landmark ahead and measures the angle of depression to be 20 degrees. He flies another 800 feet towards the landmark, remaining at the same altitude. The angle of depression from his new location to the same landmark is now 21.4 degrees. What is the glider's altitude?
Answer:
4,000 ftExplanation:
The figure attached shows sketches the situation described.
You have two right triangles.
For the right triangle with the plane on the position A, you can write:
tan(20º) = H/(800 + x)⇒ H = (800 + x) tan(20º)
For the right triangle with the plane on the position B, you can write:
tan(21.4º) = H/x⇒ H = x tan(21.4º)
To solve, equal both equations:
x tan(21.4º) = (800 + x) tan(20º)x tan(21.4º) = 800 tan(20º) + x tan(20º)x = 800 tan(20º) / ( tan(21.4º) - tan(20º) )x = 10,426.9 feetSubstitute in the equation H = x tan(21.4º)
H = 10,426.899856 × tan(21.4º) = 4,086 ftRounding to one signficant figure that is 4,000 ft.
Jessica is playing a board game and uses a number cube to determine how many spaces she can move for each turn.
What is the likelihood of Jessica rolling a 2 on her next turn?
explain
Answer: 1 out of 6
Step-by-step explanation: A number cube has 6 numbers on it. Only one of them is a two. If she were using two number cubes then she would have 2 out of 12 chances of landing on a number 2.
If you create a box-and-whisker plot for the data set, which expression correctly calculates the third quartile, Q3, of the data set?
{4.3, 5.1, 3.9, 4.5, 4.4, 4.9, 5.0, 4.6, 4.1, 4.6, 4.4, 4.3, 4.8, 4.4, 4.2, 4.5, 4.4}
Answer:
D)
(4.4+4.8)
2
Step-by-step explanation:
there is no step by step explanation
Which expression is equivalent to 7 b + 4 b minus 1 b?
A. 2b
B. 4b
C. 10b
D. 12b
Answer:
c
Step-by-step explanation:
Answer:
ITS CStep-by-step explanation:
10b Which sequence of transformations will verify that △EFG and △E'F'G' are congruent? A) △EFG is moved onto △E'F'G' after rotating 180° counterclockwise around the origin, and then reflecting across the x-axis. B) △EFG is moved onto △E'F'G' after rotating 180° counterclockwise around the origin, and then reflecting across the y-axis. C) △EFG is moved onto △E'F'G' after rotating 270° counterclockwise around the origin, and then reflecting across the x-axis. D) △EFG is moved onto △E'F'G' after rotating 270° counterclockwise around the origin, and then reflecting across the y-axis.
pls HELP
Answer:
C) △EFG is moved onto △E'F'G' after rotating 270 degrees counterclockwise around the origin, and then reflecting across the x-axis
Step-by-step explanation:
Brainliest answer here.
Above is right also.
Hope this helps :)
The sequence of transformations will verify that △EFG and △E'F'G' are congruent is; C) △EFG is moved onto △E'F'G' after rotating 270 degrees counterclockwise around the origin, and then reflecting across the x-axis
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs), etc.
For triangle △EFG and △E'F'G' to be congruent, we must first rotate 180° counterclockwise around the origin and then move EFG onto E'F'G'H'.
This proof of congruency is reflected across the y-axis.
The sequence of transformations will verify that △EFG and △E'F'G' are congruent is;
C) △EFG is moved onto △E'F'G' after rotating 270 degrees counterclockwise around the origin, and then reflecting across the x-axis
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Xerxes, Murray, Stav, Zeke, Cam, and Georgia are invited to a dinner party. They arrive in a random order and all arrive at different times. What is the probability that Xeres arrives first?
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
There are "6" people in total.
They can come at any place and at any time. All of them have equal chances of arriving at any place.
Similarly,
Everyone has the same chances of coming first.
Hence, the probability of Xerxes coming first is 1 out of 6 people
Hence,
Probability (Xerxes coming first) = 1/6
The answer is [tex]\frac{1}{6}[/tex]
The point (−3,15) undergoes a translation of 9 units right and 10
units down. What are the coordinates of the new point?
Answer:
6, 5
Step-by-step explanation:
-3 + 9 = 6
15-10 = 5
Answer:
(6,5)
Step-by-step explanation:
You just have to do 9-3 to get 6 or u can do -3-9
then for y you have to do 15-10
What's the answer to this equation .......
3= x÷2-1
Answer:
x=8
Step-by-step explanation:
If you subtract 3 from both sides then subtract -x/2 from both sides your equation should be simplified down to
-x/2 = -4. if you multiply the 2 on both sides the equation is -x=-8. but now you have to divide by negative 1 on both sides and you get x=8
N - 10 = 4 what does N equal
Answer:
N = 14 i hope this helps! :)
Step-by-step explanation:
given N - 10 = 4
add 10 to both sides N = 14
answer N = 14 units
Using Factors to Write Equivalent Expressions
Which expression has an equivalent value to x2 + 9x + 8 for all values of x?
(x + 1)(x + 8)
(x + 2)(x+6)
(x + 4)(x + 4)
(x + 5)(x + 4)
Answer:
(x + 1)(x + 8)
Step-by-step explanation:
I graphed the equation on the graph below to find the x values.
when quentinordered a tennis racket recently, he agreed to pay 7% shipping and handling charge. If quentin paid $9.45 in shipping and handling, how much must the racket have cost? (show your work)
PLEASE HELP ME
Answer:
$8.79
Step-by-step explanation:
9.45 × 0.07 = 0.6615
9.45 – 0.6615 = 8.7885
Round 8.7885 to the nearest tenth, 8.79
Given a triangle with side lengths of a, b, and c, where c is the longest side, which statement is true?
If b2 + c2 = a2, then the triangle is a right triangle.
If a2 + c2 = b2, then the triangle is a right triangle.
If a2 + b2 =c2, then the triangle is a right triangle.
If a2 = b2 = c2, then the triangle is a right triangle.
Answer:
It is C. If a2 + b2 =c2, then the triangle is a right triangle.
Step-by-step explanation:
If a triangle has side lengths a, b, and c, where c is the longest side, then the statement "If a2 + b2 = c2, then the triangle is a right triangle", the correct option is C.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
We are given that;
Sides of triangle are a, b and c
Now,
This statement is known as the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).
Conversely, if a triangle satisfies the Pythagorean Theorem, then it is a right triangle.
Therefore, by Pythagoras theorem the answer will be a2 + b2 = c2, then the triangle is a right triangle.
Learn more about Pythagoras theorem;
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Need help plz!!!
What is the correct answer in terms of pi
Answer:
volume of a cone = 2.82πinches³( nearest hundredth)
Step-by-step explanation:
given that the diameter of a cone = 2 3/8
diameter = radius x 2
radius = diameter /2
radius = 19/8/2 = 1.1875
height of the cone = 6inches
volume of the cone = ?
recall that the formulae for calculating the volume of a cone = πr² h/3
volume of a cone = πr² h/3
volume of a cone = π (1.1875)² x 6/3
volume of a cone = π1.410 x 2
volume of a cone = 2.8203πinches³
volume of a cone = 2.82πinches³( nearest hundredth)
Triangle C F E is shown. Angle C F E is a right angle. An altitude is drawn from point F to point D on side C E, forming a right angle. The length of F D is 9, the length of C D is 5, and the length of D E is 2 x + 3.
What is the value of x and the length of segment DE?
StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)
x =
Length of = units
What is the value of x and the length of segment DE?
StartFraction 5 Over 9 EndFraction = StartFraction 9 Over 2 x + 3 EndFraction
10x + 15 = 9(9)
Answer: Keep it simple
x =
6.6
Length of =
16.2
units
The value of x and one of the sides of the triangle are needed.
[tex]x=6.6\ \text{units}[/tex]
[tex]DE=16.2\ \text{units}[/tex]
[tex]CD=5\ \text{units}[/tex]
[tex]FD=9\ \text{units}[/tex]
[tex]DE=2x+3[/tex]
Finding CF
[tex]CF^2=CD^2+FD^2\\\Rightarrow CF^2=106\ \text{units}[/tex]
In triangle DEF
[tex]FE^2=DE^2+DF^2\\\Rightarrow FE^2=(2x+3)^2+81[/tex]
In triangle CFE
[tex]CE^2=CF^2+FE^2\\\Rightarrow (5+2x+3)^2=106+(2x+3)^2+81\\\Rightarrow (8+2x)^2=187+(2x+3)^2\\\Rightarrow 64+4x^2+32x=187+4x^2+9+12x\\\Rightarrow x=\dfrac{187-64+9}{32-12}\\\Rightarrow x=6.6\ \text{units}[/tex]
[tex]DE=2x+3=2\times 6.6+3\\\Rightarrow DE=16.2\ \text{units}[/tex]
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plsss help asap it would meannn alotttt
plss and tyyy
Answer:
Bottom left graph
Step-by-step explanation:
Since the y-coordinates are the same, but the x-coordinates are opposites, it is a reflection across the y axis.
Therefore, the bottom left graph is correct.
Answer: The Bottom Left Graph
Step-by-step explanation:
The Y coordinates are the same number, therefore, when you find the coordinates of the points, the y must be equal, making them the same height on a graph. The X coordinates on the graph must be opposites, therefore, the two dots have to be equidistant from the Y axis. The only graph that has two dots at the same height and is equidistant from the Y axis is the graph at the bottom Left Corner.
Identify the equation of the circle D with center D(−8,−1) and radius 3.
Answer:
(h+8)^2 + ( y +1)^2 = 9
Step-by-step explanation:
The equation of a circle can be written as
(x-h) ^2 +(y-k) ^2 = r^2
where (h,k) is the center and r is the radius
(h- -8)^2 + ( y - -1)^2 = 3^2
(h+8)^2 + ( y +1)^2 = 3^2
(h+8)^2 + ( y +1)^2 = 9
Answer:
(x + 8)² + (y + 1)² = 9
Step-by-step explanation:
Equation of a circle
(x - h)² + (y - k)² = r²
(x - -8)² + (y - -1)² = 3²
(x + 8)² + (y + 1)² = 9
One day a student comes to school sick and infects two students. The next day each of the two infected students come to school and infect four additional students. At this rate, how many days will it take to infect all 500 students in the school? Create an equation.
Answer:
2x=500
Step-by-step explanation:
Let x be the number of days.
Since there is a pattern, that 1 person is infected and infects two. Then two infects 4.
So it will be 2x. Since everyday it goes up.
Then, since there are 500 students in the school and the question asks for how many days, it will equal 500.
Well, I have to write 20 words, so... I think this is enough.
=====================================================
Explanation:
Each circle has a radius of 'a'. So r = a.
The area of each circle is pi*r^2 = pi*a^2
The area of each square with side length b is b^2
The two stacks have the same volume only when the circle area is equal to the square area, so whenever pi*a^2 = b^2 is true.
Solving for b leads to b = sqrt(pi*a^2) = sqrt(pi)*a
The stacks must also be the same height for the volumes to be the same, so m = n as well.
what’s the slope of this line?
Answer:
1
Step-by-step explanation:
We can find the slope by using any two points and the following formula
m = (y2-y1)/(x2-x1)
= (5-3)/(2-0)
= 2/2
=1
what is the domain of 0.0008x^5-0.0054x^4-0.1588x^3+1.0691x^2+4.7635x-26.4458
Answer:
[-infinity,infinity]
Step-by-step explanation:
If you look at the graph, the domain keeps going on forever and ever on both sides...
425/3333 is it. A rational number
Answer:
Yes
Step-by-step explanation:
Any number which can be written as a fraction of integers, is rational
in a class there are 8 students who play football and cricket 4 students who do not play football or cricket 14 students who play football 20 students who play cricket find the probability that a student chosen at random plays football or cricket or both
Answer:
Step-by-step explanation:
hello :
here is an solution :
The probability that a student chosen at random plays football or cricket or both is approximately 0.8667, or 86.67%, after considering the number of students playing each sport and accounting for those who play both.
To calculate the probability that a student chosen at random plays football or cricket or both, we can use the concept of probability along with a Venn diagram to organize our information.
First, we need to calculate the total number of students that play at least one of the sports. We know that 8 students play both football and cricket, 14 students play football, and 20 students play cricket. However, the 8 students that play both sports are included in the totals for both football and cricket. Therefore, to find the number of students who play at least one sport, we need to subtract the students counted twice because they play both sports:
Total playing football or cricket or both = (Number playing football) + (Number playing cricket) - (Number playing both)
= 14 + 20 - 8
= 26 students
We also know there are 4 students who do not play football or cricket. To find the total number of students, we add the number of students who play either sport to those who play neither:
Total number of students = 26 (playing sports) + 4 (not playing any sports)
= 30 students
The probability that a student chosen at random plays football or cricket or both is calculated by dividing the number of students who play either sport by the total number of students:
P(playing football or cricket or both) = Number of students playing sports / Total number of students
= 26 / 30
= 0.8667 (rounded to four decimal places)
The probability is approximately 0.8667, or 86.67%.
is line AB tangent to circle below
Answer:
Yes, Line AB is tangent to the circle.
Step-by-step explanation:
Look at points C and D on the graph
What is the distance (in units) between points C and D? Round your answer to the nearest hundredth
3.00
3.46
4.24
6.00
Answer:
4.24
Step-by-step explanation:
you should use the pythagorean theorem to solve this!
a^2 + b ^2 = c^2
3^2 + 3^2 = c^2 (i got 3 because it goes down three, and over three)
9 + 9 = c^2
18 = c^2
the square root of 18 is 4.24
therefore, the distance between C and D is 4.24.
hope this helps! :)
Answer: 3.00
Step-by-step explanation:
The point between 0-3 is 3 points
i need help for this equation x-2y=6
Answer:
y=1/2-3
Step-by-step explanation:
x-2y=6
-2y=-x+6
y=1/2-3
or
-2y=6
y=-3
x=6
What is the simplified form of 3 and the square root of 135?
Answer: do u still want to know this or not
Step-by-step explanation:
what is 2 1/8 take away 1/2
The equation is [tex]2\frac{1}{8} - \frac{1}{2}[/tex] .
1/2 is equivalent to 4/8, and 2 1/8 is equal to 17/8. (two full sets of 8 + 1 = 8 + 8 + 1, or 17)
The new equation is [tex]\frac{17}{8} -\frac{4}{8}[/tex] . Subtract the numerators.
17 - 4 = 13 or 13/8
The improper fraction [tex]\frac{13}{8}[/tex] simplifies to [tex]1\frac{5}{8}[/tex] .
Answer:[tex]1\frac{5}{8}[/tex]
Hope this helps :)