Answer:
86.5 m
Step-by-step explanation:
Length of the string forms the hypotenuse AC of right angle triangle ABC.
C is the kite. A is the hand of the person (or, one end of the string). CB is the perpendicular (height of the kite ) from C on the ground. BC is the horizontal.
Sin 60° = CB/AC = √3/2
height = 1.73/2 * AC = 0.865 * 100 m = 86.5 m
Given a right triangle with leg a = 6 and hypotenuse c = 10. Find the three heights, the three medians, the three bisectors, and the radii of the inscribed and circumscribed circles.
Answer:
The three heights are 4.8, 6, 8The three medians are 5, 2√13, √73The three angle bisectors are (24/7)√2, 3√5, (8/3)√10The radii of the incircle and circumcircle are 2 and 5, respectivelyStep-by-step explanation:
a) The other leg of the right triangle is ...
b = √(10² -6²) = √64 = 8
The area of the triangle is ...
A = 1/2bh = 1/2(6)(8) = 24
Then the height to the long side is ...
h = 2A/c = 48/10 = 4.8
The three heights are 4.8, 6, 8.
__
b) The medians to the hypotenuse is half its length, because that is also the radius of the circumcircle: 10/2 = 5.
The medians to the legs are computed from the Pythagorean theorem:
median to "b" = √(4² +6²) = √52 = 2√13
median to "a" = √(3² +8²) = √73
The three medians are 5, 2√13, √73.
__
c) The angle bisectors to the legs can be found in a fashion similar to the medians, using the angle bisector theorem to locate the point of intersection on the leg.
The angle bisector to "b" divides it into segments in the ratio 6:10, so the point of intersection is 6/(6+10)×8 = 3 units from the right angle. Then its length is ...
bisector to "b" = √(6² +3²) = √45 = 3√5
The angle bisector to "a" divides it into segments in the ratio 8:10, so the point of intersection is 8/(8+10)×6 = 8/3 units from the right angle. Then its length is ...
bisector to "a" = √(8² +(8/3)²) = (8/3)√10
I find it easier to compute the bisector to the hypotenuse by considering the hypotenuse to be a line with x- and y-intercepts at 8 and 6. Then its equation can be 3x+4y=24, and its intersection with the line y=x will be x = y = 24/7. The length of the segment to that point is ...
bisector to "c" = (24/7)√2
The three angle bisectors are (24/7)√2, 3√5, (8/3)√10.
__
d) The radius of the inscribed circle can be found from the formula ...
r = √((s-a)(s-b)(s-c)/s) . . . . where s is the semiperimeter = 24/2 = 12
r = √(2×4×6/12) = 2
The hypotenuse is the diameter of the circumscribed circle, so the radius of that circle is c/2 = 5.
The radii of the incircle and circumcircle are 2 and 5, respectively.
there were 632 animals gathered at the river. a herd of 187 elephants and 266 zebras left the river area. how many animals were still at the river?
Answer: There was a total of 173 animals left by the river
Step-by-step explanation:187+266 = 453
You subtract 453 from the total number of animals which is 632
632-453 = 179
if a binomial event has a probability of success of 0.5, how many successes would you expect out of 2000 trials
A.1000
B.600
C.1800
D.1400
Answer:
1000
Step-by-step explanation:
a binomial event only has two possible outcomes
P(success) = .5
Multiply the probability of success by the number of trials
.5*2000 =1000
in the coordinate plane, ABCD has vertices with coordinates A(1,-1), B(-5,3), C(-3,6),
and D(3,2)
Answer:
C
Step-by-step explanation:
Factor 24 j − 16 24j−1624, j, minus, 16 to identify the equivalent expressions.
Answer:
8(3j-2)
Step-by-step explanation:
Given the expression: 24j−16
We are required to factor the expression.
The GCD of 24 and 16 is 8. We therefore divide both terms of the expression by 8.
[tex]8(\dfrac{24j}{8}-\dfrac{16}{8})\\\\=8(3j-2)[/tex]
An equivalent expression therefore is: 8(3j-2)
A group of dancers raised some money for a charity here is some information about the money raised
One of the dancers is chosen at random to give the money raised to the charity
What is the probability that this dancer raised less then £10
Answer:
19/30
Step-by-step explanation:
out of 60 people 38 dancers earned less than 10, so the fraction is 38/60 and simplified its 19/30
A greenhouse contained both 6-inch high geraniums and 3 inch high geraniums. The 6-inch high geraniums were taken out of the greenhouse in early spring and grew at a rate of 1 inch per week. The 3 inch high geraniums remained in the greenhouse and grew at a rate of 1 (1/2) inches per week. After the 6-inch high geraniums were taken outside, in how many weeks were both groups of geraniums the same height.
Answer:
6 weeks
Step-by-step explanation:
Let the number of weeks be x.
Then we have an equation:
6 + 1*x = 3 + 1 1/2 x6 + x = 3 + 1.5x1.5x - x = 6 - 30.5x = 3x = 3/0.5x = 6 weeksSo after 6 weeks both 6-inch and 3-inch geraniums will have same height
The bar graph below shows the number of aluminum cans collected by students in the month of October. How many cans did seigi and Ariel collect together
Answer:
1 2 3 4 5 6 7 8 9 10 bars are there
please answer quick ! 6 9/10 - 2 2/9 = ?
Answer:
4 61/90
Step-by-step explanation:
6 - 2 = 4
9 / 10 - 2 / 9 = 61 / 90
4x-k=17 solve for x
Answer:
k = -17 + 4x
Step-by-step explanation:
Simplifying
4x + -1k = 17
Reorder the terms:
-1k + 4x = 17
Solving
-1k + 4x = 17
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-4x' to each side of the equation.
-1k + 4x + -4x = 17 + -4x
Combine like terms: 4x + -4x = 0
-1k + 0 = 17 + -4x
-1k = 17 + -4x
Divide each side by '-1'.
k = -17 + 4x
At the Boxer carnival, you can exchange 40 tickets for various assortments of
prizes. Some of those assortments are below. How many tickets does it take
to get a single tacky mirror?
1 goldfish, 2 tacky mirrors, 1 stuffed tiger
5 goldfish, 1 stuffed tiger
2 goldfish, 3 tacky mirrors
Answer:
g = number of tickets for goldfish
t = number of tickets for tacky mirrors
s = number of tickets for stuffed tiger
1g + 2t + 1s = 40
5g + + 1s = 40
2g + 3t = 40
using the second equatin we can find a value for s
1s = 40 -5g
now substitute in the first equation to get rid of s
1g + 2t + (40-5g) = 40
-4g + 2t = 0
now use this new equation with equation 3 and solve for one of the values
-4g + 2t = 0
2g + 3t = 40
multipy the second equation by 2 and then combine
-4g + 2t = 0
4g + 6t = 80
8t = 80
t = 10 (so it takes 10 tickets to get a takcy mirror)
2g + 3(10) = 40
2g = 10
g = 5 (five tickets to get a goldfish)
s = 40 -5(5)
s = 15 (fifteen tickets for a stuffed tiger)
1(5) + 2(10) + 1(15) (substitute back in the first equation)
5 + 20 + 15
40 it works!
Round 43.597 to nearest hundred
The radii of Earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively.
URGENT
Approximately how many spheres the size of Pluto does it take to have the same volume as Earth?
A.121
B. 154
C. 165
D.176
E.189
Answer:
A
Step-by-step explanation:
What is the area of triangle QRS?
7 square units
9 square units
10 square units
13 square units
Answer:
A 7
Step-by-step explanation:
Last week, Maria bought k pounds of cherries at the regular price of $2.75 per pound. This week, cherries were on sale for 20 percent off, and maria bought twice as many pounds as she bought last week, which of the following is the total in dollar, Maria paid for the cherries last week and this week
Answer:
$7.15k
Step-by-step explanation:
So the first week, she used $2.75k
Then, you can calculate the amount for one pound the next week by doing 0.8 * 2.75 = 2.2
So the second week she used 2 * 2.2 * k = $4.4k
$4.4k + $2.75k = $7.15k
Might be wrong so check it.
What is the range of possible sizes for side x?
8.8
Answer:
The size of side x can range from 0.5 < x < 16.5.
The size of side x cannot take on values 0 and 16.5, but it ranges between those two values for side x to complete a triangle with those two other sides.
Step-by-step explanation:
Complete Question
What is the range of possible sizes for side x? One Side is 8.5 the other is 8.0.
Solution
With the logical assumption that the three sides are to form a triangle
Let the two sides given be y and z
And the angle between y and z be θ
The angle θ can take on values from 0° to 180° without reaching either values.
As θ approaches 0°, (x+z) becomes close to equaling y. (x + z) < y
It can never equal y, because θ can never be equal to 0°, if a triangle is to exist.
Hence, x > (z−y)
x > 8.5 - 8.0
x > 0.5
As θ approaches 180°, x approaches the sum y+z, θ can never equal 180° if a triangle is to exist, so x never equals (y+z).
Hence x < (y+z)
x < 8 + 8.5
x < 16.5
Hope this Helps!!!
solve the equation 12x+6y=24 for x ? i need help
Answer:
x= -1/2y+2
Step-by-step explanation:
Let's solve for x.
12x+6y=24
Step 1: Add -6y to both sides.
12x+6y+−6y=24+−6y
12x=−6y+24
Step 2: Divide both sides by 12.
12x
12
=
−6y+24
12
x=
−1
2
y+2
Answer: x= -1/2y+2
Hope this helps.
Answer:
x=2−y/2
Step-by-step explanation:
which type of graph would you use to show the number of candy bars collected by each trick or treater in the neighborhood
Answer:
bar graph
Step-by-step explanation:
y axis = number of kids
X axis = types of candy bars
Sparkle Cleaners uses 2/3 of a jug of window cleaner in 3 weeks. How much window cleaner do they use in 1 week?
Answer: 2/9th of a bottle
Step-by-step explanation:
2/3 of a jug = 3 weeks
1 week =( 1 x 2/3) / 3
= 2/3 x 1/3 = 2/9
They use 2/9 of a jug of window cleaner in 1 week.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now it is given that,
Cleaner used = 2/3 of a jug
Number of weeks = 3
So, Cleaner used in 1 week = Cleaner used / Number of weeks
⇒ Cleaner used in 1 week = (2/3) / 3
⇒ Cleaner used in 1 week = 2/9 of a jug
Thus,they use 2/9 of a jug of window cleaner in 1 week.
To learn more about fractions:
brainly.com/question/445498
#SPJ2
What is the value of | -9 | ?!!!!
Answer:
9
Step-by-step explanation:
Step-by-step explanation:
|-9|=9
..
because inside | | numbers are always positive
Which Function is shown in the Graph?
Answer:
A is the correct answer
Step-by-step explanation:
Hope i helped :)
Sphere A has a radius of 24 centimeters, and sphere B has a diameter of 42 centimeters. The radius of sphere A is
multiplied by what factor to produce the radius of sphere B?
0을
o
Noo
100
Na
If you were to roll one die, one time what is the probability it will land on a number other than 3?
Answer:
3
Step-by-step explanation:
Answer:
1/6 (16.667%)
Step-by-step explanation:
there is six sides on on the dice. So there is only one side of the dice that has the number 3. 1/6 is the probability.
what is the solution for x^2 +14x +15
Step-by-step explanation:
the solution are
x = 1 or x = -15
x^2 + 14x - 15 =0
x^2 + 14x = 15
to write the left hand side as a perfect square we add 49 to both sides :
x^2 + 14x + 49 = 15 + 49
x^2 + 2.x.7 + 7^2 = 64
using the identity (a^2 + b^2) = a^2 + 2ab + b^2
(x + 7)^2 = 64
x + 7 = √64 or x + 7 = -√64
x = 8 - 7 or x = - 8 - 7
= 1 = - 15
A bag contains 4 red marbles, 2 blue marbles, 1 purple marble, and 3 green marbles.
If a single marble is pulled out of the bag, how many outcomes are in the sample space?
Answer:
10 outcomes
Step-by-step explanation:
The number of outcomes is the number of marbles in the bag since we are taking out one marble
4+2+1+3 = 10
There are 10 outcomes
Answer:
10 Thank you Person above me I knew the answer but I am saying thank you because my cousin is happy that you showed your answer to them and answered for them Have a good day or a good life hopefully life don´t do bad things in life
Step-by-step explanation:
8. Simplify the rational expression.
3x-27
3x + 3
Answer:
below
Step-by-step explanation:
3(x-9)
3(x+1)
divide by a gcf and place it outside the parenthesis.
Mr. Toshiro manages a company that supplies a variety of domestic and imported nuts to supermarkets. He received an order for 120 bags of cashews, 310 bags of walnuts, and 60 bags of Brazil nuts. The prices per bag for each type are $29, $18, and $21, respectively. Represent the number of bags ordered and the cost as vectors.
Answer:
n = 120i + 310j + 60k
p = 29i + 18j + 21 k
Total cost = $10,320
Step-by-step explanation:
Let n and p represent the vectors for number of products and prices respectively.
Also, the coordinates i,j and k represent cashews, walnut and Brazil nut respectively.
The vector form of the total number of bags ordered and the cost are;
n = 120i + 310j + 60k
p = 29i + 18j + 21 k
We can obtain the total cost by obtaining the dot product of the two vectors.
Total cost = n.p = (120i + 310j + 60k).(29i + 18j + 21 k)
C = 120×29 + 310×18 + 60×21
C = $10,320
What is the y-coordinate of the point that divides the directed
line segment from J to K into a ratio of 2:3?
K(8,11)
J(-3,1)
*7
*-6
*5
*-5
Answer:
(D)5
Step-by-step explanation:
Given the point J(-3,1) and K(8,11).
The line segment that divides the segment from J to K in any given ratio can be determined using the formula.
[tex]P(x,y)=\left(\dfrac{mx_2+nx_1}{m+n} ,\dfrac{my_2+ny_1}{m+n}\right)[/tex]
In the given case:
[tex](x_1,y_1)=(-3,1), (x_2,y_2)=(8,11)[/tex], m:n=2:3
Since we are to determine the y-coordinate of the point that divides JK into a ratio of 2:3, we have:
[tex]\dfrac{my_2+ny_1}{m+n}=\dfrac{2*11+3*1}{3+2}\\\\=\dfrac{22+3}{5}\\\\=\dfrac{25}{5}\\\\=5[/tex]
The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.
The correct option is D.
Answer:
The answer is actually C(5) not D
Step-by-step explanation:
PLZ HELP ME
The graph shows the solution to which system of inequalities?
A) y < -2x + 4 and y < 2x + 4
B) y < -2x + 4 and y ≤ 2x + 4
C) y > -2x + 4 and y ≤ 2x + 4
D) y ≤ -2x + 4 and y ≤ 2x + 4
Answer:
see below
Step-by-step explanation:
The shading is below the line in both cases. The dashed line has negative slope, so the inequality associated with it is ...
y < -2x +4 . . . . . . note that the < symbol has no "or equal to"
The solid line has positive slope, so its inequality is ...
y ≤ 2x +4
Both these inequalities are found in choice B.
Question 3 (1 point)
What is the value of x in the equation 8+4 = 2(x - 1)?
a
11/2
b
13/2
c
5
d
7
Answer:
D. 7
Step-by-step explanation:
(8+4) = 2(x-1) multiply (x-1) by 2
(8+4) = 2x-2 add 8 and 4
12 = 2x-2 add 2 on both sides
14 = 2x divide both sides by 2
7 = x