The circle is inscribed in the triangle. Find the perimeter of the triangle.
A. 20 cm
B. 24 cm
C. 35 cm
D. 48 cm
Answers
The perimeter of the triangle will be 48 cm. The correct option is D.
What is a perimeter?A perimeter is the total length of the boundary or outer edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
For example, the perimeter of a rectangle is the sum of the lengths of all four sides, while the perimeter of a circle is the distance around its circumference. The perimeter is usually measured in units such as meters, centimeters, inches, or feet, depending on the context of the problem.
Whenever we have two tangents outside the circle and they are in contact with each other, it means their lengths are the same
The perimeter of the triangle will be calculated as,
Perimeter = sum of all the sides
Perimeter = ( 11 + 11 + 7 + 7 + 6 + 6 )
Perimeter = 48 cm
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Related Questions
What is the constant of proportionality in the equation 6y=3x6y=3x6, y, equals, 3, x?
Answers
6y = 3x
From here, we must clear the value of y.
We have then:
y = (3/6) x
Rewriting we have:
y = (1/2) x
The proportionality constant is:
k = 1/2
Answer:
the constant of proportionality in the equation 6y = 3x is:
1/2
Find the equation of the line whose x-intercept is 8 and y-intercept is -2. write the equation in slope-intercept form.
Answers
0-(-2)
m = ---------- = 1/4
8-0
The equation of the line is then y-0 = (1/4)(x-8), or y = (1/4)X - 2 (in slope-intercept form).
To determine the equation of the line with x-intercept 8 and y-intercept -2, the slope is calculated to be 1/4. Thus, the line's equation in slope-intercept form is y = (1/4)x - 2.
To find the equation of a line with an x-intercept of 8 and a y-intercept of -2, we'll first determine the slope of the line (m) and then use the slope-intercept form (y = mx + b).
Two points on this line are (8,0) and (0,-2). The slope (m) of a line is calculated by the change in y divided by the change in x, which in this case is
(0 - (-2)) / (8 - 0) = 2 / 8 = 1 / 4.
Now we know the slope is 1/4 and the y-intercept (b) is -2, so the equation of the line in slope-intercept form is:
y = (1/4)x - 2
A right triangle has sides measuring 5 inches, 12 inches, and 13 inches. What is the area, in square inches, of this triangle ?
Answers
a + b + c
s = -------------------
2
Then calculate A:
A = sqrt[ s(s-a)(s-b)(s-c) ]
Final answer:
The area of a right triangle with sides of 5 inches and 12 inches as the base and height, respectively, is 30 square inches, calculated using the formula A = (base × height) / 2.
Explanation:
The area of a right triangle is calculated by multiplying one-half the base by the height: A = (base × height) / 2.
In the case of a right triangle with sides measuring 5 inches, 12 inches, and 13 inches, the 5-inch and the 12-inch sides are the legs and thus can be used as the base and height. Using the formula for the area of a right triangle:
A = (5 × 12) / 2
A = 60 / 2
A = 30 square inches
Therefore, the area of this triangle is 30 square inches.
Steve buys 14 ounces of kiwis and 2 pounds of peaches.How many more ounces do the peaches weigh then the kiwis?
Answers
2 pounds x 16 ounces = 32 ounces for the peaches.
32 ounces - 14 ounces = 18
The peaches weigh 18 more ounces.
At Martina's auto shop, it takes her 15 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Martina can do in at most 3 hours ( 180 minutes).
Answers
You want to know how much she can do in 180 minutes
She can do an oil change in 15 minutes
She can do a tire change in 18 minutes
Based on this information you can make the inequality
[tex]15x + 18y \leq 180[/tex]
The answer is [tex]15x + 18y \leq 180[/tex]
Hope this helps!
It's at most 180 minutes so left side is 'less than or equal to 180'.
Find the surface area
Answers
now the rectangles are just 4x9 each, so their area is just 6(4*9) for all 6.
the hexagons has a distance from the center perpendicular to a side of 7.8, namely the apothem is 7.8, and since each side is 9 km long, the perimeter is 9+9+9+9+9+9.
since the area of a regular polygon is (1/2)(apothem)(perimeter), we can simply get the area of those two hexagons and the area of the rectangles, sum them up, and that's the surface area of the hexagonal prism.
[tex]\bf \stackrel{\textit{6 rectangles}}{6(4\cdot 9)}~~~~+~~~~\stackrel{\textit{2 hexagons}}{2\left[ \cfrac{1}{2}(7.8)(54) \right]}[/tex]
Two angles of a triangle have the same measure and the third angle is 72degrees greater than the measure of the other two. find the measure of each angle.
Answers
The longer anger = 108 degrees.
Let me know if you would like me to explain how I got this.
Please help I really need an answer fast!!!
A, toy company manufactures arcade games. They are marketing a new pinball machine to children. It is similar in size to the adult version of the same game.
Adult pinball machine GAME with base ME measuring 35 inches and sides measuring 56 inches. Child pinball machine G prime A prime M prime E prime with base M prime E prime measuring 14 inches
If the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime? Type the numeric answer only in the box below.
Answers
first of all you need to find the missing length on the adult version.
so the work would be:
-add up all the known sides of adult so
(56+56+35)=147
-then take the total perimeter and subtract so
167-147=20
-then you need to compare the two known sides of both the adult and kids version. so that would be the bottom line EM.
They are 35 and 14 so divide
35/14=2.5
Now you know the dilation so you can figure out the missing side GA on the childs by taking the missing side from the adult dividing by the dilation 2.5 to get the answer so
20/2.5= 8
the answer is 8.
I got this correct on the quiz.
For these two rules, the second number in the ordered pair is always three times greater than the first number. If the relationship between the two numbers in each ordered pair is the same, the graph will be: Not graph-able A straight line A circle An exponential curve A parabolic curve
Answers
In how many ways can the letters of the word BANANA be rearranged such that the new word does not begin with a B?
Answers
First arrange the words in order:
AAABNN
so there are 3 A's, 1 B and 2 N's.
If there were no constraints,
Number of permutations = (3+1+2)!/(3!1!2!)=6!/(6*1*2)=720/(6*2)=60
Number of words that begin with B is to take out the B, that leaves us with
AAANN => 3 A's and 2 N's
=> 5!/(3!2!) = 120/(6*2)=10
Therefore the number of words that do NOT begin with B is
60-10 = 50 ways
Find the 12th term in the following geometric sequence. 0.75, 1.5, 3, 6, . . .
Answers
Answer:
1536
Step-by-step explanation:
Given : A geometric sequence 0.75, 1.5, 3, 6, . . .
To Find:Find the 12th term
Solution:
0.75, 1.5, 3, 6, . . .
First term =a = 0.75
Common difference = [tex]r = \frac{a_3}{a_2} =\frac{a_2}{a_1}=\frac{1.5}{0.75}=\frac{3}{1.5}=2[/tex]
nth term of G.P. = [tex]a_n=a r^{n-1}[/tex]
Where a = First term = 0.75
r = common difference = 2
Substitute n = 12
[tex]a_{12}= 0.75 (2)^{12-1}[/tex]
[tex]a_{12}= 0.75 (2)^{11}[/tex]
[tex]a_{12}= 1536[/tex]
Hence the 12th term in the geometric sequence. 0.75, 1.5, 3, 6, . . . is 1536.
From 1992 through 2007, the purchasing power of a dollar decreased by about 3.5% per a year. Using 1992, as the base for comparison, what was the purchasing power of a dollar in 2007? Formula: y=C(1−r)t
$0.48
$0.57
$0.44
$0,59
Answers
Explanation:
1) Given formula: y=C(1−r)^t
I will change t for x just due to editor limitations: y = C(1-r)ˣ
2) In that:
C =$1,
r = 3.5% = 3.5/100 = 0.035
x = t = 2007 - 1992 = 15
3) Compute
y = $1 (1 - 0.035)¹⁵ = $1 (0.965)¹⁵ = $0.586 ≈ $0.59
Answer: $0.59
An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8). Which equation represents this ellipse?
Answers
Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.
Then
a² will go with the y part of the equation
Also, since the focus is 8 units below the center, then c = 8
since the vertex is 17 units above, then a = 17
The equation b² = a² – c² gives me
b²=17²-8²-----> b²=225
the equation is
y²/a²+x²/b²=1------> y²/289+x²/225=1
the answer is
y²/289+x²/225=1
see the attached figure
Answer:
D
Step-by-step explanation:
Gina is a tour boat operator and she wants to know the mean age of all the people in her tour group.
She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34.
What is the best estimate of the mean age of all the people in the tour group?
Round to the nearest whole number.
Answers
19 + 27 + 25 + 21 + 44 + 22 + 45 + 34 = 237
237 / 8 = 29.625 = 30 years
A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex. which terms describe the degenerate conic section that is formed? select each correct answer. degenerate parabola pair of intersecting lines point line degenerate hyperbola degenerate ellipse
Answers
pair of intersecting lines
degenerate hyperbola
Answer with explanation:
It is given that, a plane intersects a double-napped cone such that the plane intersects both Nappes through the cone's vertex.It also depends on how thick or thickness of the plane:
1.We can surely say that degenerate hyperbola will be formed,whatever be the thickness of Plane.
2. Two parallel lines=pair of intersecting lines ,because both ,A double napped cone and Plane is three dimensional shape.Instead of intersecting lines ,two parallel lines which we call pair of intersecting lines, will be formed.
Which graph shows a polynomial function of an even degree?
Answers
A function is even if, for each x in the domain of f, f (- x) = f (x).
The even functions have reflective symmetry through the y-axis.
We have then that the graph that meets this definition is:
graph 1 (from left to right)
Answer:
graph 1 (from left to right)
match each graph with its corresponding equation
Answers
The graphs match the equations as follows:
Graph A: (−x+3)^2 -2
Graph B: (x−2)^2+3
Graph C : −(x+2)^2 +3
Graph D : 2(x−2)^2 +3
Equation (−x+3)^2 -2:
This equation is in the form of a quadratic function, y=a(x−h) ^2+k, where (h ,k) is the vertex of the parabola.
The vertex of the parabola is at (3,1), which matches the vertex of Graph A.
The coefficient a is negative, which tells us that the parabola opens downward.
The constant term k is −2, which tells us that the minimum value of the parabola is −2.
Equation (x−2)^2+3 :
This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h, k) is the vertex of the parabola.
The vertex of the parabola is at (2,3), which matches the vertex of Graph B. The coefficient a is positive, which tells us that the parabola opens upward.
The constant term k is 3, which tells us that the minimum value of the parabola is 3.
Equation −(x+2)^2 +3:
This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h, k) is the vertex of the parabola.
The vertex of the parabola is at (−2,3), which matches the vertex of Graph C.The coefficient a is negative, which tells us that the parabola opens downward.
The constant term k is 3, which tells us that the maximum value of the parabola is 3.
Equation 2(x−2)^2 +3 :
This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h ,k) is the vertex of the parabola.
The vertex of the parabola is at (2,3), which matches the vertex of Graph D. The coefficient a is positive and multiplied by 2, which tells us that the parabola opens upward and is stretched vertically by a factor of 2.
The constant term k is 3, which tells us that the minimum value of the parabola is 3.
Mr ong spent $960 of his salary on food and transport.He spent 1/4 of his remaining money on clothes.He then had 1/3 of his salary left.How much was his salary?
Answers
49601
43
culculate the value approximate
×11.53,51163
I hope his helps
What values for xx and yy make △MNO≅△PRT▵MNO≅▵PRT?
Triangles MNO and PRT
Answers
However, I can help you understand how to solve such problem and you can apply the explanation in the triangles you have.
Now, when writing congruent triangles, the order of the letters is very important. This is because each side/angle in the first triangle is congruent to the corresponding side/angle in the second one.
In the given, we have:
ΔMNO ≈ ΔPRT
This means that:
angle M = angle P
angle N = angle R
angle O = angle T
MN = PR
NO = RT
MO = PT
Now, to get x and y, all you have to do is make use of the above equal angles/sides.
Equate the corresponding angles/sides having the variables x and y and solve for them
Hope this helps :)
A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?
Answers
[tex]sin\left(75^{\circ} \right)=\frac{h}{60}[/tex]
[tex]h=60\cdot sin\left(75^{\circ} \right)=58\:feet[/tex]
The maximum height that the ladder can safely reach is closest to 58 feet.
Final answer:
Using trigonometry and the sine function, the maximum height that the ladder can reach when raised to a 75-degree angle with a length of 60 feet is approximately 58 feet.
Explanation:
To determine the maximum height that a fire truck ladder can safely reach when it is extended to 60 feet in length and raised to a maximum angle of 75 degrees with the horizontal, we would use trigonometry, specifically the sine function. The sine of an angle in a right triangle is equal to the opposite side (height in this case) divided by the hypotenuse (the length of the ladder).
Therefore, the maximum height (h) can be calculated using the formula:
h = Ladder Length × sin(Angle)
Where:
Ladder Length is 60 feet
Angle is 75 degrees
Plugging in our values we get:
h = 60 feet × sin(75 degrees)
Using a calculator, we find that:
sin(75 degrees) is approximately 0.9659.
Therefore:
h ≈ 60 feet × 0.9659
h ≈ 57.95 feet
The maximum height the ladder can safely reach when disregarding the height of the fire truck itself is approximately 58 feet.
The ratio of gold charms to silver charms is 1:3. Which statement does not describe the relationship?
Answers
The ratio of gold charms to silver charms is 1:3, with 1 representing the number of gold charms and 3 representing the number of silver charms. The statement that does not describe the relationship is the one that does not accurately represent this ratio.
Explanation:The ratio of gold charms to silver charms is 1:3. In this ratio, the first number (1) represents the number of gold charms, and the second number (3) represents the number of silver charms. Therefore, the statement that does not describe the relationship is the one that does not accurately represent this ratio.
Given the arithmetic sequence an = 3 + 2(n − 1), what is the domain for n?
A. All integers where n ≥ 0
B. All real numbers
C. All integers where n ≤ 1
D. All integers where n ≥ 1
Answers
One hundred employees of a company are asked how they get to work and whether they work full time or part time. The table below shows the results. If one of the 100 employees is randomly selected, find the probability of getting someone who carpools or someone who works full time.
Full time Part time
Public Transportation 7 10
Bicycle 4 3
Drive alone 30 31
Carpool 6 9
Answers
These events are not mutually exclusive, meaning they can happen at the same time. This means we use
P(A or B) = P(A) + P(B) - P(A and B)
P(carpool or full time) = P(carpool) + P(full time) - P(carpool & full time)
There are 6+9=15 people out of 100 that carpool.
There are 7+4+30+6=47 people out of 100 that work full time.
There are 6 people out of 100 that carpool and work full time.
This gives us
15/100 + 47/100 - 6/100 = 56/100
The probability of getting someone who carpools or someone who works full time is 0.36.
Explanation:To find the probability of getting someone who carpools or someone who works full time, we need to add the probabilities of the two events.
The probability of getting someone who carpools is 6/100 and the probability of getting someone who works full time is 30/100.
So the probability of either event happening is (6/100) + (30/100) = 36/100 = 0.36.
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If a rectangle measures 8 feet on the short side and 9.8 feet on the long side what is the area of the rectangle in square feet
Answers
where
[tex]A[/tex] is the area of the rectangle
[tex]w[/tex] is the width of the rectangle
[tex]l[/tex] is the length of the rectangle
Since the short side of a rectangle is the width of the rectangle, [tex]w=8ft[/tex]. Similarly, the long side a rectangle is the length of the rectangle, so [tex]l=9.8ft[/tex]. Now we can replace those values in our formula to find [tex]A[/tex]:
[tex]A=wl[/tex]
[tex]A=(8ft)(9.8ft)[/tex]
[tex]A=78.4ft^2[/tex]
We can conclude that the area of our rectangle is 78.4 square feet.
Use the graphs of f(x) =2/x and g(x)=1/-3-x to determine the solutions to f(x) = g(x).
A) (-2, -1)
B) (-2, 1)
C) (2, -1)
Answers
f(x) =2/x
and
g(x)=1/(-3-x)
we know that
the solutions to f(x) = g(x) is the intersection of both graphs
the intersection of both graphs is the point (-2,-1)
the answer is the option
A) (-2, -1)
see the attached figure
a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red
Answers
1/10 = 0.1.
The probability of choosing a red marble is 0.1, or 10%
[tex] |\Omega|=10\\
|A|=1\\\\
P(A)=\dfrac{1}{10}=10\% [/tex]
please help asap 50 pts
Answers
Steps:
1. Factor 11 out of 11g
6g^2 + 11 (g) - 35
2. Rewrite 11 as -10 plus 21
6g^2 + (-10 + 21) g - 35
3. Apply the distributive property
6g^2 + (-10g + 21g) - 35
4. Remove parentheses
6g^2 - 10g + 21g - 35
5. Group the first two and the last two terms
(6g^2 - 10g) + (21g - 35)
6. Factor out the greatest common factor from each group
2g (3g - 5) + 7 (3g - 5)
7. Factor out the greatest common factor, 3g - 5
(3g - 5) (2g + 7)
Therefore the answer is A
Answer: A. (3g - 5)(2g + 7)
If two angles are both vertical and supplementary, can we determine the angles? If so, what are they?
Answers
if A and B are vertical angles
so
angle A is equal angle B
A=B
and
if A and B are supplementary angles
so
angle A +angle B is equal to 180 degrees
A+B=180°
therefore
A=B
A+A=180-----> 2A=180-----> A=90°
the answer is
the angles are 90 degrees
Answer:
Step-by-step explanation:
45
A) how many ways can the letters in the word computer be arranged in a row?
b.how many ways can the letters of the word computer be arranged if the letters co must remain next to each other as a unit?
Answers
The are 8 total letters:
8!= 8*7*6*5*4*3*2*1
=40320
B.
The are still 8 total letters, but the 1st 2 are constants, CO. So what would scramble the remaining letters as such.
6!= 6*5*4*3*2*1
=720
Hope this helps
The permutation is defined as the arrangement number or order in which rearrangement of element in an order list.
(a) The letters in the word computer be arranged in a row is 40320.
(b) The letters of the word computer be arranged 5040 ways.
Given:
The given latter is COMPUTER.
How to find the permutation of latter?(a)
There are 8 letter in word COMPUTER. Calculate the number of ways in which we can arrange 8 letters.
[tex]8!=8\times7\times6\times5\times4\times3\times2\times1\\8!=40,320.[/tex]
Thus, the letters in the word computer be arranged in a row is
(b)
As per the question if we treat CO as a unit then there will only seven letters effective.
[tex]7!=7\times6\times5\times4\times3\times2\times1\\7!=5,040[/tex]
Thus, the letters of the word computer be arranged 5040 ways.
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Orville traveled at a speed that was twice as fast as randy, Orville traveled 240 miles in one hour less than it took randy to travel 150 miles. What were the speed and time it took for both Orville and randy?
Please answer will give brainliest
Answers
x-------> Orville speed
y-------> Randy speed
t--------> Randy time
we know that
speed=distance /time
Orville traveled at a speed that was twice as fast as randy
so
x=2y------> equation 1
speed Orville
x=240/(t-1)------> equation 2
speed Randy
y=150/t------> equation 3
substitute equation 1 in equation 2
2y=240/(t-1)------> y=120/(t-1)----------> equation 4
equate equation 3 and equation 4
150/t=120/(t-1)------> 150*(t-1)=120*t----> 150*t-120*t=150
30*t=150-----> t=5 hours
Orville speed and time
x=240/(t-1)-----> 240/(4)----> 60 miles/hour
Orville speed is 60 miles/hour
Orville time is (t-1)----> 5-1-----> 4 hour
Randy speed and time
y=150/t-----> 150/5----> 30 miles/hour
Randy speed is 30 miles/hour
Randy time is t-----> 5 hours
the answers are
a) Orville speed is 60 miles/hour
b) Orville time is 4 hours
c) Randy speed is 30 miles/hour
d) Randy time is 5 hours