Answers
Given:
The figure of triangle GHI and a circle M inscribed in the triangle.
To find:
The perimeter of the triangle.
Solution:
We know that the lengths of the tangent on a circle from same exterior point are always equal.
[tex]JH=HK[/tex] (Tangent from point H)
[tex]6x-11=2x+9[/tex]
[tex]6x-2x=11+9[/tex]
[tex]4x=20[/tex]
Divide both sides by 4.
[tex]x=\dfrac{20}{4}[/tex]
[tex]x=5[/tex]
Now,
[tex]JH=6x-11[/tex]
[tex]JH=6(5)-11[/tex]
[tex]JH=30-11[/tex]
[tex]JH=19[/tex]
In the same way,
[tex]GJ=GL[/tex] (Tangent from point H)
[tex]IK=IL[/tex] (Tangent from point H)
From the figure, it is clear that,
[tex]IL=GI-GL[/tex]
[tex]IL=40-GJ[/tex]
[tex]IL=40-23[/tex]
[tex]IL=17[/tex]
The perimeter of the triangle GHI is:
[tex]Perimeter=GH+HI+GI[/tex]
[tex]Perimeter=(GJ+HJ)+(HK+IK)+(GL+IL)[/tex]
[tex]Perimeter=(23+19)+(19+17)+(23+17)[/tex]
[tex]Perimeter=118[/tex]
Therefore, the perimeter of the triangle GHI is 118 units.
Related Questions
After 7 examinations Jordeen's average mark was 62. Her next result increased her average to 64. What was the next mark?
Answers
Answer:
Step-by-step explanation:76
ayme built a box in the shape of a rectangular prism with the dimensions shown. What is the volume of the box, in cubic inches? A rectangular prism has a length of 8 inches, a width of 2 inches, and a height of 4 inches. Use the formula V = l w h, where V represents the volume, l represents the length, w represents the width, and h represents the height. Inches cubed
Answers
Answer:
[tex]64(in)^{3} [/tex]
Step-by-step explanation:
The volume of a box is equal to the length l times the width w times the height h.
[tex](lenght) \times (width) \times (height)[/tex]
Substitute the values of the length l=8, the width w=2, and the height h=4 into the formula.
[tex]8 \times 2 \times 4[/tex]
Multiply 8 by 2.
[tex]16 \times 4[/tex]
Multiply 16 by 4.
[tex]64 {in}^{3} [/tex]
Hence, the volume of the rectangle prism is 64(in)³.
Answer:
64 in³Step-by-step explanation:
Given dimensions:
l = 8 inw = 2 inh = 4 inVolume of the prism is:
V = lwhV = 8*2*4 = 64 in³there are 96 boys and 120 girls in grade 9. write down the ratio of the number of boys to the number of girls in the class.
Answers
Step-by-step explanation:
96/120=8/12
=2/3
ratio of boys to girls in the class
=2:3
What is 73 as a decimal?
Answers
Answer
Step-by-step explanation:
What is the solution of the equation 3/4x + 5 = -9 ?
Answers
Answer:
x = -56/3
And that will be ur answer
Anyone know What 4/3 divided by 16 is
Answers
Answer:
1/12
Step-by-step explanation:
That's the same as
4/3 * 1/16
3 x 16 = 48
4/48
simplify
1/12
Answer:
4/3 divided by 16 is 0.0833333333333
Step-by-step explanation:
Difference in the 2 in 92.5 and the 4 in 8.49
Answers
Step-by-step explanation:
Raja Dilip aashram Mein Gaye
15f=45 find the variable
Answers
15f = 45
/15 /15
F = 3
Does anyone know what the answer
Answers
Angle DBC is 51 degrees
Good luck
if these two shapes are similar, what is the measure of the missing length X?please answer i’ve been doing IXL for 3 hours
Answers
11 (4) + 33
Help pls
Answers
Answer:
11 (4) + 33
= 11 × 4 + 33
= 44 + 33
= 77
Answer:
77
Step-by-step explanation:
11(4)+33=? Multiply 11 by 4 [when a number is in parentheses it means to multiply it by the number in front of it]
44+33=77
PLEASE HELP ME ASAP WITH WORK!! I WILL GIVE BRIANLIEST!!
Ba) Xander needs to collect at least 120 cans for a food drive to earn
community service credit. He has already collected 64 items. Write and
solve an inequality to represent the number of cans, c, that Xander must
still collect.
8b) describe the graph of the solution set for the question above. Be sure to describe the circle and tell the direction on the arrow
Answers
Answer:
he needs to collect at least 56 more
Step-by-step explanation:
c+64[tex]\geq[/tex]120
c[tex]\geq[/tex]120-64
c[tex]\geq[/tex]56
Answer:56 more
Step-by-step explanation:
A pat check Math. This is a assignment
Answers
The sum of 42 and x is equal to 97.45. What's the equation for the sentence?!! Help!
Answers
Answer:
X = 97.45 - 42
Step-by-step explanation:
If 42 + X = 97.45, X needs to be 97.45 - 42
you can do the same thing with smaller numbers, for example:
5 + X = 7
7 - 5= 2 and you can check for sure that this is the answer by adding them together 5 + 2= 7 so it's definitely the right answer
so for this question, 97.45- 42 = 55.45 so that's X
you can check that by 55.45 + 42 and if the answer is 97.45 that's the right answer!
I hope that makes sense
f(x)= -2x^2+3x-7, calculate the average rate of change on the interval [1, 1+h]
Answers
Answer:
[tex]Rate = -2h-1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = -2x^2 + 3x - 7[/tex]
[tex]Interval: [1,1+h][/tex]
Required
The average rate of change
This is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
Where:
[tex][a,b] = [1,1+h][/tex]
So, we have:
[tex]Rate = \frac{f(1+h) - f(1)}{1+h - 1}[/tex]
[tex]Rate = \frac{f(1+h) - f(1)}{h}[/tex]
Calculate f(1+h) and f(1)
[tex]f(x) = -2x^2 + 3x - 7[/tex]
[tex]f(1) = -2 * 1^2 + 3 * 1 - 7 = -6[/tex]
[tex]f(1+h) = -2 * (1+h)^2 + 3 * (1+h) - 7[/tex]
Evaluate squares and open bracket
[tex]f(1+h) = -2 * (1+h+h+h^2) + 3+3h - 7[/tex]
[tex]f(1+h) = -2-2h-2h-2h^2 + 3+3h - 7[/tex]
[tex]f(1+h) = -2-4h-2h^2 + 3+3h - 7[/tex]
Collect like terms
[tex]f(1+h) = -2h^2-4h +3h-2+ 3 - 7[/tex]
[tex]f(1+h) = -2h^2-h-6[/tex]
So, we have:
[tex]Rate = \frac{f(1+h) - f(1)}{h}[/tex]
[tex]Rate = \frac{-2h^2-h-6 - -6}{h}[/tex]
[tex]Rate = \frac{-2h^2-h-6 +6}{h}[/tex]
[tex]Rate = \frac{-2h^2-h}{h}[/tex]
Factorize the numerator
[tex]Rate = \frac{h(-2h-1)}{h}[/tex]
Divide
[tex]Rate = -2h-1[/tex]
The perimeter of the figure below is 219.1 cm. Find the length of the missing side.
14.6 cm
15-5 cm
15-5 cm
15.5 cm
15.5 cm
15-5 cm
15-5 cm
15-5 cm
15-5 cm
32 cm
32 cm
?
Answers
Answer:
16.5
Step-by-step explanation:
Adam thinks of a number.
He multiplies it by 8, adds 6 and then divides it by 2.
He ends up with 131.
What was the number he started with?
Answers
The number Adam started with is 32.He ends up with 131.
Let's denote the number Adam started with as "x." After multiplying by 8, we have 8x.
He adds 6 to the result.
The expression becomes 8x + 6.
He divides the result by 2.
The expression becomes (8x + 6) / 2.
The final result is 131.
Setting up the equation:
(8x + 6) / 2 = 131
To find x, we can solve this equation.
Multiplying both sides by 2:
8x + 6 = 262
Subtracting 6 from both sides:
8x = 256
Dividing both sides by 8:
x = 32
Therefore, the number Adam started with is 32.
To know more about number click here:
https://brainly.com/question/17480172
#SPJ2
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
∠KJL and ∠KJG
Step-by-step explanation:
Write the equivalent fraction with a denominator of 100.
What number will go in the numerator? 9/10=
1) 10
2) 50
3) 90
Answers
Answer:
90/100
Step-by-step explanation:
Hope this helps you...
Answer:
9/10 = 9×10/10×10 = 90/100
3) 90
In the image above x=4 cm and y=8 cm. Find the surface area of the figure. (Note: Figure is not to scale.)
Answers
Answer:
96
Step-by-step explanation:
4×8×3=96 is the surface area
Find how many quarts of 5% butterfat milk and 2% butterfat milk should be mixed to yield 45 quarts of 3% butterfat milk.
The mixture should contain quarts of the 5% butterfat milk.
Answers
Answer:
It would take 4 quarts of 5% buttermilk and 41 quarts of 2% buttermilk to make 45 quarts of 3% buttermilk.
Step-by-step explanation:
Let the number of 5% quarts = x
Let the number of 2% quarts = y
x+y=45
y=45-x
(.05)x+(.02)y=(0.03)45
5x+2y=102
5x+2(45-x)=102
5x+90-2x=102
3x=12
x=4
y=45-x=45-4=41
So it would take 4 quarts of 5% buttermilk and 41 quarts of 2% buttermilk to make 45 quarts of 3% buttermilk.
What is the arithmetic mean of the following numbers?
8, 1, 2, 6, 1, 4
Answers
Answer:
mean = 8+1+2+6+1+4= 22÷ 6 (the total number of digits )
= 3.606
Answer:
Mean = 8+1+2+6+1+4 = 22÷6( The total number of digits)
= 3.606
has a $50 bill and wants to buy a pair of shoes for $48. If the sales tax is 6% how much more does she need to buy the shoes?
Answers
Answer:
He will ned 1 dollar more
Step-by-step explanation:
50x.06=3 so that is the sales tax subtract it by 2 and he will need 1 more dollar
Answer:
He would be off 88 cents.
It would take ___ hours to drive 240 miles from Boston to New York, if one drives at a constant speed of 40 mph.
Answers
Answer:
6 hours.
Step-by-step explanation:
To find how many hours it would take to drive a 240 mile distance at a constant speed of 40 miles per hour, you'd divide 240 by 40 and the result of that is 6.
Answer:
6 hours
Explanation:
240/40= 6
How many times larger than
(8 + 22) is 8 x (8 + 22)?
Answers
Answer:
8
Step-by-step explanation:
8+22 = 30
In order to solve 8 • (8+22), we'll need to use the order of operations. First, complete what is in parenthesis.
8 • (8+22)
30
Then, multiply 30 by 8.
30 • 8 = 240.
So, you can then divide to find your answer. If you divide 240 by 30, you will find that 8 • (8+22) is 8 times larger than 8+22.
Answer:
8 times larger
Step-by-step explanation:
PLEAS HELP ASAP :)))))
Answers
Answer:
18 inches
Step-by-step explanation:
54*1/3=18(inches)
Assume that you have obtained a sample mean of 56 Pa, a test statistic of -2.02 and a p-value of 0.095. Which of the statements below are correct interpretations of the p-value?
a. There is a 9.5% chance of making a mistake by rejecting the null hypothesis of the mean elasticity being as per design specification.
b. Assuming the mean elasticity is as per design specification, the probability of observing a sample mean as small or smaller than 56 Pa is 0.095.
c. Assuming the mean elasticity is as per design specification, the probability of observing a sample mean as large or larger than 56 Pa is 0.095.
d. Assuming the mean elasticity is as per design specification, the probability of obtaining a test statistic as small or smaller than -2.02 is 0.095.
e. Assuming the mean elasticity is as per design specification, the probability of obtaining a test statistic as large or larger than -2.02 is 0.095.
f. There is a 0.095 probability that the results are due to chance.
g. None of the above.
Answers
Answer:
options : B and D
Step-by-step explanation:
Given that the sample mean = 56 pa , test statistic = -2.02 and the p-value = 0.095 . the correct statements about the interpretations of the p- value are :
Assuming the mean elasticity is as per design specification, the probability of observing a sample mean as small or smaller than 56 Pa is 0.095. Assuming the mean elasticity is as per design specification, the probability of obtaining a test statistic as small or smaller than -2.02 is 0.095.help pls what is 4.05 × 0.8
Answers
Answer:
3.24
Step-by-step explanation:
character requirement
Answer:
3.24
Step-by-step explanation:
You could have used a calculator my dude. XD
Thirty students are at soccer practice. Each group of three students needs a soccer ball and two field cones . How many balls and cones are needed in all? balls ___. cones ____.
Answers
Answer:
10 soccer balls
20 cones
Step-by-step explanation:
30/3=10 groups
10*2=20
Plz help me with this it’s really important
Answers
Answer:
axis of symmetry is 2
vertex is (2,-4)
Step-by-step explanation:
I hope this helps.