1.What is the value of x?
2.What is the value of x?
Enter your answer as a decimal.
3.What is the value of x?
4.What is the value of x?
5.The area of a right triangle is 210 in². The height of the right triangle is 35 in.
What is the length of the hypotenuse of the right triangle?
Enter your answer in the box.
Answers
Let p = distance from V to Y
By the angle bisector theorem, we can form the proportion
VT/VY = TK/KY
57/p = 129.2/68
57*68 = p*129.2
3876 = 129.2p
3876/129.2 = 129.2p/129.2
30 = p
p = 30
Use the value of p to find x
x = VY+YK
x = p+68
x = 30+68
x = 98
Answer: 98 mm
===========================================
Problem 2)
The triangles are similar, so we can form a proportion of the corresponding sides
MN/MA = MP/MB
67.2/(67.2-32) = 81.9/x
67.2/35.2 = 81.9/x
67.2*x = 35.2*81.9
67.2*x = 2882.88
67.2*x/67.2 = 2882.88/67.2
x = 42.9
Answer: 42.9 meters
===========================================
Problem 3)
Similar to problem 1, we use the same theorem
EG/GD = EH/HD
44.8/(x+4) = 56/35
44.8*35 = 56(x+4)
1568 = 56x+224
1568-224 = 56x+224-224
1344 = 56x
56x = 1344
56x/56 = 1344/56
x = 24
Answer: 24 millimeters
===========================================
Problem 4)
We'll use a similar idea used in problem 2
9/(9+72) = (3x-20)/((3x-20)+56)
9/81 = (3x-20)/(3x+36)
1/9 = (3x-20)/(3x+36)
1*(3x+36) = 9(3x-20)
3x+36 = 27x-180
3x+36+180 = 27x-180+180
3x+216 = 27x
3x+216-3x = 27x-3x
216 = 24x
24x = 216
24x/24 = 216/24
x = 9
Answer: 9 centimeters
===========================================
Problem 5)
Area of triangle
A = 0.5*b*h
Plug in A = 210 and h = 35; solve for b
A = 0.5*b*h
210 = 0.5*b*35
210 = 0.5*35*b
210 = 17.5*b
12 = b
b = 12
Now use the base and height to find the hypotenuse
a^2 + b^2 = c^2
h^2 + b^2 = c^2
35^2 + 12^2 = c^2
1369 = c^2
c^2 = 1369
sqrt(c^2) = sqrt(1369)
c = 37
Answer: 37 inches
The base of the triangle is calculated to be 12 inches using the area and height. Then, through the Pythagorean theorem, the hypotenuse is found to be approximately 36.06 inches.
Explanation:The subject of the question is related to the calculation of a triangle's hypotenuse using the area and height of a right triangle. Given that the area of a triangle is calculated by halving the product of the base and the height (Area = 1/2 * base * height), we can use the given area to find the base of the right triangle.
First, we call the base of the triangle 'x'. The area is 210 square inches and the height is 35 inches.
We rearrange the formula for the area of a triangle to find 'x' as follows: base = (2*Area) / height.
Our calculation then becomes x = (2*210) / 35. This simplifies to x = 12 inches.
Next, we use the Pythagorean Theorem, that states: a² + b² = c², where 'c' represents the hypotenuse. Here, 'a' is the base found (12 inches), 'b' is the height (35 inches), and 'c' is the hypotenuse we're seeking.
Plugging the values into the theorem, we get c = √(12² + 35²). Hence, the hypotenuse of the right triangle is approximately 36.06 inches.
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Related Questions
Which reason supports the true statement that angle1 and angle8 are supplementary?
m || n with
transversal t
Answers
Hope this helps!!
Line t is called a transversal line, because it intersects 2 parallel lines.
t divides the straight angle formed by m alone, forming the linear pair of angles (1) and (8), whose sum is 180 °, that is they are supplementary.
Answer: (1) and (8) are linear pairs
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains
4
liters of natural oil for every
5
liters of synthetic oil. If
296
liters of natural oil are used, how many liters of Petrolyn oil will be made?
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What is the length of hn¯¯¯¯¯¯ ? segment a n with point h between a and n. congruency markings on segment a h and segment h n. segment a n is labeled as being 38 units long enter your answer in the box?
Answers
Answer:
The length of HN is 19 unit.
Step-by-step explanation:
Consider the provided information:
It is given that the length of line segment AN is 38 units.
Now consider figure 1:
It is given that the point H is in between A and N. Also with the concurrency markings on segment AH and segment HN.
Therefore, the length of the segment AH = HN
AH + HN = AN
Consider the length of AH = HN = x
Therefore,
[tex]x+x=38[/tex]
[tex]2x=38[/tex]
[tex]x=\frac{38}{2}[/tex]
[tex]x=19[/tex]
Hence, the length of HN is 19 unit.
Matt paid 55$ at a restaurant. the amount included a 10% tip. What was the check amount before the tip?
Answers
As 50 + 5 (10% of $50) = $55.
Workmen used 5/8 of a pallet of pavers to build 5 steps leading up to the mansion. Each step they built was the same size. How many pallets did they use for each step?
Answers
= = 5/8 * 1/5 = 5/10 = 1/8 answer
The picture is the answer i forgot it last time
Answers
because (4, -6) is true, and it lies on both lines, which makes both equations true
hope this helps
What do you do to check whether a number is rational or irrational? In your explanation, use an example of an irrational and rational number.
Can someone check my answer, please? I would deeply appreciate it.
"Rational numbers are numbers that can be written in fraction form. The numbers are all integers. Irrational numbers are numbers that cannot be written as a fraction. They are non-repeating and nonterminating decimals. For example 6.12385546972578945213666479952145412639854845256987452874526874125874........ Is an irrational number. And 1/6, 2,9, and 3/4 are all rational numbers."
Answers
Circle K has a diameter of 24 inches. Find the exact length of semicircle HJI. In your final answer, include all of your calculations.
Answers
First find the circumference: [tex]c = 2\pi\r[/tex]
r = radius = 24/2 = 12
Now plugin 12 for r
[tex]c = 2\pi\r[/tex]
[tex]c = 2\pi12[/tex]
Now solve
[tex]c = 2\pi12[/tex]
Now divide in half
[tex]c = 2\pi12 = 75.398[/tex]
[tex]sim-c = \frac{2\pi12}{2} = 37.6991 [/tex]
OR
[tex]sim-c = \frac{75.398}{2} = 37.6991 [/tex]
Answer:
12 π inches
Step-by-step explanation:
1) Since semicircles = 180 degrees, semicircle HJI = 180 degrees.
2) Make a ratio: 180/360. Simplify it: 1/2.
3) Then do: 1/2 x π d --> 1/2 x π 24. You should get: 12 π.
4) So, the exact length of semicircle HJI = 12 π inches.
(The reason you are supposed to leave it 12 π centimeters is because only if the question asks you to find the approximate length of the arc, then you can use 3.14 instead of π. But if the question asks you to find the exact length of the arc, you have to leave it as said above because you would still have to round the answer (if you multiply 12 by pi), which makes it an approximate answer, not an exact answer.)
pi (π) = 3.14159265359......................
Pi is an endless number.
Hope this helps! :)
Rita and Tina each make $11 an hour working as cashiers at a supermarket. Last week, Rita worked r hours while Tina worked t hours. Rita also worked overtime hours during the week, for which she was paid an extra $32 flat wage. Which expressions represent the total weekly wages of both Rita and Tina? Rita and Tina's total weekly wages can be represented as 11(r)(t) + 32 (11r + 32) + 11t (11t + 32r) + 11r , 11(r + t) + 32 11(r + t) + 32r 11(rt) + 32 , or 11r + 11t + 32 11rt + 32 11r + 32t + 11
Answers
Rita's Total Wages = 11r + 32
Tina's Total Wages = 11t
write the multiplier or divisor for each pair of equivalent fractions 1/4 = 7/28
Answers
the multiplier or divisor for the equation is 7
if we divide to each pair of equation with 7 equation we get the same answer
like when we 7 is divisor in 1 / 4 we get the answer 1/ 28
and with 7/ 28, we also get the answer 1 / 28
and the when we multiply 7 with 1/4 we get the answer 7/4 and with 7 /28, also the answer is 7/4.
What is 1507 million in standard form?
Answers
One billion, five hundred seven million
Answer:
1,507,000,000
Step-by-step explanation:
We are asked to write 1507 million in standard form.
We know that 1 million equals 1,000,000.
To convert 1507 million in standard form, we will multiply 1507 by 1,000,000 as shown below:
[tex]\text{1507 million in standard form}=1507\times 1,000,000[/tex]
[tex]\text{1507 million in standard form}=1,507,000,000[/tex]
Therefore, 1507 million in standard form would be 1,507,000,000.
Given that cosθ = - and θ is in the second quadrant, find cscθ.
Answers
= 144/169+sin²x=1. Subtracting 144/169 from both sides, we get 25/169=sin²x. Square rooting both sides, we get 5/13 as sinx (since √25=5 and √169=13,as well as that it's in quadrant 2 - if it was in quadrant 3 or 4, it would be -5/13). Since cscx=1/sinx, we can plug (5/13) in for sinx to get 13/5 as our answer
Given: E is the midpoint of DF
Prove: 2DE = DF
Answers
Since it's half that means DE and EF have the same length.
Therefore DE multiplied by 2 is DF.
Considering DF is the full length.
Answer:
2DE = DF.
Hence Proved.
Step-by-step explanation:
Given : E is the midpoint of DF.
To Prove : 2DE = DF
Proof :
We have given a line DF .
D____________F.
Mid point = E
Mid point : It is that point that divide the line in to two equal parts .
D______E______F.
So, DE = EF.
We can say DE= [tex]\frac{1}{2}DF[/tex].
On multiplying both sides by 2.
2DE = DF.
Hence Proved.
Therefore, 2DE = DF.
Hence Proved.
88,999 Round to the nearest ten thousand
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90,000.
Storage rack hold 22 DVDs for 21$ how much would it cost to hold 127
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paige deposited $490.28 in a savings account that earns 3.7% simple interest. what is paige’s account balance after eleven years
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Hope I helped :)
If the absolute value of a nonzero real number is equal to the opposite of the number, the number is __________.
positive
negative
zero
irrational
Answers
For example, the absolute value of -5 is +5 or just 5. This means the distance from -5 to 0 on the number line is 5 units. We can write it as |-5| = 5.
The general rule being used is
|x| = -1*x = -x
only if x < 0; otherwise |x| = x
(5ab-4a-6)-(4ab-1) find the sum please fast
Answers
We need to get rid of expression parentheses.
If there is a negative sign in front of it,
each term within the expression changes sign.
Otherwise, the expression remains unchanged.
Numerical 'like' terms will be added. There is only one group of like terms
the answer is: ab-4a-5
binomial ( 5x - y ) ^ 10 terms ax ^ 2 y ^8
Answers
now, how do we get the coefficients? well, the first coefficient is 1, any subsequent is " the product of the current terms's coefficient and the exponent of the first element, divided by the exponent of the second element in the next term", now that's a mouthful, but for example,
how did get 210 for the 5th expanded term? well is just 120 * 7 / 4
how about 252 of the 6th term? 210 * 6 / 5.
how about 45 of the 9th one? 120 * 3 / 8.
of course, the exponents for each is simple, as you'd already know from the binomial theorem.
so, just expand away the 9th expanded term.
The amount of jen's monthly phone bill is normally distributed with a mean of $76 and a standard deviation of $9. what percent of her phone bills are between $49 and $103
Answers
Approximately 99.73% of Jen's phone bills are between $49 to $103. This is calculated by transforming the prices into z-scores regarding the normal distribution and then checking these z-scores in a standard normal distribution table.
Explanation:The problem is a question about the normal distribution. Using the properties of a normal distribution, we can solve it as follows:
First, transform the phone bill amounts into z-scores. The z-score is the number of standard deviations from the mean.For $49, the z-score is (49 - 76) / 9 = -3.For $103, the z-score is (103 - 76) / 9 = 3.Next, look up these z-scores in a standard normal distribution table or use a calculator that can calculate areas under the normal distribution.The table or the calculator will give you the percent of all observations falling below these two scores.The area to the left of z = 3 (or to the right of z = -3) is about 99.865%, and the area to the left of z = -3 is about 0.135%. Finally, subtract the percentages to get the percent of phone bills between $49 and $103.This is 99.865% - 0.135% = 99.73%.In conclusion, about 99.73% of Jen's phone bills are between $49 and $103.
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99.74% of Jen's monthly phone bills are between $49 and $103.
To answer this question, we need to understand the properties of the normal distribution. For a normally distributed variable with a mean (μ) of $76 and a standard deviation (σ) of $9, we can use the Z-score formula:
[tex]Z = \frac{(X - \mu)}{\sigma}[/tex]
We now convert $49 and $103 to Z-scores:
For $49:
[tex]Z = \frac{(49 - 76)}{9} = -3[/tex]
2. For $103:
[tex]Z = \frac{(103 - 76)}{9} = 3[/tex]
Next, we use the Z-table to find the probabilities corresponding to these Z-scores:
For Z = -3, the probability is 0.0013 (or 0.13%)
For Z = 3, the probability is 0.9987 (or 99.87%)
To find the percentage of phone bills between $49 and $103, we subtract these values:
[tex]P(49 < X < 103) = 0.9987 - 0.0013 = 0.9974[/tex]
Finally, converting this to a percentage, we get:
[tex]0.9974 \times 100\% = 99.74\%[/tex]
Therefore, 99.74% of Jen's monthly phone bills are between $49 and $103.
Factor the expression -24x+32
Answers
-8 (3x-4)
How many times can 167 go into 1135.
Answers
Good luck! :D
Find an equation of the circle that satisfies the given conditions:
Endpoints of a diameter are P(-1,3) and Q(7,-7)
Answers
A snowmobile traveled 32 miles in 2 1/3 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the snowmobile? Enter your answer in the box.
Answers
divide 32 miles by 2 1/3 hours
32/2.33333 = 13.7143
to nearest tenth = 13.7 miles per hour
Answer: [tex]13.7\text{ miles per hour}[/tex].
Step-by-step explanation:
Given : A snowmobile traveled 32 miles in [tex]2\dfrac{1}{3}[/tex] hours i.e.[tex]\dfrac{7}{3}[/tex] hours.
The distance is the product of the rate and the time.
i.e. The formula we use to find the average speed is given by :-
[tex]\text{Average Speed}=\dfrac{\text{Distance}}{\text{Time}}\\\\\Rightarrow\ \text{Average Speed}=\dfrac{32}{\dfrac{7}{3}}=\dfrac{32\times3}{7}=13.7142857143\approx13.7\text{ miles per hour}[/tex]
Hence, the average speed of the snowmobile was [tex]13.7\text{ miles per hour}[/tex].
How do I do this? Due tomorrow please help
Answers
first, you need to get rid of the denominators to ease up calculations. you can do that by miltiplying all terms by 12 (which is the result of 3x4)
so the experession now becomes:
8+12y=3
12y=3-8
12y=-5
y= -5/12
Which of the following is not true regarding sets of numbers?
A-All rational numbers are integers.
B-All whole numbers are rational numbers.
C-All irrational numbers are real numbers.
D-All integers are rational numbers.
Answers
Answer:
A:All rational numbers are integers
Step-by-step explanation:
We are given that a set of numbers
We have to find not true statement about the regarding set of numbers
We know that all integers are rational number but all rational number .
are not integers.
All whole numbers are rational number but all rational number are not whole numbers.
All irrational numbers are real numbers but all real numbers are not irrational numbers.
Hence, option A is true.
Answer:All rational numbers are integers.
Simplify (-2n - 7n4 + 7n3) - (-2n4 - 6n3 + 6n)
Answers
The simplification of the given algebraic expression is -8n -5n^4 + 13n^3 by combining like terms.
Explanation:The simplification of (-2n - 7n4 + 7n3) - (-2n4 - 6n3 + 6n) involves combining like terms and subtraction. First, change the signs of each term in the second parentheses due to the negative sign in front of the parentheses. This becomes: -2n - 7n4 + 7n3 + 2n4 + 6n3 - 6n. Now, combine like terms to simplify: (-2n - 6n) + (-7n4 + 2n4) + (7n3 + 6n3). The final answer is -8n -5n4 + 13n3.
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3(20-b)=36
I need help on this question!!
Answers
60 - 3b = 36
-3b = 36 - 60
-3b = - 24
b = -24/-3
b = 8 <==
What does this mean
Answers
You have to get the R by itself
Answers
A(2L) = r/2L(2L) (multiply 2L to both sides to isolate r)
A(2L) = r is your answer
hope this helps
2L cancels itself out and the new equation is (A)(2L) = r.