Answers
➝ Hypotenuse of triangle ( a ) = 21.63 mm
➝ Hypotenuse of triangle ( b ) = 150 mm
➝ Hypotenuse of triangle ( c ) = 111.80 mm
[tex] \quad\rule{300pt}{1.5pt}\quad[/tex]
Solution:We have to find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
Pythagoras theorem states that :" In a right angled triangle, the square of hypotenuse side is equal to the sum of square of other two sides "
[tex] \qquad \bull \:{\pmb{\mathfrak{ h^2 = b^2 + p^2}}}[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
For triangle ( a )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex]
[tex] :\implies\qquad \sf{ h= \sqrt{144 + 324}}[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{468}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}}[/tex]
For triangle ( b )[tex] :\implies\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex] :\implies\qquad \sf{h =\sqrt{b^2 + p^2} }[/tex]
[tex] :\implies\qquad \sf{ h = \sqrt{(90)^2+(120)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{8100+14400}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{22500}}[/tex]
[tex] :\implies\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} }[/tex]
For triangle ( c )[tex] :\implies\qquad \sf{h^2 = b^2 + p^2 }[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{b^2 + p^2}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{(100)^2)+(50)^2}}[/tex]
[tex] :\implies\qquad \sf{ h=\sqrt{10000+2500}}[/tex]
[tex] :\implies\qquad \sf{ h =\sqrt{12500}}[/tex]
[tex] :\implies\qquad \underline{\underline{\pmb{\sf{h = 111.80mm}}} }[/tex]
Hypotenuse of triangle ( a ) = 21.63 mm
Hypotenuse of triangle ( b ) = 150 mm
Hypotenuse of triangle ( c ) = 111.80 mm
Explanation :find the length of hypotenuse in the given 3 triangles, which can be done by using Pythagoras theorem.
[tex]h^2 = b^2 + p^2[/tex]
And we have to convert the answer to the units indicated in red i.e, in mm.
Since 1cm = 10 mm, we will convert the given values of length of side in mm before putting the values in the formula
[tex]For \: \: triangle ( a )
\qquad \sf{ h^2 = b^2 + p^2}[/tex]
[tex]\qquad \sf{ h =\sqrt{b^2 + p^2}}[/tex][tex]\qquad \sf{h=\sqrt{ (12)^2 + (18)^2 }}[/tex][tex]\qquad\sf{h=\sqrt{ (12)^2 + (18)^2 }} \\ \\ \qquad \sf{ h= \sqrt{144 + 324}} \\ \\ \qquad \sf{ h = \sqrt{468}}
\\ \\\qquad\underline{\underline{\pmb{ \sf{ h = 21.63 mm}}}} \\ \\ For \: \: triangle ( b ) \qquad \sf{ h^2 = b^2 + p^2} \\ \\ \qquad \sf{h =\sqrt{b^2 + p^2} } \\ \\ \qquad \sf{ h = \sqrt{(90)^2+(120)^2}} \\ \\ \qquad \sf{ h=\sqrt{8100+14400}} \\ \\
\qquad \sf{ h =\sqrt{22500}} \\ \\\qquad\underline{\underline{\pmb{ \sf{h = 150mm}}} } \\ \\ For \: \: triangle ( c ) \qquad \sf{h^2 = b^2 + p^2 } \\ \\ \qquad \sf{ h=\sqrt{b^2 + p^2}} \\ \\\qquad\sf{ h=\sqrt{(100)^2)+(50)^2}} \\ \\\qquad\sf{ h=\sqrt{10000+2500}} \\ \\ \qquad \sf{ h =\sqrt{12500}} \\ \\
\qquad\underline{\underline{\pmb{\sf{h = 111.80mm}}} } [/tex]
Related Questions
If the area of a circular cricket ground is 15,400 m2, then find its circumference. (Take π≈22/7)
Answers
Answer:
440m^2
Step-by-step explanation:
15400/(22/7)=4900, which is r^2, so r=70. Now we can find the circumference by doing 22/7*2*70, which is 440.
Find the radius of the circle:
Area of a circle = pi x r^2
15,400 = 22/7 x r ^2
Divide both sides by 22/7
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Take the square root of bothe sides:
R = 70
The radius of the circle is 70 meters.
now find the circumference:
Circumference = 2 x pi x radius
Circumference = 2 x 22/7 x 70
Circumference = 440 meters
answer: 440 meters
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Answer:
Step-by-step explanation:
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Answers
Answer:
5 ft
Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Hey there!
5x-4<0
=> 5x < 0 + 4
=> 5x < 4
Divide both sides by 5
=> 5x/5 < 4/5
=> x < 4/5
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Graph in image
help worth a lot of pounts
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Answers
Answer:
See below.
Step-by-step explanation:
Let x = amount of money you have in your account.
The money in your account plus the $125 extra that you need equals the total cost of the computer.
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x + 125 = 2250
Now we solve the equation by subtracting 125 from both sides.
x = 2125
Answer: You have now $2125 in your account
Answer:
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answers
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Answers
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Step-by-step explanation: hope this helps
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Answers
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How are samples classified?Samples may be classified as:
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Answers
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Answers
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Answers
The volume of the figure is the amount of space in the figure
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Hence, the volume of the figure is 10488 cubic inches
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Answer:
The answer is D: 10488
Step-by-step explanation:
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Answers
Answer:
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Answer:
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Answers
Step-by-step explanation:
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HOPE it helps
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Answer:
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Hope this helps, mate!
Step-by-step explanation:
Hope this helps, mate! :)
Please show the steps as well.
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Answer:
x = 4Step-by-step explanation:
Rewrite the equation as
[tex]2^{x -1}=8\\[/tex][tex]2^{x -1}=2^3[/tex]Powers are equal if bases are same
[tex]x -1=3[/tex][tex]x=3+1[/tex][tex]x=4[/tex]~Hello! I will try to help you!
[tex] \Rightarrow \sf {2}^{x - 1} = 8[/tex]
»Convert the number 8 to a power of 2, then:-
[tex] \Rightarrow \sf {2}^{x - 1} = {2}^{3} [/tex]
»Because the bases on the right and left are the same, we will cross out the bases to produce a linear equation.
[tex] \Rightarrow \sf \cancel2 {}^{x - 1} = { \cancel2}^{3} [/tex]
»Let's find the value of x in the above equation!
[tex] \Rightarrow \sf x - 1 = 3 \\ \Rightarrow \sf x = 3 + 1 \\ \Rightarrow \bf x = 4[/tex]
With this it's done!
PLEASE HELP ASAP!!! Draw the image of the following segment after a dilation centered at the origin with a scale factor of 5/3.
Answers
How long will it take Eniola to save $5,000 if she started with $500 and found a rate of 6. 2%? Round to the nearest whole number
Answers
Answer:
38.28 years
Step-by-step explanation:
The computation of the time period is shown below:
Given that
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sue got to the library at 10:30 am.
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then she walked home.
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Answers
Answer:
he arrived at 11:05 am.....
Answer:
12:25pm
Step-by-step explanation:
10:30 + 40 minutes = 11:10
11:10 + 1hr and 15 mins = 12:25
a. Find the slope of the line that passes through these points.
The slope is
(Type an integer or a simplified fraction.)
b. Is the slope between (1,4) And (3,12) the same as the slope between (3,12) and (4,16)?
Explain.
O A. Yes. Both slopes are equal to
(Type an integer or a simplified fraction.)
O B. No. The slope between (1,4) and (3,12) is equal to (4,16)
. The slope between (3,12) and
th
Answers
slope formula : [tex]\bold{ \sf \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
a. coordinates : (3,12) and (4,16)
[tex]\sf \rightarrow \dfrac{16-12}{4-3}[/tex]
[tex]\sf \rightarrow \dfrac{4}{1}[/tex]
[tex]\sf \rightarrow 4[/tex]
b. coordinates : (1,4) and (3,12)
[tex]\sf \rightarrow \dfrac{12-4}{3-1}[/tex]
[tex]\sf \rightarrow \dfrac{8}{2}[/tex]
[tex]\sf \rightarrow 4[/tex]
⇒ A. Yes. Both slopes are equal to 4
log2 (10x+5) - log2 5 =5
PLEASE SOLVE AND SHOW WORK
THANKS A TON
Answers
Answer:
[tex]\sf x =15.5[/tex]
Step-by-step explanation:
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=5[/tex]
[tex]\sf log_2\left(10x+5\right)\:-\:log_2\:5\:=log_2 (32)[/tex]
[tex]\sf log_2\left\dfrac{(10x+5)}{5} =log_2 (32)[/tex]
[tex]\sf 2x+1 =32[/tex]
[tex]\sf 2x+1 -1=32-1[/tex]
[tex]\sf 2x =31[/tex]
[tex]\sf x =15.5[/tex]
Answer:
Step-by-step explanation:
[tex]log_{a}[/tex] [tex]x_{1}[/tex] - [tex]log_{a}[/tex] [tex]x_{2}[/tex] = [tex]log_{a}[/tex] [tex]\frac{x_{1} }{x_{2} }[/tex]
[tex]log_{a}[/tex] x = b ⇒ [tex]a^{b}[/tex] = x
~~~~~~~~~~~~~~
[tex]log_{2} (10x+5)[/tex] - [tex]log_{2} 5[/tex] = 5
[tex]log_{2} \frac{10x+5}{5}[/tex] = 5
[tex]\frac{10x+5}{5}[/tex] = [tex]2^{5}[/tex]
10x + 5 = 32 × 5
2x + 1 = 32
x = 15.5
Which expression is equivalent to 16 4 6 a x , when a > 0 and x > 0?
Answers
The expression of [tex]\sqrt{[/tex](16a^4x^6) is an algebraic expression
The equivalent expression of [tex]\sqrt{[/tex](16a^4x^6) is 4a^2x^3
How to determine the equivalent expression?The expression is given as:
[tex]\sqrt{[/tex](16a^4x^6)
Expresss 16 as the square of 4
[tex]\sqrt{[/tex](16a^4x^6) = [tex]\sqrt{[/tex](4^2a^4x^6)
Evaluate the square root of each factor in the expression
[tex]\sqrt{[/tex](16a^4x^6) = 4a^2x^3
Hence, the equivalent expression of [tex]\sqrt{[/tex](16a^4x^6) is 4a^2x^3
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A simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. What is the 90% confidence interval for the population mean? Use the table below to help you answer the question. Confidence Level 90% 95% 99% z*-score 1. 645 1. 96 2. 58 Remember, the margin of error, ME, can be determined using the formula M E = StartFraction z times s Over StartRoot n EndRoot EndFraction. 128. 75 to 147. 25 130. 98 to 145. 02 132. 10 to 143. 90 137. 38 to 138. 62.
Answers
The 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
How to find the confidence interval for population mean from large samples (sample size > 30)?
Suppose that we have:
Sample size n > 30Sample mean = [tex]\overline{x}[/tex]Sample standard deviation = sPopulation standard deviation = [tex]\sigma[/tex]Level of significance = [tex]\alpha[/tex]Then the confidence interval is obtained as
Case 1: Population standard deviation is known[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Case 2: Population standard deviation is unknown.[tex]\overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}[/tex]
For this case, we're given that:
Sample size n = 90 > 30Sample mean = [tex]\overline{x}[/tex] = 138Sample standard deviation = s = 34Level of significance = [tex]\alpha[/tex] = 100% - confidence = 100% - 90% = 10% = 0.1 (converted percent to decimal).At this level of significance, the critical value of Z is: [tex]Z_{0.1/2}[/tex] = ±1.645
Thus, we get:
[tex]CI = \overline{x} \pm Z_{\alpha /2}\dfrac{s}{\sqrt{n}}\\CI = 138 \pm 1.645\times \dfrac{34}{\sqrt{90}}\\\\CI \approx 138 \pm 5.896\\CI \approx [138 - 5.896, 138 + 5.896]\\CI \approx [132.104, 143.896] \approx [130.10, 143.90][/tex]
Thus, the 90% confidence interval for the population mean of the considered population from the given sample data is given by: Option C: [130.10, 143.90]
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