in triangle ABC, bisectors of angle A and angle C cross each other in point M. find angle ABC if it is half of AMC. (no shape given)
Answers
Answer:
[tex]\angle ABC=60[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ image\ attachment.]\\We\ are\ given\ that,\\AM\ is\ the\ Angle\ Bisector\ of\ \angle BAC.\\Hence,\\\angle BAM= \angle MAC\\CM\ is\ the\ Angle\ Bisector\ of\ \angle BCA.\\Hence,\\\angle BCM= \angle MCA.\\Also,\\\angle AMC=2 \angle ABC[/tex]
[tex]Now,\\As\ we\ can\ observe\ that,\\\angle BCM + \angle MCA= \angle BCA\\\angle MCA+ \angle MCA= \angle BCA\ [\angle BCM = \angle MCA]\\Hence,\\2 \angle MCA= \angle BCA\\Or, \\\angle MCA=\frac{\angle BCA}{2} \\\\Similarly,\\\angle BAM + \angle MAC= \angle BAC\\\angle MAC + \angle MAC= \angle BAC\\2 \angle MAC = \angle BAC\\Or,\\\angle MAC=\frac{\angle BAC}{2}[/tex]
[tex]Through\ the\ Angle\ Sum\ Property\ of\ a\ Triangle,\ we\ know\ that:\\'The\ Sum\ of\ all\ interior\ angles\ of\ a\ triangle\ is\ 180.'\\Hence,\\In\ \triangle BAC,\\\angle ABC + \angle BCA + \angle CAB=180\\In\ \triangle MAC,\\\angle MAC+ \angle ACM + \angle AMC=180[/tex]
[tex]Hence,\\As\ \angle AMC= 2 \angle ABC, \angle MCA=\frac{\angle BCA}{2}, \angle MAC=\frac{\angle BAC}{2},\\2 \angle ABC+\frac{\angle BCA}{2}+\frac{\angle BAC}{2}=180\\By\ resolving\ the\ denominators,\\\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}=180\\\\By\ comparing\ the\ Sum\ of\ angles\ in\ both\ the\ triangles,\\We\ find\ that\ the\ RHS\ of\ both\ the\ equations\ are\ equal\ i.e.180,\\The\ LHS\ of\ the\ equations\ are\ equal\ too.\\[/tex]
[tex]Hence,\\\angle ABC+ \angle BCA + \angle BAC=\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}\\Hence,\\2(\angle ABC+ \angle BCA + \angle BAC)=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle ABC+ 2 \angle BCA + 2 \angle BAC=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle BCA + 2 \angle BAC-\angle BCA- \angle BAC=4 \angle ABC- 2 \angle ABC\\Hence,\\\angle BCA+\angle BAC= 2\angle ABC[/tex]
[tex]Lets\ get\ back\ to\ the\ Angle\ Sum\ of\ \triangle ABC,\\\angle ABC + \angle BAC + \angle ACB=180\\Hence,\\As\ \angle BCA + \angle BAC= 2 \angle ABC,\\\angle ABC + 2 \angle ABC=180\\Hence,\\3 \angle ABC=180\\\angle ABC=\frac{180}{3}=60[/tex]
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amid has gained weight he now weighs 88kg which is 10% higher than his normal weight. what is his normal weight?
Answers
Answer:
88*0.9= 79.2 (since it's 10% higher, multiply by .9 to find out what 90% of 88 is
you also could've done 88*0.1=8.8 and then subtract 8.8 from 88 and get 79.2
either way his normal weight is 79.2kg
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation: hope this helps
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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I have 10 goats, n of which are male. I need to choose 2 of them to make a casserole.
The probability both of my choices are male is 2/15
Use the information to form an appropriate quadratic equation N square + an + b = 0, specifying the constants a and b.
Answers
Answer: There are 4 male goats.
Step-by-step explanation:
We know that n of the 10 goats are male.
The probability that in a random selection, the selected goat is a male, is equal to the quotient between the number of male goats (n) and the total number of goats (10)
The probability is;
p = n/10
Now the total number of goats is 9, and the number of male goats is n -1
then the probability of selecting a male goat again is:
q = (n-1)/9
The joint probability (the probability that the two selected goats are male) is equal to the product of the individual probabilities, this is
P = p*q = (n/10)*((n-1)/9)
And we know that this probability is equal to 2/15
Then we have:
(n/10)*((n-1)/9) = 2/15
(n*(n-1))/90 = 2/15
n*(n-1) = 90*2/15 = 12
n^2 - n = 12
n^2 - n - 12 = 0
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For an equation:
a*x^2 + b*x + c = 0
The two solutions are given by:
[tex]x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}[/tex]
For our case, the solutions will be:
[tex]n = \frac{1 +- \sqrt{(-1)^2 - 4*1*(-12)} }{2*1 } = \frac{1+- 7}{2}[/tex]
The two solutions are:
n = (1 - 7)/2 = -3 (this solution does not make sense, we can not have a negative number of goats)
The other solution is:
n = (1 + 7)/2 = 4
This solution does make sense, this means that we have 4 male goats.
A recipe code lasagna calls for 3 pounds of tomatoes to serve 5 people. A caterer wants to make enough lasagna to serve 110 people. How many pounds of tomatoes does he neeed
Answers
Answer:
66 pounds of tomatoes
Step-by-step explanation:
A recipe code lasagna calls for 3 pounds of tomatoes to serve 5 people. A caterer wants to make enough lasagna to serve 110 people. How many pounds of tomatoes does he neeed
From the above question:
5 people = 3 pounds of tomatoes
110 people = x pounds of tomatoes
Cross Multiply
5 people × x pounds = 110 people × 3 pounds
x pounds = 110 people × 3 pounds/5 people
x pounds = 66 pounds of tomatoes
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
34.1 - 8.6 = 25.5
[tex]42.7^{\circ}F[/tex]
Subtract the number with the smallest value from the number with the biggest value to determine the difference between two numbers.
Temperature in a town during the day [tex]=34.1^{\circ}F[/tex]
Temperature in a town during the night [tex]=-8.6^{\circ}F[/tex]
Therefore,
Difference in temperatures [tex]=34.1-(-8.6)[/tex]
[tex]=42.7^{\circ}F[/tex]
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https://brainly.com/question/20671719?referrer=searchResults
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer: A
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Given that:
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Recall :
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Answers
Answer:
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Step-by-step explanation:
First, our ratio is sugar:flour or 2:5, so our question is 1:? We find ? by finding how we got to 1 on the other side.
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Line 2 : Undefined
Line 3 : Zero
Line 4 : Negative
Explanation:
Look at the line. Starting from the left side, is it going up or down? Up means it is positive. Down means it is negative. The other two lines you just have to remember which one is undefined and which one is Zero.
Answer:
see explanation
Step-by-step explanation:
A line sloping upwards from left to right has a positive slope.
Line 1 is in this category.
A line sloping downwards from left to right has a negative slope.
Line 4 is in this category.
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Line 2 is in this category.
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Answers
A summer camp cookout is planned for the campers and their families. There is room for 200 people. Each adult costs 4, and each camper costs4,and each camper costs3. There is a maximum budget of $750. Write the system of inequalities to represent this real-world scenario, where x is the number of adults and y is the number of campers.
A. \begin{gathered}x + y \leqslant 200 \\ 4x + 3y \leqslant 750\end{gathered}x+y⩽2004x+3y⩽750
B. \begin{gathered}x + y \leqslant 750 \\ 4x + 3y \leqslant 200\end{gathered}x+y⩽7504x+3y⩽200
C. \begin{gathered}x + y \leqslant 200 \\ 3x + 4y \leqslant 750\end{gathered}x+y⩽2003x+4y⩽750
D. \begin{gathered} x + y \leqslant 750 \\ 3x + 4y \leqslant 200\end{gathered}x+y⩽7503x+4y⩽200
Answers
Answer:
Option A
The system of inequalities
x + y ≤ 200
4x + 3y ≤ 750
Step-by-step explanation:
Let the
Number of Adults = x
Number of campers = y
A summer camp cookout is planned for the campers and their families.
There is room for 200 people.
x + y ≤ 200
Each adult costs $4, and and each camper costs $3. There is a maximum budget of $750.
Maximum means the total cost is equal to or less than $750
$4 × x + $3 × y ≤ $750
4x + 3y ≤ 750
The system of inequalities
x + y ≤ 200
4x + 3y ≤ 750
Option A is correct
Tyson is 6 feet 2 inches tall. There are 2.54 centimeters in 1 inch. What is Tyson's height in centimeters?
Answers
Answer:
187.96 cm
Step-by-step explanation:
Given hat
Tyson is 6 feet and 2 inches tall
Also
There is 2.54 cm in 1 inch
Now the tyson height in the centimeter is
= 6.16666 × 30.48
= 187.96
Hence, the Tyson height in the centimeter is 187.96
Answer:
187.96
Step-by-step explanation:
(answer d)