Answers
Answer:
MO = 8 units
MP = 4 units
Step-by-step explanation:
[tex] In\: \triangle MOP, \\
\angle P = 90\degree ... (given) \\
\angle M = 60\degree ... (given) \\
\therefore \angle O = 30\degree(3^{rd} \: \angle \: of\: \triangle) \\
Let \huge\purple {MO = x \: units}... (1)\\
\therefore MP = \frac{1}{2} \times MO\\(side\: opposite \: to\: 30\degree) \\\\
\therefore MP = \frac{1}{2} \times x\\\\
\huge\red {\therefore MP = \frac{1}{2} x}.... (2)\\\\
\therefore PO = \frac{\sqrt 3}{2} \times MO\\(side\: opposite \: to\: 60\degree) \\\\
\therefore PO = \frac{\sqrt 3}{2} \times x\\\\
\huge\orange{\therefore PO = \frac{\sqrt 3}{2}x} \\\\
\because MP + PO + MO = P(\triangle MOP) \\\\
\therefore \frac{1}{2} x+\frac{\sqrt 3}{2}x+ x = 12+4\sqrt 3\\\\
\therefore \frac{1}{2} x+x+\frac{\sqrt 3}{2}x= 4(3+\sqrt 3)\\\\
\therefore \frac{3}{2} x+\frac{\sqrt 3}{2}x= 4(3+\sqrt 3)\\\\
\therefore \frac{(3+\sqrt 3)}{2} x= 4(3+\sqrt 3)\\\\
\therefore x = 4(3+\sqrt 3)\times \frac{2}{(3+\sqrt 3)}\\\\
\therefore x = 4\cancel{(3+\sqrt 3)}\times \frac{2}{\cancel {(3+\sqrt 3)}}\\\\
\therefore x = 4\times 2\\\\
\therefore x = 8\\\\
\huge\purple {\boxed{\implies MO = 8}} \: \\ [From\: equation \: (1)]\\\\
\because MP = \frac{1}{2} x \:
\\ [From\: equation \: (2)]\\\\
\therefore MP = \frac{1}{2} \times 8\\\\
\huge\red {\boxed{\therefore MP = 4 \: units}}
[/tex]
Related Questions
during the 20 year study, a law was passed that banned the use of pesticides known to be harmful to the fruit bat. predict the year the law was passed
Answers
What is m∠P?
(NEED URGERENT HELP!!)
Answers
Step-by-step explanation:
Sum of angles in this pentagon = 540°.
Therefore 13x + 241 = 540, x = 23
Hence Angle P = 4(23) + 2 = 94°.
The measure of angle P is 94°
What is pentagon?"It is a polygon with five vertices and five sides."
For given example,
We know, the sum of all interior angles of a pentagon is 540°
⇒ ∠P + ∠Q + ∠R + ∠S + ∠T = 540°
⇒ (4x + 2)° + (132)° + (4x - 10)° + (5x - 11)° + 128° = 540°
⇒ 4x + 4x + 5x + 2 + 132 - 10 - 11 + 128 = 540
⇒ 13x + 241 = 540
⇒ 13x = 299
⇒ x = 23
So, the measure of angle P would be,
4x + 2
= 4 (23) + 2
= 94°
Therefore, the measure of angle P is 94°
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Evaluate the following equation, when x=20:
x/5 + x – 10
Answers
Which descriptions from the list below accurately describe the relationship between AQRS and ATUV? Check all that apply. 284 -28 12 12 76" 176 176 1764 6 V Q A. Same sides B. Same size C. Similar D. Congruent
Answers
Answer:
All A to D
Step-by-step explanation:
The attachment completes the question
From the attachment,
it can be seen that QRS and TUV are of the same i.e. trianglesAlso, from the attachment, the sides of each are:
[tex]RQ = UT = 22[/tex]
[tex]QS = TV = 30[/tex]
[tex]RS = UV = 23[/tex]
And the angles are:
[tex]\angle Q = \angle T = 50[/tex]
[tex]\angle R = \angle U = 83[/tex]
[tex]\angle S = \angle V = 47[/tex]
The above show that QRS and TUV are:
similarsame sidesand they are congruent25 points
What type of graph is best to use to compare two sets of data over time?
Answers
Answer:
Bar Graph
Step-by-step explanation:
Bar graphs are used to compare things between groups or tracks. They are the most efficient because the set data is set to change at any time
time sensitive!! i really need help thanksss
Answers
Answer:
-x -y = 5
Step-by-step explanation:
the Answer will be 5
There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7in or 12in. The diameter of all 15 plates combined is 140in. Which system of equations can be used to find the number of 7in plates, x , and the number of 12in plates, y , that are in the cabinet?
Answers
Answer:
Number of 7 inch plate = 8
Number of 12 inch plate = 7
Step-by-step explanation:
There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7in or 12in. The diameter of all 15 plates combined is 140in. Which system of equations can be used to find the number of 7in plates, x , and the number of 12in plates, y , that are in the cabinet?
Given that :
Total Number of plates = 15
Diameter of each plate : 7 in or 12 in
Diameter of all 15 plates = 140 in
Let number of 7 in and 12 in diameter plates = x and y respectively ;
x + y = 15 - - (1)
7x + 12y = 140 - - - (2)
x = 15 - y
Substitute x = 15 - y in (2)
7(15 - y) + 12y = 140
105 - 7y + 12y = 140
105 + 5y = 140
5y = 140 - 105
5y = 35
y = 7
From x = 15 - y
x = 15 - 7
x = 8
Number of 7 inch plate = 8
Number of 12 inch plate = 7
Samantha purchased dinner at a restaurant and spent $38 on food and beverages. Her sales tax was 7%. How much will Samantha pay for sales tax in dollars and cents?
Answers
Given:
Samantha purchased dinner at a restaurant and spent $38 on food and beverages.
Rate of sales tax = 7%
To find:
How much will Samantha pay for sales tax in dollars and cents?
Solution:
Amount spent on food and beverages = $38
Rate of sales tax = 7%
Sales tax = 7% of $38
[tex]\text{Sales tax}=\dfrac{7}{100}\times 38[/tex]
[tex]\text{Sales tax}=\dfrac{266}{100}[/tex]
[tex]\text{Sales tax}=2.66[/tex]
Therefore, the sales tax is $2.66.
Find the solution to the systems of equations using the elimination method.
2x + 3y = 11
5x + 3y = 14
Answers
Answer:
x=1
Step-by-step explanation:
-3x=-3
On Monday, the low temperature outside was 32 degrees above zero. On Christmas, it was 5 degrees below zero. What is the difference in the two temperatures?
Answers
Answer:
Difference in temperatures = 37 degree
Step-by-step explanation:
Given:
Temperature above zero = 32 degree
Temperature below zero = -5 degree
Find:
Difference in temperatures
Computation:
Difference in temperatures = Temperature above zero - Temperature below zero
Difference in temperatures = 32 - (-5)
Difference in temperatures = 37 degree
Huilan's age is three times Thomas's age. The sum of their ages is 64. What is Thomas's age?
Answers
Answer:
16
Step-by-step explanation:
Answer: 16 years old
Step-by-step explanation:
1
1
Consider the polynomial function:
p(x) = 3x3 + 10x2 + ax - 6
where a is an unknown real number.
If
(x + 3)
is a factor of this polynomial what is the value of a? Show all the steps below.
Answers
Step-by-step explanation:
By Factor Theorem, p(-3) = 0.
Therefore 3(-3)³ + 10(-3)² + (-3)a - 6 = 0 and a = 1.
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Answers
(0,0) and (2,3)
(3-0)/(2-0) = 3/2 slope
Solution: y = 3/2x
Solve 20/420 and remember to add the partial quotients to find the actual quotient.
Answers
Answer:
0.0476
Step-by-step explanation:
To solve 20/420,
We first reduce the numerator and denominator to its lowest terms(we are not using long division method) :
In the fraction 20/420, we cancel out the zeros =2/42
In the fraction 2/42, 2 will divide numerator and denominator so =1/21
To find the actual quotient, we are sure to get a result of decimal number since numerator is already smaller than denominator,
Therefore 1/21= 0.0476 to 4 decimal places
Note : we add zero to the numerator till it can be divided by 21(even with a remainder) hence the "0.0" before 4
Simplify the expression. 14 + (-3) -3/7j - 6/7j + 6
Answers
Because you would group all of the non fractions together ( 14-3+6 =17) and then group the fractions together ( 9/7j)
Answer:
[tex]t^{14}[/tex] + 3 + − [tex]\frac{3j}{7}[/tex] + 7 + -[tex]\frac{6j}{7}[/tex]
Step-by-step explanation:
A company ships its drink mix in a box in the shape of a rectangular prism. The base of the
prism is a rectangle with a length of 4 meters and a width of 1.5 meters. The height of the
container is 2.5 meters. What is the volume of the box in cubic meters?
Answers
Answer:
6 cubic meters
Step-by-step explanation:
Find the GCF of 74 and 154.
Answers
Answer: 2
Step-by-step explanation:
2
74: 2 37
154: 2711
GCF:2
5/9 x 6/15 x 15/4=
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Answers
Answer:
5/6
Step-by-step explanation:
Joaquin lives 0.4 mile from Keith. Layla lives 0.3 as far from Keith as Joaquin.
How far does Layla live from Keith? Enter an equation to solve.
Answers
from Keith as Joaquin.
solve.
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Answer:
answer D looks good :)
Step-by-step explanation:
how many teaspoons are f vanilla will i use?
Answers
Answer:
9 teaspoons of vanilla
Step-by-step explanation:
12/4=3
3*3=9
Answer:
teaspoons of vanilla =9
Step-by-step explanation:
we can make it as a ratio
So we have (3 for teaspoons and 4 tablespoons)
3:4
Then x : 12
x=(12/4)*3=9
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In a bowl of fruit, there are green grapes and black grapes in the ratio of 3:5. If there are 27 green grapes, how many black grapes are there.
Answers
Answer:
45
Step-by-step explanation:
27 DIVIDED BY 3 IS 9
SO 9 MULTIPLIED BY 5 IS 45
SO THE ANSWER IS 45
The two-way table below displays information about passengers on a commercial flight.
Passenger Data
First Class
Coach
Checked Bags
10
81
Did Not Check Bags
14
57
What percentage of coach passengers did not check bags? Round to the nearest tenth.
35.2%
41.3%
70.4%
80.3%
Answers
The percentage of coach passengers who did not check their bags will be 43.82 %.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that the total number of passengers is, 162 of which 71 bags didn't check while 91 bags got checked.
We have to find the percentage of coach passengers who did not check their bags.
It is found by dividing the total number of passenger bags not checked by the total number of passengers.
=71 / 162 × 100
=43.82 %
Thus, the percentage of coach passengers who did not check their bags will be 43.82 %.
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what is the solution of the system of equations 2x-5y=11 and -2x+3y=-9
Answers
x = (5y+11)/2
Substitute equation 1 to 2:
-2((5y+11)/2)+ 3y=-9
-2/2 = -1 thus -1(5y+11)
Continue...
-(5y+11)+3y=-9
-5y-11+3y =-9
(-5+3)y= 11-9
-2y = 2
y=-1
Substitute y into equation 1:
x=(5*-1+11)/2
x = 6/2=3
So y=-1 and x =3
Answer:
Step-by-step explanation:
In order for us to be able to get our (x,y) value, we need to show our work step-by-step.
Solving for Y:
-2x + 3y = -9
+ (2x - 5y = 11)
_____________________
-2y = 2
-2 -2
In order for us to be able to find our y value, we need to divide -2 both sides.
y = -1
Solving for X:
2x-5(-1) = 11
2x + 5 = 11
- 5 -5
_____________________
2x = 6
2 2
In order for us to find our x value, we need to divide 2 both sides.
x = 3
Our equation set or (x,y) value will be equal to:
(3,-1)
3.2 geometry worksheet
Answers
Answer/Step-by-step explanation:
9. 17x = 16x + 5 (alternate exterior angle)
17x - 16x = 5
x = 5
Measure of bolded angle = 17x = 17 * 5 = 85
10. 21x - 6 = 20x (corresponding angels)
21x - 20x = 6
x = 6
Measure of bolded angle = 20x = 20(6) = 120
11. (x + 95) + (x + 105) = 180 (linear pair angles)
2x + 200 = 180
2x = 180 - 200
2x = -20
Divide both sides by 2
x = -10
Measure of bolded angle = x + 105 = -17 + 105 = 88°
12. 12x - 4 = 11x + 3 (vertical angles)
Collect like terms
12x - 11x = 4 + 3
x = 7
Measure of bolded angle = 11x + 3 = 77 + 3 = 80°
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Answers
Answer:
8 is 1
Step-by-step explanation: Multiply
An infant playpen is in the shape of a circle. If the playpen has a diameter of 2 meters, what is the approximate area of the playpen?
Answers
Answer:
π meters
Step-by-step explanation:
The diameter is 2 meters. Then the radius is 1 meter. So:
A=πr²
=π(1)²
=π meters ...............
Answer:
3.14
Step-by-step explanation
the formula of a circle is A=πrxr
2 divided by 2 is 1
1 x 1 = 1
3.14 x 1 = 3.14
thats is!
In ΔBCD, \text{m}\angle B = (4x-14)^{\circ}m∠B=(4x−14) ∘ , \text{m}\angle C = (x-1)^{\circ}m∠C=(x−1) ∘ , and \text{m}\angle D = (6x+8)^{\circ}m∠D=(6x+8) ∘ . What is the value of x?X?
Answers
Answer:
x = 17Step-by-step explanation:
The sum of angle in the triangle BCD is 180 degrees
Given;
<B = 4x -14
<C = x - 1
<D = 6x + 8
Required
Find x
Since <B + <C + <D = 180, hence;
4x - 14 + x - 1 + 6x + 8 = 180
11x -7 = 180
11x = 180+7
11x = 187
x = 187/11
x = 17
Hence the value of x is 17
Find the value of x in the parallelogram.
Answers
Step-by-step explanation:
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Answers
Answer:
Solid line y is less than or equal to -1+4
Dashed line y is greater than or equal to 1/3
Step-by-step explanation:
PLZ MARK BRAINLIEST
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h bjwkjdfrekojfhrkeifcuhenjdc
Step-by-step explanation: