Given that the measure of angle a is 30 degrees and the length of segment c is 5cm. Fill in the missing measurements
Answers
Given:
\(\begin{gathered} \angle a=30\degree \\ c=5 \end{gathered}\)Required:
To find the missing information.
Explanation:
Since ABC is a right angle triangle.
\(\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 30\degree+90\degree+\angle C=180\degree \\ 120\degree+\angle C=180\degree \\ \angle C=180\degree-120\degree \\ \angle C=60\degree \end{gathered}\)Now by using the trigonometric ratios we will find the values of a and b.
\(\begin{gathered} cos\theta=\frac{adj.}{hyp.} \\ cos30\degree=\frac{5}{b} \\ \frac{\sqrt{3}}{2}=\frac{5}{b} \\ b=\frac{10}{\sqrt{3}} \\ b=\frac{10}{1.732} \\ b=5.77 \\ b\approx5.8 \end{gathered}\)\(\begin{gathered} tan\theta=\frac{opp.}{adj.} \\ tan30\degree=\frac{a}{5} \\ \frac{1}{\sqrt{3}}=\frac{5}{a} \\ a=5\sqrt{3} \\ a=5(1.732) \\ a=8.66 \\ a\approx8.7 \end{gathered}\)Final answer:
\(\begin{gathered} a=8.7 \\ b=5.8 \\ \angle C=60\degree \end{gathered}\)
Related Questions
match each linear equation with the name of its form
Answers
Answer:
2x - 5y = 9 // standard form
y + 6 = -3 (x-1) // point slope form
y = -x + 8 // slope intercept form
Step-by-step explanation:
find the value of x and give reasoning in the following image
Answers
Answer:
x = 75°
Step-by-step explanation:
Quadrilateral ABCD is a parallelogram.
\(\implies seg\: AB|| seg\: DC\)
(Opposite sides of a parallelogram)
\(\implies m\angle A + m\angle B=180\degree\)
(Interior angles on the same side of transversal)
\(\implies 105\degree + m\angle B=180\degree\)
\(\implies m\angle B=180\degree-105\degree\)
\(\implies m\angle B=75\degree\)
\(seg \: AB || seg\: EF.....(Given)\)
\(\implies m\angle B =m\angle BEF\)
(Alternate angles)
\(\implies 75\degree =x \)
\(\implies \huge\red{\boxed{x =75\degree}} \)
22. What prime number is greater than 88 and less than 95?
Answers
Answer:
89
Step-by-step explanation:
The answer is 89.
Step-by-step explanation:
A prime number is only numbers that has two factors
Solve for f
F/2 -11 =-21
Answers
\(\frac{F}{2}=-21+11\\\frac{F}{2}=-10\\\frac{F}{2}(2)=-10(2)\\F=-20\)
BRAINLEAST HELPPP MEEEEEEEEEREEEE
Answers
Answer:
i think it is 676
Step-by-step explanation:
Someone help on this question ASAP
Answers
Answer:
\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)
Step-by-step explanation:
For a dilation at the origin, multiply each of the coordinates by the scale factor.
\(Q(-2,3) \longrightarrow Q'(-1/3, 1/2) \\ \\ R(-3,1) \longrightarrow R'(-1/2, 1/6) \\ \\ T(2,-1) \longrightarrow T'(1/3, -1/6) \\ \\ W(2,4) \longrightarrow W'(1/3, 2/3)\)
The coordinates of the vertices of DEF are D(2,3), E(4,0), and F(1,−2). The coordinates of the vertices of TVW are T(0,3), V(−2,0), and W(1,−2).
Answers
Answer:
To find the equation of the line containing the segment DE, we can use the coordinates of D and E to find the slope:
slope = (change in y) / (change in x) = (0 - 3) / (4 - 2) = -3/2
We can use the point-slope form of the equation of a line, using either D or E as the point:
y - 3 = (-3/2)(x - 2)
Simplifying this equation, we get:
y = (-3/2)x + 6
Similarly, to find the equation of the line containing the segment EF, we can find the slope using the coordinates of E and F:
slope = (change in y) / (change in x) = (-2 - 0) / (1 - 4) = 2/3
Using either E or F as the point, we can write the equation in point-slope form:
y - 0 = (2/3)(x - 4)
Simplifying, we get:
y = (2/3)x - (8/3)
To find the equation of the line containing the segment TV, we can find the slope using the coordinates of T and V:
slope = (change in y) / (change in x) = (0 - 3) / (-2 - 0) = 3/2
Using either T or V as the point, we can write the equation in point-slope form:
y - 3 = (3/2)(x - 0)
Simplifying, we get:
y = (3/2)x + 3
Finally, to find the equation of the line containing the segment VW, we can find the slope using the coordinates of V and W:
slope = (change in y) / (change in x) = (-2 - 0) / (1 - (-2)) = -2/3
Using either V or W as the point, we can write the equation in point-slope form:
y - 0 = (-2/3)(x - (-2))
Simplifying, we get:
y = (-2/3)x + (4/3)
Answer:
are reflection across the y-axis and translation 2 units right.
Step-by-step explanation:
HELP!! ILL MARK BRRAINLIST
Answers
Answer:
I think answer is D but it could be wrong not sure
In the diagram below, the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, & the first aid station, F. The campground is 0.35 mile from the lifeguard chair. The straight paths from both the campground and first aid station to the park ranger station are perpendicular.
If the path from the park ranger station to the campground is 0.65 mile, determine and state, to the nearest
hundredth of a mile,
a. Find the length of PL
Answers
Whwn the line of sight from the park ranger station, P, to the lifeguard chair, L, the length of PL is 0.76 miles.
How to calculate the valueIt should be noted that since the line of sight from the park ranger station, P, to the lifeguard chair, L, on the beach of a lake is perpendicular to the path joining the campground, C, and the first aid station, F, then the path from the park ranger station to the lifeguard chair is the hypotenuse of a right triangle with legs of 0.35 miles and 0.65 miles.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. Therefore, the length of PL is equal to:
= ✓(0.35² + 0.65²)
= 0.76 miles.
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Simplify the expression. Write the answer using scientific notation.
a) 2.52 × 10–3
b) 2.52 × 10–2
c) 2.52 × 10–1
d) 4.3 × 10–2
Answers
Answer:
b) 2.52 x 10^(-2)
Step-by-step explanation:
0.7 X 3.6 = 2.52
2.52 X 10^(-2)
A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 75 cubic yards. Rectangular prism
B has a length of 7 yards and a width of 3 yards. The total volume of the solid figure is 180 cubic yards. What is the height of
rectangular prism B?
Answers
The height of rectangular prism B is 5 yards.
Let's first find the volume of rectangular prism B:
The volume of the solid figure = Volume of prism A + Volume of prism B
180 = 75 + length × width × height of prism B
105 = length × width × height of prism B
We know that the length of prism B is 7 yards and the width is 3 yards,
Substitute those values:
105 = 7 × 3 × height of prism B
105 = 21 × height of prism B
height of prism B = 105/21
height of prism B = 5
Therefore, the height of rectangular prism B is 5 yards.
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the pants cost $45.Gina had a coupon for 15% off. How much money did she save
Answers
Step by step
Maximizing Profit: Tutorial
? Question
Buzz and Hover Electronics is a company that sells a variety of flying drones. For one model of drone, the cost and revenue
can be described by the given functions and graphs, where x is the number of drones.
R(x) = 180x
C(x) = 65x+13,800
Total (dollars)
+40,000
+35,000
+30,000
+25,000
+20,000
+15.000
D
+10,000
Answers
The company cannot maximize profit because the cost of producing outweighs the revenue or profit made
How should they maximize profit?
The profit function is given by P(x) = R(x) - C(x), where R(x) is the revenue function and C(x) is the cost function:
P(x) = R(x) - C(x) = 180x - (65x + 13,800) = 115x - 13,800
To maximize the profit, we need to find the value of x that maximizes P(x). We can do this by finding the vertex of the parabola that represents the profit function. Since the coefficient of the x² term is negative (-115), the parabola opens downward and the vertex represents the maximum value of the function.
The x-coordinate of the vertex is given by x = -b/2a, where a and b are the coefficients of the x² and x terms, respectively. In this case, a = -115 and b = 0, so x = 0.
Therefore, the maximum profit occurs when x = 0, which means that the company should not produce any drones. This is because the cost of producing each drone (65x + 13,800) is greater than the revenue generated by selling each drone (180x) for all values of x.
In other words, the company will lose money for each drone produced, so it should not produce any at all.
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SUSTAINIBILTY COUNTS! ENERGY CHALLENGE WHAT TO DO: COMPARITIVE STUDY OF CONSECUTIVE ELECTRIC BILLS o of post summer break with all calculations.
SUSTAINIBILTY COUNTS! ENERGY CHALLENGE
WHAT TO DO: COMPARITIVE STUDY OF CONSECUTIVE ELECTRIC BILLS HOW TO DO: 1) Examine your electricity bills of pre summer break.
2) List the various electrical appliances used in your home.
3) Find out the power consumption, duration for the device in use.
Do estimate calculation of your bills as per power consumption.
4) Make an energy reduction plan and determine how far you could implement it.
5) Re – examine your electricity bill of post summer break with all calculations.
6) WRITE your reduction plan & change in the bill.
Answers
Given statement solution is :-
1) Gather your electricity bills from the period before the summer break.
2) Create a comprehensive list of all the electrical appliances used in your home.
Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.
3) Research or locate the power consumption information for each appliance.
4) Identify areas where energy consumption can be reduced, such as:
Turning off lights when not in use.
Setting air conditioner temperatures at an optimal level.
Using energy-efficient appliances.
5) After the summer break, collect your electricity bill for the corresponding period.
6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.
Provide recommendations for further improvements or adjustments to achieve even greater sustainability.
To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:
Examine your electricity bills of pre-summer break:
Gather your electricity bills from the period before the summer break.
Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.
List the various electrical appliances used in your home:
Create a comprehensive list of all the electrical appliances used in your home.
Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.
Find out the power consumption and duration for each device in use:
Research or locate the power consumption information for each appliance.
This information is typically provided on the appliance itself or in the user manual.
Note down the power rating of each device in watts (W) or kilowatts (kW).
Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).
Calculate the estimated electricity consumption and cost:
Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).
Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.
Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.
Sum up the estimated costs for all appliances to get the total estimated electricity bill.
Make an energy reduction plan and determine implementation:
Identify areas where energy consumption can be reduced, such as:
Turning off lights when not in use.
Setting air conditioner temperatures at an optimal level.
Using energy-efficient appliances.
Unplugging devices when not in use.
Determine the feasibility of implementing these energy reduction measures in your home.
Re-examine your electricity bill of post-summer break:
After the summer break, collect your electricity bill for the corresponding period.
Calculate the actual energy consumption and cost using the same method as in step 4.
Compare the actual post-summer break bill with the estimated pre-summer break bill.
Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.
Document your reduction plan and changes in the bill:
Write a report summarizing your findings and observations.
Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.
Provide recommendations for further improvements or adjustments to achieve even greater sustainability.
By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.
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-61=-3(1-5p)+4(-8-7p)
Answers
Answer: hello! have a good day! :)))
P = 2
You choose one spade, one club, one heart, and one diamond from a standard deck of playing cards. Count the number of elements in the event that each card has a different face value.
Answers
Answer:
17,160
Step-by-step explanation:
10x+4x-15=145
What is x?
Answers
Answer:
x=11.429
Step-by-step explanation:
10x+4x-15=145
14X=160
x=11.429
Answer:
11.43
Step-by-step explanation:
Combine like terms 10x and 4x to get 14x.your new equation is 14x-15=145 add 15 on both sides and then you get 14x=160. 160/14 = 11.43 rounded to the nearest hundredth
If X1 = 440, Y1 = 220, and X2 = 360, what’s the value of Y2
Answers
Answer:
140 is the answer for y2 because x1 is 80 more than x2 so you would subtract y2 by 80
Answer:
Y2 = 180
Step-by-step explanation:
two numbers are in the ratio 7:5 and their difference in 22. find the number
Answers
Step-by-step explanation:
it's step by step explanation
PLEASE HELPPPPPP!!!!!!
Answers
The term of each of the following diagram is below;
Line CA = radiusAngle ADB = 1/2 of ACBAngle ACB = 2 time angle ADB.Line EF = TangentWhat is the term of each diagram?Line CA = radius
Angle ADB = 1/2 of ACB
Angle ACB:
AC = CB equal radius
Angle Angle CAB = Angle CBD (isosceles triangle)
Angle ACB = 2 time angle ADB.
Line EF = Tangent
The tangent of a circle is a line drawn to be perpendicular to the radius of a circle because they are always at a right angle.
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A line passes through the points (-7, 3) and (5,-5) Which is the slope of the
line?
ASAP
Answers
Answer:
slope is -2/3
Step-by-step explanation:
hope that helps!
Answer:
-8:12 or -2:3 slope
Step-by-step explanation:
the difference in the x values is 12 and the difference in the y values is 8
the length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is . the length of the arc intercepted by a central angle of in a circle of radius 15 is
Answers
The length of the arc intercepted by a central angle of 3 radians in a circle of radius 76 is 228 and the length of the arc intercepted by a central angle of 2 radians in a circle of radius 15 is 30.
Explain:
The following formula determines the length of an arc that a circle's central angle intercepts:
Arc length is equal to (central angle / 2) 2r r r
where r denotes the circle's radius. We can determine the length of the two arcs using the following formula:
For the first circle, with a radius of 76 and a center angle of 3 radians:
Arc length = 3 x 76 = 228
Therefore, in a circle with a radius of 76, the length of the arc that is intercepted by a central angle of 3 radians is 228.
For the second circle, whose radius is 15, and whose center angle is 2 radians:
Arc length = 2 x 15 = 30
As a result, the length of the arc in a circle with a radius of 15 is 30 when it is intercepted by a central angle of 2 radians.
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radius is 18.4, what is the diameter?
9.2
36.8
34.8
338.56
Answers
Answer:
B. 36.8
Step-by-step explanation:
Seventy-five 6th- grade students chose to watch a movie on the last day of school. This is 25% of the 6th-grade class. How many total students are in the 6th grade?
Answers
25% = 75/x
To solve for x, we can cross-multiply:
0.25x = 75
Then, we can divide both sides by 0.25:
x = 300
Therefore, there are 300 6th-grade students in total.
(SAT Prep) Find the value of x.
Please help me
Answers
Answer:
lelelleleellelelellelellelelelrlrlelel
Subtract using the number line.
−2−(+7)
Select the location on the number line to plot the point.
Answers
Answer:
-9Step-by-step explanation:
see attached
-2 -7 = -9
A
B
C
D
37. What is the length of side P in the figure below?
6.7 cm
11 cm
15 cm
45 cm
20 cm
25 cm
P
Answers
The length of the side P is 15 cm. And the right option is C.
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
To calculate the length of side P we use Pythagoras theorem's formula
Pythagoras formula:
a² = b²+c²......................... Equation 1Where:
a = Diagonal of the rectangleb = Length of the rectanglec = Width of the rectangleFrom the diagram,
Given:
a = 25 cmb = 20 cmc = p cmSubstitute these values into equation 1
25² = 20²+p²p² = 25²-20²p² = 225p = √225p = 15 cmHence, the right option is C 15 cm.
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A round cake has a diameter of 30 cm. Angela places the cake on a circular cake board with a diameter 5 cm
longer than that of the cake.
What is the circumference of the cake board?
Give your answer in terms of T.
cm
Stuck? Watch a video or use a hint.
Report a problem
Doble
Answers
Answer: Circumference of cake board is 35π cm.
Step-by-step explanation:Since we have given that
Diameter of a round cake = 30 cm
Diameter of a cake board is 5 cm longer than the diameter of a round cake.
So, Diameter of a cake board = 30+5=35 cm
So, radius of a cake board will be
As we know the formula for " Circumference of Circle ":
So, According to question, we get,
Hence, Circumference of cake board is 35π cm.
Answer: 35π cm
Step-by-step explanation:
in 2012 the population of california was 38,041,430, and the population living in the united states but outside california was 275,872,610. during the year, it is estimated that 748,252 persons moved from california to elsewhere in the united states, while 493,641 persons moved to california from elsewhere in the united states.
Answers
The migration matrix that has been found is
[0.98033 0.00179
0.01967 0.99821 ] by matrix method.
The 2012 populations of California and the US minus California are 38,041,430 and 275,872,610, respectively, according to the exercise statement. Let's represent these quantities by the variables c and u. What we want are two vectors m1 and m2 such that
cm 1+um 2 = [ 2013 population of California
2013 population of US minus California ]
m1 = [ 0.98033 0.01967 ] and m2 = [ 0.00179 0.99821]
Now that we have the two vectors for equation ,we use the fact that a vector equation of the form
au + bv = w
is equivalent to a matrix equation of the form
[ u v ] [a b] = w
to get our migration matrix for this system.
[0.98033 0.00179
0.01967 0.99821 ]
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The complete question is :
In 2012 the population of California was 38,041,430, and the population living in the United States but outside California was 275,872,610. During the year, it is estimated that 748,252 persons moved from California to elsewhere in the United States, while 493,641 persons moved to California from elsewhere in the United States. Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California. Let your work show how you produced the migration matrix.
evaluate the function at the given value of the independent variable. simplify the results. (if an answer is undefined, enter undefined.)f(x) = 1/√(x-4)f(x) - f(5) / x - 5
Answers
The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).
Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealised relationship between two changing quantities.
We have given function as ,
f(x) = 1/√(x-4)
We have to find f(x) - f(5)/x-5
f(x) = f(5)/x-5 = 1/√(5-4)/(x-5)
= 1/√(5-4)/(x-5)
= (x-5)/√(5-4)
= (x-5)
Therefore, The function at the given value of the independent variable, f(x) = 1/√(x-4)f(x) - f(5) / x - 5 is (x-5).
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