What is the measure of a?
In the figure below, C D bisects ∠A C B
AB=B C
∠ B E C=90° and
∠D C E=42°
Find the measure of ∠A
Answers
The measure of "a" in the above-given right-angled triangle is 32°
What is a triangle?Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Key properties of a right-angled triangle to note are:
One angle is always 90° or a right angle.The side opposite angle of 90° is the hypotenuse.The hypotenuse is always the longest side.The sum of the other two interior angles is equal to 90°.The other two sides adjacent to the right angle are called base and perpendicular.The Sum of all three interior angles is equal to 180°To solve for "a" recall the following. It is given that:
AB = BC
∠BEC=90°
∠DCE=42°
Because CD bisects ∠ACB, Hence,
∠ACD = ∠DCB = x.............................1
∠DCE= ∠BCE + ∠DCB .....................2
= ∠BCE + x = 42° ................................3
To find ∠A, we use deductive reasoning to state:
∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)
Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:
∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°
Recall equation 2, where ∠DCB = x, hence
∠A +∠E +x + x + ∠BCE = 180°
Recall equation three where 3 where ∠BCE + x = 42°, hence
∠A +∠E +x + (x + ∠BCE) = 180°
⇒ ∠A +∠E + x + 42° = 180°
Recall that ∠E = 90° so
⇒ ∠A +90° + x + 42° = 180° (Collect like terms)
⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence
∠A + x = 48°...........................4
Recall that in Δ ABC
AB = BC (given)
Hence, ABC is an Isosceles triangle. Since this is true, then
⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)
Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°
3x = 48
x = 48/3
x = 16°
Recall that
∠A = 2x...........equation 5, hence,
∠A = 2 * 16
∠A = 32°
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Related Questions
Melissa bought 10 party subs and 3 cases of water for a party she's hosting. The subs cost $47 each, and each case of water cost $7 How much did Melissa
spend on subs and water?
Answers
Answer:
melissa spent approximately $491 in total
Subs = $47/each
47 x 10 = $470 (total cost for subs)
7 x 3 = $21 (total cost for water cases)
470
+ 21
———
491
Melissa spent $491 on subs and water
5. Given the following lengths, determine if the shape is a RIGHT triangle: 14, 16, 18 (2 points: 1 point for the correct answer, 1 point for showing your work) Your answer
Answers
To be able to determine if the figure is a right triangle.
The given length must satifies the given conditions,
a.) The sum of the two sides must always be lesser than the other side. We get,
[tex]\text{ a + b }>\text{ c ; b+ c }>\text{ a ; a + c }>b[/tex]Given: a = 14 ; b = 16 ; c = 18
Let's check,
a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria
b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria
a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria
b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,
[tex]\begin{gathered} \text{ c}^2=a^2+b^2 \\ 18^2=14^2+16^2 \\ 324\text{ = }196\text{ + }257 \\ 324\text{ }\ne\text{ 457} \end{gathered}[/tex]Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.
PLEASEEE HELP ME
find the inverse of f(x)=1/x+5 -1 and it’s domain
Answers
Answer:
C
Step-by-step explanation:
HOPE IT HELPS MARK BRAINLEIST PLS
In an apartment 40%read the nation 25%read the standard 5%read both .if a random resident is selected calculate the probability that
Answers
What happens to the surface area of a sphere if the radius is doubled?b. What happens to the surface area of a sphere if the radius is tripled?
Answers
Given:
a) The radius is doubled.
b) The radius is tripled.
To find:
The changes to the surface area of a sphere
Explanation:
Let us take the original radius as r.
The surface area of the original sphere is,
[tex]A=4\pi r^2[/tex]a) The new radius will be,
[tex]R=2r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(2r)^2 \\ =4\pi(4r^2) \\ A=4(4\pi r^2) \\ A=4\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes four times the original surface area if the radius is doubled.
b) The new radius will be,
[tex]R=3r[/tex]So, the surface area of the sphere with the new radius is,
[tex]\begin{gathered} A=4\pi R^2 \\ =4\pi(3r)^2 \\ =4\pi(9r^2) \\ A=9(4\pi r^2) \\ A=9\times Surface\text{ area of old sphere} \end{gathered}[/tex]Therefore, the surface area of a sphere becomes nine times the original surface area if the radius is tripled.
Juan rides the bus to school each day. He always arrives athis bus stop on time, but his bus is late 80% of the time.Juan runs a simulation to model this using a randomnumber generator. He assigns these digits to the possibleoutcomes for each day of the week:• Let 0 and 1 = bus is on time• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is lateThe table shows the results of the simulation.
Answers
B. 2/10 = 20%
Explanations:The total number of weeks shown in the simulation = 10
By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3
The number of weeks that Juan was late everyday = 2
The estimated probability that Juan will be late evryday of next week = 2/10 = 20%
Marcus has an aquarium with three different types of fish. 1/9 of the fish are goldfish. 5/9of the fish are angelfish. • The rest of the fish are guppies. What fraction of the fish are guppies?
Answers
The fraction of fishes which are guppies in Marcus's aquarium is 2/3
Number of gold fishes in the aquarium = 1/9
Number of angelfish in the aquarium = 5/9
Fractions: A numerical value that designates a portion of a whole is used to represent fractions. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Let x be the total number of fishes in Marcus's aquarium:
Number of guppies = Total fishes - Number of gold fishes - Number of angelfishes
= x - 1/9 - 5/9
= x - 6/9
x = 6/9 or 2/3
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74/5+1 9/10 what is the the lowest denominata to use to solve?
Answers
A lowest denominator to solve the given equation is 10.
What are fractions?
Fraction are ratios in which numerator and denominator are both integers and denominator is not zero.
We are given a equation
[tex]\frac{74}{5}+1\frac{9}{10}[/tex]
Upon solving we get the following
[tex]\frac{74}{5}+\frac{19}{10}[/tex]
If we multiply both numerator and denominator of the first term by 2 we get
[tex]\frac{148}{10}+\frac{19}{10}[/tex]
Hence after this we can add
Hence A lowest denominator to solve the given equation is 10
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Two trains for Palwal leave Kanpur at 10 am and 10:30 am and travel at the speeds of 60Kmph and 75Kmph respectively. After how many kilometers from Kanpur will the two trains be together?
Answers
Answer:
150 km
Step-by-step explanation:
You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.
SetupAt t hours after 10 am, the distance of the first train from Kanpur will be ...
distance = speed × time
distance = 60t
At t hours after 10 am, the distance of the second train from Kanpur will be ...
distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am
These distances will be equal when ...
60t = 75(t -1/2)
SolutionThe time at which the trains meet will be the solution to the above equation.
60t = 75t -37.5 . . . . eliminate parentheses
0 = 15t -37.5 . . . . . . subtract 60t
0 = t -2.5 . . . . . . . . . divide by 15
2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves
The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:
60t = 60(2.5) = 150 . . . . km
The two trains will be together 150 km from Kanpur.
The linear function
M= 10- 1.44p represents the amount m (in dollars)
of money that you have after printing p photographs.
(See Example 5.)
a. Interpret the terms and coefficient in the equation.
b. Find the domain of the function. Is the domain
discrete or continuous? Explain.
c. Graph the function using its domain.
Answers
Considering the given linear function, it is found that:
a)
The intercept is of 10, meaning that initially you have $10.The slope is of -1.44, meaning that the cost of printing each photo is of 1.44.b) The discrete domain of the function is: {0, 1, 2, 3, 4, 5, 6, 7}.
c) The graph of the function is given at the end of the answer.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule given below:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).The amount of money you have remaining after printing p photographs is modeled by the following function:
M(p) = 10 - 1.44p.
Hence the coefficients are as follows:
The intercept is of b = 10, meaning that initially you have $10 to spend on printing photos.The slope is of -1.44, meaning that the cost of printing each photo is of 1.44, that is, for each photo you print, you are going to lose $1.44 from your amount.The number of photos printed is a discrete number, as this number cannot assume decimal values, hence the domain is also discrete.
You cannot print a negative value of numbers, neither can M(p) be negative, hence the domain, which is the number of photos you can print, is:
{0, 1, 2, 3, 4, 5, 6, 7}.
Considering the above domain, the graph of the function is given by the image at the end of the answer.
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Order from least to greatest5/6 4/50.82
Answers
Okay, here we have this:
Considering the provided set of numbers we are going to organize the numbers from smallest to largest, so we obtain the following:
Remember that 5/6 is approximately 0.83 and 4/5 is 0.8, then:
Considering the number line and that the smaller numbers are further to the left and the larger numbers are further to the right, we are left with the following order from least to greatest: 4/5, 0.82, 5/6.
help meeeeeee pleaseee !!!!
Answers
The linear equation that passes through the two points (0, 360) and (10, 560) is:
y = 20*x + 360
How to find the linear equation?Remember that the slope-intercept form of a linear equation is:
y = a*x + b
Where b is the y-intercept and a is the slope or rate of change.
If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
[tex]a = \frac{y_2 -y_1}{x_2 - x_1}[/tex]
Here the line must pass through (0, 360) and (10, 560), so the slope is:
[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]
And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:
y = 20*x + 360
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Solve the inequality for x
(x+8)(x-3)^2(x-7)^3<0
Answers
The solution for the given inequality is −8<x<3 or 3<x<7.
The given inequality is (x+8)(x-3)²(x-7)³<0.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality can be solved as follows
Solve for x by simplifying both sides of the inequality, then isolating the variable.
Inequality Form: x+8<0
x<-8 (Subtract 8 on both the sides of the inequality)
(x-3)²<0
⇒ x-3<0
⇒ x<3 (Add 3 on both the sides of the inequality)
(x-7)³<0
⇒ x-7<0
⇒ x<7 (Add 7 on both the sides of the inequality)
Solution is −8<x<3 or 3<x<7
Therefore, the solution for the given inequality is −8<x<3 or 3<x<7.
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Alice is saving to buy a house and currently has$2,000 in her savings account. She's planning tocontribute $150 to the account each month,Identify the function that describes therelationship between the number of monthsthat pass (n) and the balance of her savingsaccount,f(n).
Answers
Alice plans to buy a house. She has $2,000 in her savings account.
She plans to contribute $150 to the account each month.
We know that with each month, n, she deposits $150 and so, each month, her savings account balance increases by $150.
This simply means that after n months, her savings account balance would have increased by:
150 * n = 150n
Her initial balance was $2000, therefore, her balance after n months will be the sum of 150n and the amount that was initially there.
That is:
f(n) = 2000 + 150n
This is the function that describes the relationship between the number of months and her balance.
find the perimeter of the hallway
Answers
Answer: 17x - 39
Step-by-step explanation:
1) Find all sides of the hallway.
P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1
2) Add it together
P= 17x - 39
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯¯¯¯
K
M
.
Answers
Answer L
The part 1 picture of the same question the part 2Because is a little long.
Answers
The answer would be B.
The relationship is proportional. The constant of proportionality is 5.
Math
-2-(-7) = ?
Bookmark
Answers
Answer:
5
Step-by-step explanation:
We know that - (-7) = +7, so
-2 - (-7) = -2 + 7 = 5
The length of the hypotenuse of a right triangle is 13 cm. The length of one leg is 5 cm. Find the length of the other leg. i think its 12
Answers
Answer: Correct! The answer is 12.
Step-by-step explanation:
1) Draw the triangle.
Drawing a triangle usually helps you see the problem better!
| \
| \ 13 cm
| \
|______\
5 cm
2) Solve the other leg
To find the other leg, we need to use the Pythagorean theorem. Which goes like this
[tex]a^2+b^2=c^2[/tex]
We will then substitute the numbers into the equation
[tex]5^2+b^2=13^2[/tex]
Simplify
[tex]25+b^2=169[/tex]
Set the variable on one side
[tex]b^2=144[/tex]
Get rid of the squared in the b by square rooting both sides.
[tex]b=12[/tex]
The answer is 12.
A company prints designs on T-shirts. They charge $40 for set-up costs plus $12 per shirt. Write the equation for the situation.
Answers
The equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.
According to the situation,
We have the following information:
The company charges $40 for set-up costs plus $12 per shirt.
So, the basic charge is added to every t-shirt.
Now, let's take the number of T-shirts on which the company prints designs on shirts to be x.
So, we have the charge for x number of t-shirts is:
$(40+12x)
Hence, the equation for the situation a company prints designs on T-shirts is (40+12x) when x is the number of T-shirts.
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2.Graph and complete the t-chart for the function y=2/3 x +5.
Answers
Recall that to complete the table we have to evaluate the given function at every value of x:
[tex]\begin{gathered} y(-3)=\frac{2}{3}(-3)+5=-2+5=3, \\ y(3)=\frac{2}{3}(3)+5=2+5=7, \\ y(6)=\frac{2}{3}(6)+5=4+5=9. \end{gathered}[/tex]Answer:
Table:
Graph:
find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (hint: let (x,y) be the unknown endpoint. apply the midpoint formula, and solve the two equations for x and y.) midpoint (-15, -6), end point (-16,-3)
Answers
The coordinates of the other endpoint of the segment, given its midpoint and one endpoint are (-14, -9)
How to find the midpoint coordinate of a Line?The Midpoint Formula for a line with endpoints as (x₁, y₁) and (x₂, y₂) is;
((x₁ + x₂)/2, (y₁ + y₂)/2)
We are given the following;
Midpoint (-15,-6)
End point (-16,-3)
Let x₁ = -16, the x coordinate of the endpoint
Let x₂ = the x coordinate of the unknown endpoint
Let y₁ = -3, the y coordinate of the endpoint
Let y₂ = the y coordinate of the unknown endpoint
Thus, for the x coordinate of the unknown endpoint;
(x1 + x2)/2
(-16 + x₂)/2 = -15
-16 + x₂ = -30
x₂ = -14
For the y coordinate of the unknown endpoint;
(y1 + y2)/2
(-3 + y₂)/2 = -6
-3 + y₂ = -12
y₂ = -12 + 3
y₂ = -9
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The sum of three consecutive even integers
is –78. What are the integers?
Describe how you would use the strategy of writing an equation to solve the given problem.
Answers
Answer:
- 28, - 26 and - 24Step-by-step explanation:
The difference between two consecutive even integers is 2.
Let the first of the three integers is x, then the following ones are:
x + 2 and x + 4.
The sum of the three is - 78. Express it as equation and solve for x:
x + x + 2 + x + 4 = - 783x + 6 = - 783x = - 84x = - 84/3x = - 28The integers are - 28, - 26 and - 24
Solve 3x - 2y = - 6 if the domain is {-2, -1, 0, 2, 3).
Write your answer as ordered pairs.
Answers
The solution of equation as ordered pairs can be given as {0, 3/2, 3, 6, 15/2}.
Domain may be defined as the input variable x for any of the given function which gives a suitable set of output variables y. The input variable is called the independent variable whereas the output variable is called the dependent variable. The equation given in the question 3x - 2y = -6 can also be expressed as y = (3x + 6)/2. The ordered pairs of Domain are {-2, -1, 0, 2, 3}. Now if we put these values as values of x we get the values of y as,
At x = -2, y = 0, at x = -1, y = 3/2, at x = 0, y = 3, at x = 2, y = 6 and at x = 3, y = 15/2.
These are the values of outputs, and the ordered pair will be expressed as
{0, 3/2, 3, 6, 15/2}.
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Calculate the mean of the electric bills for Family A. Round your answer to the nearest cent.
Month Family A Family C
January
February
March
April
May
June
July
August
September
October
November
December
$
Answers
Answer:
78.59$
Step-by-step explanation:
What is the number of terms in the polynomial -y4 + 7y³
Answers
-y^4 is the first, or leading term in the polynomial. The second term is 7y^3. This is considered a binomial.
A football team has a 60% chance of winning a league trophy each season it competes. What would be its probability of winning two times in three consecutive seasons?
Answers
Answer:
P(X = 2) = 43.2%
Step-by-step explanation:
P(X = 2) = 3 * 0.6^2 * (1 - 0.6)^(3 - 2)
P(X = 2) = 54/125
P(X = 2) = 0.432
P(X = 2) = 43.2%
write in standard form the equation of the line through each pair of points
9. (0,1) and (3,0)
10. (1/2,2/3) and (-3/2,5/3)
11. (-3,-2) and (1,6)
Answers
The equation of the line 3y + x = 3 through pair of points (0,1) and (3,0), the equation of the line 6y = 2x +3 through pair of points (1/2,2/3) and (-3/2,5/3) and the equation of the line y = 2x + 4 through pair of points (-3,-2) and (1,6)
The equation of the line through pair of points (0,1) and (3,0)
⇒ y - y₁ = [(y₂ - y₁)/(x₂ -x₁ )](x - x₁ )
Here x₁ = 0 and y₁ = 1
x₂ = 3 and y₂ = 0
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 1 = [(0-1)/(3-0)](x -0)
⇒ y - 1 = (-1/3)x
⇒ 3y - 3 = x
⇒ 3y + x = 3
The equation of the line through pair of points (1/2,2/3) and (-3/2,5/3)
⇒ y - 2/3 = [(5/3 -2/3)/(-3/2-1/2)](x -1/2)
⇒ y - 2/3 = [(3/3)/(-4/2)](x -1/2)
⇒ y - 2/3 = (1/3)(x -1/2)
Multiply by 6 both sides of the equation,
⇒ 6y - 4 = 2(x -1/2)
⇒ 6y = 2x -1 + 4
⇒ 6y = 2x +3
The equation of the line through pair of points (-3,-2) and (1,6)
⇒ y - (-2) = [(6-(-2))/(1-(-3))](x -(-3))
⇒ y + 2= (8/4)(x + 3)
⇒ y = 2x + 6 -2
⇒ y = 2x + 4
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( – 5q–1)–( – 2q–8)
help meeeee
Answers
The value of expression ( – 5q–1)–( – 2q–8) is -3q + 7.
As per the known fact, the similar signs are consequently takes as positive for calculation. So, the two negative signs will be takes as positive. So, rewriting the expression to solve and find its value.
Value of expression = (-5q - 1) + 2q + 8
Rearrange the expression
Value of expression = - 5q + 2q - 1 + 8
Performing addition of numerals written with q and subtraction of constant values
Value of expression = - 3q + 7
Thus, the value of expression mentioned in question is -3q + 7.
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Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat. What is the probability that you, Shirley, and Matthew are chosen? Enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The probability that you, Shirley, and Matthew are chosen is 0.0001
Probability:
Probability refers the measure of the likelihood of an event to occur.
The formula of Probability is
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Given,
Suppose that your boss must choose three employees in your office to attend a conference in Jamaica. Because all 28 of you want to go, he decides that the only fair way is to draw names out of a hat.
Here we need to find the probability that you, Shirley, and Matthew are chosen.
Here we have assuming that the selection process is fair;
We know that, the total number of employees is 28
Therefore, the probability of selecting each employee is,
=> 1/28
So, the probability of selecting yourself, Shirley, and Matthew is calculated as,
=> 1/28 x 1/27 x 1/26
=> 1/19656
=> 0.00005
When we round off it into four decimal place then we get,
=> 0.0001
Therefore, the probability that you, Shirley, and Matthew are chosen 0.0001.
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