Please help thanks, Which postulate can be used to prove the two triangles are congruent?
Answers
The postulate that can be used to prove the two triangles are congruent is the HL this is the last option
What is HL?HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.
The theorem says that, two angles of a right angle triangle that have equal
hypotenuse andany one legthen two triangles are congruent
The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal
Therefore, this theorem says that the two triangle are congruent
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Related Questions
Sofia is 38 years old. Write an equation that relates Sofia's age to Tony's age, t. How old is Tony?
(Sofia’s age is 2 times the combined ages of Carlos and Lily - Carlos’s age is 4 more years than Tony’s age - and Lily’s age is one more than 6 times Tony’s age)
Answers
Answer:
Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.
c + y = 2s ------ equation (1)
t + 4 = c ------ equation (2)
6t + 1 = y ------ equation (3)
Since Sofia is 38 years old, substitute s = 38 into equation (1):
c + y = 2(38)
= 76 ------ equation (4)
Substitute equations (2) and (3) into equation (4):
t + 4 + 6t + 1 = 76
7t + 5 = 76
7t = 71
∴ t = 10 (to the nearest whole number)
∴Tony is 10 years old (to the nearest whole number).
how many different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6? repeated digits are allowed.
Answers
There will be 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6 when repeated digits are allowed by fundamental counting principle.
What is fundamental counting principle?A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting simplifies the approach to selection by taking into account all of the possible choices and their combinations in order to calculate the Probability.
Here,
Since there are 6 digit given,
In first place, there are 6 ways to arrange the digits. In second place, there are 6 ways to arrange the digits. In third place, there are 6 ways to arrange the digits.
This way,
6×6×6=216 ways
When repeated digits are allowed by the fundamental counting principle, 216 different 3-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6.
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Solve the equation:
3/2=4x
x= ____________
Answers
3/8 or 0.375
Answer:
x = [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{2}[/tex] = 4x ( multiply both sides by 2 to clear the fraction )
3 = 8x ( divide both sides by 8 )
[tex]\frac{3}{8}[/tex] = x
Matilda walks from a castle's tower to its drawbridge by heading 624 m due
east and then heading due south.
The straight-line distance from the tower to the drawbridge is 927 m.
Work out the bearing of the drawbridge from the tower.
Give your answer to the nearest degree.
Answers
Answer:
138° (nearest degree)
Step-by-step explanation:
Bearing: The angle (in degrees) measured clockwise from north.
The given scenario can be modelled as a right triangle (see attachment).
Therefore, the bearing is 90° + θ (shown in green on the attached diagram).
To find angle θ, use the cosine trigonometric ratio:
[tex]\implies \cos{\theta}=\dfrac{A}{H}[/tex]
[tex]\implies \cos{\theta}=\dfrac{624}{927}[/tex]
[tex]\implies \theta=\cos^{-1}\left(\dfrac{624}{927}\right)[/tex]
[tex]\implies \theta=47.69018863...[/tex]
[tex]\implies \theta=48^{\circ}\; \; \sf (nearest\;degree)[/tex]
Therefore, the bearing of the drawbridge from the tower is:
[tex]\begin{aligned}\implies \sf Bearing&=90^{\circ}+\theta\\&=90^{\circ}+48^{\circ}\\&=138^{\circ} \end{aligned}[/tex]
Answer:
The bearing of the drawbridge from the tower is 138° SE-----------------------------
The segments that are formed by Matilda walking from the tower to drawbridge form a right triangleHorizontal leg = 624 m,Hypotenuse = 927 m.Find the angle x between the two segmentscosine = adjacent / hypotenusecos x = 624/927x = arccos (624/927)x = 48° (rounded to the whole degree)Find the bearing of the drawbridge from the towerAdd 90° to the angle measure we just found, since bearing is counted from the north direction:
48° + 90° = 138° SEPLEASE HELP!!!!!!!!!!!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
Answers
a) These ramp dimensions do not meet the ADA guidelines.
b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
What is a slope?The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:
The vertical change is of: 3 feet.The horizontal change is of: 15 feet.The ratio between the vertical change to the horizontal change is of:
3/15 = 1/5.
Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.
If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:
3 feet vertical.39 feet horizontal.As the ratio would be of:
3/39 = 1/13 < 1/12.
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graph the solution of the inequality x ≤ 3
Answers
The solution of x ≤ 3 depicts that all the value of x is either less than 3 or equal to 3, so option C is correct.
What is number line?In mathematics, numbers are shown visually as a straight line on a number line. The numerals on a number line are positioned in a specific order and spaced out equally throughout its length. Since it can go on forever in any direction, it is frequently presented horizontally.
The expression x ≤ 3 depicts that the value of x is less than 3 or equal to 3, this can be represented in the image attached below.
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Helen draws a random circle.
She then measures
its diameter and circumference.
She gets a
circumference, C, of 405 mm correct to 3 significant figures.
She gets a diameter, d, of 130 mm
correct to 2 significant figures.
Helen wants to find the value of rt using the formula
T= G
Calculate the upper bound for Helen's value of TC.
Give your answer correct to 3 decimal places.
Answers
If Helen wants to find the value. the upper bound for Helen's value of TC is 3.123 and lower bound is 3.092.
How to find upper and lower bound?Upper bound
405 = 405.999
130 =130.99
Lower bound
405 = 405.001
130 =130.01
Now let find the upper and lower bound
Upper bound = 405.999/130.01
Upper bound =3.123
Lower bound = 405.001 /130.99
Lower bound = 3.092
Therefore the upper bound is 3.123.
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what is the quotient of 84/0.729
Answers
Answer:
115.226337449
Step-by-step explanation:
84/0.729= 115.226337449
And thank you and your welcome
Answer: the quotient of 84/0.729 is 115.226337
A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
Answers
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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Write
y − 2 = (x + 6) in
standard form.
Answers
.
.
.
.
answer: y=x+8
a package of 4 erasers costs $0.39. At this rate, how much would 54 erasers cost, in dollars and cents?
Answers
Answer:
Step-by-step explanation:
5 dollars and 25 cents
can anyone help with this???
Answers
Answer:
L=66 degrees
KL=3.5
LM=8.7
Sophia spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -2.1°F. Between 9am and noon, the temperature increased by 10.8°F. Between noon and 3pm, the temperature decreased by 13°F. Between 3pm and 6pm, the temperature dropped 18.4°F. What was the temperature at 6pm? PLEASE
Answers
Answer:
Step-by-step explanation:
-22.7
If you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually? Is there anything you could change in the problem that would make you change your answer?
Answers
a. I would rather compound annually at 5 % interest
b. I would increase the simple interest rate if i were to change my answer
a. How to determine which option to choose?Since you have $200 to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually, we need to determine the amount of each type of interest after 10 years.
Since you have $200 to invest for 10 years at 7% simple interest, using the simple interest formula for the amount, we have
A = P(1 + rt) where
P = principal amount = $ 200, r = rate = 7% = 0.07 and t = time = 10 yearsSubstituting the values of the variables into the equation, we have
A = P(1 + rt)
A = 200(1 + 0.07 × 10)
A = 200(1 + 0.7)
A = 200(1.7)
A = 340
Also, since you have $200 to invest for 10 years at 5% interest compounded annually, using the compound interest formula for the amount, we have
A' = P(1 + r)ⁿ where
P = principal amount = $ 200, r = rate = 7% = 0.07 and n = time = 10 yearsSubstituting the values of the variables into the equation, we have
A' = P(1 + r)ⁿ
A' = 200(1 + 0.07)¹⁰
A' = 200(1.07)¹⁰
A' = 200(1.9672)
A' = 393.43
Since A' = $393.43 > A = $340, i would rather compound annually at 5 % interest
b. Is there anything you could change in the problem that would make you change your answer?To change my answer, I would increase the simple interest rate if i were to change my answer
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What is the area of the parallelogram shown?
A= In^2
Answers
6.6 in^2
Explanation:
Area = Length x height (width)
= 2.2 x 3
= 6.6 in^2
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The fraction of a mile that Evan has to hike and the fraction he has hiked, gives the completed statement as follows;
[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex]. So the difference is closest to [tex]\frac{1}{2}[/tex]
What is a fraction in mathematics?A fraction is a representation of the part of a whole of an item or collection of items. The distance Evan's hiking trail of [tex]\frac{5}{6}[/tex] miles is a fraction of a mile.
The length of the trail = [tex]\frac{5}{6}[/tex] mile
The distance Evan has hiked = [tex]\frac{2}{5}[/tex] mile
The distance Evan has left to hike is given by the difference between the length of the trail and the distance Evan has hiked as follows;
Distance remaining = [tex]\frac{5}{6} -\frac{2}{5} = \frac{13}{30}[/tex]
Representing the numbers in decimal form, we have;
[tex]\dfrac{5}{6} = 0.8\overline 3[/tex]
The value of [tex]\frac{5}{6}[/tex] is close to 1
[tex]\dfrac{2}{5} = 0.4[/tex]
The value of [tex]\frac{2}{5}[/tex] is closest to 0.5
[tex]\dfrac{13}{30} = 0.4\overline 3[/tex]
The difference between [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{5}[/tex], which is [tex]\frac{13}{30}[/tex] is therefore closest to [tex]\frac{1}{2}[/tex]
The completed statement is therefore;
[tex]\frac{5}{6}[/tex] is closest to 1 and [tex]\frac{2}{5}[/tex] is closest to [tex]\frac{1}{2}[/tex] so the difference is closest to [tex]\frac{1}{2}[/tex]
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William buys 5 small boxes of oat porridge and some large boxes too
in total he buys 6825 grams of porridge
work out the number of large boxes of oat porridge William buys
small boxes = 325 grams each
large boxes = 650 grams each
Answers
The number of large boxes of porridge that William bought, using a system of equations, was of:
8.
What is a system of equations?A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem.
For this problem, the variables are defined as follows:
Variable x: number of small boxes bought.Variable y: number of large boxes bought.William buys 5 small boxes of oat porridge, hence:
x = 5.
The total weight of his purchase is of 6825 grams, hence, considering the weight of each box, the following equation is built:
325x + 650y = 6825.
It is already stated on the problem that x = 5, hence the value of y can be obtained as follows:
325(5) + 650y = 6825.
y = (6825 - 325(5))/650
y = 8 large boxes.
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URGENT
We're doing some experiments to work out how fast our agents can accelerate
Using v = u + at, work out the acceleration when v = 40, u = 20 and t = 10
Answers
First rearrange the equation so that a=(v-u)/t
g(a)=3a+2; find g(-3) HELP PLEASE!!
Answers
The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.
What is the output value of g( -3 ) in the given function?A function is simply a relationship that maps one input to one output. For relation to qualify as a function, each x-value can only have one y-value.
Given the data in the question;
g( a ) = 3a + 2g( -3 ) = ?To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.
g( a ) = 3a + 2
g( -3 ) = 3( -3 ) + 2
Multiply 3 and -3
g( -3 ) = -9 + 2
Add -9 and 2
g( -3 ) = -7
Therefore, the output value is -7, this forms an ordered pair of (-3,-7).
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match to form complementary angle pairs. sin(14) cos(37) sin(49) cos(66) sin(41) cos(24)
cos(76) —>
sin(66)—>
sin(53)—>
cos(49)—>
Answers
Answer:
see explanation
Step-by-step explanation:
using the cofunction identities
cos x = sin(90 - x)
sin x = cos(90 - x)
then
cos76° = sin(90 - 76)° = sin14°
sin66° = cos(90 - 66)° = cos24°
sin53° = cos(90 - 53)° = cos37°
cos49° = sin(90 - 49)° = sin41°
The Matched values are
cos(76) —> sin (14)
sin(66)—> cos (24)
sin(53)—> cos (37)
cos(49)—> sin (41)
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
For complementary angle,
a+ b= 90
So, sin (14)
= cos (90 - 76)
= cos 76
and, cos (37)
=sin (90 - 53)
= sin (53)
and, sin (49)
= cos (90- 41)
= cos 41
and, cos (66)
= sin (90 - 24)
= sin 24
Then, the Matched values are
cos(76) —> sin (14)
sin(66)—> cos (24)
sin(53)—> cos (37)
cos(49)—> sin (41)
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Given that
7
x
−
3
y
=
23
Find
x
when
y
=
−
2
Answers
Answer: [tex]\frac{17}{7}[/tex]
Step-by-step explanation:
7x - 3y = 23
3y = -2 × 3 = -6
7x + 6 = 23
7x = 23 - 6
7x = 17
x = [tex]\frac{17}{7}[/tex]
Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.
How many miles apart are the cyclists in 45 minutes?
PLEASE HELPPPPPP!!!!!!!!!!!
Answers
The distance between two cyclists after 45 minutes as described in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.
Speed, distance and time.It follows from the task content that the distance between the two cyclists after 45 minutes is to be determined from the given parameters.
Given; the speed of the first cyclist is; 12 miles per hour, while the speed of the second cyclist is b miles per hour greater than that of the first.
The speed of the second cyclist is therefore; (b + 12).
On this note, since the distance covered by each cyclist is given by;
Distance = Speed × Time where, Time = 45 minutes = 0.75 hours.
Therefore, the total distance between the two cyclists can be determined from the expression as follows;
7 + 0.75 (12) + 0.75 (b + 12).
Therefore, the distance between the two cyclists as required in the task content is; 7 + 0.75 (12) + 0.75 (b + 12) miles.
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Please Help ASAP!!!!!
Answers
Answer:
the forth (7,2).........
Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season. What is his batting average for the whole season, written as a decimal?
Answers
Answer:123
Step-by-step explanation:
7328x3424
Steven battling average for the whole season he played was 0.45
How to solve an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Steven hit the ball 12 times out of 26 at bats in the first half of the season and 6 times out of 14 at bats in the second half of the season.
Hence:
Batting average = (total number of time he hit the ball in both season half) / (total number of balls thrown)
Therefore:
Battling average = (12 + 6)/ (26 + 14) = 18 / 40 = 0.45
Steven battling average was 0.45
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A youth group is planning a trip to a local amusement park. They are taking a van which holds 10 people. It will cost $25 for parking and tickets to enter the park are $18 per person. Create a table to represent the situation, showing the possible total costs for the various numbers of people who could go?
Answers
Factor −4x2 + 12x. PLease help
Answers
Answer:
-4x(x-3)
Step-by-step explanation:
-4x^2+12x
divide by -4x
-4x(x-3)
Alexa drive a motorcycle 200 kilometers in 3 hours. If she drove at this constant speed, how fat could she travel in 9 hours?
Answers
Answer:600
Step-by-step explanation:
i think
14x²y – 21xy² + 28x²y²
Answers
Answer:
7xy(2x-3y+4xy)
Step-by-step explanation:
14÷7=2
21÷7=3
28÷7=4
they all have 7, x and y so that would be on the outside
show algebraically the sum of two consecutive numbers is always odd
Answers
the sum of two odd integers will always be resulted in an odd digit.
What are odd numbers?Odd numbers are entire numbers that can't be isolated precisely into matches. Odd numbers, when separated by 2, leave a rest of 1. , 3, 5, , 9, 11, , 15 are consecutive odd numbers.
These are added together to get n + n+1, or 2n+1. Since +1 make it odd, 2n is even. Any two successive integer sums are hence odd. According to the solution is "2n + (2n + 1) = 4n +1."
Even numbers result from the addition of two fractions, but still only digits result from the addition of one odd number with one even number. In order to only receive an odd number, add one odd as well as one even.
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Carmen has taken out a loan for $800 to buy a car. She plans to pay back the loan at a rate of $40 per month. Ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month.
How long will it take Ramona to pay back her loan?
a.
25 months
b.
20 months
c.
15 months
d.
10 months
Answers
Answer:
Carmen will have her loan paid back in 20 months
