Answers
∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.
In the given question we have to prove ∆GHJ congrurnce ∆KLM.
Given that: ∠G≅∠K, ∠J≅∠M, [tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex].
As given that;
∠G≅∠K
∠J≅∠M
[tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex]
So from the angle sum property of triangle
∠G+∠H+∠J=180................(1)
∠K+∠L+∠M=180.................(2)
Now equation equation 1 and 2
∠G+∠H+∠J=∠K+∠L+∠M
As we know that ∠G=∠K, ∠J=∠M
So now the expression is
∠G+∠H+∠J=∠G+∠L+∠J
After solving ∠H=∠L (3rd Angle Theorem)
Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,
∆GHJ≅∆KLM
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Related Questions
See picture-multiple choice.
Answers
From the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞
From the given graph
The x axis represents the values of x, and the y axis represents the value of y
From the graph,
When the value of x moves from 0 to - ∞, then the value of f(x) is moves from 0 to - ∞
Similarly, when the value of x moves from 0 to ∞, the the value of f(x) is increased to positive values and then decreased to - ∞.
Hence, from the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞
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A five-gallon tank full of water starts draining at t = 0 at a rate of 1/(1 + t) gallons per hour. How long until the tank is empty?
Answers
1. It will take 5 hours for the five-gallon tank full of water to become empty at the drainage rate of 1/(1 + t) gallons per hour.
2. A correct setup of the equation problem above in terms of function is D. None of these will give the correct solution.
What is an equation?An equation is a mathematical statement that shows that two or more mathematical expressions share equality or are equivalent.
Functions, which are mathematical expressions involving one or more variables known as domain (or the independent variable) and range (or the dependent variable), using the equation symbol to show that two expressions are equal.
Drainage rate per hour = 1/(1 + t) gallons
t = 0
The capacity of the tank = 5 gallons
1/(1 + t) gallons
= 1/(1 + 0) gallons
= 1/1 gallons
= 1 gallon per hour
Since the tank is 5 gallons, it will take = 5 hours (5/1)
Thus, based on the drainage equation rate, the five-gallon tank will empty in 5 hours.
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4.8 is what percent of 12
Answers
Answer:
40%
Step-by-step explanation:
4.8 * 100 = 480
480 / 12 = 40
= 40%
I hope this helps.
Please HELP..
Our class is studying the effects of mindfulness on mental health. To help with data collection, we will have the support of ten grade 9, eleven grade 10, twelve grade 11 and thirteen grade 12 students. Showing your calculations,how many different groups of 12 volunteers can we make if:
a) the group must have the same number of students from each grade?
b) the group must have at least two grade 9 students? [2A]
c) the group must have James and Lucy (both grade 11 students) in it? [2A]
Answers
The number of groups, using the combination formula, for each case, is given as follows:
a) Same number of students from each grade: 1,245,816,000
b) At least two grade nine students: 31,650,886,995.
c) James and Lucy are in it: 2,481,256,778.
How to obtain the number of groups?The number of groups is obtained for the three cases using the combination formula, as the order in which the students are chosen is not important.
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For item a, the same number of students is taken from each class, hence 3 students are taken from each class, as 12 students are taken from 4 classes, hence 12/4 = 3.
Hence the number of groups, considering the number of students in each class, is of:
[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]
For item b, we use complementary events, first obtaining the total number of students that can be taken, and then removing the combinations that do not have at least two grade nine students.
The total number of groups is obtained as follows:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
(as there are 10 + 11 + 12 + 13 = 46 students, and 12 are taken).
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
(removing the 10 students from grade 9).
The number of groups with one student from grade 9 is:
[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]
(one from grade 10 and the remaining from the other classes).
This the number of groups with at least two grade 9 students is calculated as follows:
38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.
For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set containing the 44 remaining students, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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I don't know what I'm doing! HELP!!!
Answers
Booker's father amount of commission earned is 668.31 dollars.
Sophia needs to make sells of 16744 dollars in order to earn at least 1800 dollars in commission.
How to find how much commission Booker's father will earn?Booker's father sells computer software and earns a 4.25% commission on every software package he sells.
The amount of commission he will earn after selling a software package of $15, 725 can be calculated as follows:
amount of commission earned = 4.25% of 15725
amount of commission earned = 4.25 / 100 × 15725
amount of commission earned = 66831.25 / 100
Therefore,
amount of commission earned = 668.3125
amount of commission earned = 668.31 dollars
Sophia needs to earn at least 1800 dollars each month to cover her living expenses.
The minimum she needs to sell in order to earn at least 1800 dollars if she earns 10.75% commission can be calculated as follows:
let
x = amount she needs to sell
Therefore,
10.75% of x ≥ 1800
10.75 / 100 x ≥ 1800
multiply both sides by 100
10.75x ≥ 180000
divide both sides by 10.75
x ≥ 16744.1860465
x ≥ 16744
Therefore, she needs to sell 16744 dollars worth of goods.
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P(H)=
P(T)=
let me know if you know how to do this
Answers
Answer:
Step-by-step explanation:
they are asking for probability
so they want to know, what's the probability of getting a "heads" on a coin toss. What do you think it is? You probably know this intuitively.
P(H) = ?
P(T) = ?
They are asking for fractions, so just say what you already know to be how often you'll get a "heads" in words, then just make that a fraction. :)
Find three even numbers less than 400, each of which can be expressed as a sum of consecutive positive odd numbers in at least six different ways.
Answers
Answer:
394, 396 and 398
Step-by-step explanation:
Question 10
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A
pollster contacts 93 people in the 18-21 age bracket and finds that 79 of them respond and 14 refuse to
respond. When 251 people in the 22-29 age bracket are contacted, 219 respond and 32 refuse to respond.
Assume that 1 of the 344 people is randomly selected. Find the probability of getting someone in the 18-21
age bracket or someone who responds.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
P(18-21 or responds) =
(Hint: It might be helpful to organize the data into a table first.)
Submit Question
%
Answers
The probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.
The total number of people in the 18-21 age bracket is 93. The number of people in this bracket who responded is 79. The number of people in this bracket who refuse to respond is 14. The total number of people in the 22-29 age bracket is 251. The number of people in this bracket who responded is 219. The number of people in this bracket who refuse to respond is 32.
A person is randomly selected from all the people surveyed. We need to find out the probability of getting someone in the 18-21 age bracket or someone who responds. Let the variables E1 and E2 represent the events.
E1 is the event of getting a person from the 18-21 age bracket.
E2 is the event of getting a person who responds.
P(E1∪E2) = P(E1) + P(E2) - P(E1∩E2)
P(E1∪E2) = (93/344) + [(79 + 219)/344] - (79/93)
P(E1∪E2) = 0.27035 + 0.86628 - 0.84946
P(E1∪E2) = 0.28717
Hence, the probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.
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Solve for x
-21 = -7x
Simplify your answer as much as possible.
Answers
Answer:
Step-by-step explanation:
-21 = -7x
-21 divided by -7 = -7 divided by -7
3=x
Hi can someone please help me? Thank you so much have a good day/night! ;)
Answers
Answer:
136 cm
Step-by-step explanation:
area of rectangle-- width x length--- 112
area of triangle-- base x height divided by 2--- 24
please mark brainiest
How far up the wall does the ladder reach (round your answer to the nearest tenth) enter only the numerical answer no label
Answers
Answer: 8.7m
Step-by-step explanation:
We can use the Pythagorean theorem to solve this,
[tex]a^2+b^2 = c^2[/tex]
We have a (5m) and c (10m) so we're looking for b.
We can rearrange the equation to find b into,
[tex]b^2 = c^2-a^2[/tex]
[tex]b^2=10^2-5^2[/tex]
[tex]b^2 = 100-25[/tex]
[tex]b^2=75[/tex]
[tex]b=8.66025404[/tex]
Rounded to the nearest tenth is 8.7m.
solve the equation for y
5x+7y=35
Answers
Answer:
[tex]y=-\frac{5}{7}+5[/tex]
Step-by-step explanation:
the goal is to isolate y on one side
5x+7y=35
-5x. -5x
7y=35-5x
/7. /7. /7
y=-5/7x+5
Hopes this helps please mark brainliest
c. Write two different expressions you could use to represent the
combined area of the Description and Small Diagram sections.
What information about the combined area does each
expression show
Answers
500
Step-by-step explanation:
research
I need help please and thank you.
Answers
The inequality that relates [tex]LN[/tex] and [tex]OQ[/tex] is [tex]LN>OQ[/tex].
A group of 15 athletes participated in a golf competition. Their scores are below:
Score (points) 1 2 3 4 5
Number of Athletes 1 2 3 4 5
Would a line plot or a histogram best represent the data presented here? Why?
Histogram, because a large number of scores are reported as ranges
Histogram, because a small number of scores are reported individually
Line plot, because a large number of scores are reported as ranges
Line plot, because a small number of scores are reported individually
Answers
The solution is Option D.
Line plot , because a small number of scores are reported individually
What is a line plot?
A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.
If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions
Given data ,
Total number of athletes = 15
The score points of athletes = { 1 , 2 , 3 , 4 , 5 }
The number of athletes = { 1 , 2 , 3 , 4 , 5 }
The best option to plot the line plot because of the data set
The line plot , a data visualization chart that more accurately represents the small data set, is chosen.
And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation
Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps
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Answer:D
Step-by-step explanation:
Apply the distributive property to the following expression: 2n (5m -1)
I need HELP!! ASAP!!
Answers
By using the distributive property, we will rewrite the expression as:
2n*(5m -1) = 10*n*m - 2n
How to apply the distributive property?
The distributive property of the multiplication says that the product:
A*(B + C)
Can be rewritten as:
A*(B + C) = A*B + A*C
So we are "distributing" the product.
In this case, we have the expression:
2n*(5m - 1)
If we apply the distributive property, then we will get:
2n*(5m - 1) = (2n)*(5m) + (2n)*(-1)
Now we can simplify this expression to get:
(2n)*(5m) + (2n)*(-1) = 10*n*m - 2n
That is what we wanted to get.
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The figure is cut into 12 equal pieces. Shade 2/3 of the figure.
Answers
Answer:
Step-by-step explanation:
OK:
I won't be able to draw this but if I can I will
1. Find 2/3 of the 12 pieces
2/3*12=
24/3=
8
2. Answer: Shade 8 out of 12 pieces
or Each morning, Sleepwell Hotel offers its guests a free continental breakfast with pastries and orange juice. Last year, the hotel served a total of 490 gallons of orange juice to its guests. This year, the hotel served 931 gallons of orange juice. What is the percent of increase in the amount of orange juice served yearly?
Answers
Answer:
90% increase
Step-by-step explanation:
490-931=-441
931-490=441
931/490=1.9
therefore, 190% of 441=931
Answer:90% increase
What is answer? Tell me pls :)
Answers
Answer:
when y=20
x=unknown number
x-y=16
x=16+y
x=16+20
x=36
Step-by-step explanation:
b) On the grid draw the graph of x+y=6 for values of c between -2 and 3
Answers
PLEASE PLEASE HURRY What is −12÷2/3? Responses −36 negative 36 −24 negative 24 −18 negative 18 −8 negative 8
Answers
Answer: -18
Step-by-step explanation:
im not 100% sure but good luck :)
Answer: -12/2/3=-2
Step-by-step explanation:
Helppp!
Triangle FJE and GKH are similar right triangles. Which statements about the slopes of FE and GH is true?
Answers
G(-2,1)
H(4,9)
F(-5,-3)
E(-8,-7)
Therefore we can find the slope by using the formula : y1-y2/x1-x2
Let’s find slope GH
1-9/-2-4=-8/-6=4/3
Let’s find slope FE
-3-(-7)/-5-(-8)=4/3
The slope FE is equal to the slope of GH
B) is the right answer
A shelf and bracket are shown below. The shelf is
perpendicular to the wall.
Note: The figures is not drawn to scale
What angle (x), in degrees, does the bracket make with the wall?
Answers
60 degrees is he angles which are made by bracket with the wall
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The shelf is perpendicular to the wall.
The shelf makes an angle of 90 degree to the wall because when the shelf is perpendicular then the wall and shelf should be ninety degrees.
From the shelf edge to wall there creates an angle x.
We need to find the angle x.
As it forms a right angle triangle one angle is 90 degrees and the other angles should be 60 degrees and 60 degrees.
Hence 60 degrees is the angles which are made by bracket with the wall
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For a pole-vaulter in training, the height the athelete will be able to pole-vault after t months of training is given by
H(t) = 17-11e^-0.02t
After how many months will she be able to vault 11 ft?
Answers
The number of months after which she will be able to vault 11 feet is 30 months.
For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by a mathematical formula. The formula is given below.
H(t) = 17 - 11e^(-0.02t)
We need to find the number of months after which she will be able to vault a height equal to 11 feet. We will substitute the value of height in the given equation.
11 = 17 - 11e^(-0.02t)
11e^(-0.02t) = 17 - 11
11e^(-0.02t) = 6
e^(-0.02t) = 6/11
Now, we will take the natural logarithm on both sides of the equation.
-0.02t = -0.606
t = 0.606/0.02
t = 30.3
Thus, she will be able to vault 11 feet in approximately 30 months.
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Which of the following is an example of the identity property of 1?
1.11(0)=0
0+2 4/5=2 4/5
11/15(1)=11/15
3-2=1
Answers
Answer:
i think third answer is write
In QRS, RS QR and m/Q = 46°. Find m/S.
Answers
In triangle QRS, ∠S=67⁰ if ∠R =∠S and ∠Q=46⁰
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common endpoint, and are referred to as the sides of the angle. Two planes intersecting at an angle also produces an angle.
A measure of an angle or of a rotation is also referred to as an angle. The ratio of a circular arc's length to radius is known as this quantity. When it comes to a geometric angle, the arc's vertex serves as its center and its sides as its boundaries. When there is a rotation, the arc is defined by the rotation's image and any other point other than the rotation's center.
In triangle QRS,
And from the figure,
∠R=∠S
Therefore,
∠R+∠S+∠Q=180⁰
2∠S+46⁰=180⁰
2∠S=134⁰
∠S=67⁰
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The height of a triangle is 8 centimeters greater than the base. The area of the triangle is 356.5 square centimeters. Find the length of the base and the height of the triangle.
Answers
The lengths of the base of the triangle are 31cm while the height of the triangle is 39cm
A triangle is a polygon that has 3 sides, three angles and three vertices whose sum of angles equal to 180 degrees.
How to find the lengths and height of a triangle?
from the statement,
h=b+8Area = 256.5 square centimetersA=1/2bh
A=1/2 xbx(8+b)
cross multiplying,
713 = 8b+b²
rearrange the function
b²+8b-713=0
Simplyfying the equation,
(b²+23b)-(31b-713)=0
b(b+23)-31(b+23)=0
b-31=0 or b+23 =0
b=31 or b=-23
length cannot be negative. therefore base = 31cm
Recall the h= b+8
this implies that h=8+31
h=39cm
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Answers
Answer:should be 40 because WxL=area soooo try 40
Step-by-step explanation:
Answer:
Area = width x height
Area = 4cm x 10cm
Area = 40 cm²
Carter shared his post with 10 friends, who each share with only 2 people each day. Carter shared his post with 10 friends, who each share with only 2 people each day.
write an exponential function to represent the spread of carters social media post.
Answers
The exponential function will be equal to y = 20ˣ.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carter shared his post with 10 friends, who each share with only 2 people each day.
The exponential function will be written as,
y = abˣ
y = 10(2)ˣ
y = 20ˣ
Therefore, the exponential function will be equal to y = 20ˣ.
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Answer:
f(x) = 10(2)^x
Step-by-step explanation:
Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.
The temperature gauge in your car records the temperature to be 27°C. What is that temperature to the nearest degree Fahrenheit?
Answers
===============================================
Work Shown:
F = (9/5)*C + 32
F = (9/5)*27 + 32
F = 80.6
F = 81
Side note: 9/5 = 1.8
Answer:
81 degrees Fahrenheit.
Step-by-step explanation:
Using the standard Fahrenheit-Celsius conversion formula.
27 * 9/5 = 48.6.
48.6 + 32 = 80.6.
Rounded to 81.
Therefore 81 degrees Fahrenheit.