Answers
Based on given question question, following are the answers of blanks based on Midpoint Theorem.
- ∠ECD ≅ ∠BCA [Vertically opposite angle]- ∠D ≅ ∠A [Alternate interior angle]Given, ∠DEC ≅ ∠ABCC is the midpoint of D and A1.) Definition of midpoint
The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side.
2.) ∠ECD ≅ ∠BCA [Vertically opposite angle]
Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other.
3.) ∠D ≅ ∠A [Alternate interior angle]
When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
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Related Questions
Find the values of x and y. 4y 112° 7x +7°
Answers
If m = 7x + 7, m = 4y, and m = 112
since m = 112
112 = 7x + 7
112 - 7 = 7x
105= 7x
x = 15
112 = 4y
y = 28
Solve the equation below for x by graphing
3x =8_2x
Answers
The solution to the equation 3x = 8 - 2x is x = 1.6.
To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:
Express the equation in the form of y = f(x). Rearrange the equation:
3x + 2x = 8
5x = 8
x = 8/5 or 1.6
Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.
Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.
The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).
Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.
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A standard pair of six sided dice is rolled what is the probability of rolling a sum greater than or equal to 11
Answers
The diagram below shows all the possible outcomes from rolling a pair of six sided dice.
The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.
Total number of outcomes = 36
Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3
Thus, the probability of rolling a sum greater than or equal to 11 is
3/36 = 1/12
what is p^-2 divided by p^n equal to?
Answers
Answer:
p^2+n
Step-by-step explanation:
When you divide exponents, you subtract them and keep the base (the large number attached to the exponent) the same.
If we subtract two negatives (in this case it's p^-2 - p^n) the answer ends up being positive. So, the answer is p^2+n.
Hope this helped!
A recipe calls for 2 cup of brown sugar for every 6 cups of white sugar. How many cups of brown sugar are required for every 12 cups of white sugar?
(PLEASE HELP!!)
Answers
There are 4 cups of brown sugar are required for every 12 cups of white sugar.
A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:
2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar
To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:
2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar
24 cups brown sugar = 6x cups brown sugar
x = 24/6
x = 4
So, 4 cups of brown sugar are required for every 12 cups of white sugar.
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Chris burrows $124 from a friend to get his chainsaw repaired. If Chris agrees to pay his loan in 6 months at 4% simple interest, then how much interest does Chris pay?
Answers
Chris borrows $124 from a friend for 6 months with a simple interest of 4%, the total interest that he would pay is given by:
\(\begin{gathered} \text{Total interest=\#months}\times(Borrowmoney)(\text{interest rate)} \\ \text{Total interest}=6\times(124)(\frac{4}{100})=29.76\text{ usd} \end{gathered}\)Chris pays $29.76 interest in 6 months.
len Love: by Can Themba
Your response should be 80-100 words in length.
The is story about two people who loved each other deeply and had
to hide their feelings. Micheal is black and Dora is coloured.
The two lovers are eventually exposed when Dora's little brother
Bobby is told at his school that his sister is in a relationship with a
native.
A fight follows and Menner Carelse (school teacher) who is in love
with Dora finds out. He tries to convince the Principal that her family
must be told, and much against the Principal's wishes, he goes to
tell the whole community about what they considered "scandal".
Put yourself in Dora's shoes and write TWO diary entries on
how she feels about the meeting between the two families. One
entry must express her feelings. BEFORE Micheal's beating by
Davie and his friends. The other must express how she felt
AFTER Salome presents evidence in the form of love letters
that Davie has written to her.
[20]
Answers
Expression P + 2p +3p +4p whats the equivalent expression
Answers
Answer:
10p
Step-by-step explanation:
p + 2p + 3p + 4p
= 10p
Answer:
10p
General Formulas and Concepts:
Algebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define
p + 2p + 3p + 4p
Step 2: Simplify
Combine like terms (p): 10pWhat is 30 ÷ 14 written as a fraction?
Answers
Answer: A fraction is Quite literally division so 30 divided by 14 is 30/14 as a fraction, you can also simplify that to 15/7
The value of the expression is 15/7.
What is division?Division is the process of dividing a number by a given number.
The given expression is 30 ÷ 14.
Solve the expression as follows:
30 ÷ 14
= 30/14
= 15/7
Hence, the value of the expression is 15/7.
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Does the function f(x) = (0.68)^x represent exponential growth, decay, or neither?
Answers
Answer:
The function is always Decreasing
Step-by-step explanation:
By graphing the polyminal in order to determine the intervals over which it is increasing or decreasing we find that it always decreasing.
The test results for a class with 24 students are normally distributed with a mean of 82 and a standard deviation of 8.9. What is the probability that a randomly chosen student earned a B or higher on the test (score of 80 or higher)?
Answers
Answer:
The value is \(P( X > 80 ) = 0.58901\)
Step-by-step explanation:
From the question we are told that
The sample size is n = 24
The mean is \(\mu = 82\)
The standard deviation is \(\sigma = 8.9\)
Generally the probability that a randomly chosen student earned a B or higher on the test (score of 80 or higher ) is mathematically represented as
\(P( X > 80 ) = P( \frac{ X - \mu }{\sigma } > \frac{ 80 - 82 }{ 8.9 } )\)
\(\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )\)
=> \(P( X > 80 ) = P(Z > -0.225 )\)
From the z table the area under the normal curve to the right corresponding to -0.225 is
\(P(Z > -0.225 ) = 0.58901\)
=> \(P( X > 80 ) = 0.58901\)
5. Aaron sold 126 boxes of cookies. This is 14 more than twice the
number of boxes his sister, Victoria, sold. How many boxes of
cookies did Victoria sell?
Answers
Answer:
56 boxes
Step-by-step explanation:
1. First subtract 14 from 126 to get 112 boxes
2. Now divide 112 by 2 to get Victoria's total of 56
Aircraft A has 105 more seats than aircraft B. If their total number of seats is 701, find the number of seats for each aircraft.
Aircraft A has how many seats?
Answers
Answer:
Aircraft A: 403 seats
Aircraft B: 298 seats
Step-by-step explanation:
Let's x represent the seats in Aircraft B
We have the equations:
Aircraft A: (x + 105)
Aircraft B: x
We Know
Their total number of seats is 701; find the number of seats for each aircraft.
We Take
x + (x + 105) = 701
2x + 105 = 701
2x = 596
x = 298 seats
So, there are 298 seats in Aircraft B
Aircraft A has how many seats?
We Take
701 - 298 = 403 seats
So, there are 403 seats in Aircraft A
Final Answers:
Aircraft A: 403 seats
Aircraft B: 298 seats
Please help!!!!! Find the value of the variables
Answers
Answer:
x = 24
y = 8√3
Step-by-step explanation:
This is a special right triangle with angle measures 30° 60° 90°
The side length that sees 90° is represented by 2a, the side length that sees angle 60° is represented by a√3 , and the side length that sees angle 30° is represented by a
16√3 ÷ 2 = 8√3 this is the value of y
8√3 × √3 = 24 this is the value of x
Rosa Bought some place mats costing $17.16 and some napkin ring’s costing $10.36.If there were 4 place mats and 4 napkin ring’s what was the total cost for 1 place mat and 1 napkin ring?
Brian is trying to lose at least 2 pounds a week by eating less and walking 2 miles each day. For the past 3 weeks,he lost 2.4 pounds,1.9,and 3.2 pounds. what was the average number of pounds he lost?
Can someone answer these?
Answers
9514 1404 393
Answer:
$6.882.5 poundsStep-by-step explanation:
1. In this case, it appears that "some" means "4". The total cost of 4 place mats and 4 napkin rings is apparently ...
$17.16 +10.36 = $27.52
Then the total cost of 1 of each is 1/4 this amount, or ...
$27.52/4 = $6.88
__
2. The average of three numbers is their sum, divided by 3.
(2.4 + 1.9 + 3.2)/3 = 7.5/3 = 2.5
Brian lost an average of 2.5 pounds per week.
Hi guys! PLEASE HELP! I'm back with another probability problem I've struggling on. Please DO NOT leave any links or you will be reported.
Please help explain what I'm doing wrong and what I'm suppose to do. This is confusing me.
Pizza parlor A advertises 35 different three-topping pizzas. How many individual toppings does Pizzeria A actually use? Pizzeria B advertises 55 different two-topping pizzas. How many toppings does pizza parlor B actually use? (Hint: In these problems, you are given the total number of combinations, and you must find the number of toppings that are used.)
Pizza parlor A uses _____ nothing different toppings. (Type a whole number.)
Thank to anyone who decides to help :)
Answers
Answer:
Possibly 105?
Step-by-step explanation:
35 becuase (35 different three-topping pizzas) so 35x3=105?
Peter had 208 Canadian stamps and 186 Mexican stamps for sale. The stamps were mixed up and sold in packets of 6. How many packets of stamps were there? How many stamps were left over?
Answers
Answer:
65 packets and 4 stamps
Step-by-step explanation:
The first thing we see is that the stamps are mixed... which means they must be added.
208 + 186 = 394 stamps total
Now we see that each packet has 6 stamps. So we divide the number of stamps in total by 6.
394/6= 65.66667
Now we see from that number that the stamps can't quite make 66 packets, so there are 65 packets.
Now we find the number of stamps left over by multiplying the number of packets by 6.
65 x 6= 390
Now we take the total number of stamps minus the number of stamps in packets.
394 - 390 = 4
Therefore, there are four stamps left over.
Hope this helps!
The surface area of a sphere is 900pi cubic cm. What is the length of its diameter.
Answers
The length of the diameter of the sphere is 30 cm.
The surface area of a sphere is given by the formula:
\(A = 4\pi r^2\)
where A is the surface area and r is the radius of the sphere.
We are given that the surface area of the sphere is 900π cubic cm. Therefore:
\(A = 4\pi r^2 = 900\pi\)
Dividing both sides by 4π, we get:
\(r^2 = 225\)
Taking the square root of both sides, we get:
r = 15
The diameter of the sphere is twice the radius, so:
d = 2r = 30
Therefore, the length of the diameter of the sphere is 30 cm.
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4 x 5 - (2² - 2) =?
(18 ÷ 3) + (3² - 7) =?
Answers
(18/ 3) + (3 (2) - 7) 8
London found an equivalent ratio to the ratio shown below by multiplying both side of 7. What is the equivalent ratio London found? Use the ratio format (a/b) when inputting your answer. 5:2
Answers
Answer:
It can also be expressed as 35/14.
Step-by-step explanation:
Equivalent Ratio
A ratio is a relation between two numbers a, b in the format a:b and it's equivalent to the division a/b.
Since it's equivalent to a division or a fraction, it can be simplified or amplified by multiplying or dividing both sides by the same number.
The ratio 5:2 can be amplified by multiplied by 7 as follows:
5*7:2*7 = 35:14.
It can also be expressed as 35/14.
in a sale, normal prices are reduced by 25% the normal price of a cost is reduced by £12
work out the normal price of the coat
Answers
Answer:
£16
Step-by-step explanation:
Let's assume the normal price of the coat is represented by the variable "P."
According to the information given, the normal price of the coat is reduced by £12. This can be expressed as:
P - £12
Additionally, in the sale, normal prices are reduced by 25%. This reduction can be calculated by multiplying the normal price by 25% (or 0.25):
0.25P
To find the sale price after the 25% reduction, we subtract the reduction amount from the normal price:
P - 0.25P = £12
Simplifying the equation:
0.75P = £12
To solve for P, we divide both sides of the equation by 0.75:
P = £12 / 0.75
Performing the calculation:
P = £16
Therefore, the normal price of the coat is £16.
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
help please help please
Answers
Answer:
+7 or 7
Step-by-step explanation:
an integer is a whole number. So the question asks what whole number represent this real world situation. A positive charge to an atom can not be represent by a negative number (number below zero). Therefore, it has to be positive.
Answer:
-7
Step-by-step explanation:
.
11. Together, Andy and Ben can re-roof a certain house in six days. When Ben works alone, it takes him 9 days longer than when Andy works by himself. How long does it take each person to re-roof the same house independently?
Answers
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the population of a town grows at a rate proportional to the population present at time t. the initial population of 500 increases by 15% in 10 years. what will be the pop ulation in 30 years? how fast is the population growing at t 30?
Answers
Using the differential equation, the population after 30 years is 760.44.
What is meant by differential equation?In mathematics, a differential equation is a relationship between the derivatives of one or more unknown functions. Applications frequently involve a function that represents a physical quantity, derivatives that show the rates at a differential equation that forms a relationship between the three, and a function that represents how those values change.A differential equation is one that has one or more functions and their derivatives. The derivatives of a function define how quickly it changes at a given location. It is frequently used in disciplines including physics, engineering, biology, and others.The population P after t years obeys the differential equation:
dP / dt = kPWhere P(0) = 500 is the initial condition and k is a positive constant.
∫ 1/P dP = ∫ kdtln |P| = kt + C|P| = e^ce^ktUsing P(0) = 500 gives 500 = Ae⁰.
A = 500.Thus, P = 500e^ktFurthermore,
P(10) = 500 × 115% = 575sO575 = 500e^10ke^10k = 1.1510 k = ln (1.15)k = In(1.15)/10 ≈ 0.0140Therefore, P = 500e^0.014t.The population after 30 years is:
P = 500e^0.014(30) = 760.44Therefore, using the differential equation, the population after 30 years is 760.44.
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what is 2,606 + 7,025?
Answers
Answer:
2606 + 7025 = 9631
Pls mark me brainliest
Answer: 9631
2606
+7025
9631
Is f(x)= 7e^-21 an example of exponential growth or decay?
Answers
Answer:
\(\small\mathfrak\green{here \: is \: your \: answer...} \\ \\ \small\mathfrak\pink{exponential \: decay...} \\ \\ \small\mathfrak\green{hope \: it \: helps...}\)
joe spend 1 1/3 hours studying for his math test. randy studied for 1/2 the amou t the time that joe did. what fraction of an hour did randy spend studying
Answers
Step-by-step explanation:
Lets convert 1 1/3 into improper fraction.
\(1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} \\ = \frac{4}{3} \)
Since Randy studied half the above time,
Randy Studied:
\( \frac{1}{2} \times \frac{4}{3} \\ = \frac{1 \times 4}{2 \times 3} \\ = \frac{4 \div 2}{6 \div 2} \\ = \frac{2}{3} hours\)
Can Wendell make a triangular garden using pieces D, E, and F? Why or why not?
Answers
If the sides of the triangle are given. Then Wendell can make a triangular garden using pieces D, E, and F.
What is the construction of the triangle?The process of making a triangle is known as the construction of the triangle.
Wendell makes a triangular garden using pieces D, E, and F.
Where D, E, and F may be a side of the triangle or angle of the triangle.
To make a triangle we need at least one side of the triangle.
If all the angles of the triangle is given then we can not make a triangle because the side of the triangle is unknown.
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Answer:
If the sides of the triangle are given. Then Wendell can make a triangular garden using pieces D, E, and F.
Step-by-step explanation:
the length of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of 0.7 minutes. what is the probability that a conversation lasts longer than 6 minutes?
Answers
The probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
What is probability?
The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.
We can use the standard normal distribution to solve this problem by standardizing the variable using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that a conversation lasts longer than 6 minutes, so x = 6, μ = 5, and σ = 0.7. Substituting these values into the formula, we get:
z = (6 - 5) / 0.7 = 1.43
Next, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than 1.43. Using a standard normal distribution table, we find that this probability is approximately 0.0764.
Therefore, the probability that a conversation lasts longer than 6 minutes is approximately 0.0764 or 7.64%.
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