Select the correct answer from each drop-down menu. A triangle ABC with base AC is shown. A line DE, parallel to line AC, passes through vertex B. Interior angle at vertex A is labeled 1, at vertex C is labeled 3, and at vertex B is labeled 2. The exterior opposite angles at vertex B are 4 and 5. Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ΔABC is 180°. Statement Reason Points A, B, and C form a triangle. given Let be a line passing through B and parallel to . definition of parallel lines ∠3 ≅ ∠5 and ∠1 ≅ ∠4 m∠1 = m∠4 and m∠3 = m∠5 m∠4 + m∠2 + m∠5 = 180° angle addition and definition of a straight line m∠1 + m∠2 + m∠3 = 180° substitution
Answers
The statement to prove that the sum of the interior angles of ΔABC is 180° should be completed as follows;
Statements Reasons
Points A, B, and C form a triangle. ⇒ Given
Let DE be a line passing through B and parallel to AC. ⇒ definition of parallel lines
∠3 ≅ ∠5 and ∠1 ≅ ∠4 ⇒ alternate interior angle theorem.
m∠1 = m∠4 and m∠3 = m∠5 ⇒ congruent angles have equal measures.
m∠4 + m∠2 + m∠5 = 180° ⇒ angle addition and definition of a straight line
m∠1 + m∠2 + m∠3 = 180° ⇒ substitution
What is the congruence of angles?In Mathematics, congruence of angles can be defined as a theorem which states that two (2) angles are congruent when the measure of their angles are equal.
This ultimately implies that, two (2) congruent angles would always have equal measures as depicted in triangle ABC with line DE;
m∠1 = m∠4 and m∠3 = m∠5
By applying the Alternate Interior Angles Theorem to triangle ABC and line DE, we have the following:
∠3 ≅ ∠5 and ∠1 ≅ ∠4
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Related Questions
What is the best approximation of the solution to the system to the nearest integer values?
Answers
Answer:
(-2, 6)
Step-by-step explanation:
3x - 4y = -32
3x + 5y = 24
-9y = -56
y = [tex]\frac{56}{9}[/tex] = 6
3x - 4*[tex]\frac{56}{9}[/tex] = -32
3x - [tex]\frac{224}{9}[/tex] = -32
3x = -32 + [tex]\frac{224}{9}[/tex]
3x = -[tex]\frac{288}{9}[/tex]+ [tex]\frac{224}{9}[/tex]
3x = -[tex]\frac{64}{9}[/tex]
x = -[tex]\frac{64}{27}[/tex] = -2
Need help with this one
Answers
Answer:
The answer is a.2x/9Step-by-step explanation:
[tex] \frac{x {}^{2} }{3y} \div \frac{3x}{2y} \\ \frac{x {}^{2} }{3y} \times \frac{2y}{3x} \\ \frac{x {}^{2} }{3} \times \frac{2}{3x} \\ \frac{x}{3} \times \frac{2}{3} = \frac{2x}{9} [/tex]
look at the pictures
Answers
Factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)
Inequality functionsFor us to determine if a set of inequality function has a solution, we will equate the functions and determine the point of intersection if there are any,
Given the inequalities
y ≤ x^2 - 3
y > -x^2 + 2
Equate
x^2 - x = -x^2 + 2
Collect like terms
2x^2 - x - 2 = 0
In order to determine the value of x, we will factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)
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Difference of Squares gives which complex factors for the expression x² +11?
A. (x+√11)2(x-i√11)²
B. (x+√11)(x+√11)
C. (x-i√11)(x-√11)
D. (x+√11)(x - √11)
Answers
Answer:
Step-by-step explanation:
Discussion
i has to appear somewhere. That lets D and B out. They are both wrong.
C has only one i. It can't be right either. You need 2 i-s which will multiply to +1 when squared. That leaves you with a.
The way a is written, it can't be the answer either. For one thing, that 2 makes the answer question at best.
I would say there is no correct answer. Could you check the question? Also it would be a good idea to ask your instructor how this works, in case I'm wrong.
4/10x - 2x + 8/5 = 4/5
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]
Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$}[/tex]Subtract 8/5 from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}[/tex]Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}[/tex]Subtract 8 from 4 to get -4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$}[/tex]Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$}[/tex]Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}[/tex]Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf x=\frac{1}{2} \end{gathered}$}}[/tex]Good luck in your studies10 points please answer correctly (due soon)
Let’ pretend that in an American city there were 2000 new cases on Monday which is a 12% decrease from two weeks ago.
1. Write a linear/exponential equation that
models this situation (consistent with the data
provided). Time is the explanatory variable, and
New Cases is the response variable.
B) Explain what the slope/multiplier (consistent
with your choice above) means in this context
of the problem. Be sure to use units.
Answers
The exponential equation of the model is A(t) = 2583 * 0.88^t and the multiplier means that the number of new cases in a week is 88% of the previous week
The function that models the dataThe given parameters are:
New, A(t) = 2000
Rate, r = 12%
The function is represented as:
A(t) = A * (1 - r)^t
So, we have:
2000 = A * (1 - 12%)^t
This gives
2000 = A * (0.88)^t
2 weeks ago implies that;
t = 2
So, we have:
2000 = A * 0.88^2
Evaluate
2000 = A * 0.7744
Divide by 0.7744
A = 2583
Substitute A = 2583 in A(t) = A * 0.88^t
A(t) = 2583 * 0.88^t
Hence, the exponential equation of the model is A(t) = 2583 * 0.88^t
The interpretation of the multiplierIn this case, the multiplier is 88% or 0.88
This means that the number of new cases in a week is 88% of the previous week
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p(m) = 2m² − 4m + 3, find p(1/3)
Answers
Answer:
17/9
Step-by-step explanation:
Plug in 1/3 as m.
2*(1/3)^2 - 4(1/3) + 3 = 17/9
IQ scores are approximately normally distributed with a mean of 100 and a standard
deviation of 15. What IQ score is about 1.5 standard deviations above the mean?
A. 77.5
B. 120
OC. 115
D. 122.5
Answers
The IQ score of 122.5 is about 1.5 standard deviations above the mean.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.
The z score is given by:
z = (raw score - mean) / standard deviation.
Given a mean of 100 and standard deviation of 15. The IQ score that is 1.5 standard deviations above the mean corresponds to a z score of 1.5, hence:
1.5 = (x - 100)/15
x = 122.5
The IQ score of 122.5 is about 1.5 standard deviations above the mean.
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Using traditional methods, it takes 103 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 60 students and observed that they had a mean of 102 hours. Assume the variance is known to be 9. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.
Answers
The test statistic based on the probability illustrated is -2.57.
How to calculate the probability?The basic training is given as 103 hours. The variance is also given as 9.
The test statistic will be:
= (102 - 104/3/✓60)
= -1/(3/7.7)
= -2.57.
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while sshopping ,you see a jacket mark down 20%.if the original price of the jacket $175.what is the sale price of the jacket?
Answers
The sales price of the jacket is $140.
What is a markdown price?A price markdown is a planned decrease in the retail item's selling price. It is used to accelerate an item's sales rate, usually for clearing at the closing of a season or to get rid of outdated goods when their useful lives have passed.
Markdown prices are reductions in a product's selling price from its initial selling price expressed as a rate called markdown percentage. Markdown prices are more commonly referred to as discounts.
From the given information:
The markdown price of the jacket = 20% of the original price.If the original price of the jacket is $175.Then the sales price of the jacket is:
= $175 - (20% of $175)
=$175 - $35
= $140
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100 Points! Which shorts should I get?
Answers
The wheel of the average bicycle is 28 inches in diameter. How many feet will be covered in 9
turns of the wheel?
Answers
Answer:
Approximately 66 feet
Step-by-step explanation:
Given d = 28 inFind the circumference:
C = πd = 3.14*28 = 87.92 inFind the distance covered by 9 turns:
9C = 9*87.92 = 791.28 inConvert inches to feet:
1 foot = 12 in791.28 in = 791.28/12 ft = 65.94 ft ≈ 66 ftSolve equation -1/9 / (-1/3)
Answers
Answer: 1/3
Step-by-step explanation:
-1/9 / -1/3 = ?
Keep: -1/9
Change: *
Flip: -3/1
Solve: -1/9 * -3/1 = 3/9
Simplify: 1/3
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]
[tex]\huge\textsf{Convert:}[/tex]
[tex]\mathsf{= -\dfrac{1}{9} \times -\dfrac{3}{1}}[/tex]
[tex]\huge\textsf{Multiply:}[/tex]
[tex]\mathsf{= \dfrac{-1\times3}{9\times -1}}[/tex]
[tex]\mathsf{= \dfrac{-3}{-9}}[/tex]
[tex]\mathsf{= \dfrac{-3 \div -3}{-9\div-3}}[/tex]
[tex]\mathsf{= \dfrac{1}{3}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{\dfrac{1}{3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
10) Find the mean of the data set.
O a.) 5
Ob.) 9
O c.) 10
O d.) 13
Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
Answers
Answer:
b
Step-by-step explanation:
the mean is calculated as
mean = [tex]\frac{sum}{count}[/tex]
= [tex]\frac{5+8+12+6+7+10+14+6+13}{9}[/tex]
= [tex]\frac{81}{9}[/tex]
= 9
Answer:
9
Step-by-step explanation:
The mean is also known as the average. To find it, we add up all of the data and divide it by how many numbers were added.
5 + 8 + 12 + 6 + 7 + 10 + 14 + 6 + 13 = 81
81/9 = 9
Brainliest, please :)
A 28-metrelong guy wire is attched to a point 24 m up the side of a tower. How far from the base of the tower is the guy wire attached
Answers
The distance between the guy and the wire attached is 14.42m
Pythagoras theoremThe square of the longest side is equal to the sum of the square of other two sides.
In order to determine the length of base of the tower, we will use the expression below:
b² = 28² - 24²
b² = 208
b = 14.42
Hence the distance between the guy and the wire attached is 14.42m
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Simplify the following
Answers
= 4×8 +2×3 -1+9
___________
20
= 8+6-9
_______
20
= 14 - 9
_______
20
= 5
____
20
Find the sum of the arithmetic series 8 +13 +...+ 58.
a) 726
Ob) 1914
Oc) 330
d) 363
Answers
Answer:
363 (d)
Step-by-step explanation:
Sum = (a1+an)(n)/2
n = (an-a1)/d +1 = 11
Plug into the sum formula.
Sum = 363
A function and its inverse are shown on the same graph. A function and its inverse are shown on the same graph.
Which statement describes the relationship between the function and its inverse?
The slope of f–1(x) is the same as the slope of f(x).
The slope of f–1(x) is the opposite as the slope of f(x).
The x-intercept of f–1(x) is the same as the y-intercept of f(x).
The x-intercept of f–1(x) is the opposite as the y-intercept of f(x).
Answers
Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
Which statement is the correct one?
On the image, we can see two linear equations, such that the orange one is f(x) and the blue one is the inverse.
If you follow the orange line, you can see that the y-intercept of f(x) is y = 1.If you follow the blue line, you can see that the x-intercept of the inverse is x =1.Then the x-intercept of the inverse is the same as the y-intercept of f(x), this means that the correct statement is the third option.
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A machine can pack 5000 articles in 24 hours.How long will 3 such machine take to pack the same number of articles
Answers
The time taken for 3 machines to pack 5000 articles is 8 hours.
What are word problems?Word problems are mathematical problems expressed completely in words.The given problem is the rate of work done kind of word problem.To solve a word problem, first, observe the data given in words and apply the basic algebraic operations.The basic algebraic operations are addition, subtraction, multiplication, and division.How long will 3 such machines take to pack 5000 articles?It is given that,
A machine can pack 5000 articles in 24 hours. I.e,
1 machine → 5000 articles → 24 hours
3 machines → 5000 articles → 24/3 hours
Thus, 3 of such machines can pack the same number of articles in
24 ÷ 3 = 8 hours.
Therefore, 3 of such machines take 8 hours to pack 5000 articles.
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A line graph titled Meals per Day has number of days on the x-axis, and number of meals prepared on the y-axis. At 5 days there are 30 meals prepared; at 10 days, 60 meals; at 15 days, 90 meals; at 20 days, 120 meals.
Use proportional reasoning to find the constant of proportionality for the relationship shown on the graph.
What is the value of y when the value of x is 1?
Answers
The constant of proportionality is 6.
How to calculate the constant?From the information given, the constant will be:
30 meals ÷ 5 days = 6
60 meals ÷ 10 days = 6
90 meals ÷ 15 days = 6
120 meals ÷ 20 days = 6
The constant of proportionality is 6. Therefore, the function will be:
y = kx
y = 6x
The value of y when x is 1 will be:
y = kx
y = 6 × 1 = 6
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Answer:
what they said
Step-by-step explanation:
Special Right Triangles
Find x.
Answers
Answer:
8
Step-by-step explanation:
The cos of 30 is [tex]\sqrt{x}[/tex] / 2. Since the adjacent angle is 4 times that. We would multiply 2 x 4 and get 8
wwqrwqretertertreterterter
Answers
Answer:
answer: no spam please
oly questions
The value of Kayla's investment can be modeled by the equation y=2650(1.05)x where x is the number of years invested and y is the value in dollars. What will be the value of the investment after 25 years? Round your answer to the nearest dollar.
Answers
Answer:
8,974 dollars
Step-by-step explanation:
y=2650.(1.05)^x
x=25
2650(1.05)^25 = 8974 dollars
5x6-3x²+7-2x6-3x6+4x² for x = -10
Answers
Answer:
Hope you like it. I have just wrote answers
What expression could be used to add 3/4+1/6
Answers
The expression that could be used to add 3/4+1/6 is [tex]\frac{9 + 2}{12}[/tex]
How to determine the expression?The sum expression is given as:
3/4 + 1/6
Rewrite properly as:
[tex]\frac 34 + \frac 16[/tex]
Take the LCM.
The LCM of 4 and 6 is 12.
So, we have:
[tex]\frac{9 + 2}{12}[/tex]
Hence, the expression that could be used to add 3/4+1/6 is [tex]\frac{9 + 2}{12}[/tex]
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Can someone please explain the steps to get too the second answer also please answer too thank you
Answers
Explanation :
So y = x × 9. Then if x = 9, mutiply it by 9 and equals 81.
Hope it helps !
Which of the following functions has an initial value of -1/2 and a rate of change of 0?
A.
2
x
B. y=−12x
y
=
−
1
2
x
C. y=−12x
y
=
−
1
2
x
D. y=−12
Answers
The function that has the given initial value and rate of change is: D. y = -1/2.
What is the Initial Value and Rate of Change of a Function?A function is given as, y = mx + b, where, m is the rate of change, and b, which is a constant is the initial value.
Given the following:
b = -1/2
m = 0
Plug in the values into y = mx + b
y = 0(x) + (-1/2)
y = -1/2
Therefore, the function is: D. y = -1/2.
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What is the midpoint of 125 and 12?
Answers
For an example; finding the midpoint of 4 and 12 you may simply insert the equation : 4+12/2 which equals 8. Meaning your mid point is 8.
For your question; 125 + 12 = 137/2 = 68.5
The mid point of 125 and 12 is 68.5.
Koos spent 3/7 of his monthly pocket money during the first week. The following week he spends two- thirds of what he had spent the previous week. The fraction of the pocket money that is still left is.
Answers
Answer: 2/7
Step-by-step explanation:
The total amount of pocket money he has is 7/7.
He spent 3/7 of his pocket money during the first week.
He then spends 2/3 of what he spent the previous week, 2/3 * 3/7 which is 2/7.
What he has left is 7/7 - 3/7 - 2/7 = 2/7.
You buy almond milk in 1 gallon containers. One portion of waffles requires 2.5 ounces of almond milk. How many portions can be made with one container
Answers
Answer:
61 portions
Step-by-step explanation:
First, the conversion between gallon and ounces is:
1 Gallon = 153.722 ounces (oz)
GIven 1 portion of waffles requires 2.5 ounces of milk
Number of portions of waffles = Total amount of milk / milk required per portion of waffles
= 153.722 / 2.5
= 61.489 portions
Of course, we are unable to make part portions in this case, so we will take the highest possible whole number, which is 61 portions.