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According to the converse of corresponding angles theorem, the statement that allows Carmen to conclude that lines p and q are parallel is: ∠2 ≅ ∠6.
What is a Transversal?A transversal is a line that crosses two straight lines. For example, line t is a transversal that crosses the lines p and q in the given diagram above.
What are Parallel Lines?Parallel lines are lines that do not meet each other at any point and are of equal distant to each other.
When a transversal intersects two parallel lines, they form angle pairs. One of such angle pairs is, corresponding angles, which are always congruent to each other.
Thus, if corresponding angles are formed and are equal to each other, then the lines they lie on must be parallel lines based on the corresponding angles converse theorem.
Angles 2 and 6 are corresponding angles that are formed by the transversal that intersects lines q and p. If they are congruent angles, then the lines are parallel.
Therefore, Carmen can use the statement, ∠2 ≅ ∠6 to show that lines q and p are parallel.
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Related Questions
| В Find the measure of ZA in AABC. Since we are given information here, we can use the following equation to solve for MZA. 55 DONE 35 А C 50
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#1 - Find the inverse of the function shown. *y = ( 6х + 12)/2
Answers
The given function is expressed as
y = (6x + 12)/2
In order to determine the inverse of the given function, we would substitute x for y and y for x. Then we would solve for y. It becomes
x = (6y + 12)/2
x = 3y + 6
3y = x - 6
y = (x - 6)/3
y = x/3 - 2
The inverse is
y = x/3 - 2
Find the GCF if the following terms . (30x^5 ,60x^3)
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The coefficient of the GCF of a set of algebraic terms, wil be the GCF of the coefficients of the terms.
Notice that the coefficients in this case, are 30 and 60.
The greatest comon factor of this set, is 30, since:
[tex]\begin{gathered} 30=30\cdot1 \\ 60=30\cdot2 \end{gathered}[/tex]On the other hand, the variable x appears with an exponent of 5 in one case and an exponent of 3 in the other case. The greatest common factor for the variable x will be the lowest power, in this case, 3. Notice that:
[tex]\begin{gathered} x^3=x^3\cdot1 \\ x^5=x^3\cdot x^2 \end{gathered}[/tex]Then, we can factor out the following:
[tex]30x^3[/tex]Notice that each term can be written as a product of this factor:
[tex]\begin{gathered} 30x^5=30x^3(x^2)^{}^{}^{}_{} \\ 60x^3=30x^3(2)^{}_{} \end{gathered}[/tex]Therefore, the greatest common factor (GCF) is:
[tex]30x^3[/tex]Prove that 3x + y = 7 + y and 3(x + y) = 2 + 3x are perpendicular
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Answer:
Since one line is vertical, and one line is horizontal, the lines are perpendicular.
Step-by-step explanation:
The product of the slopes of perpendicular lines is -1.
We find the slopes of the 2 lines and multiply them together.
If the product equals -1, then the lines are perpendicular.
To find the slopes of the lines, we write each equation in the y = mx + b form, where m is the slope. In other words, we solve each equation for y.
3x + y = 7 + y
Subtract y from both sides.
3x = 7
x = 7/3
This is not the y = mx + b form since there is no y in the equation. A line with equation x = k, where k is a number, is a vertical line that passes through the point (k, 0), and the x-coordinate of all points on the line is k.
3(x + y) = 2 + 3x
3x + 3y = 2 + 3x
Subtract 3x from both sides.
3y = 2
y = 2/3
y = 0x + 2/3
Slope = m = 0
A line with 0 slope is a horizontal line.
Since one line is vertical, and one line is horizontal, the lines are perpendicular.
help it’ll be greatly appreciated:(
Answers
Answer:
hola como estas soy de guatemala
Craig is training to try out for the wrestling team at his school. Each week he records the number of sit-ups he can do in 1 minute so that he can track his improvement. The table shows his results over the first 3 weeks.
Week Number of Sit-Ups
1 40
2 44
3 47
Find the percent of change from Week 1 to Week 2 and from Week 2 to Week 3. Round to the nearest tenth percent if necessary.
Percent of change from Week 1 to Week 2:
%
Part B
Fill in the blank question.
Percent of change from Week 2 to Week 3:
%
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The percent of change from Week 1 to Week 2 is 10%.
The percent of change from Week 2 to Week 3 is 6.8%
What is the percentage change?Percentage is the ratio of an amount that is expressed as a number out of 100. Percentage is a measure of frequency. The sign that is used to represent percentage is %.
The percent of change from Week 1 to Week 2 = (number of sit ups in week 2 / number of sit ups in week 1) - 1
(44 / 40) - 1 = 0.1 = 10%
The percent of change from Week 2 to Week 3 = (number of sit ups in week 3 / number of sit ups in week 2) - 1
(47 / 44) - 1 = 0.068 = 6.8%
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-8+19+8 witch is the value of the expression
Answers
The expression given as -8+19+8 has a value of 19
How to evaluate the expression?From the question, the expression is given as
-8+19+8
Rewrite the expression properly
This is rewritten as follows
-8 + 19 + 8
Collect the like terms in the above expression
So, we have the following equation
-8 + 19 + 8 = 8 - 8 + 19
Evaluate the like terms in the above expression
So, we have the following equation
-8 + 19 + 8 = 0 + 19
Finally. we add 0 and 19
So, we have the following equation
-8 + 19 + 8 = 19
Hence, the valye of the expression is 19
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The obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.
What are Arithmetic operations?In mathematics, the addition, subtraction, division, and multiplication of built-in expressions can also be used to specify arithmetic operations.
The expression which is given in the question is below
⇒ -8 + 19 + 8
Rearrange similar terms in the above expression,
⇒ 8 - 8 + 19
Apply the subtraction operation,
⇒ 0 + 19
Apply the addition operation to get the answer,
⇒ 19
Hence, the obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.
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Find the range and standard deviation of the set of numbers.38, 47, 43, 44, 44, 41, 44The range is 9.The standard deviation is__(Round to the nearest tenth as needed.)
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To find the standard deviation of this set of numbers, we will use the formula
[tex]s=\sqrt{\frac{\sum_^(x-\text{ }x_{mean})^2\text{ }}{n-1}}[/tex]let us explain the parts of this formula, as follows:
[tex]x_{mean}\text{ is the mean of the data \lparen we have to calculate\rparen}[/tex][tex]n\text{ is the total quantity of numbers \lparen in this example 7\rparen}[/tex]We will proceed by parts, the first thing to do is find the mean of the data
Calculating the mean
To find the mean, we will sum all the numbers and divide by the total quantity of numbers, as follows:
[tex]x_{mean}=\frac{\Sigma x}{n}=\frac{38+47+43+44+44+41+44}{7}=\frac{301}{7}=43[/tex]That is, the mean of the set is 43. Now we proceed to find the difference between the data and the mean, and the add them to the power of two, in symbols we have:
[tex]\begin{gathered} \Sigma(x-x_{mean})^2=(38-43)^2+(47-43)^2+(43-43)^2+3\times\text{ }(44-43)^2+(41-43)^2 \\ \text{ =\lparen-5\rparen}^2+4^2+0^2+3\times\text{ }1^2+(-2)^2 \\ =25+16+3+4 \\ =48 \end{gathered}[/tex]Now we introduce this result into the formula for the standard deviation, we find:
[tex]s=\sqrt{\frac{\Sigma(x-x_{mean})^2}{n-1}}=\sqrt{\frac{48}{7-1}}=\sqrt{\frac{48}{6}}=\sqrt{8}\approx\text{ 2.8}[/tex]That is, after approximate to the nearest tenth, we found that the standard deviation of the set of numbers is 2.8
Is 5.67 < > = to 1.93
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Answer: 5.67> 1.93
Step-by-step explanation:
Let's think of it this way, if you have five apples and another person has one apple. Do you think you have a greater amount of apples?
Of course because 5.67 is a larger number than 1.93. You can always make a number line.
1-9.b.C.GROWING, GROWING, GROWING, PART ONECopy the tile pattern shown below onto graph paper.Figure 2Figure 3Figure 4Draw the 1st, 5th, and 6th figures on your paper.How is the pattern changing?What would the 100th figure look like? How many tiles would it have?How can you justify your prediction?
Answers
Answer:
Explanation:
a) To draw the 1st , 5th and 6th figures, we need to know the count of squares
For the first figure, we would have 3 squares
The fifth figure would have 35 squares
The sixth figure will have 48 squares
The way to get this is to add 2 to the odd number difference between the last two terms
b) Here, we want to know how the pattern is changing
From the information provided, the first pattern has 8 squares, the second has
15 squares while the last has 24 squares
We can have a formula as follows:
[tex][/tex]what is the answer for this equation 20x2-45=0
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Answer:
-5
Step-by-step explanation:
Evaluate using your knowledge of the unit circle:cot 120°
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We are asked to evaluate cot 120,
[tex]\begin{gathered} \cot 120^0=\frac{1}{\tan 120^0} \\ 120^0\text{ falls in the second quadrant. } \\ \tan 120^0=-\tan (180^0-120^0)=-\tan 60^0 \\ \end{gathered}[/tex][tex]\Rightarrow\cot 120^0=-\frac{1}{\tan 60^0}=-\frac{1}{\sqrt[]{3}}=-\frac{\sqrt[]{3}}{3}[/tex]Select all of the expressions equivalent to (m + m)(-4.2m).
Answer choices
2m(-4.2m)
-4.2m³
-2.2m²
4.2m²+4.2m²
-4.2m²+(-4.2m²)
-8.4m²
Answers
Answer:
2m(-4.2m)
-4.2[tex]m^{2}[/tex] + - (4.2[tex]m^{2}[/tex])
-8.4[tex]m^{2}[/tex]
Step-by-step explanation:
2m(-4.2m) = -8.4 [tex]m^{2}[/tex]
-4.2 [tex]m^{2}[/tex] + (-4.2 [tex]m^{2}[/tex]) = 8.4[tex]m^{2}[/tex]
math worksheet , sets
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The elements of the set given by A∩B is {12,18} .
Set theory, a branch of mathematical logic, studies sets, which are essentially collections of objects.
Despite the fact that every form of object may be turned into a set, set theory is a branch of mathematics that primarily deals with issues that are relevant to mathematics as a whole.
The foundation of set theory is a straightforward binary link between an object o and a set A.
If o is a component (or member) of A, it is expressed as o A. When listing members of a set, commas are used to indicate their separation, or brackets are used to surround a property of those parts.
Since sets are objects, they can be connected by the membership relation.
Given set U = {11,12,13,14,15,16,17,18,19,20}
A = {12,14,16,18,20}
B = {12,15,18}
A∩B = {12,18}
A∪B = {12,14,15,16,18,20}
A' = {11,13,15,17,19}
Therefore the elements of the set given by A∩B is {12,18} .
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If a one-person household spends an average of $52 per week on groceries, find the maximum and minimum amounts spent per week for the middle 50% of one-person households. Assume the standard deviation is $14 and the variable is normally distributed. Round your answers to the nearest hundredth.Minimum: $Maximum: $
Answers
Solution
For this case we have the following random variable:
X= amount spend on average for groceries by one person
And we have the following properties:
mean= 52
sd= 14
The distribution of the variable is normal
We can find the middle 50% using a graph like this one:
We can find two quantiles from the normal distribution that accumulates 25% of the area on each tail of the distribution and we have:
Z= -0.674 and 0.674
Now we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma},x=\mu\pm z\cdot\sigma[/tex]So then we have:
Minimum= 52 - 0.674*14 = 42.56
Minimum= 52 + 0.674*14 = 61.44
how to solve for x and round it up to tenth
Answers
Answer:
4.6
Explanation:
The diagram shown is a right triangle having the following sides;
Opposite = 17
Adjacent = x
Angle of elevation = 75 degrees
Using SOH CAH TOA identity
Tan theta = opposite/adjacent
Tan 75 = 17/x
x = 17/tan 75
x = 17/3.73205
x = 4.6
Hence the value of x to the nearest tenth is 4.6
A number when rounded to 3 decimal places, is equal to
0.029
Find the upper and lower bound of
The number
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A storage tank has a height of 10 feet and a diameter of 6 feet. The tank is half filled with oil. 6 ft Approximately how much oil, in cubic feet, is currently in the cylindrical tank? A 90 ft B 360r ft3 C 455 Ft D 180rt ft3
Answers
ok
Volume of a cilinder = pi*r^2*h
Substitution
Volume of a cilinder = 3.14*3^2* 6
Simplification
Volume of a cylinder = 170 ft^3
Approximately, there are 180 ft^3 of oil
if you have 1/4 cup how many eighths do you have
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MATHEMATICALLY WE SAY
BE AWARE THAT EIGHTHS IS
[tex] \frac{1}{8} [/tex]
THEY ARE ASKING HOW MANY
[tex] \frac{1}{8} [/tex]
ARE THERE IN
[tex] \frac{1}{4} [/tex]
[tex] = \frac{1}{4} \div \frac{1}{8} \\ = \frac{1}{4} \times \frac{8}{1} \\ = \frac{8}{4} \\ = 2[/tex]
YOU HAVE 2 .The Wilsons want to tile their kitchen floor. The floor is 12 feet by 15 feet. The tiles are nine-inch squares.
12 feet = _____ inches
15 feet = _____ inches
Total square inches of the floor = ______ square inches
One tile = _____ square inches
Total number of tiles needed =______ tiles
Answers
The number of tiles required to cover the floor is 2880 tiles.
What is the number of Tiles Needed?To solve this problem, we can find the number of tiles by calculating the area of a rectangle:
We have to convert the dimensions from feet to inches will be
1 feet = 12 inches
12 feet = 12 * 12 = 144in
15 feet = 12 * 15 = 180in
The area of the rectangle can be calculated as:
A = l * w
A = 180 * 144
A = 25920in²
The tiles are 9 squared inches, we can divide the area by 9 to find the number of tiles needed:
25920/9= 2880
Hence, The number of tiles needed will be 2880 tiles
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A mother need 6 pieces of ribbon, with lengths of 25 cm each, for her daughter's hair. If the ribbon is only sold per full meter, how many meters does she need to buy?
Answers
Given:
The length of each ribbon is 25 cm.
The number of ribbon need by mother is 6.
Explanation:
Determine the length of ribbon for daughter's hair.
[tex]\begin{gathered} 25\cdot6=150\text{ cm} \\ =1.5\text{ m} \end{gathered}[/tex]Since length is in decimal so we need to find multiple of 25 such that it is more than 150 and multiple of 100.
The multiples of 25 are 25,50, 75, 100, 125, 150, 175, 200, ...
Since 200 is more than 150 and multiple of 100 also.
Determine the length of 200 cm in terms of meters.
[tex]200\text{ cm}\cdot\frac{1\text{ m}}{100\text{ cm}}=2\text{ m}[/tex]So mother needs to buy 2 meters of ribbon.
Answer: 2 meters
What is the decay percentage rate of t h(x) = 20(175)” ?A75%oB.75%Oс25%0D.25%
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Given the function :
[tex]h(x)=20(0.75)^x[/tex]So, the decay percentage rate :
[tex]\frac{\triangle h}{\triangle x}=0.75[/tex]convert the decimal to percentage: 0.75 = 75%
So, the answer is option A) 75%
bill saved 3,500 to take a vocation. if he pays 816 for his plane ticket, 125 per day for hotel accommodation, 100 per day for food, and 95 per day for sightseeing, at most how many days will bill be able to stay on vocation
Answers
Answer:
7 day
Step-by-step explanation:
Pa brainlest po plsss
Answer: 8 days
Step-by-step explanation:
1) Set up an equation. Let x be the day
3,500 >= 2(816) + x(100+95)
The 816 is just two times (Plane ticket back and forth) so it doesn't go into the x. 100 and 95 do as it is one day.
2) Solve the equation
3,500 >= 2(816) + x(100+95)
1868 >= 195x
9.57 >= x
3) Rounding
Since the x has to be less than 9.57, our next option is 8
help meeeeeee pleaseee !!!!
Answers
So, we are writing a function. c(x) is the manufacturing costs, and x is the amount of bikes manufactured. The y-intercept is 1908 because when no bikes are manufactured it still costs 1908 to run the factory. The slope is 75 because it costs $75 to create a bike. So, y = mx + b, where m is the slope and b is the y-intercept is:
c(x) = 75x + 1908
Latoya opened a savings account and made an intial deposit. After the intial deposit, she added money into the account each week she added the same amount each week with out any withdrawals after the forth week she had $450 by the ninth week she had $825 what was latoya's intial deposit?
Answers
She made an initial deposit that we will call "D", as it is one of the unknowns.
We know that she made a weekly deposit (lets call this amount "w").
After 4 weeks she had $450 in the account balance and this is the sum of the initial deposit and 4 weekly deposits, so we can write:
[tex]D+4w=450[/tex]At the ninth week she had $825, that correspond to the initial deposit and 9 weekly deposits. This can be written as:
[tex]D+9w=825[/tex]We have a system of linear equations that we will solve by elimination: we will substract the first equation from the second and then find w.
[tex]\begin{gathered} (D+9w)-(D+4w)=825-450 \\ 5w=375 \\ w=\frac{375}{5} \\ w=75 \end{gathered}[/tex]Now that we know "w", we can calculate D with any of the two equations:
[tex]\begin{gathered} D+4w=450 \\ D+4\cdot75=450 \\ D+300=450 \\ D=450-300 \\ D=150 \end{gathered}[/tex]Answer: the initial deposit was $150.
Evaluate the expression 14-16+8+12\3
Answers
Let's evaluate the given expression:
[tex]\text{ 14 - 16 + 8 + }\frac{\text{ 12}}{\text{ 3}}[/tex][tex]=\text{ 14 - 16 + 8 + 4}[/tex][tex]\text{ = -2 + 8 + 4}[/tex][tex]\text{ = -2 + 12}[/tex][tex]\text{ = 1}0[/tex]Therefore, the answer is 10.
A fluorescent lighting panel is 12 5/8 inches wide. If three of
the panels are installed next to each other, what will be the
width in inches of the combined panels?
Answers
The width of the combined three panels when installed next to each other is [tex]37\frac{7}{8}[/tex] inches.
What is the width of the combined panels?In order to determine the width of the three combined panels, multiply the width of one fluorescent lighting panel by the total number of panels.
Multiplication is the mathematical operation that is used to calculate the product of two or more numbers. The sign that represents multiplication panel is ×.
Width of the combined panels = width of one panel x number of panels
[tex]12\frac{5}{8}[/tex] × 3
[tex]\frac{101}{8}[/tex] x 3 = [tex]\frac{303}{8}[/tex] = [tex]37\frac{7}{8}[/tex] inches
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f(t)= 2t/3 For what value of t is f(x)=64?
Answers
We are given the following function
[tex]f(t)=\frac{2t}{3}[/tex]We are asked to find out the value of t which results in f(t) = 64
Let us substitute f(t) = 64 into the above function and solve for t
[tex]\begin{gathered} f(t)=\frac{2t}{3} \\ 64=\frac{2t}{3} \\ 3\cdot64=2t \\ 192=2t \\ \frac{192}{2}=t \\ 96=t \\ t=96 \end{gathered}[/tex]Therefore, the value of t is 96
Please help!! Find the values of x and y.
Answers
The values of x and y will be 100° and 10° when two parallel lines are being cut by a transversal line.
According to the question,
We have a figure where two parallel lines are being cut by a transversal line.
Now, we know that the angles formed on a straight line is 180° and vertically opposite angles are equal.
The sum of consecutive interior angles is 180°.
Now, we will use these three statements in finding the values of x and y.
Now, adding (2x-70)° and (5y)° will give 180° because the angles made are on a straight line.
(2x-70)°+(5y)° = 180°
2x+5y = (180+70)°
2x+5y = 250° .... (1)
Now, (x+30)° will be the interior angle consecutive to 5y° because they are vertically opposite angles.
So, we have:
(x+30)°+5y° = 180°
x+5y = (180-30)°
x+5y = 150°
5y = 150-x
Now, putting this value of 5y in equation 1:
2x+5y = 250
2x+150-x = 250
x+150 = 250
x = (250-150)°
x = 100°
Now, we will find the value of y:
5y = 150-x
5y = 150-100
5y = 50
y = 50/5
y = 10°
(Note that the values of x and y will be in ° because angles are measured in degree.)
Hence, the value of x is 100° and the value of y is 10°.
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Help me! i need this answer now i am so dead. if i get it worng please help help please
Answers
Answer:
70.4
Step-by-step explanation:
c = 2[tex]\pi[/tex]r
c = 2(3.142)(11.2)
c = 70.3808 Rounded to 1 decimal place
c = 70.4
70.4
Explanation:
Circumference = 2 (3.142) radius
Circumference = 2 x 3.142 x 11.2
Circumference = 70.3808
Round ur answer to 1 d.p:
=70.4