Use the following figure and information to complete the proof. Given: m∥n Line l is a transversal of lines m and n. Prove: ∠3≅∠5
Answers
Answer:
1. Given.
2. Definition of vertical angles.
3. Vertical angles theorem.
4. Definition of corresponding angles.
5. Corresponding angles postulate.
6. Transitive property of congruence.
Explanation:
1. This statement is the given part of the problem
2. vertical angles are the pair of opposite angles that are formed when two line segments intersect. Angles 1 and 3 verify this definition, thus they're vertical angles.
3. The vertical angles theorem states that a pair of two vertical angles have the same measure.
4. Corresponding angles are the angles that are formed in matching corners with the transversal when two parallel lines are intersected by another line. Thus, angles 1 and 5 are corresponding angles.
5. The corresponding angles postulate states that, when two parallel lines are cut by a transversal, the resulting corresponding angles are congruent. Thus, angles 1 and 5 are congruent.
6. The transitive property of congruence states that if a is congruent to b and b is congruent to c, then a is congruent to c.
This means:
[tex]\angle3\cong\angle1\cong\angle5\Rightarrow\angle3\cong\angle5[/tex]
Related Questions
A researcher is interested in whether using mental imagery can help people remember specific details when given information. To conduct the experiment, the researcher asks 100 volunteers to participate. The researcher places everyone’s name in a hat and randomly selects 50 names, making sure to sure to mix the names between each selection.
Which component is missing from the researcher’s process?
The researcher did not use enough randomization in the process.
The researcher used volunteers instead of randomly selected people from the population.
The researcher did not assign the 50 names to the treatment group or the control group.
The researcher should have used numbers instead of names for confidentiality reasons.
Answers
The 50 names were not allocated to either the treatment group or the control group by the researcher.
What is research?A problem must be thoroughly investigated in order to meet specific planned research objectives.
Research involves a certain process. The definition of the issue that will be studied during the research process is one of the crucial procedures.
After doing that, the researcher must decide whether there is enough knowledge about the issue that he or she plans to study.
Scientific research is research done with the intention of advancing science by the methodical collection, analysis, and evaluation of data—and that too in a planned manner: This research is being done by a researcher.
The instruments of observation, experimentation, and conclusion are essential components of the scientific method.
In this instance, the researcher should have randomly assigned the volunteers to the treatment group and the control group.
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a dime has a diameter of 17.91 millimeters. What is the area of the face of the dime? use 3.14 for π. Round to the nearest hundredth if necessary
Answers
The area of a circle is:
[tex]A=\pi\cdot r^2[/tex]As you have the diameter, use it to find the radius: the radius of a circle is equal to the half of the diameter:
[tex]\begin{gathered} r=\frac{d}{2} \\ \\ r=\frac{17.91\operatorname{mm}}{2}=8.955\operatorname{mm} \end{gathered}[/tex]Then, the area is: 251.80 millimeters[tex]\begin{gathered} A=(3.14)(8.955mm)^2 \\ A=251.80\operatorname{mm} \end{gathered}[/tex]Allison drew a map of where she and her friends live. Allison's house is at point A, and her friends live at points B, C, and D. She only wrote some of the distances, in blocks, on the map. Also, AD¯¯¯¯¯¯¯¯ is a perpendicular bisector of BC¯¯¯¯¯¯¯¯. Allison wants to know the distance between her house and point C.What is the measure of AC?
Answers
Solution:
Given that;
Allison drew a map of where she and her friends live.
Allison's house is at point A, and her friends live at points B, C, and D
Where, line segment AD is a perpendicular bisector of BC,
And a perpendicular bisector is a line segment which bisects another line segment at 90 degrees, and divides it into two equal parts..
Since, AD is a perpendicular bisector of BC, then
[tex]\begin{gathered} BD=CD=3 \\ \angle ADB=\angle ADC \\ And,\text{ }AD=CD \\ Thus, \\ \Delta ADB\cong\Delta ADC\text{ \lparen SAS\rparen} \end{gathered}[/tex]Hence,
[tex]AB=AC=4.24[/tex]The measure of AC is 4.24
Which of the following ordered pairs is a solution to the graph of the system of inequalities? Select all that apply(5, 2)(-3, -4)(0, -3)(0, 1)(-4, 1)
Answers
ANSWER
(5, -2) and (0, -3)
EXPLANATION
We want to find which of the ordered pairs is a solution to the system of inequalities.
Ordered pairs are written in the form (x, y), this means, whichever ordered pair is a solution, when inserted into the system of inequalities, should be true.
This means that the values of x and y must be true for both inequalities in the system.
The system of inequalities is:
[tex]\begin{cases}-2x-3\leq\text{ y} \\ y-1<\text{ }\frac{1}{2}x\end{cases}[/tex]A. (5, -2)
[tex]\begin{gathered} -2(5)\text{ - 3 }\leq-2\Rightarrow\text{ -10 - 3}\leq-2\Rightarrow\text{ -13 }\leq-2 \\ -2\text{ - 1 < }\frac{1}{2}(5)\Rightarrow\text{ -3 < }\frac{5}{2} \end{gathered}[/tex]Since both inequalities are correct, this is a solution.
B. (-3, -4)
[tex]-2(-3)\text{ - 3 }\leq-4\Rightarrow\text{ 6 - 3 }\leq-4\Rightarrow\text{ 3}\leq-4[/tex]Since the first inequality is already incorrect, we do not need to go further.
It is not a solution
C. (0, -3)
[tex]\begin{gathered} -2(0)\text{ - 3 }\leq\text{ -3 }\Rightarrow\text{ -3 }\leq\text{ -3} \\ -3\text{ - 1 < }\frac{1}{2}(0)\Rightarrow\text{ -4 < 0} \end{gathered}[/tex]Since both inequalities are correct, this is a solution.
D. (0, 1)
[tex]\begin{gathered} -2(0)\text{ - 3 }\leq\text{ 1 }\Rightarrow\text{ -3 }\leq\text{ 1} \\ 1\text{ - 1 < }\frac{1}{2}(0)\Rightarrow\text{ 0 < 0} \end{gathered}[/tex]Since 0 is not less than 0, this is not a solution.
E. (-4, 1)
[tex]-2(-4)\text{ - 3 }\leq\text{ 1}\Rightarrow\text{ 8 - 3 }\leq1\Rightarrow\text{ 5 }\leq1[/tex]Since 5 is not less than 1, this is not a solution.
Therefore, the solutions are (5, -2) and (0, -3)
Write a equation of the line described
Passes through (4,8)
Parallel to the line y=-7/4x-4
Answers
Answer:
y=-7/4x+15
Step-by-step explanation:
Parallel line so has the same gradient:
y=-7/4x+c
Substitute (4,8) into above equation
8=(-7/4 x 4)+ c
rearrange to find c
8=-7+c
c=15
New equation: y=-7/4x+15
Hope this helps!
Trying to use a model or number line for fractions for a 4th grader
Answers
Given:
[tex]\frac{76}{100}-\frac{50}{100}[/tex]Solve:
[tex]\begin{gathered} \frac{76}{100}-\frac{50}{100} \\ so\colon \\ =\frac{76-50}{100} \\ =\frac{26}{100} \end{gathered}[/tex][tex]\begin{gathered} =\frac{26}{100} \\ =0.26 \end{gathered}[/tex]In number line 0.26 lies in between 0 to 1.
Question 15 of 31In a 45-45-90 right triangle, what is the ratio of the length of one leg to thelength of the other leg?A. 2:1B. 1:2C. 2:1O D. 1:1SUBMIT
Answers
Ratio = 1:1 (option D)
Explanation:We use an illustration to answer the question
One leg = 1
Another leg = 1
When we compare the two images, the ratio of the leg of the 45-45-90 right triangle:
Ratio = 1/1
Ratio = 1:1 (option D)
A store has clearance items that have been marked down by 45%. They are having a sale, advertising anadditional 50% off clearance items. What percent of the original price do you end up paying?%Give your answer accurate to at least one decimal place.
Answers
We have clearance items that have two discounts applied to its price.
We can use a $1 item to find the final discount.
If we apply a 45% mark down, we will obtain a price of:
[tex]1-1*0.45=0.55[/tex]The discounted price is $0.55.
To this price we apply a 50% off. This can be expressed as:
[tex]0.55(1-0.5)=0.55*0.5=0.275[/tex]This is the final price.
We can calculate the percentage of the original price as:
[tex]\frac{P_d}{P_0}=\frac{0.275}{1}=0.275=27.5\%[/tex]Answer: 27.5%
there are four marbles in a vase blue blue red and green jenny pulls out two marbles without replacement list tge sample space
Answers
Let' begin by listing out the information given:
Number of marbles = 4; blue, blue, red, and green
Jenny pulls out two marbles without replacement. We have:
[tex]\begin{gathered} S=\mleft(Blue,Blue\mright),(Blue,Red),(Blue,Green) \\ S=(Red,Blue),(Red,Green) \\ S=(Green,Blue),(Green,Red) \\ \therefore S=\mleft\lbrace(BB),(BR),(BG),(RB),(RG),(GB),(GR)\mright\rbrace \end{gathered}[/tex]use three letters to name (a) the plane on which the square pyramid sits and (b) a plane represented by one of the sides.
Answers
Use three letters to name
(a) The plane on which the square pyramid sits and ABC
Why : because ABC is at the base of the square pyramid
b) A plane represented by one of the sides. ABG
Why : Because ABG represents the triangle of one of the 4 sides of the pyramid
What is the perimeter of the figure Assume that all angles are right anglesA) 23 yardsB) 30 yardsC) 32 yardsD) 26 yards
Answers
The perimeter of the figure is the sum of the lengths of its sides. Find the missing side lengths to calculate the perimeter of the figure.
The length of then missing horizontal side is 6yd because it must add up to 8yd with the 2yd segment.
The length of the missing vertical side is 4yd because it must add up to 7yd with the 3yd segment.
Then, the perimeter of the figure is:
[tex]\begin{gathered} P=7yd+8yd+3yd+2yd+4yd+6yd \\ =30yd \end{gathered}[/tex]Therefore, the correct choice is option B) 30 yards.
f(x) = -x^2 - 4x + 13find f(3)
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
f(x) = -x^2 - 4x + 13
f(3) = ?
Step 02:
f(x) = - x² - 4x + 13
f(3) = - (3)² - 4(3) + 13
f(3) = - 9 - 12 + 13
f(3) = - 21 + 13
f(3) = - 8
The answer is:
f(3) = - 8
Log5b=1.61 then log5b
Answers
The solution to the Logarithmic Expression Log ₅ 8 given that Log 5 = 1.61 And Log 8 = 2.08 is; 1.29
How to solve logarithmic expressions?Some of the rules of logarithm are as follows;
Rule 1; Log (M*N) = Log M + Log N
Rule 2; Log (M/N) = Log M - Log N
Rule 3; Log (M)ⁿ = nLog(M)
Rule 4; Log 1 = 0
Rule 5; Logₐ a = 1
Now, we are given that Log 5 = 1.61 And Log 8 = 2.08. We want to find Log ₅ 8.
From the rules of logarithm, we can say that;
Logₐ7 = (Log 7)/(Log a)
Thus;
Log ₅ 8 = (Log 8)/(Log 5)
= 2.08/1.61
= 1.29
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Complete question is;
If Log 5 = 1.61 And Log, 8 = 2.08, Then Log ₅ 8 = O 3.25 O 3.35 10 0.47 O 2.69 O 1.29
55. Use the effective tax rate method to calculate the property tax on a $112,500 home. The assessment rate is 43%. The property tax rate is$32.89 per $1,000 of assessed value. Round the effective tax rate to threeplaces. What is the property tax?
Answers
Let's begin by listing out the given information:
Home (Property Value) = $112,500
Assessment rate = 43% = 0.43
Property tax rate = $32.89 per $1,000 of assessed value
The Property tax is calculated using the formula:
[tex]\begin{gathered} AssessedValue=112,500\times0.43=48,375 \\ PropertyTax=\frac{32.89}{1,000}\times48,375=1591.05375\approx1591.05 \\ PropertyTax=\text{ \$}1591.05 \end{gathered}[/tex]The effective tax is calculated using the formula:
[tex]\begin{gathered} ETR=\frac{TaxesPaid}{TaxableIncome} \\ ETR=\frac{PropertyTax}{AssessedValue}=\frac{1591.05}{48,375}=0.0329 \\ ETR=0.0329=3.29\text{ \%} \\ ETR=3.29\text{ \%} \end{gathered}[/tex]Which answer choice correctly represents 1.436363636…?A) 1.436 _B) 1.436 __D) 1.436 ___C) 1.436
Answers
Given: The number below
[tex]1.436363636\ldots[/tex]To Determine: The simplified form of writing the given number
It can be observed the given number that 36 keeps recurring indefinitely
Hence, the nuumber can be written as
[tex]1.436363636\ldots=1.4\bar{36}[/tex]Hence, option C is the correct answer
Last week, Thor ran 30 laps around the lake. Shaq ran 5/9 as many laps around the lake as Thor did. How many laps around the lake did Shaq run?
Answers
Explanation:
Thor: 30 laps
Shaq: 5/9 Thor's laps.
To find how many laps Shaq did, we have to multiply Thor's laps by 5/9:
[tex]30\times\frac{5}{9}=\frac{30\times5}{9}=\frac{150}{9}[/tex]And simplify the fraction:
[tex]\frac{150}{9}=\frac{50}{3}[/tex]It's an improper fraction. Written as a mixed number:
[tex]\frac{50}{3}=16\frac{2}{3}[/tex]Answer:
Shaq did 16 2/3 laps around the lake
There are 167 students taking a foreign language at North HighSchool. Based on the graphic above, how many students are takingSpanish?
Answers
59 (1st option)
Explanation:Given:
Total students taking the foreign language = 167
To find:
The number of students taking Spanish
To determine the number of students for Spanish, we will do an estimation:
The Spanish region is represented by the red region
The blue and red region is approximately half of the circle. This means half of the total students
Half of the students = 1/2(167) = about 83 students
The blue region in the half of the circle is about 1/3. The red represents the remaining part (2/3)
The Spanish region = 2/3 × 83
The Spanish region = 55.3
The closest number to this in the options is 59 (1st option)
helllllppppppppppppppppp
Graph the function f(x)=3(0.25)x.
How can features of the graph be described?
Select from the drop-down menus to correctly complete the statements.
The function is an example of exponential
Choose...
.
As x
Choose...
without bound, the function approaches y = 0. As x
Choose...
without bound, the function
Choose...
without bound.
Answers
The required graph of the given exponential function f(x) = 3(0.25)ˣ which has been attached below.
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function is given in the question following as:
f(x) = 3(0.25)ˣ
As per the attached graph, can see that the domain of the given function is all real numbers that are (-∞, ∞) in the interval notation. The range of the given function is (0, ∞) in the interval notation.
The required graph of the given exponential function f(x) = 3(0.25)ˣ which has been attached below.
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In right triangle ABC, m 2 A = 32°, m 2 B= 90°, andAC = 6.2 cm. What is the length of BC, to the nearesttenth of a centimeter?
Answers
Given Data:
In a triangle ABC,
[tex]\begin{gathered} \angle A=32^{\circ} \\ \angle B=90^{\circ} \\ AC=6.2\text{ cm.} \end{gathered}[/tex]From the triginometry,
[tex]undefined[/tex]Help me asap I'm so stressed it's a Yes Or No questionstheres 7 questions in the image each one is a yes or no answer pls help I'm super stressed
Answers
Explanation:
A relation is a function if every value of x is related to just one value of y.
So, number 6 is not a function because -4 is related to 9 and -4 is also related to 0.
Number 7 is a function because every value of x (first coordinate) is related to one value of y (second coordinate).
In the same way, we can say that number 8 is also a function and number 9 is not a function because number 7 is related to 0, -5, -8, 4, and 3.
Finally, for the graph of numbers 10, 11, and 12 we need to identify the coordinates of every point.
So, number 10 is equivalent to:
{(-7, -1), (-2, -7), (0, 2), (4, 2), (6,6)}
It means that number 10 is a function
For number 11, we get:
{(-5, -4), (-3, 5), (2, -1), (2
answer this for methe other to answers are c.the slope is 3/2,and the y-intercept is -2d.the slope is 3/2,and the y-intercept is 3
Answers
We are given a line that passes through the points (3,0) and (0,-2) (from the graph) from that information we can find the slope of the line using the following formula:
[tex]m=\frac{y_{2\text{ }}-y_1}{x_{2\text{ }}-x_1}[/tex]where
[tex]\begin{gathered} (x_1,y_1);\text{ } \\ (x_2,y_2) \end{gathered}[/tex]Are the points through which the line passes. Replacing
[tex]m=\frac{-2-0}{0-3}=\frac{2}{3}[/tex]Since the intercept is the point of the line when x = 0, and the line passes through (0,-2), the intercept is -2.
The slope is 2/3 and the intercept -2
gabrielle wants to buy a new pair of jeans. if the jeans were originally $25.00, but are on sale with a $15 discount, how much will gabrielle have to pay for the jeans.
Answers
the same thing i did when my dad died in a motorcycle crash and my mom had a stroke in her arms when i got to work in a hospital
25-15=10
abubububuvuv
M Find the range of possible diagonal lengths in a parallelogram with the given side lengths. 4. 3 and 12 5. x and 2x 6. x and x 812a, 25) F C12a + 2c, 25) The area of a parallelogram is given by the formula A=bh, where A is the area, b is the length of a base, and h is the height perpendicular to the base. ABCD is a parallelogram. E, F, G, and Hare the midpoints of the sides. 7. Show that the area of EFGH is half the area of ABCD. G A(0,0) D(200)
Answers
Here, we want to find the range of the diagonal length of a parallelogram measuring x by x units
From what we have, we can see that the sides are equal and what this mean is that we have a square with equal diagonal length from any of the sides
So to get the diagonal length, we use the Pythagoras' theorem since the dsigonal splits the square into two equal parts
Thus, we have;
[tex]\begin{gathered} d^2=x^2+x^2 \\ \\ d^2=2x^2 \\ \\ d\text{ = x}\sqrt[]{2} \end{gathered}[/tex]If you don’t need further explanation on this question, we can end the session. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks and have a great day!
Stretch or compress each linear function. Let g(x) be a vertical compression of f(x)=8x+6 by a factor of 1/4. Write the rule for g(x).
Answers
we have
f(x)=8x+6
we know that
The rule for a vertical compresion of f(x) is equal to
(x,y) -------> (x, ay)
where a is the factor
so
(x,f(x)) -------> (x,1/4f(x))
thet means
g(x)=1/4{8x+6}
g(x)=2x+1.5
Given the point A(-3,-2) and B(6, 1),find the coordinates of the point Pon directed line segment ABthat partitions AB in the ratio 2:1.
Answers
1) Let's pick the points A(-3,-2) B(6,1)
2) Let's visualize it to better understand
Suppose Julia spends $932 on her credit card. Calculate the amount of interest she would owe in one month if she does NOT pay off her balance in full by the due date. Julia's APR is 16.99%. Estimate the interest charges using the monthly periodic rate
Answers
Answer:
The amount of interest she would owe in one month if she does not pay off her balance in full by the due date is $13.2
Explanation:
Given that Julia's APR is 16.99%
Suppose she spends $932 on her credit card, the amount of interest she would owe in a year is 16.99% of $932, this amounts to
0.1699 * 932
= $158.3468
To know the interest in a month, we divide the last result by 12
158.3468/12
= $13.196
This is approximately $13.2
Find the value of xa. 13 b. 14/5 c. 5 d. 8
Answers
Given that
There is a figure of the circle and we have to find the value of x.
Explanation -
Since the two chords of the circle are given and they are intersected making four parts. And we have to find the value of x.
So by using Intersecting Chords Theorem
If AC and BD are the chords intersecting at E. Then,
AE x EC = DE x EB
So in the given figure we have,
[tex]\begin{gathered} 4\times10=x\times8 \\ 40=x\times8 \\ x=\frac{40}{8} \\ x=5 \end{gathered}[/tex]
So C is the correct option.
Final answer -
Therefore the final answer is 5.Select the correct answer from each drop-down menu.y 10+816+4AETBBية1+60-8106A sequence of transformations maps AABCO ABC. The sequence of transformations that maps ABC onto ABC is a✓ followed by
Answers
Explanation:
To find the transformation
We will first have to write out the coordinates of ABC
The coordinates of ABC are:
[tex]\begin{gathered} A=(-4,4) \\ B=(-8,2) \\ C=(-6,6) \end{gathered}[/tex]Next, we will write the equation of the image
[tex]\begin{gathered} A^{\prime}=(4,-2) \\ B^{\prime}=(2,2) \\ C^{\prime}=(6,0) \end{gathered}[/tex]From the given coordinates of the image and pre-image
When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x, y) to (-y, x) and graph the rotated figure.
To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x)
Also, there was a
Comparing Relationships with Tables1. Decide whether each table could represent a proportional relationship.If the relationship could be proportional, what would the constant ofproportionality be?a. How loud a sound is depending on how farDistance toaway you are.Listener (ft)Sound Level(dB)85791020407367Costb. The cost of fountain drinks at Hot Dog Hut.Volume(fluid ounces)($)$1.4920$1.59$1.8930
Answers
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
Verify each table
table a
Let
x ----> distance
y ----> sound level
For each ordered pair calculate the value of k
k=y/x
so
(5,85) -----> k=85/5=17
(10,79) ----> k=79/10=7.9
the values of k are differents
that means
the table nor represent a proportional relationship
table b
let
x ----> volume
y ----> cost
k=y/x
(16,1.49) ----> k=1.49/16=0.093125
(20,1.59) ----> k=1.59/20=0.0795
the values of k are differents
that means
the table nor represent a proportional relationship
it is due today!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
The value of 5/9x - 2/3y + xy when x = 3/5 and y = 1/2 is 3/10
We need to evaluate the expression
5/9x - 2/3y + xy
x = 3/5 and y = 1/2
(5/9)(3/5) - (2/3)(1/2) + (3/5)(1/2)
(15/45) - (2/6) + (3/10)
1/3 - 1/3 + 3/10
= 3/10
Therefore, the value of 5/9x - 2/3y + xy when x = 3/5 and y = 1/2 is 3/10
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