In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work. (5 points)
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal. (5 points)
Answers
Answer:
Part A
x is 46°
Part B
Alternate angles are angles that are in relatively opposite locations relative to a transversal
Step-by-step explanation:
Part A
∠DRP = 110° (Given)
∠QPA = 64° (Given)
∠QPR =
Given that AB is parallel to CD, we have;
∠DRP is congruent to ∠APR (Alternate angles to a transversal RP of parallel lines AB and CD)
Therefore, ∠APR = 115°
∠APR = ∠QPA + ∠QPR (Angle addition postulate)
∴ 115° = 64° + ∠QPR
∠QPR = 110° - 64° = 46°
x = 46°
Part B.
Given that AB is parallel to CD, the lines common (that intersects) both lines are the transversal lines
The angles formed between the parallel lines and the transversal lines have special relationships based on their position with respect to each other
In the question, the angle 110° given between CD and the transversal RP, is found to at an alternate position to the angle ∠APR between the same transversal RP and AB and given that alternate angles are always equal, angle ∠APR is therefore also equal to 110°.
Related Questions
Lorenzo’s test scores are shown below.
Lorenzo’s Test Scores
A dot plot titled Lorenzo's Test Scores. A number line going from 80 to 90. 0 dots are above 80, 81, and 82, there is 1 dot above 83, 2 above 84, 2 above 85, 2 above 86, 2 above 87, 0 above 88 and 89, and 1 above 90.
Anika’s test scores are shown below.
Anika’s Test Scores
A dot plot titled Anika's Test Scores. A number line going from 80 to 90. There are 0 dots above 80, 81, 82, and 83, 3 dots above 84, 2 above 85, 2 above 86, 3 above 87, and 0 dots above 88, 89, and 90.
Which statement compares the shape of the two dot plots?
There is a gap in both plots.
There is a gap in Anika’s scores, but not in Lorenzo’s scores.
The data is widely spread across both plots.
The data is more widely spread for Lorenzo’s scores than for Anika’s.
Answers
Answer:
The data is more widely spread for Lorenzo’s scores than for Anika’s.
Step-by-step explanation:
Answer:
The data is more widely spread for Lorenzo’s scores than for Anika’s.
Step-by-step explanation:
In other words "D" trust me
Need Help Please with q2 & q4!!
Question 2: ARITHMETIC SEQUENCES AND SERIES
Tamara has decided to start saving for spending money for her first year of college. Her money is currently in a large suitcase under her bed, modeled by the function s(x) = 450. She is able to babysit to earn extra money and that function would be a(x) = 6(x − 2), where x is measured in hours. Explain to Tamara how she can create a function that combines the two and describe any simplification that can be done.
Question 4: GEOMETRIC SEQUENCES
Tommy has $350 of his graduation gift money saved at home, and the amount is modeled by the function h(x) = 350. He reads about a bank that has savings accounts that accrue interest according to the function s(x) = (1.04)^x−1. Explain how Tommy can combine the two functions to model the total amount of money he will have in his bank account as interest accrues after he deposits his $350. Justify your reasoning.
Answers
Answer:
Question 2: The first function represents the amount of money she'll have from her 450 under her bed.
s(x) = 450
The second function represents the amount of money she'll earn from babysitting per hour (x):
a(x) = 6(x - 2)
To figure the combined amount, we can add the two functions:
f(x) = s(x) + a(x)
f(x) = 450 + 6(x - 2)
From there, she can simplify the function by distributing, then combining the like terms to simplify:
f(x) = 450 + 6x - 12
f(x) = 438 + 6x
Answer:
f(x) = 438 + 6x
Question 4: His functions are;
h(x)=$350
s(x)=(1.04)^x-1
To find total amount of money in Tommy's account using the functions above, we substitute the first equation x=$350 in the second function.
does this make sence to anyone
Answers
HELPPPPP PLEASE
(04.02 MC)
What is the solution to the following system of equations?
4x + 2y = 6
x - y = 3
(2, 1)
(-2, -1)
(2, 4)
(2, -1)
Answers
======================================================
Explanation:
Double everything in the second equation to go from x-y = 3 to 2x-2y = 6.
So we have this equivalent system of equations
[tex]\begin{cases}4x+2y = 6\\2x-2y=6\end{cases}[/tex]
We can then add straight down. The x terms add to 6x. The y terms go away because they add to 0. The stuff on the right hand sides add to 12.
After those three sets of addition operations, we have the new equation 6x = 12 which solves to x = 2 after dividing both sides by 6.
Now use x = 2 with any of the equations mentioned that have x,y involved so we can solve for y.
4x+2y = 6
4(2)+2y = 6
8+2y = 6
2y = 6-8
2y = -2
y = -2/2
y = -1
or we could say
x-y = 3
2-y = 3
-y = 3-2
-y = 1
y = -1
Either way, we get the same y value.
Since x = 2 and y = -1 pair up together, we get the ordered pair solution (x,y) = (2, -1). Therefore, the answer is choice D.
If you were to graph the two equations, as shown below, the two lines intersect at (2,-1). This point is on both lines at the same time. This is visual confirmation that the point is a solution to both equations. Though you should still algebraically check each original equation.
Plz help, asap!!
This is a triangular prism
perimeter of the base is:
Height is:
Base area is:
Volume is:
Surface area is:
Answers
Answer:
Perimeter of base: 50 cm
Height: 30 cm
Base area: 60 cm
Volume: 21,600 cm
Surface area: I am sorry I forget how to do surface area, but I hope everything else helps.
Step-by-step explanation:
perimeter of base: 50 cm
13+13=26+24=50
Height: 30 cm
already shows height.
Base area: 60 cm
1) 24/2=12 2) 5*12=60
Volume: 21,600 cm
Length*Base*height/2=24*60*30=43,200/2=21,600
surface area:
Sorry I forget how to do surface area.
Answer:
Perimeter of base: 50 cm
Height: 30 cm
Base area: 60 cm
Volume: 21,600 cm
Surface area: I am sorry I forget how to do surface area, but I hope everything else helps.
Step-by-step explanation:
perimeter of base: 50 cm
13+13=26+24=50
Height: 30 cm
already shows height.
Base area: 60 cm
1) 24/2=12 2) 5*12=60
Volume: 21,600 cm
Length*Base*height/2=24*60*30=43,200/2=21,600
Evaluate 4 - x, when x = -6
Answers
Answer:
10
Step-by-step explanation:
4--6
4+6=10
10
step-by-step
4–6
4+6
PLZ HELP 10 POINTS
The slope of a line through the points (-2, 4) and (6, b) is –3/2 . What is the value of b? Explain your method for
calculating b.
Answers
Answer:
b = -2
Step-by-step explanation:
please help me find the answer or at least give me the formula
Answers
Answer:
[tex]2\sqrt{2x}[/tex] or [tex]8x^2[/tex]
Step-by-step explanation:
first you find the distance between P and O which is 4n (use the distance formula -- [tex]\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)}[/tex])
then find the distance between O and Q also using the distance formula; it gives you 4n
then find the hypotunuse by using the pythagorean theorem, [tex]a^2+b^2=c^2[/tex] which would be [tex]4n^2+4n^2=hypotenuse[/tex] and when you simplify it, you get [tex]8x^2[/tex] and if you need it in radical form, it would be [tex]2\sqrt{2x}[/tex]
Answer:
[tex]Hypotenuse = 4n \sqrt{2} [/tex]
Step-by-step explanation:
Catethus1=4n
Catethus2=4n
Hypotenuse=?
[tex]Hypotenuse= \sqrt{{(catethus1)}^{2} + {(catethus2)}^{2}} \: = \sqrt{{(4n)}^{2} + {(4n)}^{2}} \: = 4n \sqrt{2} [/tex]
please help thank you!!!
Answers
Answer:
y = -180 + 3x
Step-by-step explanation:
Because AB = AC -> ABC is a isosceles triangle -> B = C
Because AB = BD -> ABD is an isosceles triangle -> A = D -> x = D
We have ADB + ADC = 180 -> x + ADC = 180 -> ADC = 180 - x (1)
We have x = D, and BAD + ADB + ABD = 180 -> ABD = 180 - 2x but B = C -> C = 180 - 2x (2)
With (1) and (2) We have DAC + ACD + ADC = 180
-> y + 180 -2x + 180 -x = 180
-> y + 360 - 3x = 180
-> y = -180 + 3x
Answer:
y=3x-180
Step-by-step explanation:
Above working is my step by step solution. Thank you.
The sum of twice a number and 13 is 47. Find the number.
Answers
Answer: 17
Step-by-step explanation:
In this problem, the phrase "a number" can be interpreted as a variable. In this case, let the variable be "x."
Thus, "twice a number" = "2x"
"and 13" = "+ 13"
"is 47" = "= 47"
Thus, the problem is simply 2x + 13 = 47.
Then, simply subtract 13 from both sides to get 2x = 34.
Then, simply divide both sides by 2 to get x = 17.
Because "the number" is "x," the number is 17.
Hope it helps :) <3 and lmk if you need more help
17
Step-by-step explanation:
you represent the unknown by a variable
for example X
2x +13=47
Is the triangle obtuse, acute, equilateral or right?
Answers
9514 1404 393
Answer:
obtuse
Step-by-step explanation:
The law of cosines tells you ...
b² = a² +c² -2ac·cos(B)
Substituting for a²+c² using the given equation, we have ...
b² = b²·cos(B)² -2ac·cos(B)
We can subtract b² to get a quadratic in standard form for cos(B).
b²·cos(B)² -2ac·cos(B) -b² = 0
Solving this using the quadratic formula gives ...
[tex]\cos(B)=\dfrac{-(-2ac)\pm\sqrt{(-2ac)^2-4(b^2)(-b^2)}}{2b^2}\\\\\cos(B)=\dfrac{ac}{b^2}\pm\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}[/tex]
The fraction ac/b² is always positive, so the term on the right (the square root) is always greater than 1. The value of cos(B) cannot be greater than 1, so the only viable value for cos(B) is ...
[tex]\cos(B)=\dfrac{ac}{b^2}-\sqrt{\left(\dfrac{ac}{b^2}\right)^2+1}[/tex]
The value of the radical is necessarily greater than ac/b², so cos(B) is necessarily negative. When cos(B) < 0, B > 90°. The triangle is obtuse.
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.
Simplify the given polynomials. Then, classify each polynomial by its degree and number of terms.
Answers
Have attached the picture which has the answers plus explains the solution...
Hope that helps
The simplification, its degree and number of terms of the given polynomials is given below.
What is polynomial?
Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer
Given:
1. (x-1/2)(6x+2)
Simplified form: 6x²-x-1
Name by degree : Quadratic
Number of terms: Polynomial.
2. (7x²+3x)-1/3(21x²-12)
Simplified form: 3x+4
Name by degree : Linear
Number of terms: Binomial.
3. 4(5x²-9x+7)+2(-10x²-18x-13)
Simplified form: 2
Name by degree : constant
Number of terms: monomial.
Learn more about polynomial here:
https://brainly.com/question/11536910
#SPJ2
A theater wants to build movable steps that they can use to go on and off the stage. They want the steps to have enough space inside so they can also be used to store props.
How much space is inside the steps?
Give an exact answer (do not round).
Give correct answer and I will give you brainlist
Answers
Answer:
0.045 m^3
Step-by-step explanation:
0.2 m x 0.15 m x 0.5 m = 0.015 m^3
0.2 m x 0.3 m x 0.5 m = 0.03 m^3
0.045 m^3
The blue shape is a dilation of the black shape. What is the scale factor of the dilation? Simplify your answer and write it as a fraction or whole number.
Answers
Answer:
3 or 3/1 (the 1 is the denominator)
Step-by-step explanation:
the shape got 3 times bigger. let me know
(02.02 MC)
Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of water?
one over ten
one over five
two over seven
two over five
Answers
Answer:
2/5 or two over five
Step-by-step explanation:
2:5
Divide each by 5
2/5 : 1
2/5 * 1
2/5
Answer: 2 over 7
Step-by-step explanation:
2/(2+5) = 2/7
plz help me with the attcahment below
Answers
Step-by-step explanation:
...............MaRk As BrAiNeSt
Answer:
cos theta = BC/AC
Step-by-step explanation:
The cosine function is the ratio of the length of the adjacent side of one of the angles of a triangle to the length of the hypotenuse:
cos theta = BC/AC
What is the format of this proof? Given: ∠ABC is a right angle, ∠DBC is a straight angle Prove: ∠ABD is a right angle
Answers
Answer:
Step-by-step explanation:
abd
Aryona’s ship is 43 miles west off the dock. Aleena’s yacht is 25 miles north from Aryona. How far is Aleena from the dock?
Answers
Answer:
79 miles :p
Step-by-step explanation:
43 + 25
Tyrone has a fish tank that measures 36in. long, 24in. high, and 18 in. wide. He wants to fill the fish tank to a height of 14 inches. What will be the volume of water in the tank?
Answers
Answer:
Step-by-step explanation:
volume of water=l×w×h
l=length of tank=36 in
w=width of tank=18 in
h=height of water=14 in
volume=36×18×14
=9072 in³
What are some transformations that would map DFE to ABC on this coordinate plane? Other than a unit movement
Answers
Answer: You could use a translation since the shape is maintaining its orientation and size. All it’s doing is moving to the right.
The distance between port M and port N is 162 mi. A ship left port M with a speed of 45 mph. In 45 minutes another ship left port N and went towards the first ship with a speed of 36 mph. How long after the departure of the first ship will the two ships meet?
Answers
Answer:
900 minutes
To get explanation go here:
https://brainly.com/question/14424494
Give correct answer and I will give you branlist
Answers
Hello!
Space = 5 cm + 10cm + 10cm + 20cm + 22cm + 30cm => space = 15cm + 10cm + 20cm + 22cm + 30cm => space = 25cm + 20cm + 22cm + 30cm => space = 45cm + 22cm + 30cm => space = 67cm + 30cm => space = 97cm²
Good luck! :)
Answer:
97cm square
Step-by-step explanation:
Need Help!!
Graph the first 6 terms of a sequence where a1 = −3 and d = 4.
Answers
Answer:
thats what i got hope you have a good day :)
Step-by-step explanation:
a1=3
d=-10
………………….
HELP ASAP I WILL MARK BRAINLIEST AND GIVE POINTS!!!!!! (FAKE ANSWERS REPORTED)
The following figures are not drawn to scale but AB and CD if present) are straight lines. Find x:
Answers
Answer:
x=60
Step-by-step explanation:
y=x
90-30=y
60=y
x=60
180 - 90(A&C right angle) =90
90 -30 (from B) = 60
Thus x = 60
The answer is 60
Drag each tile to the correct box.
Find the decreasing functions and arrange them in order from least to greatest y-intercept.
y = 2.5x + 10
y = -0.5x + 0.5
y = -4.5x + 3
y = -0.5x − 5
y = -2x + 7
y = -5x − 12
↓
↓
↓
↓
Answers
y = -5x - 12
y = -0.5x - 5
y = -0.5x + 0.5
y = -4.5x + 3
y = -2x + 7
y = 2.5x + 10
Answer:
from least to greatest y-int
y = -5x - 12
y = -0.5x - 5
y = -0.5x + 0.5
y = -4.5x + 3
y = -2x + 7
y = 2.5x + 10
Step-by-step explanation:
Eva conducted a survey to find out the amount of time high schoolers spend surfing the Internet. From the data collected, the range of time spent was 3 hours. What does this range say about the data?
A. The quotient between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
B. The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
C. All the students surveyed spend exactly 3 hours surfing the Internet.
D. All the students surveyed spend an average of 3 hours surfing the Internet.
Answers
Answer
The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
Explanation
The meaning of range is the difference between the largest and smallest numbers in a set.
In this case, it's possible that one of the students spends no time surfing the internet, and another student spends 3 hours. The range of the data would be 3. It's also possible that some students spend 20 hours surfing the internet, and other students spends 23 hours surfing the internet (although, that's obviously unreasonable).
Answer:
B. The difference between the greatest amount of time and the least amount of time spent surfing the Internet is 3 hours.
Step-by-step explanation:
I'm going to leave this person anonymous, but they have deleted 2 of my answers and I'm sick of it, so please stop deleting my answers I'm not trying to violate brainly's rules in any way, shape, or form.
Complete a b and c if you do one it would mean alot
Answers
Answer: I don't see what your talking about here, so I can't help you.
Step-by-step explanation:
B .50 cents less for each yard with ez excavation
C. She should go with ez excavation it’s cheaper for the buyer and her
Which of the following correctly simplifies the expression 3 to the power of 2 multiplied by 5 to the power of 0 whole over 4, the whole squared.?
3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 1 squared over 4 squared. = 1 over 6.
3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 0 over 4 squared. = 0
3 to the power of 2 multiplied by 0 whole over 4, the whole squared. = 3 to the power of 1 multiplied by 0 over 4 squared. = 0
3 to the power of 2 multiplied by 1 whole over 4, the whole squared. = 3 to the power of 4 multiplied by 1 squared over 4 squared. = 81 over 16.
Answers
simplify
(x^a)^b-c×(x^b)^c-a×(x^c)^a-b
step by step...
Answers
Answer:
= (xa+b)a-b .(xb+c)b-c. (xc+a)c-a
Or
= x(a+b)(a-b). x(b+c)(b-c) .x(c+a)(c-a)
Answer:
[tex]\left(x^a\right)^b-c\left(x^b\right)^c-a\left(x^c\right)^a-b[/tex]
[tex]=x^{ab}-cx^{bc}-a\left(x^c\right)^a-b[/tex]
[tex]=x^{ab}-cx^{bc}-ax^{ac}-b[/tex]
-------------------------
Hope it helps...
Have a great day!!
lets evaluate (3^6)^1/2
step by step.
Answers
Answer:
27Step-by-step explanation:
[tex]\bigg(3^6\bigg)^{\frac{1}{2}}[/tex]
use
[tex](a^n)^m=a^{n\cdot m}[/tex]
[tex]\bigg(3^6\bigg)^{\frac{1}{2}}=3^{6\cdot\frac{1}{2}[/tex]
simplify
[tex]6\!\!\!\!\diagup^3\cdot\dfrac{1}{2\!\!\!\!\diagup_1}=3\cdot\dfrac{1}{1}=3\cdot1=3[/tex]
other
[tex]6\cdot\dfrac{1}{2}=\dfrac{6\cdot1}{2}=\dfrac{6}{2}=3[/tex]
therefore
[tex]\bigg(3^6\bigg)^{\frac{1}{2}}=3^{6\cdot\frac{1}{2}}=3^3=\underbrace{3\cdot3\cdot3}_{3}=27[/tex]
[tex]\displaystyle\bf \boldsymbol{\boxed{(a^n)^m=a^{n\cdot m}}} \\\\(3^6)^{\frac{1}{2}} =3^{\frac{6}{2} }=3^3=\boldsymbol{{\boxed {27}}}[/tex]
