Answers
Answer:
1) x = 55°
2) x = 30°
3) x = 68°
Step-by-step explanation:
In the given set of questions where it requires to find the unknown value of x to prove that v ||w:
Definition of Consecutive Interior Angles Theorem:The Consecutive Interior Angles Theorem states that for any given two parallel lines cut by a transversal, the measures of a pair of consecutive interior angles have a sum of 180°. Hence, the pair of consecutive interior angles are supplementary.
Question 11.) In the given diagram, the two consective interior angles are m ∠70° and m ∠ 2x°. As defined by the Consecutive Interior Angles Theorem:
m ∠70° + m ∠ 2x° = 180°
Solve for x algebraically:
70° + 2x° = 180°
Subtract 70° from both sides:
70° - 70° + 2x° = 180° - 70°
2x° = 110°
Divide both sides by 2 to solve for x:
[tex]\LARGE\mathsf{\frac {2x^{\circ}}{2}\:=\:\frac{110^{\circ}}{2}}[/tex]
x = 55°
Verify whether the value for x is valid:
70° + 2x° = 180°
70° + 2(55)° = 180°
70° + 110° = 180°
180° = 180° (True statement).
Question 2:2) In the given diagram, the two consective interior angles are m ∠2x° and m ∠ 4x°. As defined by the Consecutive Interior Angles Theorem:
m ∠2x° + m ∠ 4x° = 180°
Solve for x algebraically:
2x° + 4x° = 180°
Add like terms:
6x° = 180°
Divide both sides by 6 to solve for x:
[tex]\LARGE\mathsf{\frac {6x^{\circ}}{6}\:=\:\frac{180^{\circ}}{6}}[/tex]
x = 30°
Question 3:The Consecutive Interior Angles Theorem still applies in this question. The two consective interior angles are m ∠90° and m ∠ (x + 22)°. As defined by the Consecutive Interior Angles Theorem:
m ∠90° + m ∠ (x + 22)° = 180°
Solve for x algebraically:
90° + x° + 22 = 180°
Combine like terms:
112° + x° = 180°
Subtract 112° from both sides to isolate x:
112° - 112° + x° = 180° - 112°
x = 68°
Verify whether the value for x is valid:
90° + x° + 22 = 180°
90° + 68° + 22 = 180°
180° = 180° (True statement).
Related Questions
I don’t get it and I’m struggling to answer it.
Answers
Multiply that together and he has 84 ft left
ang Find any three rational numbers between 2 and 3
Answers
Answer:
5/2, 9/4 and 19/7.
Step-by-step explanation:
Rational numbers can be written as a/b where a and b are integers ( b not = 0).
Line m passes through points (10, 7) and (3, 4). Line n is parallel to line m . What is the slope of line ?
Answers
Answer:
The slope is 3/7 or ~0.43
Step-by-step explanation:
The equation for slope is y2-y1/x2-x1
7-4=3
10-3=7
3/7=0.428
The product of two consecutive positive odd numbers is 195.By constructing a quadratic equation and solving it, find the two numbers
Please help
Answers
Step-by-step explanation:
x = one odd number
the second odd number is (x+2), as both are consecutive.
so,
x × (x + 2) = 195
x² + 2x = 195
x² + 2x - 195 = 0
the formula to solve this is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -195
x = (-2 ± sqrt(4 - 4×1×-195))/(2×1) =
= (-2 ± sqrt(4 + 4×195))/2 = (-2 ± sqrt(784))/2 =
= (-2 ± 28)/2 = -1 ± 14
x1 = -1 + 14 = 13
x2 = -1 - 14 = -15 which is invalid as the numbers are positive.
so, the two numbers are 13 and 15.
PLEASE HELP ME!!
Find the domain, in interval notation too.
Answers
I sadly do not have an answer to this problem but, have a great explanation for a similar problem. (I really am sorry that I don't have the answer, in a bit of a time constraint)
Step-by-step explanation:
Example (graph found below):
The domain of a function f(x) is the set of values of x for which f(x) has a defined value.
In the graph we can see that we have two asymptotes: one vertical and one slant asymptote.
The slant asymptote does not affect the domain, but the vertical asymptote at x = 0 implies that f(x) does not have a defined value at x = 0.
Then, x = 0 is not part of the domain of f(x). All the real numbers different from 0 are part of the domain.
Then, we can write the domain as x ≠ 0 or, in interval notation, as (-∞,0) ∪ (0,∞).
Answer: the domain is all the real numbers different from 0.
NOTE:
If we want to know the range of the function, we have to look at the values that f(x) can take for the domain for which it is defined.
In this case, we can see that there is no limitation for the values f(x) can take: f(x) can take all real numbers, so the range is all real numbers.
Answer:
[tex]D = (-\infty, -1) \ \cup \ (-1, 2) \ \cup \ (2, \infty)[/tex]
Step-by-step explanation:
This function is rational function that's meaning that is of the form:
[tex]\frac{1}{x}[/tex]
So you have to take care when [tex]x[/tex] is equal to 0 because the function is undefine in that number (is represented with an asymptote and means that go to positive or negative infinity).
In the given graph there are 2 asymptotes in -1 and 2 so you have to avoid this two points in the notations by intervals. You can achieve this using the parenthesis indicating that you don't take the value in account.
Evaluate.
−[−1 2/5÷0.7(1.8)]−2/3
What is the value of the expression?
Enter your answer as a simplified mixed number in the box.
Answers
Answer: the answer is 2 14/15
Step-by-step explanation:
The solution of the expressions will be 0.44.
What is Number system?
A system of writing to express the number is called number system.
Given that;
The expressions are,
⇒ −[−1 2/5 ÷ 0.7 (1.8) ] − 2/3
Now,
Solve the expression as;
⇒ −[−1 2/5 ÷ 0.7 (1.8) ] − 2/3
Using the BODMAS rule to solve the expressions as;
⇒ −[−1 2/5 ÷ 0.7 (1.8) ] − 2/3
⇒ −[−1 2/5 ÷ 1.26 ] − 2/3
⇒ - [ - 7 / 5 ÷ 1.26 ] − 2/3
⇒ - [ - 7 / 5 x 1 / 1.26 ] - 2 / 3
⇒ - [ - 7 / 6.3 ] - 2/3
⇒ 1.1 - 2/3
⇒ 1.1 - 0.66
⇒ 0.44
Therefore,
The solution of the expressions will be 0.44.
Learn more about the mathematical expression visit:
https://brainly.com/question/2164351
#SPJ5
the ratio of adult to children in the spot club is 5:3 There are 120 people in the club. how many children are there
Answers
Answer:
5:3=8
3/8 x 120
3/1 x 15
3 x 15=45
Step-by-step explanation:
hope this helps
sorry
3x+5x=120
Then combine like terms
8x=120
Divide 8 by both sides
x=15
Now that we have that we can figure out how many children and adults there are
Children: 3x15=45 children
Adults: 5x15=75 adults
Also, you can type this in your calculator for a faster method
Children : 120 x(3/8) =45
because eight is the sum of the ratio 5+3
And Adults : 120 x(5/8)=75
So the answer to your question is 45 children.
Hope this helps!!!
Which point is a solution for the inequality 3x – 2y < 5
a (3, 2)
b (2, 3)
c (5, 2)
d (8, 5)
how do I solve this?
Answers
3*3 - 2*2 < 5
9 - 4 < 5
5 < 5
False
3*2 - 2*3 < 5
6 - 6 < 5
0 < 5
True
3*5 - 2*2 < 5
15 - 4 < 5
11 < 5
False
3*8 - 2*5 < 5
24 - 10 < 5
14 < 5
False
B. (2, 3) is the only point that worked, so that is the answer! :D
Use the following function rule to find f(0).
f(x) = 5^x− 4
f(0) =
Answers
So you just substitute 0 into the equation
f(0)= 5^0-4
=1-4
=-3
Hope I helped!
Answer:
-3
Step-by-step explanation:
Using the remainder and the factor theorem
5⁰-4
1-4
-3
What is r(-4)=(-4+1)(-4-3)? It’s apart of evaluating functions.
Answers
Answer:
21
Step-by-step explanation:
r=-5.25 btw
I need help :) pls help me:)
Answers
Answer:
A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be drawn by hand or by a computer. In the past, sometimes mechanical or electronic plotters were used.
Step-by-step explanation:
not the answer for that but ig this can help u mwa
Answer:
12.15-13.00 is 15 mins
13.00-13.30 is 30 mins
Answer-45 mins
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2
Answers
[tex]\large\red{┈──┈──┈──┈──┈──┈──┈──┈──┈─}[/tex]
The best option is B.B. The rate of change of the cost of the taxi ride is 3.00 per minute.
Determine whether the following ratios are equivalent. (9:12 and 24:18)
Answers
0111100109090909099999999999999999
Round 0.008547 to the nearest thousandth :]
Answers
Answer:
0.855
Step-by-step explanation:
Brainliest Please!Answer:
Step-by-step explanation:
The first zero in the tenth region
The second zero is in the hundreds region
The 8 is in the 1/1000 so look to the next digit.
It is a 5
So round 1 digit in the thousands higher.
Answer: 0.009
Please help me
RIGHT ANSWERS ONLY
Answers
Answer:
90 adults
Step-by-step explanation:
Let's make this an equation
We can add 5+3 giving us 8
Let's make it 8x=144
Solve for x
Divide 8x by 8 = 1x
144 ÷ 8 = 18
Now since we're looking for the adults we multiply by 5
18*5=90 adults
I just need help with these 3
Answers
Answer:
1) 11c
2) 9m - 14
3) 4x - 5
-----
4) x = 4
5) x = 2
Step-by-step explanation:
1)
10c + c
11c
2)
5m + 2( 2m - 7 )
5m + 4m - 14
9m - 14
3)
6x - ( 2x + 5 )
6x - 2x - 5
4x - 5
-----
4)
3x + 7 = -5
3x = 12
x = 4
5)
18 = 4x + 10
8 = 4x
2 = x
Hopefully this helps!
Brainliest please?
Answer:
Step-by-step explanation:
How many times larger is 4 × 1011 than 2 × 106?
Answers
Step by step Explanation:
1. 4*1011=4044
2. 2*106=212
3. 4044/212= 19.07547
4. you now have your answer.
Key:
/ means division
* means multiplication
I hope that helps
Brainliest?
help asap :)
8 1/4 as a percent
Answers
Answer:
Its 8.25% I know this because of history of math in my family
HELP ASAP!!!
x3+y3+z3
Answers
Answer:
= k
Step-by-step explanation:
If ∠ABC and ∠DBF are vertical angles we can conclude...
Answers
Answer:
We can conclude they are congruent
Step-by-step explanation:
Because of the vertical angles theorem
Use mental math to find the missing number. Enter your answer in the box.42,000 ÷ = 600
Answers
Answer:
7 is the required answer.
Step-by-step explanation:
4200 ÷ 7 = 600
Which of the following fractions has a repeating decimal expansion (other than repeating zero)
A 17/20
B 17/25
C 17/3
D 17/22
Answers
Answer:
C
Step-by-step explanation:
→ Immediately remove option A and B from the list as they convert to non recurring decimals
Option C or D are both recurring
Will give brainliet no file plz
Answers
Answer:
it would be C
Step-by-step explanation:
Time(h)
Distance (mi)
12 3 4 5
14 26 38 50 62
The table shows Eli's distance from home as he
rides his bike at a steady rate after meeting a
friend. Write an equation in slope-intercept form
that represents the miles, y, that Eli goes in x hours.
y = 12x + 2
y = 2x + 2
y = 12x + 12
y = 2x + 12
Answers
Answer:
y = 12x + 2
Step-by-step explanation:
To know:
[] These equations are in y = mx + b form
() Also known as slope-intercept form
() m is the slope
() b is the y-intercept
Now, let's solve
[] Slope / m
() Slope is "change in y over change in x," let hours be our x and distance by our y
() [tex]\frac{62 - 14}{5 - 1}=\frac{48}{4}=12[/tex]
[] Y-intercept / b
() We will plug in a set of points into our current equation, then solve for b
() y = mx + b -> y = 12x + b -> 14 = 12(1) + b -> 14 = 12 + b -> 2 = b
Last, we will find our answer
Our b is 2, and our m is 12. This leaves us with option 1, y = 12x + 2
Have a nice day! - table I made is attached
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Sorry for the spam, I really need help.
Answers
Answer:
x=8
y=18
Step-by-step explanation:
[tex](3x+13)+(7x-3)=90[/tex]
[tex]10x+10=90[/tex]
[tex]10x=90-10[/tex]
[tex]x=\frac{80}{10} =8[/tex]
[tex]3x+13=3(8)+13=24+13=37[/tex]
[tex]5y=180-37-53=90[/tex]
[tex]y=\frac{90}{5} =18[/tex]
I hope this help you
..................................
Answers
PLEASE HELP!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I think it's c
Step-by-step explanation:
because that looks like a good answer.
If sin(0) > 0, then in which quadrants could 0 lie? Select all correct answers.
Select all that apply:
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Answers
Answer:
I and IV
Step-by-step explanation:
based on the unity circle 0 and 360 is on the same plane..hope it's answerd
Please help me. What is 5 3/4 - 2 11/12? I'm almost done for the year
Answers
Answer:
2.83
Step-by-step explanation:
Mrs. Coulter has 3 / 5 yard of ribbon to tie on balloons for the festival. Each balloon will need 3 / 10 yard of ribbon. How many balloons can Mrs. Coulter tie with ribbon
Answers
Answer:
I know they are not the same name but they have the same question they are the same answerStep-by-step explanation:
#hope it helps you #happy learning