Given than line a is parallel to line b and that line c is parallel to line d, if m<13=(12x-22) & m<14=(9x-29), find m<2.
a 65
b 70
c 85
d 110
Answers
12x-22+9x-29=180
21x-51=180
x=11
m<2=m<14
m<2=70°
The measure of ∠2 is 70° .
What is corresponding angles?The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other and are equal in measure.
What is supplementary angles angles?When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.
According to the question
line a is parallel to line b and c and d are transversal for them
line c is parallel to line d and a and b are transversal for them
m∠13 = (12x - 22)°
m∠14 = (9x - 29)°
Now
As, ∠13 and ∠14 forms supplementary angles .
i.e
m∠13 + m∠14 = 180°
12x - 22° + 9x - 29° = 180°
21x - 51° = 180°
21x = 180° + 51 °
21x = 231 °
x = 11°
So,
m∠13 = 12*11 - 22° = 110°
m∠14 = 9*11 - 29° = 70°
Now,
according to corresponding angles
m∠14 = m∠6 = m∠2 = 70°
Hence, the measure of ∠2 is 70° .
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Related Questions
Evie was doing a science fair project by surveying her biology class. She found that of the 30 students in the class, 15 had brown hair and 17 had blue eyes and 6 had neither brown hair nor blues eyes. Determine the number of students who had brown hair and blue eyes.
Answers
Which of the following polynomials does not have real roots?
A. x2 - 17x - 7
B. -x4 + 4x2 + 6
C. x4 + 2x2 + 2
D. 2x2 - 13 ...?
Answers
proof
if a is a (real) is a root of x4 + 2x2 + 2, so
a4 +a2 +2 =0, it is impossible, because a4>0, a2>0 and 2>0
a4 +a2 +2 must be >0, so x4 + 2x2 + 2 doesnt have real roots
Answer:
C.
Step-by-step explanation:
x4 + 2x2 + 2 has no real roots
Below are the functions of y = |x| and y = |x| – 3. How are the functions related?
a. The functions have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –3.
b. The functions have the same shape.
c. The y-intercept of y = |x| is 0, and the y-intercept of the second function is –3.
d. The functions have the same y-intercept.
Answers
Hope this helps u!!!
WILL UPVOTE
what is the value of x in the following equation: 3x-15=4x+36
A.21
B.-51
C.-21
D.none of these
Answers
3x = 4x + 51
-x = 51
x = -51
________________________________________
Explanation:
________________________________________
Given: 3x − 15 = 4x + 36 ; Solve for "x" .
________________________________________
Let us subtract: "3x" from EACH side of the equation; AND
add: "15 to EACH side of the equation:
__________________________________________
→ 3x − 15 − 3x + 15 = 4x + 36 − 3x + 15 ;
__________________________________________
to get:
__________________________________________
→ 0 = x + 51 ;
___________________________________
→ Subtract "51" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;
___________________________________
→ 0 − 51 = x + 51 − 51 ;
__________________________
→ - 51 = x ; ↔ x = - 51 ; which is: "Answer choice: [B]: -51".
___________________________________
→ Now, let us check our answer, "x = -51 ; by plugging in "-51" for "x" in the original equation, and seeing in both sides of the equation hold true when x = - 51 ;
______________________________
→ Given: 3x − 15 = 4x + 36 ;
→ Substitute "- 51 for "x" ;
→ Start with the "left-hand side" of the equation:
→ 3x − 15 = (3*-51) − 15 = -153 − 15 = -168 ; when x = -51 ;
→ Then, let us examine the "right-hand side" of the equation:
__________________________________________
→ 4x + 36 ; Substitute "-51" for "x" ;
→ (4*-51) + 36 = -204 + 36 = -168
→ Does the "left hand side" of equation = the "right-hand side of the equation" when: x = -51???
______________________________
→ That is, when x = -51, does: - 168 =? -168 ?? Yes!
_________________________
Which of the following is not equivalent to the other three?
A) 1/6
B) 1.66666666.....
C) .17
D) .16
Answers
Which answer describes the type of sequence?
3, 4, 5, 6, ...
A. neither arithmetic nor geometric
B. geometric
C. arithmetic
Answers
What is the simplified form of each expression?
1. (–5.1)^0
1
0
–5.1
–1
2. 3g^-2 b^2
3b^2 over g^2
3g^2b^-2
3gb^-4
b^2 over 3g^2
Answers
The perimeters of a rectangle and an equilateral triangle are equal. The length of the rectangle is twice the width, and the side of the triangle is 8 more than the width of the rectangle. Which statements about this scenario are true if we use the variable w to represent the width of the rectangle?
Answers
The perimeter of rectangle is w+w+2w+2w = 6w
Set them equal to solve for w:
6w = 3w +24
3w = 24
w = 8
Answer:
for online school people it will be 2,3,4
Step-by-step explanation:
i did the assigment
water flows from a faucet at a rate of 5 liters every 25 seconds. At this rate, how much water will flow form the faucet in 45 seconds. Make a table.
Answers
A bag of 29 tulip bulbs contains 10 red tulip bulbs, 11 yellow tulip bulbs, and 8 purple tulip bulbs.
What is the probability that two randomly selected tulip bulbs are both red?
What is the probability that the first bulb selected is red and the second is yellow?
What is the probability that the first bulb selected is yellow and the second is red?
Answers
So, your final answer is 45/406
2) It would be: 10/29 * 11/28 = 110/812 = 55/406
So, your final answer is 55/406
3) It would be: 11/29 * 10/28 = 110/812 = 55/406
So, your final answer is 55/406
Hope this helps!
Answer:
The probability that two randomly selected tulip bulbs are both red is 0.11
The probability that the first bulb selected is red and the second is yellow is 0.13
The probability that the first bulb selected is yellow and the second is red is 0.13
Step-by-step explanation:
A bag of 29 tulip bulbs contains:
10 red tulip bulbs
11 yellow tulip bulbs
8 purple tulip bulbs
Part 1:What is the probability that two randomly selected tulip bulbs are both red?
No. of red tulips = 10
So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{10}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
And that 1 bulb is drawn from red bulbs . So, remaining red bulbs = 9
So, probability of getting red bulb in second draw = [tex]\frac{9}{28}[/tex]
Thus the probability that two randomly selected tulip bulbs are both red:
= [tex]\frac{10}{29}\times\frac{9}{28}[/tex]
= [tex]\frac{45}{406}[/tex]
= [tex]0.11[/tex]
Hence the probability that two randomly selected tulip bulbs are both red is 0.11
Part 2: What is the probability that the first bulb selected is red and the second is yellow?
No. of red tulips = 10
So, probability of getting red tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{10}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
No. yellow bulbs =11
So, probability of getting yellow bulb in second draw = [tex]\frac{11}{28}[/tex]
Thus the probability that the first bulb selected is red and the second is yellow
= [tex]\frac{10}{29}\times\frac{11}{28}[/tex]
= [tex]\frac{55}{406}[/tex]
= [tex]0.13[/tex]
Hence the probability that the first bulb selected is red and the second is yellow is 0.13
Part 3: What is the probability that the first bulb selected is yellow and the second is red?
No. of yellow tulips = 11
So, probability of getting yellow tulip in first draw = [tex]\frac{\text{Favorable events}}{\text{Total events}}[/tex]
= [tex]\frac{11}{29}[/tex]
Since 1 bulb is drawn . So, total no. of bulbs remaining = 28
No. red bulbs =10
So, probability of getting red bulb in second draw = [tex]\frac{10}{28}[/tex]
Thus the probability that the first bulb selected is red and the second is yellow
= [tex]\frac{11}{29}\times\frac{10}{28}[/tex]
= [tex]\frac{55}{406}[/tex]
= [tex]0.13[/tex]
Hence the probability that the first bulb selected is yellow and the second is red is 0.13
Karina solves the system using linear combination and arrives at the equation 116y = 96.28. She then solves this equation for y. Which statement explains Karina’s solution?
a. The cost of electricity is $0.17 per unit.
B. The cost of natural gas is $0.20 per unit.
C. The cost of electricity is $0.72 per unit.
D. The cost of natural gas is $0.83 per unit.
Answers
Answer:
The correct option is D. The cost of natural gas is $0.83 per unit.
Step-by-step explanation:
Consider the provided equation.
[tex]116y = 96.28[/tex]
We need to solve the above equation for y.
Divide both the sides by 116.
[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]
[tex]y=0.83[/tex]
Now consider the provided options.
Hence, the correct option is D. The cost of natural gas is $0.83 per unit.
An equation that sets two fractions equal to each other is called a ____.
Answers
Final answer:
An equation that sets two fractions equal to each other is known as a proportion, where equivalent ratios or fractions indicate the same value. This maintains the equality governed by the rules of algebra, important when performing operations on both sides of an equation.
Explanation:
An equation that sets two fractions equal to each other is called a proportion. This type of equation indicates that two ratios or fractions are equivalent. For example, if we have ½ on one side of the equation and 2/4 on the other, we have a proportion because both fractions represent the same amount.
When we have fractions with the same value in the numerator and the denominator, such as ¹¹/₁₀⁰ for micrometers to meters, we can simplify this to 1 because the quantities cancel each other out. This is true by the rules of algebra, specifically the property that if we perform the same operation on both sides of an equality, the equation remains balanced. This concept is crucial when working with proportions and equations involving fractions.
It's also important to remember that when adding fractions, they must have a common denominator. Ratios and percentages are other forms of expressing relative sizes or amounts which can also be related back to fraction and proportion concepts.
A statement we accept without proof is called a:
theorem
definition
postulate
term
Answers
For postulates, no evidence/proof is needed. It is always believed to be true.
Answer:
C. Postulate.
Step-by-step explanation:
We are asked to find the term that defines the given statement.
Theorem: We know that a theorem is proved by a chain of reasoning. Ir is not self evident.
Definition: We know that definition is a statement of the exact meaning of a word.
Postulate: We know that a postulate is a statement that is taken to be true without any proofs, therefore, postulate is the correct choice.
how do you round 17.92 to the tens
Answers
∧ ∧ this is the ones place
this is the tens place
if the ones place is lower then 5 you keep the tens the same. if the ones place is higher then 5 you round the tens place up one. so the answer is 17.90
What decimal is represented by this expanded form? 5 x 10,000 3 x 1,000 2 x 10 8 x 1 6 1/1,000 4 x 1/,000?
Answers
NEED HELP I SUCK AT MATH AND LIFE IN GENERAL =)
2 .A relation is plotted as a linear function on the coordinate plane starting at point C (0,−1)(0,−1) and ending at point D (2,−11)(2,−11) .
What is the rate of change for the linear function and what is its initial value?
Select from the drop-down menus to correctly complete the statements.
Options for rate of change: a. -11 b. -5 c. 0 d. 5
options for initial value: a. -11 b. -2 c. -1 d. 0
3. Maria is saving money so she can go to a professional football game. Maria has $25. She saves $5 a week.
Graph a ray to represent the amount she saved over time.
( i am really bad at graphs but you're just graphing this i guess???)
4. The temperature decreases by 0.5 degrees every hour.
5. x −2−2 −1−1 0 1 2
y −6−6 −4−4 −2−2 0 2 how would you put that onto a graph???
9. What is the equation of a line with a slope of 1212 and a point (3, 1) on the line?
Express the equation in the form of y=mx+by=mx+b where m is the slope and b is the y-intercept.
10.What does the initial value mean for this function?
Roberta saves $10 each week.
After 4 weeks, Roberta has $90.
Roberta had $50 before she started to save money each week.
Roberta had no money until she started to save $10 a week.
Answers
If you have two points, (x1, y1) and (x2, y2), the rate of change or slope would be
[tex] \frac{y2-y1}{x2-x1} [/tex].
In your problem, the given points are (0, -1) and (2, -11).
Using the formula for rate of change, the rate of change would be:
[tex] \frac{-11+1}{2-0} = \frac{-10}{2}=-5 [/tex].
The "initial value" is the y-intercept - where the graph intersects the y-axis and also where x = 0. The given point (0, -1) has x = 0, so the initial value is -1.
4. Remember the model equation for a graph of a line is
y = mx + b,
where m is slope and b is y-intercept - where the graph intersects the y-axis and also where x = 0.
The x-axis of the graph would be number of weeks, since it is independent.
The y-axis of the graph would be how much money she has.
Since she starts (at 0 weeks) at $25, the first point would be (0, 25). Notice here that it is the y-intercept since x = 0. The value of b in the model equation of a line y = mx + b would be 25.
The rate of change, or slope, is $5/week. This is m in the model equation of a line y = mx + b.
Putting b = 25 and m = 5 into the model equation y = mx + b (remember we use this equation because it works for all lines), the equation would be
y = 5x + 25.
4.
The slope of this will be -0.5degrees/hr, or just -0.5 if it is used as m in the
y = mx+b equation. The slope is negative because it "decreases".
5.
Plot each point and connect the dots. Remember the first number corresponds to the x-axis and the second to the y-axis.
For example in the table for x = -2 and y = -6, the point is (-2, -6), and from the origin (0,0) you go left 2 on the x-axis and down 6 to plot the point.
9.
I think you can do this if you can do #3, but now you have to find b by plugging in given values.
y = mx + b
y = 1212x + b
We can plug in the given point (3,1) to find b.
1 = 1212(3) + b
b = -3625
y = 1212 - 3625
10. Don't know which function you are referring to.
The slope is $10/week, or m = 10.
A point is (4, 90) because "After 4 weeks, Roberta has $90."
The y-intercept is 50 because x (weeks) = 0 at that time.
y = mx + b
y = 10x + 50
What additional information would you need to prove that ΔABC ≅ ΔDEF by ASA
Answers
The additional information needed to prove that ΔABC ≅ ΔDEF by ASA is two pairs of congruent angles and the included side between the two pairs of congruent angles.
We are given that;
The two triangles ΔABC and ΔDEF
Now,
To prove that ΔABC ≅ ΔDEF by ASA (Angle-Side-Angle) congruence criterion, we need the following information:
Two pairs of congruent angles.
The included side between the two pairs of congruent angles.
If two angles and one side of one triangle are equal to two angles and one side of another triangle, then they are congruent. For example, in ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E and BC= EF then ΔABC ≅ ΔDEF by AAS criteria
Therefore, by congruent triangles answer will be two pairs of congruent angles and the included side between the two pairs of congruent angles.
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Need help solving for X
Answers
tan 75 = P / B
3.73 = 300 / x [ tan 75 = 3.73 ]
x = 300 / 3.73
x = 80.42
After round-off to the nearest tenth, it would be 80.4
So, your final answer is x = 80.4
Hope this helps!
Write five and three eights as an improper fraction and as a mixed number
Answers
43/8 (improper fraction)
5.375 (decimal)
At a hockey game a vendor sold a combined total of 145 sodas, the number of hot dogs sold was 33 less of sodas sold, Find the number of Sodas and Hot dogs sold?
Answers
The number of sodas sold is 145, and the number of hot dogs sold is 112. (145 sodas, 112 hot dogs)
Let's denote:
- s as the number of sodas sold.
- h as the number of hot dogs sold.
Given that the total number of sodas sold is 145, we have:
[tex]\[ s = 145 \][/tex]
And we know that the number of hot dogs sold is 33 less than the number of sodas sold:
[tex]\[ h = s - 33 \][/tex]
Now, substitute the value of s into the equation for h :
[tex]\[ h = 145 - 33 \]\[ h = 112 \][/tex]
So, the number of hot dogs sold is 112, and the number of sodas sold is 145.
Tony invested $5,500 in a four-year CD that paid 4.8% interest, but later needed to withdraw $475 early. If the CD’s penalty for early withdrawal was three months’ worth of interest on the amount withdrawn, how much of a penalty did Tony pay?
a.
$5.70
b.
$22.80
c.
$60.30
d.
$66.00
Answers
Answer:
It's A-$5.70 :))))
Step-by-step explanation:
The penalty will be $5.70 which corresponds to option A.
The question is about calculating the penalty for early withdrawal from a Certificate of Deposit (CD). Tony invested $5,500 in a CD at a 4.8% interest rate and withdrew $475 early.
To calculate the penalty, we first need to find three months' worth of interest on the amount withdrawn.
The annual interest on $475 at 4.8% is:
Interest = Principal × Rate × Time
Interest = $475 × 0.048 × 1 = $22.80
Since the penalty is three months' worth, we divide the annual interest by 4 (because there are four 3-month periods in a year):
Penalty = $22.80 / 4
= $5.70
if x>2, then x^2-a-6 / x^2-4=
Answers
We have to factorize the numerator and the denominator:
x² - x - 6 = x² - 3 x + 2 x - 6 = x ( x - 3 ) + 2 ( x - 3 ) = ( x - 3 ) ( x + 2 )
x ² - 4 = ( x - 2 ) ( x + 2 )
[tex] \frac{(x-3)(x+2)}{(x-2)(x+2)}= \frac{x-3}{x-2} [/tex]
Sara is burdened with debt and runs the risk of defaulting on her car loan. She is also late with her credit card payments. What action should Sara take to help her situation?
Answers
Dan put's 11 dollars or his allowance in his savings account every week. how much money will he have affter 15 weeks
Answers
You multiply 11 and 15 in order to get your answer.
Hope this helps..
How do I convert 4/5 to a percent
Answers
= 80%
=0.8
3x + 2y = 5
5x + 2y = 7
Based on the given system of equations, which of the following is not true?
Answers
5x + 2y = 7
(eliminate the equation)
-2x = -2
x = 1 . . . .(put x in equation and you will get that y is also 1)
So the one that is not true is the one where x and y is not 1, like :
8x = 12
Hope this helps
solve 9x + 7 = 7x - 5
Answers
9x - 9x + 7 = 7x -9x - 5
7 = -2x - 5
7 + 5 = -2x - 5 + 5
12 = -2x
12/-2 = -2x/-2
-6 = x
The solution of equation 9x + 7 = 7x - 5 is -6.
The equation 9x + 7 = 7x - 5 can be solved by first isolating x on one side. To do this, we subtract 7x from both sides of the equation, which gives us 2x + 7 = -5. Next, we subtract 7 from both sides to get 2x = -12. Finally, we divide both sides by 2 to find that x = -6. This single solution can be checked by substituting x back into the original equation to verify that both sides equal out, confirming it is an identity. Therefore, the correct solution is x=-6.
To validate the result, we substitute -6 back into the original equation:
9(-6) + 7 = 7(-6) - 5
-54 + 7 = -42 - 5
-47 = -47, which is indeed an identity.
Valerie drives to and from work 5 days a week. the distance from her home to work is 6 miles. over the course of 5 days, her car uses 1/4 of a tank of gas.
Answers
how to solve 4m+6p-8mp
Answers
Final answer:
The provided algebraic expression 4m+6p-8mp cannot be solved or simplified further without additional context, such as specific values for m and p or instructions for solving for one variable in terms of the other.
Explanation:
The original question, "how to solve 4m+6p-8mp", seems to be a request for simplification or to apply given values to an algebraic expression. Without specific values or instructions to solve for one of the variables, the expression cannot be "solved" in the conventional sense of finding a numerical answer. However, we can explore quick ways to simplify or rearrange such an expression if additional context or information were provided, such as values for m and p or instructions on solving for one variable in terms of the other.
The shortest known adult woman is about 24 inches tall and tallest known adult woman is about 92 inches tall. Write an absolute value equation that represents the minimum and maximum heights. Use x to represent the heights.
Answers
Final answer:
The absolute value equation that represents the minimum and maximum heights of adult women, with heights represented by x, is |x - 58| = 34.
Explanation:
To write an absolute value equation representing the minimum and maximum heights of adult women, where the shortest known adult woman is about 24 inches tall and the tallest known adult woman is about 92 inches tall, we can use the variable x to represent an adult woman's height. The midpoint between the smallest and largest height is (24 + 92) / 2 = 58 inches. The distance from this midpoint to each extreme is 34 inches, because 92 - 58 = 34 and 58 - 24 = 34. So, the absolute value equation would be |x - 58| = 34. This equation represents that the height of an adult woman can deviate from 58 inches by 34 inches to be either at the minimum or maximum height recorded.
Final answer:
The absolute value equation representing the minimum and maximum heights of adult women is |x - 58| = 34, where x is the height in inches.
Explanation:
The objective is to write an absolute value equation to represent the minimum and maximum heights of adults.
Using the heights given for the shortest and tallest known adult women, 24 inches and 92 inches respectively, we set the variable x to represent an unknown height.
To express this as an absolute value equation, we identify the midpoint between these two heights, which is (24 inches + 92 inches) / 2 = 58 inches.
The distance from the midpoint to either extreme is (92 inches - 58 inches) = 34 inches, which is the absolute difference.
Therefore, our absolute value equation is |x - 58| = 34.
This equation tells us that the height x must be either 34 inches above or below 58 inches, which corresponds to the minimum and maximum heights of 24 inches (58 - 34) and 92 inches (58 + 34) respectively.