Answers
Answer:
x= 80
y= 130
Step-by-step explanation:
The correct values of x and y that make k || j and m || n are x = 130 and y = 130.
To find the values of x and y, we need to use the fact that if two lines are parallel, their corresponding angles are equal.
Given that k is parallel to j, we have:
x = 50 (corresponding angles)
Since m is parallel to n, we have:
y + 80 = 210 (corresponding angles)
Solving for y:
y = 210 - 80
y = 130
Now, we have the value of x as 50 and the value of y as 130. However, we also know that the angles x and y are supplementary because they form a straight line. Therefore, their sum must be 180 degrees.
x + y = 180
50 + y = 180
y = 180 - 50
y = 130
This confirms that y is indeed 130 degrees. Since x and y are supplementary and both equal to 130 degrees, we have a contradiction because the sum of x and y should be 180 degrees.
To resolve this contradiction, we must re-evaluate our initial assumption that x = 50 degrees. Since x and y are supplementary, and we have correctly determined that y = 130 degrees, we must have:
x + y = 180
x + 130 = 180
x = 180 - 130
x = 50
This is incorrect because we initially assumed x = 50 degrees based on corresponding angles, but we did not consider that the angle adjacent to x on line k is not given and could be different from the corresponding angle of 50 degrees on line j.
To correct this, we should consider the angle adjacent to x on line k, which must sum up with x to 180 degrees because of the straight line. Let's call this angle x'. Since k is parallel to j, x' corresponds to the angle of 130 degrees on line j. Therefore, we have:
x' + x = 180
130 + x = 180
x = 180 - 130
x = 50
Now, considering that x and y are supplementary:
x + y = 180
50 + y = 180
y = 180 - 50
y = 130
Thus, we have x = 50 degrees and y = 130 degrees, which are indeed the values that make k || j and m || n. However, since x and y are supplementary, they must both be 130 degrees to satisfy the conditions of the problem.
Therefore, the correct values are x = 130 degrees and y = 130 degrees.
Related Questions
Write a two-column proof given 2x + 6 96 prove: x = 46
Answers
Salma drove 605 miles in 11 hours at the same rate how long would it take her to drive 385
Answers
Time = 11 hours
Velocity = distance/time
Velocity = 605miles/11 hours
Velocity = 55mph
385miles/55miles/hour= 7hours.
Or
605 = 11
385 = x
Solving for x =(385/605)*11
X= 7 hours
divide 605 by 11 to find her speed
605/11 = 55 ( she drove 55 miles per hour )
now divide 385 by 55 to find time
385/55 = 7 hours
what is
7x-4=-2x+1+9x-5
Answers
remember, you can do anything to an equation as long as you do it to both sides
7x-4=-2x+1+9x-5
group like terms
7x-4=-2x+9x+1-5
add like terms
7x-4=7x-4
add 4 to both sides
7x=7x
divide both sides by 7
x=x
true
x=all real numbers
since it sipmlifies to x=x (it could somiplify to 0=0 as well), it is an identity and all real numbers work for x
The equation 7x-4=-2x+1+9x-5 has infinitely many solutions
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is 7x-4=-2x+1+9x-5
We have to take the variable terms on one side and constant on other side
In the given equation x is the variable and plus comma minus are all operators.
We need to solve for x.
7x+2x-9x=1-5+4
9x-9x=0
0=0
So the equation has infinitely many solutions
Hence, the equation 7x-4=-2x+1+9x-5 has infinitely many solutions
To learn more on Equation:
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Which ordered pair is a solution to the system of inequalities?
A. (0,4)
B. (-2, -3)
C. (1, 4)
D. (-3, 5)
Answers
if p - 4 = 2, find the value of 5p - 20
Answers
p-4=2
+4 +4
then p=6
5p-20
5(6)-20
30-20
the answer is 10
What else would need to be congruent to show that triangle ABC is congruent to triangle DEF by ASA?
Answers
answer
D. m<B = m<E
Answer:
Option D. ∠B ≅ ∠E
Step-by-step explanation:
In ΔABC and ΔDEF,
Measure of side AB = Measure of side DE = 10 units
∠A ≅ ∠ D ≅ 45°
Now we have to prove ΔABC ≅ ΔDEF by the property of congruence ASA.
Since one angle and one side are equal.
So other angle based on sides AB and DE will be the adjacent angles ∠B and ∠E
Therefore, Option D. ∠B ≅ ∠E will be the answer.
A bicyclist traveled with a speed of 12 km/h from a camping ground to a station, located 60 km away. Write a formula expressing the dependence of the variable s on t, where s is the distance between the bicyclist and the station in km, t - the duration (time) of his travel in hours. Using the formula, find:
Answers
[tex]s=60-12t [/tex]
Now you can answer questions such as "how far was the bicyclist from the station after 3 hours?" Substitute 3 for t. s = 60 - 12(3) = 60 - 36 = 24 km.
Answer:
s=18
Step-by-step explanation:
First of all, the formula is s=60-12t. thanks to the person who answered this question first (teehee)
S=distance and t=duration.
We also know that the distance is 60 km, the bicyclists's speed is 12 km/h, and the duration for this example is 3.5 hours.
So, using the formula, we substitute all the variables and s=18.
Thanks!
Also, for how the formula is what it is, look at the previous answer cuz yea.
Maybe this helped?
hehe- EG
A student writes the difference between 15 and the product of 5 and y to describe the expression 5y - 15. Explain the error
Answers
Determine the value of y in the equation: -5y-9=-(y-1) (show all work)
Answers
The value of y in the equation is -2.5.
Explanation:To determine the value of y in the equation -5y-9=-(y-1), we can start by distributing the negative sign to both terms within the parentheses. This gives us -5y-9=-y+1. Next, we can combine like terms by adding y to both sides of the equation. This simplifies the equation to -4y-9=1. To isolate y, we can subtract 9 from both sides of the equation, resulting in -4y=10. Finally, we divide both sides of the equation by -4 to find the value of y, which is -2.5.
thalia is packing a moving box she has a square frame poster with an area of 9 square feet the cube shaped box has a volume of 30 cubic feet will the poster lie flat in the box
Answers
Total employment for sheet metal workers in 2016 is projected to be 201,000. If this is a 6.3% increase from 2006, approximately what was the total employment in 2006? a. 214,000 b. 188,000 c. 195,000 d. 189,000
Answers
1+(6.3/100) = 1.063
Then divide the final number by the original multiplier:
201,000 / 1.063 = 189087
So the answer is d
Hope this helps! :)
Answer:
189,000
Step-by-step explanation:
Twice a number is 24 less than 4 times the number find the number
Answers
2n + 24 = 4n
24 = 4n - 2n
24 = 2n
n = 24/2
n = 12
The question asks for a number which when multiplied by 2 gives a result that is 24 less than the result of the number when multiplied by 4. The solution to this problem is the number 12.
Explanation:The student's question asks about algebraic expression and solving for a value. This could be written as an equation:
2x = 4x - 24
First, let's simplify this equation by subtracting 2x from both sides, this gives you:
2x = 24
Then, solve the equation by dividing both sides by 2, and we find that the number is:
x = 12
So, the number that the student is searching for is 12. Twice this number is 24, which is indeed 24 less than 4 times the number (48).
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The half-life of a substance is how long it takes for half of the substance to decay or become harmless (for certain radioactive materials). The half-life of a substance is 8.6 days and there is an amount equal to 15 grams now. What is the expression for the amount A(t) that remains after t days, and what is the amount of the substance remaining (rounded to the nearest tenth) after 37 days? Hint: The exponential equation for half-life is A(t) = A0(0.5)t/H, where A(t) is the final amount remaining, A0 is the initial amount, t is time, and H is the half-life.
Answers
A(t) = 15(0.5)37/8.6
Hope this helps!
Final answer:
The amount of a substance remaining after a period of time can be calculated using the half-life formula A(t) = [tex]\frac{A0(0.5)t}{H}[/tex]. After 37 days, with a half-life of 8.6 days starting with 15 grams, approximately 2.2 grams will remain.
Explanation:
The half-life of a substance is the amount of time it takes for half of the substance to decay. For a substance with a given initial amount, the expression for the amount A(t) that remains after t days is A(t) = [tex]\frac{A0(0.5)t}{H}[/tex], where A0 is the initial amount, t is the time in days, and H is the half-life.
Given that the half-life H is 8.6 days and the introductory sum A0 is 15 grams, able to utilize this condition to discover the remaining sum after a certain number of days. To decide the sum of the substance remaining after 37 days, we substitute these values into the equation: A(37) = [tex]\frac{15(0.5)37}{8.6}[/tex]
Calculating this expression, we get that approximately 2.2 grams remain after 37 days, rounded to the nearest tenth.
what is the simplified form of 3abc/abc, when abc does not equal 0? explain using the properties of real numbers
Answers
3abc/abc = 3 .....when abc does not equal 0
the properties is : (ac/bc = a/b ... c ≠ 0 )
The perimeter of a triangle is 465 cm. The length of the sides are consecutive integers. Find the length of the smallest side.
Answers
x=180/3
x=60 cm. for the shortest side.
60+2=62 cm. for the middle side.
60+4=64 cm. for the longest side.
side B= 155cm
side C= 154cm
Livia’s bill for lunch came to $8 before tax and tip. The restaurant included a 7 percent sales tax, and she left a 15 percent tip, which she calculated on the bill before the sales tax was added. What was the total cost of Livia’s lunch?
$8.56
$8.68
$9.20
$9.76
HELPPPPPP PLZZZ
Answers
Answer:
Total cost $9.76 of Livia's lunch.
Step-by-step explanation:
Livia's bill for lunch came = $8.00
The restaurant included a 7% sales tax = 7% of $8.00
= 0.07 × 8 = 0.56
She left a tip of 15% = 15% of $8 =
= 0.15 × 8 = $1.20
Now add tip and tax to the lunch bill
Bill (Pre tax) = $8.00
Tax 7% = $0.56
Tip 15% = $1.20
= 8.00 + 0.56 + 1.20 = $9.76
Total cost of Livia's lunch was $9.76
d•r=r•d what’s the property
Answers
hope this helps
Marty is helping make floral centerpieces for the sports banquet. The guidelines tell him how many of each flower to use in one centerpiece. If he follows the guidelines, which statement is true?
-2 lilies
-1 rose
-3 carnations
-2 daffodils
-1 iris
Answers
What type of math is adding subtracting of positive and negative numbers
Answers
It is Arithmetic.
Hope This Helps You!
Good Luck :)
Final answer:
Adding and subtracting positive and negative numbers falls under the subject of arithmetic in mathematics. The rules for addition and subtraction of integers depend on the signs of the numbers being operated on.
Explanation:
In mathematics, adding and subtracting positive and negative numbers falls under the subject of arithmetic. This concept is also known as integer addition and subtraction.
When you add two positive numbers, the answer is positive. When you add two negative numbers, the answer is negative. When you add numbers with different signs, you subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.
Similarly, when you subtract a positive number from another positive number, or a negative number from another negative number, you follow the same rules. However, when you subtract a negative number from a positive number, you can think of it as adding a positive number, resulting in a larger positive number.
The height of a triangle is 3cm less than the length of its base and is area is 27m,find the height
Answers
27= x(x-3)/2
27= (x^2-3x)/2
54= x^2-3x
x^2-3x-54=0
(x-9)(x+6)=0
x=9, x=-6.
In this case, x must equal 9 since the base cannot be a negative number.
Final answer: Height=6 m
Solve for p: 3p-2(p-4) =7p+6
Plz help asap
Thanks
Answers
3p-2p+8=7p+6
then we will separate the variable and solve for it:
3p-2p-7p=6-8
-6p = -2
6p = 2
p = 2/6 = 1/3
what are the roots to this quadratic equation?
Answers
x^2=9/18
x=sqrt(9/16)
x=3/4,-3/4
so the root of the quadratic equation are 3/4 and -3/4
Answer:
[tex]\frac34[/tex] and [tex]-\frac34[/tex]
Step-by-step explanation:
Hello!
We have to solve for x to find the roots of the quadratic.
Solve for x[tex]16x^2 = 9[/tex][tex]x^2 = \frac{9}{16}[/tex][tex]\sqrt{x^2} = \sqrt{\frac{9}{16}}[/tex][tex]x = \pm\frac{\sqrt9}{\sqrt{16}}[/tex][tex]x = \pm\frac34[/tex]The roots of the quadratic are [tex]\frac34[/tex] and [tex]-\frac34[/tex].
The roots of the quadratic is when the value of y is 0, or when the graph intersects the x-axis.
Evaluate 3|-3|. -6 6 9 -9
Answers
answer is
9
For a sample with m = 20 and s = 4, a score of x = 17 would be considered an extremely low score.
a. True
b. False
Answers
I'm going a serva between cats and dog... Do you like cats more then dogs or dogs more then cats?
Answers
Answer:I like cats better.
Step-by-step ex
please help !!!!!!!!!
Answers
Change=600-576=24
24/600=0.04= 4%
Final answer: 4%
Which graph represents the solution to the inequality?
Answers
-2x > = -17 - 3
-2x > = - 20...change the inequality sign when dividing by a negative
x < = -20/-2
x < = 10.........graph D
An artist is creating a sculpture using bendable metal rods of equal length. One rod is formed into the shape of a square and another rod into the shape of an equilateral triangle. If each side of the triangle is 2 inches longer than each side of the square, how long, in inches, is each rod?
Answers
so notice, their perimeter is the same, because the perimeter is just one rod anyway, and all rods are the same length, thus
[tex]\bf P_s=P_t\implies 4s=3(s+2)\implies 4s=3s+6\implies s=6[/tex]
Answer:
24 inches
Step-by-step explanation:
We are given that an artist creating a sculpture using bendable metal rods of equal length.
One rod is in square shape and second rod is in equilateral triangle shape.
We have to find the length of each rod
Let side of square= x inches
Length of each side of equilateral triangle =x+2 inches
We know that perimeter of square=[tex]4\times side[/tex]
Perimeter of equilateral triangle=[tex]3\times side[/tex]
Using the above formula
Then , Length of square shaped rod=perimeter of square =[tex]4x[/tex]
Perimeter of equilateral triangle =Length of equilateral shaped rod=[tex]3(x+2)[/tex]
Length of square shaped rod=Length of equilateral triangle shaped rod
[tex]4x=3(x+2)[/tex]
[tex]4x=3x+6[/tex]
[tex]4x-3x=6[/tex]
[tex]x=6[/tex]
Length of each side of square =6 inches
Length of square shaped rod=[tex]4\times 6=24 inches[/tex]
Length of each side of equilateral side=6+2=8 inches
Length of equilateral shaped rod=[tex]8\times 3=24 inches[/tex]
Find two consecutive even integers such that five times the smaller integer is ten more than three times the larger integer.
Answers
5n = 3n + 16
12n = 16
n = 8
8 is smaller integer and 10 is the larger.
The problem can be solved by setting up and solving an algebraic equation based on the given conditions. With 'x' representing the smaller integer, and 'x + 2' for the next consecutive even integer, 'x' can be found to identify these integers.
Explanation:To find the two consecutive even integers specified in the question, we should first assign variables to these numbers. Let's say the smaller even integer is 'x', then the next consecutive even integer will be 'x+2' (because even numbers increment by 2).
According to the problem, five times the smaller integer equals ten more than three times the larger integer. We can translate this into a mathematical equation: 5*x = 3*(x+2) + 10.
By simplifying this equation through multiplication and subtraction, we can make 'x' the subject to find the value of the smaller even integer. The larger integer is then x + 2. Using these formulas, we can identify the two consecutive integers that meet the criteria specified in the problem.
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One Endpoint is 9,18 and the midpoint is 14,16 what the other end point
Answers
[tex]\bf \left( \cfrac{x+9}{2}~,~\cfrac{y+18}{2} \right)=\stackrel{\textit{midpoint}}{(14,16)}\implies \begin{cases} \cfrac{x+9}{2}=14\\\\ x+9=28\\ \boxed{x=19}\\ -------\\ \cfrac{y+18}{2}=16\\\\ y+18=32\\ \boxed{y=14} \end{cases}[/tex]