In the figure shown below, lines j and k are parallel. Which equation can be used to find the value of x in the figure?
Answers
Answer:
Step-by-step explanation:
D b/c you know that the two angles add to 180°
The solution is Option D.
The value of x can be calculated from the equation
( x + 40 ) + ( 2x + 20 ) = 180
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles
Given data ,
Let the parallel lines be j and k
The transversal line is m
Now , the value ( 2x + 20 )° lies on one side of the transversal line
And the value ( x + 40 )° lies on one side of the transversal line
The total angle of a line is 180°
So ,
The sum of ( 2x + 20 )° and ( x + 40 )° will be 180°
Therefore , The solution is ( x + 40 ) + ( 2x + 20 ) = 180
Hence , The value of x can be calculated from the equation
( x + 40 ) + ( 2x + 20 ) = 180
To learn more about angles in parallel lines click :
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Related Questions
Rewrite the following equation as a function of x 2x^(4)-625-500=0
Choices are below. Will give 15 points for this.
Answers
Answer:
Option (D) is true.
Step-by-step explanation:
Given the equation
25x⁴ - 625y - 500 = 0
solving in terms of y as a function of x
[tex]25x^4\:-\:625y\:-\:500\:=\:0[/tex]
Step 1: Add -25x⁴ to both sides
[tex]25x^4\:-\:625y\:-\:500\:+\:\left(-25x^4\right)=0+\left(-25x^4\right)[/tex]
[tex]-625y-500=-25x^4[/tex]
Step 2: Add 500 to both sides
[tex]-625y-500\:+500=-25x^4\:+500[/tex]
[tex]-625y=-25x^4\:+500[/tex]
Step 3: Divide both sides by -625
[tex]\frac{-625y}{-625}=\frac{\left(-25x^4\:+500\right)}{-625}[/tex]
[tex]\:\:y=\:\frac{1}{25}x^4-\frac{4}{5}[/tex]
Therefore,
[tex]\:f\left(x\right)=\:\frac{1}{25}x^4-\frac{4}{5}[/tex]
Thus, option (D) is true.
At a school of 900 students, 20% have blue eyes. A student randomly selects 100 students and finds 17% of them have blue eyes. A second student takes another random sample of 90 students and finds 24% of them have blue eyes. Which of the following explains why there is a difference between the two percentages?
a. The sample sizes were both too small.
b.The samples were not random samples.
c. Both samples suffered from non-response bias.
d. Random error; the numbers were different due to variability inherent in sampling.
Answers
Answer:
d.
Step-by-step explanation:
Given that:
In a school;
Population mean = 900
First student:
Sample size = 100
Sample proportion = 0.17
Second student:
Sample size = 90
Sample proportion = 0.24
The difference between the two percentages is a result of the random error because numbers were not the same as a result of variability inherent in sampling.
At a pizza party, where each person had their own pizza, 12 people ate 100% of their pizza, 7 people ate 75% of their pizza, and 3 people only ate 50% of their pizza. What was the average amount of pizza eaten by all people attending the party?
Answers
Raju has some amount saved in his piggy bank. His uncle gave him Rs. 50 as a birthday gift and now Raju has Rs 123 with him.Find how much money he had earlier? ( Write an equation and solve).
Answers
123-50=73
Step-by-step explanation:
its pretty basic, subtract the amount his uncle gave him from what he has now
On a typical day, the snow on Pike Mountain melts at a rate modeled by the function
M(t), given by M(t)=π/6sin(πt/12)
A snow maker adds snow at a rate modeled by the function S, given by
S(t)=0.006t^2−0.12t+0.87
Both M and S have units in inches per hour and t is measured in hours for 0≤t≤6. At time t = 0, the mountain has 40 inches of snow.
a. How much snow will melt during the 6 hour period? Indicate units of measure.
b. Write an expression for I(t), the total number of inches of snow at any time t.
c. Find the rate of change of the total amount of snow at time t = 3.
Answers
Answer:
a. 2in
b. [tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]
c. l'(3)=0.1938 in/hr
Step-by-step explanation:
a.
In part a, the problem is asking us to find how much snow will melt during the 6 hour period. In order to do so we need to take the M(t) function and integrate it in the given period of time, so we get:
[tex]\int\limits^6_0 {\frac{\pi}{6}sin(\frac{\pi}{12}t)} \, dt[/tex]
So now we solve:
[tex]\frac{\pi}{6}\int\limits^6_0 {sin(\frac{\pi}{12}t)} \, dt[/tex]
this is a known integral, so we get:
[tex]\frac{\pi}{6}[-\frac{12}{\pi}cos(\frac{\pi}{12}t)]^{6}_{0}[/tex]
we can simplify this so we get:
[tex]-2[cos(\frac{\pi}{12}t)]^{6}_{0}[\tex]
[tex]-2[cos(\frac{\pi}{12}(6))-cos(\frac{\pi}{12}(0))][/tex]
[tex]-2[cos(\frac{\pi}{2})-cos(0)][/tex]
[tex]-2[0-1][/tex]
2 in
b)
For part b they want us to write an expression for l(t), the total number of inches of snow at any time t.
in order to do so we need to find an expression for the rate of change of snow. A snowmaker is adding some snow while another amountn of snow is melting, so this rate of change is found by subtracting the two functions, so we get:
l'(t)=S(t)-M(t)
so:
[tex]l(t)=\int {(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))} \, dt[/tex]
so we integrate this to get:
[tex]l(t)=\frac{0.006}{3}t^{3}-\frac{0.12}{2}t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]
and we can simplify this:
[tex]l(t)=0.002t^{3}-0.006t^{2}+0.87t+2cos(\frac{\pi}{12}t)+C[/tex]
so now we need to find what C is equal to, we can use the fact that l(0)=40in so we get:
[tex]40=0.002(0)^{3}-0.006(0)^{2}+0.87(0)+2cos(\frac{\pi}{12}(0))+C[/tex]
which yields:
40=2+C
so
C=40-2
C=38
So the final function is:
[tex]l(t)=0.002t^{3}-0.06t^{2}+0.87t+2cos(\frac{\pi}{12}t)+38[/tex]
c)
for part c we need to find the rate of change of the total amount of snow at time t=3, so in this case we can use the equation we found previously:
l'(t)=S(t)-M(t)
[tex]l'(t)=(0.006t^{2}-0.12t+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}t))[/tex]
and substitute t=3
[tex]l'(3)=(0.006(3)^{2}-0.12(3)+0.87-\frac{\pi}{6}sin(\frac{\pi}{12}(3)))[/tex]
which yields:
l'(t)=0.1938 in/hr
PLEASE help i’m a little confused what goes where
Answers
Answer:I think you find the mean mode miden
Step-by-step explanation:
Figure ABCD is a kite. Find the
value of x.
Answers
Answer:
X=8
Step-by-step explanation:
2x - 5 = X + 3
-x -x
X - 5 = 3
+5 +5
X=8
2x - 2x -5 = x + 2x + 3
-5 = 3x + 3
-5 -5 = 3x +3-3
-10 = 3x
-10/3 = 3x/3
-3.3333 = X
1/3 + 4 × 2/3 + (-12) ÷ 4
Answers
Write a recursive formula and an explicit formula for the following arithmetic sequence.
11, 13, 15, 17, 19, ...
A recursive formula is a = INan=.
(Simplify your answers.)
An explicit formula is an =
(Simplify your answer.)
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the sequence
11, 13, 15, 17, 19, ...
Determining the Recursive formula:
We know that a recursive formula is termed as a formula that specifies each term of the given sequence using the preceding terms.
From the given sequence it is clear that every term can be obtained by adding two to the previous term.
i.e. 13 = 11+2, 15 = 13+2, 17 = 15+2, 19 = 17+2
so
aₙ₊₁ = aₙ+2, for n ≥1
Therefore, a recursive formula is:
aₙ₊₁ = aₙ+2, for n ≥1Determining the Explicit formula:
Given the sequence
11, 13, 15, 17, 19, ...
An arithmetic sequence has a constant difference 'd' and is defined by
[tex]a_n=a_1+\left(n-1\right)d[/tex]
computing the differences of all the adjacent terms
[tex]3-11=2,\:\quad \:15-13=2,\:\quad \:17-15=2,\:\quad \:19-17=2[/tex]
The difference between all the adjacent terms is the same and equal to
[tex]d=2[/tex]
also
[tex]a_1=11[/tex]
so substituting [tex]d=2[/tex], [tex]a_1=11[/tex] in the nth terms
[tex]a_n=a_1+\left(n-1\right)d[/tex]
[tex]a_n=2\left(n-1\right)+11[/tex]
[tex]a_n=2n+9[/tex]
Therefore, the Explicit formula is:
[tex]a_n=2n+9[/tex]
Solve:
At the high school, 1/3 of the students play an instrument. Of the students who play an instrument, 2/3 play a string instrument. What fraction of the students at the high school play a string instrument?
Answers
Answer:
2/9 of the high school students play string instruments.
Step-by-step explanation:
[tex] \frac{1}{3} \times \frac{2}{3} = \frac{2}{9} [/tex]
A = {1, 3, 5, 7, 9}
B = {2, 3, 5, 7}
What is A UB?
Answers
Answer:
1234579
Step-by-step explanation:
first apply formula.then solved
Write an Inequality to represent a graph.
Answers
Answer:
nun of the 3 you gave use so the last one the 4th
Step-by-step explanation:
To take 10% of a number, move the decimal_spaces to the_.
Answers
Answer:
1 space to the right?
Step-by-step explanation:
Answer:
1 space to the left
Step-by-step explanation:
example 5.0 X 10% is the same as 5.0 x .10
5.0 x .10 = .50
Explain how you can use a model to find 6 x 17
Answers
here Multiplicand =6
Multiplier=17
First break Multiplier (17) into 1 ten and 7 ones as
17=10+7
Then Multiply 6 to both of the parts of 17 then add it,
6×17
=6(10+7)
=6×10+6×7 [Distributive property]
=60+42=102
Partial Product is a product obtained by multiplying the multiplicand by one digit of the multiplier when the multiplier has more than one digit.
Helllpp ASAP The sum of -14.3 and a number is positive. Identify a possible value for that
number. Explain your selection.
Answers
Answer: Any number larger than 14.3; one possible value is 20
Note how 20 + (-14.3) = 20-14.3 = 5.7 which is positive.
If we picked something smaller than 14.3, like say 10, then
10+(-14.3) = 10-14.3 = -4.3 which is negative.
----------------
When adding a positive to a negative, you basically subtract the two values. Then whatever the largest value is, that's the sign of your result. For 20+(-14.3), the positive 20 is larger in absolute value so the overall result is positive. On the other hand, the -14.3 is larger in magnitude compared to the 10, which is why 10+(-14.3) has a negative result.
what is 12x-7 where x=4
Answers
Answer:
41
Step-by-step explanation:
12x4=48 -7= 1 and that's my explanation
Which is equivalent to the expression below?
Answers
Answer:
A
Step-by-step explanation:
Opening the brackets, you get: 3x^2 - 2x + 5 - 2x^2 + 5x - 1
Simplifying, you get : x^2 + 3x + 4
Answer:
a
Step-by-step explanation:
3x^2 - 2x^2= x^2
-2x + 5x = 3x
5- 1 =5
What is the smallest initial velocity that is required to throw a stone 49 feet up on top of a silo?
Answers
Answer: the smallest initial velocity that is required to throw the stone is 56 ft/s
Step-by-step explanation:
We know that;
u = initial velocity
v = final velocity = 0
a = acceleration = -g = -32,
s = distance travelled = 49 feet
V² - u² = 2aS
we substitute
0² - u² = 2 × -32 × 49
0 - u² = -3136
u² = 3136
u = √3136
u = 56 ft/s
Therefore the smallest initial velocity that is required to throw the stone is 56 ft/s
11:59 is the deadline please give me the correct answer
Answers
Answer:
[tex]6 - 8x = 5x - 10x + 15 \\10x-8x-5x=15-6\\ - 3x = 9 \\ x = \frac{9}{ - 3} \\ x = - 3[/tex]
-3 is the right answer.Answer:-3
the right answer did ths on paper
If the angles of a traingle are in the ratio 2:3:4 , Find Them
Answers
Answer:
40°, 60°, and 80°
Step-by-step explanation:
We know that the sum of the angles of a triangle is equal to 180°.
We can use this equation to solve for these angles:
180 = 2x + 3x + 4x
180 = 9x
20 = x
Then substitute the solution in for x to solve for the angles:
2(20) = 40°
3(20) = 60°
4(20) = 80°
Therefore, the angles are 40°, 60°, and 80°.
Amy is applying for a job in two companies. The given table shows the salary in dollars () that Company 1 is offering
if she works x hours. Company 2 is offering $12.50 per hour plus a bonus of $80. If she plans to work 40 hours each
week, in which company will she earn more money in a week and by how much more?
A)
She will earn $20 more in Company 1.
B)
She will earn $40 more in Company 1.
C)
She will earn $20 more in Company 2.
D)
She will earn $40 more in company 2.
Eliminate
Answers
Answer: B is the correct answer
Step-by-step explanation: Lol its B
lil_chris23x 56x34 45x34?? 5yx2X
Answers
Find the missing dimensions in the table. Write the dimensions in simplest form.
Parallelogram
Base
Height
Area
Answers
Answer/Step-by-step explanation:
Parallelogram A:
Area = 5x + 20
Base = x + 4
Height = h = ?
Area of Parallelogram = base * height
Plug in the values
5x + 20 = (x + 4) * h
Divide both sides by x + 4
[tex] \frac{5x + 20}{x + 4} = h [/tex]
[tex] \frac{5(x + 4)}{x + 4} = h [/tex]
[tex] 5 = h [/tex]
Height = 5
Parallelogram B:
Area = 8x - 24
Base = b
Height = 8
Area of Parallelogram = base * height
Plug in the values
8x - 24 = b * 8
Divide both sides by 8
[tex] \frac{8x + 24}{8} = b [/tex]
[tex] \frac{8(x + 3)}{8} = b [/tex]
[tex] x + 3 = b [/tex]
Base = x + 3
Parallelogram C:
Area = 12x + 6y
Base = 6
Height = h = ?
Area of Parallelogram = base * height
Plug in the values
12x + 6y = 6 * h
Divide both sides by 6
[tex] \frac{12x + 6y}{6} = h [/tex]
[tex] \frac{6(2x + y)}{6} = h [/tex]
[tex] 2x + y = h [/tex]
Height = 2x + y
A bottle of laundry detergent costs $4.95 per bottle. If you have a coupon for $2.00 off and your total is $7.90, how many bottles of detergent did you buy? WRITE AN EQUATION AND SOLVE.
Answers
The following expression models the total money earned by setting up a food stall at a funfair, where x represents the number of cheeseburgers sold.
What does the constant term in the above expression represent?
A.
The constant -10 represents the cost of setting up the food stall even if no cheeseburgers were sold.
B.
The constant -10 represents the total money earned by setting up the food stall.
C.
The constant -10 represents the maximum number of cheeseburgers sold by the food stall at the funfair.
D.
The constant -10 represents the cost of each cheeseburger at the food stall
Answers
Answer:
C
Step-by-step explanation:
I think so im not sure sorry
A set of pencils sells for $1.75 and costs $0.40 to make. Twenty percent of the profit (the difference between the purchase price and the amount it costs to make) from each set of pencils goes to a school. If 500 sets are sold, what is the amount of money that will go to the school?
Answers
Answer:
$135
Step-by-step explanation:
If each set cost $0.40 to make and sells for $1.75, the profit for each pack is $1.35.
To get 20% of this you do the following: 1.35×0.20
20% of $1.35 is $0.27.
If 500 sets of pencil are sold and the school gets $0.27 from each pack sold, you would multiply $0.27 by 500, which would give you the answer $135.
helpppppppppp pleasssseeee
Answers
Help pleaseee I’m stuck
Answers
Answer:
Measure of angle S= 30° as both the triangles are similar and similar triangles have thier angles equal.Now,In triangle QRS,
Angle.Q+an.R+an.S=180
(Angle sum property of a triangle.)
Angle.Q+17°+30°=180
Angle.Q=180-
Answer:
7
Step-by-step explanation:
i did this before
Glen has 70 toy cars. 30% of the cars are green. How many cars are green?
a.21
b.35
c.18
d.25
Answers
Answer:
21 green cars
Step-by-step explanation:
Answer:
70 x 30/100 = 21
21 cars are green
Step-by-step explanation:
Ben has an apartment worth $425,000, a car worth $18,000, and $3,750 in his savings account. He has no other assets. His only debt is the loan he took out to buy his apartment. If Ben's net worth is $316,750, what is the amount of his loan?
Answers
Answer:
the answer is B
Step-by-step explanation:
Got it correct on Edge 2020
Answer:
its 130000
Step-by-step explanation:
i had that as my exit ticket for mathcounts :) hope it helps