Answers
Answer:
Please check the explanation.
Step-by-step explanation:
From the given diagram, we can observe that r and s are the two parallel lines intersected by the two transversal lines.
Therefore, the pairs of alternating interior angles formed by the two transversal lines are:
∠1 & ∠5 ∠2 & ∠4∠2 & ∠7 ∠3 & ∠6We know that alternating interior angles formed by a transversal line are congruent.
Thus,
∠1 = ∠5 ∠2 = ∠4∠2 = ∠7 ∠3 = ∠6Part a)
Given
m∠1 = 3x + 42
m∠5 = 8x - 8
As
∠1 = ∠5
So
3x + 42 = 8x - 8
flipe the equation
8x - 8 = 3x + 42
subtract 3x from both sides
8x - 8 - 3x = 3x + 42 - 3x
5x - 8 = 42
add 8 to both sides
5x - 8 + 8 = 42 + 8
5x = 50
divide both sides by 5
5x/5 = 50/5
x = 10.0000 (Rounded to four decimal places)
Thus, the value of x = 10.0000 (Rounded to four decimal places)
Part b)
Given
m∠6 = 12°
It is clear that angles ∠6 and angle ∠7 lie on a straight line.
Thus,
The sum of ∠6 and ∠7 is 180°.
∠6 + ∠7 = 180°
substituting m ∠ 6 = 12° in ∠6 + ∠7 = 180°
12° + ∠7 = 180°
subtract 12 from both sides
12° + ∠7 - 12° = 180° - 12°
∠7 = 168°
Thus, measure of angle ∠7 = 168°.
We already know that alternating interior angles formed by a transversal line are congruent.
∠7 and ∠2 are alternating interior angles.
Thus,
∠2 = ∠7
As ∠7 = 168°.
Therefore,
∠2 = 168°
Hence, we conclude that
∠2 = 168°
Related Questions
Write the word sentence as an inequality
The sum of a number n and 2/3 is no less than 5 1/3.
Answer and you’ll get brainliest answer if correct
Answers
Answer:
Step-by-step explanation:
n+2/3 ≥ 5 1/3
there is you answer! :)12 = 3 (g - 1)
Options are:
5
3
-5
-3
Answers
Answer:
It's 5.
Step-by-step explanation:
substituting g = 5 into the equation,
12 = 3(5 - 1)
12 = 12
5 of 5
Sushil, Alex and Peter share some sweets in
the ratio 4:2:3. Sushil gets 8 more sweets than
Peter. How many sweets does Alex get?
Check
Answers
9514 1404 393
Answer:
16
Step-by-step explanation:
If we multiply the numbers by 8, the difference between the first (Sushil) and last (Peter) will be 8.
4 : 2 : 3 = 32 : 16 : 24
This tells us Alex gets 16 sweets.
Patrick drives from P to Q at an average speed of 40 mph . His drive back from Q to P is at an average speed of 45 mph and takes two minutes less.
How far, in miles, is it from P to Q?
Answers
Answer:
12
Step-by-step explanation:
13. What is the length of the missing side, x?
Answers
Ariel makes this model to show a division equation. Which equation matches Ariel's model?
Answers
Answer
I think it's the third one :)
Step-by-step explanation:
The requried equation that matches the Ariels model are as follows,
A, 1512 / 8 = 189 and C = 1688 / 8 = 211.
The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
A division of 8 has been showing,
So the expression that matches the division of 8 would be the required expression,
So,
A, = 1512 / 8 = 189 [true]
B, = 1600/80 = 8 [false]
C = 1688 / 8 = 211 [true]
D = 1600 / 2 = 800 [false statment]
Thus, the requried equation that matches the Ariels model are as follows,
A, 1512 / 8 = 189 and C = 1688 / 8 = 211.
Learn more about models here:
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PLS HELP ME!!! which matrix represents the system of equations below {8x-9y+13z=11
{-8x-5y+5z=15
{3x+4y-8z=-10
Answers
Answer:
The answer is below
Step-by-step explanation:
The system of equations:
8x-9y+13z=11
-8x-5y+5z=15
3x+4y-8z=-10
The equations can be represented in matrix form as:
AX = B
X = A⁻¹B
Therefore:
[tex]\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}8&-9&13\\-8&-5&5\\3&4&-8\end{array}\right] ^{-1}\left[\begin{array}{c}11\\15\\-10\end{array}\right]\\[/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{19} &-\frac{1}{19}&\frac{1}{19}\\-\frac{49}{380}&-\frac{103}{380}&-\frac{36}{95} \\-\frac{17}{380}&-\frac{69}{380}&-\frac{28}{95} \end{array}\right] \left[\begin{array}{c}11\\15\\-10\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}-0.74\\-1.69\\0.13\end{array}\right] \\[/tex]
Ivy likes to buy trail mix in bulk at her local grocery store. If she paid $5.16 for 1.2 pounds of trail mix, what is the price per pound?
A. $3.96
B. 4.03
C. $4.30
D. $6.19
Answers
Answer:Step-by-step explanation:
c。4.3
ddddddddddddddddddddddddddddddd
Ivy likes to buy trail mix in bulk at her local grocery store. If she paid $5.16 for 1.2 pounds of trail mix, the price per pound would be $4.3.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
If she paid $5.16 for 1.2 pounds of trail mix
Cost 1.2 pounds of trail mix = $5.16
Cost per pound of trail mix = $5.16/1.2
= $4.3
Learn more about the unitary method;
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Don’t get this problem
Answers
Answer:
why does it say right twice? ...
Pure salt is made up of sodium and chloride. Each gram
of salt contains 0.393 g of sodium. About how much
sodium is in 55.7 g of pure salt?
24 g
29 g
9 g
90 g
Answers
Answer:
21.8901 g
Step-by-step explanation:
Given that:
1 gram of pure salt contains 0.393 g of sodium
1 gram = 0.393g
Gram of sodium in 55.7g of pure salt will be x
1g = 0.393g
55.7g = x
Cross multiply:
x = 55.7 * 0.393
x = 21.8901
55.7 g of pure salt will contain about 21.8901 g of sodium chloride
What is the expression in factored form?
2x^2+16x+24
Is it (x-2)*(x-6) or 2(x-2)*(x-6)?
Answers
Answer:
( 2x +4) ( x+6)
Step-by-step explanation:
Explanation:-
Given expression 2 x² + 16 x + 24
The factors of 48 = 12 × 4
⇒ 2 x² + 16 x + 24
⇒ 2 x² + 12 x + 4x + 24
⇒ 2 x ( x +6 ) + 4( x +6)
⇒ ( 2x +4) ( x+6)
Ramona has a booth at a craft show. She sells door
wreaths as a money making project. The booth
costs her $200, and each wreath costs her $10 for
material. If she sells each wreath for $30, how many
wreaths does she have to sell to break even?
Friday, January 8, 2021
Record your answer and fill in the bubbles on
your answer document. Be sure to use the correct
place value
Answers
Answer: 10 wreaths
Step-by-step explanation:
First identify the terms.
She has a booth that cost $200. This price will not change thus making it a Fixed cost.
Making a wreath would cost her $10 each time so this is a Variable cost.
She sells the wreath for $30 so this is the selling price.
Breakeven = Fixed Cost / Contribution margin
Contribution margin = Selling price - Variable cost
= 30 - 10
= $20
Breakeven point = 200/20
= 10 wreaths
pls answer this asap
Answers
Answer:
its c or d
Step-by-step explanation:
PLSS HELP ME!! ASAP!! I WILL GIVE YOU BRAINLYEST!!
What is the best estimate of the area of the figure in square inches?
Answers
To find the area of this figure the best action would to divide it into three different sections, finding the area of each and then adding them all together.
First, find the area of the square in the center, which would be 60in.
Second, find the area of the half circle. You would use the formula for area of a circle. You would divide this answer by 2 since this is only half of a circle. You would get 14.135in.
Last, you would find the area of the triangle. You would multiply both sides and then divide by 2, since it’s a triangle and not a square. Area for this is 12in.
And then you would add all these together.
Answer:
86.1372 -------> 86.1 (Nearest Tenths)
86.1372 -------> 86.14 (Nearest Hundreths)
86.1372 --------> 86.137 (Nearest Thousandths)
Step-by-step explanation:
Semicircle: 3.14*[tex]3^{2}[/tex]/2 = 14.1372
Triangle: 4*6 = 24/2 = 12
Rectangle: 10*6 = 60
14.1372 + 12 + 60 = 86.1372
86.1372 -------> 86.1 (Nearest Tenths)
86.1372 -------> 86.14 (Nearest Hundreths)
86.1372 --------> 86.137 (Nearest Thousandths)
You use beads to make a decision. Of the beads,1/3 are red and 1/4 are blue. The rest are white. What fraction of the beads are red or blue.
Answers
4/12= 1/3
3/12=1/4
3 + (5 + 4) = 3+ (4 + 5) illustrates which property?
Answers
Answer:
Distributive
Step-by-step explanation:
Answer:3(4+5)= 3(4)+3(5)
Step-by-step explanation:
What is m
A.51
B.129
C.134
D.141
Answers
Answer:D 141 because
The value of the internal angle m from the heptagon is given by the equation m = 141°.
What is the sum of a polygon's internal angles?The formula returns the sum of the internal angles of a polygon.
The sum of the internal angles of an n-sided polygon is n = 180° (n - 2), where n is the number of sides = angle in degrees
Given the data,
Let's call the polygon a heptagon.
The polygon has n sides, which equals 7 sides.
Now, n = 180 is the sum of the interior angles of a polygon with n sides ( n - 2 )
7θ = 180 ( 7 - 2 )
7θ = 180 ( 5 )
When we simplify the equation, we obtain 7 = 900°.
A = 900° denotes the sum of the internal angles of the polygon.
And , the value of A = 120° + m° + 148° + 90° + 142° + 130° + 129°
900° = m + 759°
Subtracting 759° on both sides of the equation , we get
m = 141°
Hence , the interior angle ∠B = 141°
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The triangles are congruent. Find the measure of x.
Answers
Match up the sides for each triangle using the little marks through the sides
1 to 1, 2 to 2 and 3 to 3
When you do this you see that x corresponds to c on the first triangle.
The 3 angles in a triangle = 180.
Find c by subtracting A and B from 180
C = 180- 29-63 = 88
Now x = c so x = 88
The answer is C. 88
Find the area and perimeter of the figure. I need help on this
Answers
Answer:
area=38cm²
perimeter=34cm
Step-by-step explanation:
I found three shapes and got
4·2=8
3·3=9
9·3=21
8+9+21=38cm²
5+6+9+4+3+2+2+3=34
Perimeter: 30
AREA - 9 * 6 = 54
6 + 4 = 10
54 - 10 = 44 sq
PERIMETER - 9 + 9 + 6 + 6 = 30
Find the slope of the line from a graph. Will give brainliest!!!
Answers
Answer:
2/1 or 2
Step-by-step explanation:
to find the slope you have to calculate the rise over run, do this by picking two spots on the line that go thourgh the corner of a square. then count the amount up the is your rise then the lateral movement, the is your run.
this means the answer is 2/1 that can be simplified to 2.
Directed line segment PT has endpoints whose
coordinates are P(-2, 1) and 1(4,7). Determine
the coordinates of pointſ that divides the segment
in the ratio 2 to 1.
Answers
Answer:
(2 , 5)
Step-by-step explanation:
point (x,y) that divides the segment PI in the ratio 2 to 1
PD=4 - (-2) = 6 PE/ED=2/1 PE=2ED PE+ED=6 3ED=6 ED=2 PE=4
coordinate of E (2,1) .... 2 is x coordinate of E
DI=7-1=6 DF/FI=2/1 DF=4
coordinate of F (4,5) .... .... 5 is y coordinate of E
CF // PD PC/CI=DF/FI=2/1
C (2,5)
Coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).
Given in the question,
Segment PT with endpoints P(-2, 1) and T(4, 7).Point (h, k) divides the segment in the ratio of 2 : 1.If the endpoints of a segment PQ have been given as[tex]P(x_1,y_1)[/tex] and [tex]Q(x_2,y_2)[/tex] and a point [tex](h,k)[/tex] divides this segment in the ratio of m : n,
[tex]h=\frac{mx_2+nx_1}{m+n}[/tex]
[tex]k=\frac{my_2+ny_1}{m+n}[/tex]
If the extreme ends of a segment PT are [tex]P(-2,1)[/tex] and [tex]T(4,7)[/tex] and a point (h, k) divides this segment in ratio of 2 : 1,
[tex]h=\frac{2(4)+1(-2)}{2+1}[/tex]
[tex]h=2[/tex]
[tex]k=\frac{2(7)+1(1)}{2+1}[/tex]
[tex]k=5[/tex]
Therefore, coordinates of the point intersecting segment PT in the ratio of 2 : 1 will be (2, 5).
Learn more,
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can someone answer the question plz?
Answers
Answer:
49π cm²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Here diameter = 14, so r = 14 ÷ 2 = 7, then
A = π × 7² = 49π cm²
Answer:
49pi cm^2
Step-by-step explanation:
[tex]a = \pi \: {r}^{2} [/tex]
Because the radius is half of the diameter, divide it by 2 to get the radius to place in the formula which is 14 ÷2 = 7
so
A = pi × 7^2
A= pi × 49cm^2
A piano has 88 keys. Fifty-two of the keys are white.
How many more white keys are there than black keys?
Answers
Answer:
36
Step-by-step explanation:
88 - 52
=36
Estimate by rounding to the nearest ten. Then, find the sum.441+345=?
Answers
345 to the nearest ten is 350
The sum is;
440 + 350 = 790
Is this a domain or range?
please help :(
Answers
Answer:
1,4
Step-by-step explanation:
its just that hoped this helped
Answer:domain
Step-by-step explanation:
How do I find the y-intercept of a graph?
Answers
Answer:
the y intercept on a graph is the line that goes up and down
Step-by-step explanation:
Step-by-step explanation:
Every point on the y-axis has 0 as its x-coordinate. The y-intercept is the point of intersection of the graph and the y-axis.
To find the y-intercept, let x = 0 in the equation of the graph and solve for y. The value of y is the y-intercept.
For example, what is the y-intercept of
2x + 3y = 6
Let x = 0.
2(0) + 3y = 6
Solve for y.
3y = 6
y = 2
The y-intercept is 2.
Can y’all help me on question 22?!
Answers
Answer:
The answer for question 22 is 40.
-
Step-by-step explanation:
[tex] \frac{8 \: red \: cars}{3 \: blue \: cars} = \frac{x}{15 \: blue \: cars} \\ \\ \frac{3x}{3} = \frac{120}{3} \\ \\ x = 40[/tex]
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5
points. If x is the number of 3-point questions and y is the number of 5-point guestions, the system shown
represents this situation
x+y= 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions
The test contains 20 three-point questions and 8 five-point questions.
Answers
Answer:
10 three point questions, 14 five point questions
Step-by-step explanation:
trial and error
Find the Y equation of the line
Answers
Answer:
Step-by-step explanation:
(-2, 0) (0, 4)
(4 - 0)/(0 + 2) = 4/2 = 2
y - 0 = 2(x + 2)
y = 2x + 4
please help! hurry, will mark brainliest
Answers
Answer:
123, angles are supplementary
Step-by-step explanation:
m<6 = 57
m<1 = 57 ## Corresponding angles
m<1 + m<2 = 180 ## Same side
180 - 57 = 123