Is this statement true or false? If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.
Answers
The statement " If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are paralle " is true.
What is Property of Parallel lines?If the corresponding angles created by any two lines are equal, then the lines are said to be parallel.If the alternate internal angles created are equal, any two lines are considered to be parallel.If the alternate outside angles created are equal, any two lines are considered to be parallel.Given:
If two lines are intersected by a transversal so that the alternate interior angles are congruent, then the lines are parallel.
We know whenever we have parallel line intersected by transversal line then we Alternate Interior Angle, Corresponding Angle, Alternate Exterior Angle, are congruent.
Thus, the statement showing when we have Alternate Interior Angle congruent then the lines were be parallel lines.
Hence, the statement is True.
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Related Questions
A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
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The correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]. Therefore the correct option is 2.
The volume [tex]\( V \)[/tex] of a pyramid is given by the formula:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]
For a square pyramid, the base area is given by [tex]\( \text{Base Area} = \text{side length}^2 \)[/tex].
In this case, the side length is [tex]\( x \)[/tex] and the height is [tex]\( y \)[/tex]. Therefore, the expression for the volume [tex]\( V \)[/tex] is:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]
Now, let's compare this with the given options:
1. [tex]\( \frac{1}{3}xy \)[/tex] cm³
2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³
3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³
4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³
Now, we can see that the correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3}x^2y \, \text{cm}^3 \][/tex]
So, the correct option is option 2: [tex]\( \frac{1}{3}x^2y \)[/tex] cm³.
The correct expression representing the volume of the pyramid is:
[tex]\[ \frac{1}{3} \times x^2 \times y \[/tex]
Complete question:
A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?
1. [tex]\( \frac{1}{3}xy \)[/tex] cm³
2. [tex]\( \frac{1}{3}x^2y \)[/tex] cm³
3. [tex]\( \frac{1}{2}xy^2 \)[/tex] cm³
4. [tex]\( \frac{1}{2}x^2y \)[/tex] cm³
What is the value of y?
Enter your answer in the box.
y =
Answers
Answer-
[tex]\boxed{\boxed{y^{\circ}=26^{\circ}\ 45'}}[/tex]
Solution-
As the triangle ABC is an isosceles triangle, with AC = BC.
So the angles A and B will be same, i.e
[tex]\Rightarrow \angle A=\angle B[/tex]
[tex]\Rightarrow 34^{\circ}=(x-5)^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=34^{\circ}+5^{\circ}[/tex]
[tex]\Rightarrow x^{\circ}=39^{\circ}[/tex]
As sum of all angles in a triangle is 180°, so
[tex]\Rightarrow \angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]\Rightarrow 34^{\circ}+39^{\circ}+4y^{\circ}=180^{\circ}[/tex]
[tex]\Rightarrow 4y^{\circ}=180^{\circ}-34^{\circ}-39^{\circ}[/tex]
[tex]\Rightarrow 4y^{\circ}=107^{\circ}[/tex]
[tex]\Rightarrow y^{\circ}=\dfrac{107^{\circ}}{4}[/tex]
[tex]\Rightarrow y^{\circ}=26.75^{\circ}[/tex]
[tex]\Rightarrow y^{\circ}=26^{\circ}\ 45'[/tex]
The diameter of a small gear is 16 cm this is 2.5 more than 1/4 of the diameter of a larger gear ehat is the diameter of the larger gear
Answers
the small one has a diameter of 16cm, we know that, this is 2.5 more than (1/4)x.
[tex]\bf 16=\cfrac{1}{4}x+2.5\implies 16-2.5=\cfrac{x}{4}\implies 13.5=\cfrac{x}{4}\implies 4(13.5)=x \\\\\\ 54=x[/tex]
A train travels from city a to city b and then to city
c. the distance from a to b is 200 miles and the distance from b to c is 70 miles. the average speed from a to b was 50 miles per hour, and the average speed from b to c was 35 mph. what was the average speed from a to c (that is for the entire trip) in miles per hour?
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Write the base of −(−6)^5.
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If Juan paid $21.30 for 7.1 pounds of salmon, what was the price of 1 pound of salmon?
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So for 1 pound of salmon its $3.
F(x) = |x − 1| find the derivative from the left at x = 1. if it does not exist, enter none.
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A graph of the function is shown below.
The function is either
f(x) = x-1, for x>1
or
f(x) = 1-x, for x<1
Therefore
f'(x) = 1, for x>1
and
f'(x) = -1, for x<1
Answer: -1
If you subtract twelve from twice a number, the result is eight. what is the number?
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2x = 8 + 12
2x = 20
x = 20/2
x = 10 <== ur number
Twice the number will be 2Y
12 is subtracted from it. That will be;
2Y-12
And it is equal to 8
2Y-12=8
-12 will go over the equality sign to become +12
2Y=8+12
2Y=20
Divide both sides by 2
Y=20/2
Y=10
The number is 10
Have a nice day
Which line is parallel to a line that has a slope of 3 and a y-intercept at (0, 0)?
line AB
line CD
line FG
line HJ
Answers
Answer:
line HJ
Step-by-step explanation:
we know that
The equation of the line that has a slope of [tex]3[/tex] and a y-intercept at [tex](0, 0)[/tex] is equal to
[tex]y=3x[/tex] -----> is a proportional relationship
Remember that
If two lines are parallel , then their slopes are the same
Find the slope of the line HJ
[tex]H(-1,-4), J(1,2)[/tex]
The formula to calculate the slope between two points is equal to
[tex]m=\frac{2+4}{1+1}[/tex]
[tex]m=\frac{6}{2}[/tex]
[tex]m=3[/tex]
therefore
The line HJ is parallel to the line [tex]y=3x[/tex]
factor by grouping: 12x^3-20x+3x-5
Answers
1,705x-5
F(x) = 4x^2+1
Group 1: 3x-5
Group 2: 12x3-20x2
This is going to take a long time to explain so the answer is just (12x2 - 12x - 5) • (x + 1)
How many numbers are divisible by 100 between 1 and 6296?
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find the sum of the first 30 terms of the equation below: an=4n+1
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We are actually looking for a_30.
a_30 = 4(30) + 1
a_30 = 120 + 1
a_30 = 121
Answer:
1,890 is the sum of the first 30 terms of the equation .
Step-by-step explanation:
[tex]a_n=4n+1[/tex]
if , n = 1
[tex]a_1=4\times 1+1=5[/tex]
If, n = 2
[tex]a_2=4\times 2+1=9[/tex]
If, n = 3
[tex]a_3=4\times 3+1=13[/tex]
The arithmetic sequence comes out to be:
5, 9, 13........
a = 5
d = [tex]a_2=a_1=9-5=4[/tex]
The sum of first 30 terms is given by:
[tex]S_n=\frac{n}{2}\times (2a+(n-1)d)[/tex]
[tex]S_{30}=\frac{30}{2}\times (2\times 5+(30-1)\times 4)[/tex]
[tex]S_{30}=1,890[/tex]
1,890 is the sum of the first 30 terms of the equation .
Which of the following points is a solution of the inequality y < -|x|?
a. (1,-2)
b. (1,-1)
c. (1,0)
Answers
You can substitute each point into the inequality which gives you the answer of a
None of the given points is the solution to the inequality y < -|x|.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given inequality,
y < -|x|
As per the given below, the dotted line is not included in the region thus, point (1,-1) is not included.
Hence "None of the given points is the solution to the inequality y < -|x|".
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A pair of shoes costs $25 to make. This means that you need to charge a price of at least ___ just to cover your cost.
Answers
Answer: $25
Step-by-step explanation: you are not trying to make a profit. You are just trying to cover your cost and they cost $25 to make.
The probability that an event will occur is 100%. Which of these best describes the likelihood of the event occurring?
Likely
Certain
Unlikely
Impossible
Answers
Answer: Certain
Step-by-step explanation:
A probability is from 0 - 1, if not 0 or 1 it is a fraction, percentage, or decimal. 100% also equal to 1 is the highest amount you can get, therefore the answer is certain.
What is the product of −412 and 212 ? Enter your answer as a mixed number, in simplified form, in the box.
Answers
It seems that the two factors are - 4 + 1/2 and 2 + 1/2.
Let's use latex for better underestanding:
[tex](-4 \frac{1}{2} ).(2 \frac{1}{2} ) = (-4 - \frac{1}{2} ).(2+ \frac{1}{2} )=(- \frac{9}{2} ).( \frac{5}{2})=- \frac{45}{4} = -( \frac{44 + 1}{4} ) = - 11 \frac{1}{4} [/tex]
Answer: - 11 1/4
What Is The Perimeter Of The triangle ? A(1,2) B(4,6) C(4,2)
Answers
you can pretty much get AC and BC right off the grid.
now, let's check how long is AB then.
[tex]\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 2}})\quad % (c,d) B&({{ 4}}\quad ,&{{ 6}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=\sqrt{(4-1)^2+(6-2)^2}\implies AB=\sqrt{3^2+4^2} \\\\\\ AB=\sqrt{9+16} \implies AB=\sqrt{25}\implies AB=5[/tex]
so the perimeter will then be AB + BC + AC.
Please help me thank you.
Answers
solve the inequality
6n-3 > -18
a. n > -2.5
b. n > -3.5
c. n < -2.5
d. n > 2
Answers
n > 2 {divided each side by -6 and changed the inequality sign}
B.) n > 2
If the area of a square is 49 square inches, how long must each side be?
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or,49 = (side)²
or,side = √49 or 7
So, each side is 7 inch long
As you may know, all sides of a square are equal.
Area = side².
In this case:
49 = side²
side = √49
side = 7.
Each side is 7 square inches.
Hope This Helps You!
Good Luck :)
- Hannah ❤
Rectangle ABCD is transformed to AB’C’D’ by a dilation .What is the scale factor used for the dilation ?
Answers
Answer: The required scale factor that is used for the dilation is 3.
Step-by-step explanation: Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.
We are to find the scale factor that is used for the dilation.
We know that
the scale factor of dilation is defined as
[tex]S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.[/tex]
From the graph, we see that
in rectangle ABCD, the length the side AB is 2 units
and
the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.
Therefore, the scale factor of dilation is given by
[tex]S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.[/tex]
Thus, the required scale factor that is used for the dilation is 3.
Solve the equation
9|9-8x|=2x+3 show work.
Answers
[tex]\bf 9|9-8x|=2x+3\implies |9-8x|=\cfrac{2x+3}{9}\\\\\\ \begin{cases} +(9-8x)=\cfrac{2x+3}{9}\\\\ -(9-8x)=\cfrac{2x+3}{9} \end{cases}\\\\ -------------------------------\\\\ 9-8x=\cfrac{2x+3}{9}\implies 81-72x=2x+3\implies 78=74x \\\\\\ \cfrac{78}{74}=x\implies \cfrac{39}{37}=x\\\\ -------------------------------\\\\ -(9-8x)=\cfrac{2x+3}{9}\implies -9+8x=\cfrac{2x+3}{9} \\\\\\ -81+72x=2x+3\implies 70x=84\implies x=\cfrac{84}{70}\implies x=\cfrac{6}{5}[/tex]
To solve the equation 9|9-8x|=2x+3, follow these steps: remove the absolute value by considering both positive and negative cases, combine like terms, solve for x, and simplify the solutions.
Explanation:To solve the equation 9|9-8x|=2x+3, we need to isolate the variable x. Let's start by removing the absolute value by considering both positive and negative cases.
Case 1: Positive
9-8x = 2x+3
Combine like terms: -8x - 2x = 3 - 9
-10x = -6
Divide both sides by -10: x = -6/-10
Simplify: x = 0.6
Case 2: Negative
-(9-8x) = 2x+3
Distribute the negative sign: -9+8x = 2x+3
Combine like terms: 8x - 2x = 3 + 9
6x = 12
Divide both sides by 6: x = 12/6
Simplify: x = 2
Therefore, the solutions to the equation are x = 0.6 and x = 2.
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How can the pythagorean theorem be used to classify acute, right, and obtuse triangles?
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Look at the figure. If doing a two-column proof, what will be the very last statement?
Question 1 options:
X = 15
MN¯¯¯¯¯¯¯ = RS¯¯¯¯¯
Division Property of Equality
3x+3 = 5x-27
Save
Answers
In the given question, we are required to prove that x = 15
Therefore, the very last statement of the two-column proof for the given figure is x = 15.
In Mrs. Johnson's class there are 28 student desks each desk measures 26.17 inches long if you were to line up all the desks end to end how long would all the desk be?
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number of desks* how long it measures = total measurement
28*26.17
=732.76 inches
Translate the following phrase into an algebraic expression or equation.
the square of the difference of two numbers
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(x - y)^2
Done.
sam and bethan share £54 pounds in the ratio 5:4 workout how much each person gets
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ratio is 5:4
5+4 =9
54 pounds divided by 9 = 6
6*5 = 30
6*4 = 24
Sam gets 30 pounds Bethan gets 24 pounds
Consider kite FGHJ. What are the values of a and b?
Answers
Answer:
Hmmm... interesting on my final I answered B: a=14, b=8 and got it wrong but, when I did it again I got C: a=17, b=6
Step-by-step explanation
Answer:
The value of a=17 cm and b=6 cm
C is correct option.
Step-by-step explanation:
Given: FGHJ is a kite.
Kite has property their adjacent sides are equal. Top two side of the kite is equal and bottom two side of the kite is equal.
FG=GH because ∠F=∠H.
30=2a-4
2a=34
a=17 cm
Similarly, ∠F=∠H
FJ=HJ
3b+6=24
3b=18
b=6 cm
Hence, The value of a=17 cm and b=6 cm
Suppose you need to buy fabric to make costumes for a school play. The budget is $16 for each costume.
You need 12 costumes made from brown fabric. Each brown costume needs 3.25 yards of fabric. You need 8 costumes made from red fabric. Each red costume needs 3.5 yards of fabric.
You have gotten prices from two stores.
Store A: Brown fabric is $4.25 per yard. Red fabric is $4.75 per yard. On any purchase over $40, you will receive a $10 coupon for your next purchase. This store is 5 miles from school.
Store B: Both fabrics are $4.50 per yard. This store is walking distance from school.
What is the maximum budget for the fabric?
Answers
Hope this helped!
20 x 16 = 320
The maximum budget for the fabric is $320
How to Graph y=4/5x-7
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To graph the equation y = 4/5x - 7, plot the y-intercept at -7 and use the slope to find a second point before drawing a line through the two points.
Explanation:To graph the equation y = 4/5x - 7, follow these steps:
Start by plotting the y-intercept at -7 on the y-axis.Use the slope 4/5 to find a second point by moving up 4 units and to the right 5 units. Plot this point.Draw a straight line through these two points to represent the graph of y = 4/5x - 7.