The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
State Alternate angle theorem?
The angles which are formed inside the two parallel lines, when intersected by a transversal, are equal to its alternate pairs. These angles are called alternate interior angles.
When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
Angles that are on opposite sides of the transversal are called alternate angles. All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent.
In the above-given figure, you can see, two parallel lines intersected by a transversal AB.
So according to the alternate angle theorem,
m∠3 = m∠6
Now moving on to the students' explanations, both logics are correct.
Hence we can say that according to the alternate angle theorem,
m∠3 = m∠6
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4 hundreds is 10 times as much as 4 thousandths
No, 4 hundreds is not 10 times as much as 4 thousandths.
How to compare 4 hundreds and 4 thousandths?Numbers in the tens are numbers that are multiples of 10, such as 10, 20, 30, 40, etc.
4 hundreds is equal to 4 × 100 = 400.
4 thousandths is equal 4/1000 = 0.004
To compare their magnitudes, we can divide 0.4 by 0.004:
400 ÷ 0.004 = 100000
So 4 hundreds (400) is significantly larger than 4 thousandths (0.004).
Therefore, 4 hundreds is 100000 times as much as 4 thousandths.
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what’s the numerator for the rational expression?
The numerator of the rational expression will be 6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 1 / b + 5 / b = x / b.
The expression will be solved as below,
E = (1/b) + (5/b)
E = ( 1 + 5 ) / b
E = 6 / b
Hence, the numerator will be equal to 6.
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7Mr's sharma spends 17/25 parts of her earning of her children education. how many childrene percent does she spends on her daughter education How many percent does she save.
If Mrs. Sharma spends 17/25 parts of her earnings on her children's education, then she is spending (17/25) x 100 = 68% of her earnings on her children's education.
If the number of children is the same, she spends 68%/number of children on her daughter education.
If she spends 68% of her earnings on her children's education, then she is saving 100 - 68 = 32% of her earnings.
So, she spends 68% on her daughter education and she saves 32% of her earning.
solve the inequality:
||x-3|-2|≤1
Answer:
-1 ≤ x ≤ 5
Step-by-step explanation:
-1 ≤ x ≤ 5 is the answer
Amina runs a small café at the festival and her piece of ground
is 6.0 m x 5.0 m. She wants to put up a tarp roof to shelter
the entire area. The angle at the central top of the roof has to be 90°.
What is the minimum length and width of the tarp in order to
cover the whole roof?
Answer:
The minimum length and width of the tarp would be the diagonal length of the café's piece of ground. To find this length, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the café's piece of ground forms a right triangle, with one side measuring 6.0 m and the other side measuring 5.0 m. So, to find the length of the hypotenuse, we can use the formula: c = √(a^2 + b^2) where c is the length of the hypotenuse and a and b are the lengths of the other two sides. Plugging in the numbers, we get: c = √(6.0^2 + 5.0^2) = √(36 + 25) = √(61) = 7.81 m
So, the minimum length and width of the tarp would be 7.81 m.
I need help ASAP!! thanks if you help <3
The integers that -3.425 lie between are -3 and -4.
The rational numbers that -3.425 lie between to the nearest tenth are -3.4 and -3.5.
The rational numbers that -3.425 lie between to the nearest hundredth are -3.42 and -3.43.
What are the integers and rational numbers ?Integers are numbers without decimals and fractions. They are whole numbers. Integers can either be positive, negative or zero. Examples of integers are -5 and 10.
A rational number is a number that can be expressed as a fraction of two integers. Examples of rational numbers are 1/4, -2/3
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How do you do this math problem involving csc? Can you do it on a ti-84 calculator?
Explanation:
The TI-84 calculator is fairly powerful and can handle things like this, but it's not needed to be honest. Any calculator will do.
"csc" is shorthand for "cosecant". It's the reciprocal of sine.
csc = 1/sin
Recall that
sin = opposite/hypotenuse
which means
csc = 1/sin = hypotenuse/opposite
What we'll need are the hypotenuse and opposite sides. Plot the points (0,0) and (-20,21). Draw a segment between them. This forms the hypotenuse of the right triangle shown below. This triangle is in the quadrant Q2 in the upper left corner. The hypotenuse 29 is found using the pythagorean theorem a^2+b^2 = c^2.
Use a = 20 and b = 21 to find c = 29.
According to that diagram, we can then say:
csc = hypotenuse/opposite = 29/21
I will give brainliest, if you get this correct
Answer: the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
Step-by-step explanation:
To obtain the regression equation for costs related to age of cars, we can use the method of least squares. This method involves finding the line of best fit that minimizes the sum of the squared differences between the predicted values and the actual values.
The equation for a linear regression line is:
y = a + bx
where a is the y-intercept and b is the slope of the line.
To find the slope of the line (b), we can use the formula:
b = (n(∑xy) - (∑x)(∑y)) / (n(∑x^2) - (∑x)^2)
To find the y-intercept (a), we can use the formula:
a = (∑y - b(∑x)) / n
Given the data provided, we can calculate the following values:
∑x = 142
∑y = 150
∑xy = 2430
∑x^2 = 10304
n = 8
By substituting these values into the formulas for b and a, we can find the slope and y-intercept of the line:
b = (8(2430) - 142(150)) / (8(10304) - 142^2) = 0.5
a = (150 - 0.5(142)) / 8 = 13.5
Therefore, the regression equation for the costs related to age of cars is:
y = 13.5 + 0.5x
To estimate the maintenance cost of cars when the age of cars is 12 years, we can substitute x = 12 into the equation and solve for y:
y = 13.5 + 0.5(12) = 16.5
So the estimated maintenance cost of cars when the age of cars is 12 years is 16.5 ( in 100 birr)
Maureen bought a new car worth $26,525 one year ago. She knows that her car's value will depreciate each year. She uses an online calculator to find that her car is worth $24,403 today. Write an exponential equation in the form y = a(b) that can model the value, y, of Maureen's car x years after purchase. Use whole numbers, decimals, or simplified fractions for the values of a and b.
The exponential equation that models the function of Maureen's car is 26,525 (0.92)
a = 26,525 and b = 0.92
What is an exponential function?Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting value
b = the base function
x = the exponents
Considering the problem,
the starting = $26,525
the base = depreciation
the exponents = x
A year ago hence x = 1
$24,403 = $26,525(b)¹
b = 24,403 / 26,525
b = 0.92
hence we can say that a = 26,525 and b = 0.92
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The actual sum is
0
A i need help for this math please
Answer:
the answer is 0
Step-by-step explanation:
because the question you asked has no digits other than 0
PLEASE HELP ME ASAP IREADY
which complex number has an absolute value of square roof of 13 ?
Answer:
There should be 8 of them
- 2 - 3i
- 2 + 3i
2 - 3i
2 + 3i
- 3 - 2i
- 3 + 2i
3 - 2i
3 + 2i
Thanks
absolute value is the real part squared + the complex part squared and the root of the things you get.
|a + ib|
= √(a²+b²)
so the sign doesn't matter
factorise 6xy - 5x squared
Answer:
see full calculations in below
Step-by-step explanation:
Answer:
don't know my dear friend
In △ABC, the length of median BM is half the length of side AB and ∠ABM measures 40°. Find m∠ABC.
Answer:
m∠ABC = 180.
Step-by-step explanation:
In a triangle, the median to the side opposite the largest angle bisects that angle.
Since BM is a median, it bisects ∠C, the angle opposite side AB.
Let's call the angle opposite side AB angle x, so x/2 = 40.
Therefore, x = 80
Since a triangle has 180 degree, then if we add all the angles in the triangle we get:
m∠ABC = m∠BAC + m∠BCA + m∠CAB = x + (180-x) + (180-x) =180
So m∠ABC = 180
9 cm Find the area of the square. Remember A = s² Area of the square cm 2
What is the slope for the graph?
A: -5
B: -1/2
C:2
D: -1/5
Answer:
Step-by-step explanation:
Since we are given two points in the graph, we can use the slope equation shown below:
(y2-y1)/(x2-x1)
reading the graph left from right (1,11) will be the first point and (3,1) the second. plug in and solve!
(1-11)/(3-1) = -10/2 = -5
The slope is -5
a negative slope makes sense since the graph is leaving the first quadrant.
hope this helps!
Answer: A) -5. Graph slope.
Step-by-step explanation:
The formula to calculate the slope of the line is:
[tex]\boldsymbol{\sf{m=\dfrac{\Delta y}{\Delta x} \iff m=\dfrac{x_2-x_1}{y_2-y_1} }}[/tex]
We have that the points are:
A (x₁, y₁) = 1, 11B (x₂, y₂) = 3,1We substitute these points in the previous formula and solve:
[tex]\boldsymbol{\sf{m=\dfrac{x_2-x_1}{y_2-y_1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{1-11 }{3-1} }}\\ \\ \\ \boldsymbol{\sf{m=\dfrac{-10}{5} }}\\ \\ \\ \boxed{\boldsymbol{\sf{m=-5}}}[/tex]
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Answer:
Step-by-step explanation:
Answer:
The Graph is Below
Step-by-step explanation:
The diagram shows a prism. 1m 2m front 2m 1m 2m side front elevation Draw the front elevation and the side elevation of the prism on the grids. Use a scale of 2 squares to 1 m. side elevation
The required Front view and a Side view of the given prism have been shown.
What is 3d geometry?3D geometry is the study of shapes in 3D space using three coordinates: x-coordinate, y-coordinate, and z-coordinate. To discover the exact location of a point in 3D space, three criteria are required.
Here,
"Front view" and "side view" refer to two different perspectives of an object or a scene. "Front view" is a perspective of the object or scene as seen from the front, and "side view" is a perspective of the object or scene as seen from the side.
Thus, the required Front view and Side view of the given prism has been shown.
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What would 1+1 equal if we add 0
Answer:
any number added to 0 is equal to itself.
Step-by-step explanation:
Answer:
... 2?
Step-by-step explanation:
1+1+0 = 2
what is the solution to this equation?
[tex](\frac{1}{4})x^+{1}=32[/tex]
[tex]\cfrac{1}{4}x+1=32\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{4}x+1 \right)=4(32)}\implies x+4=128\implies x=124[/tex]
$2750 is invested at an interest rate of 3.5% APR compounded quarterly. Determine the amount after 7 years. Round your answer to the nearest hundredth.
Answer:
The compound interest formula is A = P(1 + r/n)^(nt) where A is the final amount, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In this case, P = 2750, r = 0.035, n = 4 (because interest is compounded quarterly) and t = 7 (because we are trying to find the balance after 7 years).
So the formula becomes:
A = 2750(1 + 0.035/4)^(4*7)
By plugging the number into the formula we can find the final amount after 7 years
A = $3,974.23
So the amount of money in the account at the end of 7 years is $3,974.23, rounded to the nearest hundredth.
To which set does the number
11 belong. Choose the most descriptive answer.
O rational
O irrational
O whole
O natural
Answer:
Step-by-step explanation:
The number 11 belongs to the set of natural numbers. Natural numbers are the set of all positive whole numbers, including 0, and the number 11 is a positive whole number.
6, 12, 15, 60, 65, ?
Answer:
390
Step-by-step explanation:
The pattern here is inversing between multiplying and adding
6 to 12 = ×2
12 to 15 = +3
15 to 60 = ×4
60 to 65 = +5
This means that to get the next number you must do ×6 since the next pattern has to be × and the number must be 6!
65 × 6 = 390
Have a lovely day :)
Multiply the previous term by 3 and subtract 4 The second term of the sequence is 5. Find the difference between the first and fourth terms of the sequence.
Answer:
72
Step-by-step explanation:
Given that the second term of the sequence is 5, and that we are to multiply the previous term by 3 and subtract 4, we can use that as a recursive formula to find the other terms of the sequence.
The first term of the sequence is:
5*3-4 = 11
The third term of the sequence is:
53-4=11
113-4=29
The fourth term of the sequence is:
53-4=11
113-4=29
29*3-4=83
The difference between the first and fourth terms of the sequence is:
83-11 = 72
So the difference between the first and fourth terms of the sequence is 72.
identify the vertex of the parabola
I WILL MARK BRAINLIEST
Answer:(1,0) which is the second one in the picture
Step-by-step explanation:The vertex is in (1,0).
Find the values of k and m in the parallelogram?
Answer:
In order to find the values of k and m in a parallelogram, you would need to have additional information such as the coordinates of the points that make up the parallelogram and the formulas or equations that relate k and m to these points.
Here is one way to find the values of k and m in a parallelogram:
Label the four vertices of the parallelogram as A, B, C, and D with the opposite sides parallel to each other.
Find the slope of the line segment AB by using the formula (y2-y1)/(x2-x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Let the slope of AB be represented by k.
Find the slope of the line segment AD by using the same formula and let it be represented by m.
The values of k and m are now found.
Please note that, this method is only applicable if the Parallelogram is not degenerate i.e, it is not a rectangle or a line.
It is also important to keep in mind that different formulas or equations may be used depending on the specific context of the problem. It is also important to check that the slopes of opposite sides are equal.
Step-by-step explanation:
In ΔXYZ, x = 89 cm, z = 84 cm and ∠Z=70°. Find all possible values of ∠X, to the nearest degree.
The value of angle X Is 85° ( nearest degree)
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
the law of sines is used to solve the triangle, when we know two angles and one side or two angles and one included side. It means that the law of sines can be used when we have ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) criteria.
therefore x/sin X = z/sinZ
89/sinX = 84/sin 70
89sin70 = 84sin X
= 89× 0.94 = 84sinX
=83.66 = 84sin X
sin X = 83.66/84
sinX = 0.996
X = sin^-1 0.996
X = 85° ( nearest degree)
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Does anyonw know how to solve:
cos2a=4/5?
The value of a is 18.43°
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, cos2a=4/5
cos 2a = 4/5
2a = cos⁻¹(4/5)
2a = 36.86°
a = 18.43°
Hence, the value of a is 18.43°
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Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
Answer:
They will meet after 4 hours from the departure------------------------
The distance is 710000 km and the first spaceship has travelled 110000 km in the first hour.
The remainder of the distance is reducing by:
110000 + 90000 = 200000 km an hourTime to travel before they meet:
(710000 - 110000)/200000 = 600000/200000 = 3 hoursAdd the first hour to this to get total travel time of 4 hours.
Ill give brainiest for the answer
Answer:
m∠10 = 41°
Step-by-step explanation:
If ∠9 and ∠10 are complementary. Then ∠7 and ∠8 are complementary as well. Complementary angles meameansns they sum up to 90 degrees.
m∠7 + m∠8 = 90
m∠7 + 41 = 90
m∠7 = 90 - 41 = 49°
Given that m∠7 ≅ m∠9. So m∠9 = 49° and m∠10 = 41°.