The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.
A rectangle is a plane shape with equal opposite sides. Its area can be determined by;
Area of a rectangle = length x width
Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;
w = l + 5
But,
Area of the plot = length x width
500 = l x (l + 5)
= [tex]l^{2}[/tex] + 5l
This implies that,
500 = [tex]l^{2}[/tex] + 5l
[tex]l^{2}[/tex] + 5l - 500 = 0
Applying the quadratic formula, we have;
l = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a
a = 1, b = 5, c = -500
= (-5 ± [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2
= (-5 ± 45) / 2
l = (40) / 2 OR l = (-50) / 2
l = 20 OR l = - 25.5
So that,
l = 20
Therefore, the length of the plot is 20 feet.
Thus the width of the plot can be determined as;
w = l + 5
= 20 + 5
w = 25
The width of the plot is 25 feet.
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Figure A is a scalr image of figur B. Figure A maps to Figure B with scale factor of 2/3. what is tge value of x?
Answer:
7
Step-by-step explanation:
You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.
Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex] and that can be changed to [tex]\frac{21}{2}[/tex]
([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex]) The two's cancel out and we are left with [tex]\frac{21}{3}[/tex] Which is the same as 7.
one endpoint of a line segment is (1,2) and the midpoint of the midpoint of the segment is (-1,4) what is the other end point ?
In the figure, ABCDEF is a regular hexagon. △ BDF is drawn by joining the
alternate vertices. Show that △ BDF is equilateral
Answer:
Step-by-step explanation:
Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.
ProofAB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon
∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon
ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence
FB ≅ BD ≅ DF . . . . CPCTC
ΔBDF is equilateral . . . . definition of equilateral triangle
o trees are growing in a clearing. The first tree is 5.6 feet tall and casts a 4.2-foot shadow. The second tree casts a 42.3-foot shadow. How tall is the second tree to the nearest tenth of a foot?
The second tree is 56.4 ft tall.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.
Let the length of the tall tree be x. Thus by similarity of triangles we get,
Length of small tree/ Shadow Length of small tree =
Length of Tall tree/ Shadow Length of tall tree
Substituting the values we get,
5.6/4.2 = x/42.3
x = 56.4
Thus the second tree is 56.4 ft tall.
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Kent has two similar cylindrical pipes, pipe a and pipe b. the radius of pipe a is 6 cm, and the radius of pipe b is 2 cm. what is the ratio of the volume of pipe a to the volume of pipe b?
The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
Given that,
Radius of pipe a is 6 cm, and the radius of pipe b is 2 cm.
We know that the volume of cylinder is :- [tex]\pi r^{2}h[/tex]
where r is radius and h is height of the cylinder.
If two figures are similar then ratio of volume is equal to the cube of any dimension.
The ratio of the volume of Pipe a to the volume of Pipe b :-
[tex]\frac{V(a)}{V(b)}=\frac{6^{3} }{2^{3} }[/tex]
= [tex]\frac{27}{1}[/tex]
Hence, The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
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Solve the given differential equation by undetermined coefficients. y'' 4y = 7 sin(2x)
The solution to the given differential equation is yp=−14xcos(2x)
The characteristic equation for this differential equation is:
P(s)=s2+4
The roots of the characteristic equation are:
s=±2i
Therefore, the homogeneous solution is:
yh=c1sin(2x)+c2cos(2x)
Notice that the forcing function has the same angular frequency as the homogeneous solution. In this case, we have resonance. The particular solution will have the form:
yp=Axsin(2x)+Bxcos(2x)
If you take the second derivative of the equation above for yp , and then substitute that result, y′′p , along with equation for yp above, into the left-hand side of the original differential equation, and then simultaneously solve for the values of A and B that make the left-hand side of the differential equation equal to the forcing function on the right-hand side, sin(2x) , you will find:
A=0
B=−14
Therefore,
yp=−14xcos(2x)
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An astronaut visited mars. his weight on earth was 180 pounds, and his weight on mars was only 72 pounds. he removed a rock with a weight of 16 pounds on mars. what is the weight of the rock on earth? a. 1.4 pounds c. 6.4 pounds b. 4 pounds d. 40 pounds
Answer: d. 40 pounds
Step-by-step explanation: let e equal the number of pounds weigh on Earth and m equal the number of pounds weighs on Mars.
so
72m=180e
1m= 72m/72
e= 180/72 = 2.5
1m=2.5e
16m=1 x16
e= 16 x 2.5
e= 40
so therefore, 16m=40e
I hope this helps
What is the probability distribution of X when X~B(1,1/25)?
P(X= 0) = 0.96
P(X= 1) = 0.04
P(X= 0) = 0.75
P(X= 1) = 0.25
P(X= 0) = 0.04
P(X= 1) = 0.96
P(X= 0) = 0.25
P(X= 1) = 0.75
The probability distribution of X when X~B(1,1/25) is (Option A)
P(X= 0) = 0.96P(X= 1) = 0.04See the explanation below.
What is the explanation to the above solution?Given X~B(n,p)
P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)
Thus, X~B [1, 1/25]
1/25 = 0.04
hence, p(x=0)
= C⁰₁ * 0.04⁰ (1 - 0.04)¹
= 0.96
P (x=1)
= C¹₁ 0.04¹ (1-0.04)⁰
= 0.04
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I thought I just had to half the diameter and then put it into the volume formula for cylinders but ig I was wrong? Help please?
Answer:
10830.87 mm³
Step-by-step explanation:
Hello!
Volume of a cylinder: [tex]V = \pi r^2(h)[/tex]
[tex]\pi[/tex] = pir = radius (half diameter)h = heightThe radius for this cylinder is 9.525, after dividing 19.05 by 2.
Plug it into the volume formula to solve for the volume.
Find the Volume[tex]V = \pi r^2(h)[/tex][tex]V = \pi (9.525)^2(38)[/tex][tex]V = \pi (90.725625)(38)[/tex][tex]V = 3447.57375\pi[/tex][tex]V = 1083087236570...\approx10830.87[/tex]The volume is approximately 10830.87 cubic millimeters.
how to do questions 28-29?
thanks!
28. 1.45l ÷ 0.32l = 4.53125
so approximately 5 glasses to leave the bottle empty
29. 5.6kg + 2.5kg = 8.1kg
8.1kg ÷ 0.48 = 16.875
he can make 16 complete doughs
there will be 0.875kg of flour left
The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days: Sample No.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Temperature 40 45 49 47 52 45 51 46 44 48 51 50 56 44 48 50 49 50 46 46 49 49 51 50 Use the data above to calculate the descriptive statistics.
The descriptive statistics for the above data is given as follows:
X = 12.5
What is Descriptive Statistics?
A set of concise descriptive coefficients that describe a particular data set indicative of a whole or sample population is known as descriptive statistics.
For X (mean) = [tex]{\displaystyle X={\frac {1}{n}}\sum _{i=1}^{n}X_{i}[/tex]
= 300/24
= 12.5
For sample variance = [tex]s^2 = \frac{1}{n-1}\biggl[\, \sum_{i=1}^n X_i^2 - \frac{\Bigl(\,\sum\limits_{i=1}^n X_i\Bigr)^{\!2}}{n} \biggr][/tex]
= (1/(24-1) (4,900 - (300²/24)
= 50
Standard deviation s = √s²
= √50
= 7.0711
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Evaluate the double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d
The double integral. 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d is given as
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
What is the double integral 7x cos(y) da, d is bounded by y = 0, y = x2, x = 7 d?Generally, the equation for is mathematically given as
The area denoted by the letter D that is bordered by y=0, y=x2, and x=7
The equation for the X-axis is y=0.
y=x² ---> (y-0) = (x-0)²
Therefore, the equation of a parabola is y = x2, and the vertex of the parabola is located at the point (0,0), and the axis of the parabola is parallel to the Y axis.
The equation for a straight line that is parallel to the Y-axis and passes through the point (7,0) is x=7.
[tex]\int _D 7xcosydA\\\\\int^7_0 \int^x^2 _0 7xcosydA[/tex]
Integrating we have
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
If x equals zero, then we know that u equals zero as well.
When x equals seven, we know that u=72=49.
Therefore, by changing x2=u into our integral, it becomes from
[tex]7/2 \int^7_0 (2xsinx^2)dx[/tex]
[tex]7/2 \int^49_0 sin u dx[/tex]
Hence
=7/2(-cos49+1)
In conclusion,
[tex]\int _D 7xcosydA =7/2(-cos49+1)[/tex]
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A circle is circumscribed around a rectangle with sides lengths 6 and 8 what is the area of the circle?
A. 16[tex]\pi[/tex]
B. 20[tex]\pi[/tex]
C. 24[tex]\pi[/tex]
D. 25[tex]\pi[/tex]
E. 30[tex]\pi[/tex]
Answer:
D. 25pi
Step-by-step explanation:
"circumscribed" means the rectangle is inside the circle and just the corners (vertices) of the rectangle are touching the circle. This means the diagonal of the rectangle is the diameter of the circle. See image. If the sides of the rectangle are 6 and 8 then the third side that makes the triangle(half the rectangle) is 10. You can find this using Pythagorean Theorem or Pythagorean triples (shortcut)
6^2 + 8^2 = d^2
36 + 64 = d^2
100 = d^2
d = 10
This is the diameter of the circle. The radius would then be 5.
Area of a circle is:
A = pi•r^2
= pi•5^2
= 25pi
If the infinite curve y = e^−2x, x ≥ 0, is rotated about the x-axis. Find the area of the resulting surface.
The area of the resulting surface of this infinite curve is π units.
In this question,
The infinite curve is y = e^−2x, x ≥ 0.
The curve is rotated about x-axis.
Since x ≥ 0, the limits will be 0 to ∞.
Then the area of the resulting surface is,
[tex]A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )[/tex]
Now substitute,
u = -2x
⇒ du = -2dx
⇒ dx = [tex]-\frac{1}{2} du[/tex]
Then,
[tex]\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du[/tex]
Now substitute u and du, we get
⇒ [tex]-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx[/tex]
⇒ [tex]-\frac{-2}{2} \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex](1) \int\limits {e^{-2x} } \, dx[/tex]
⇒ [tex]\int\limits {e^{-2x} } \, dx[/tex]
Thus the area of the resulting surface is
[tex]A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx[/tex]
⇒ [tex]A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0[/tex]
⇒ [tex]A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\[/tex]
⇒ [tex]A= -\pi [0-1} \,]\\[/tex]
⇒ [tex]A= \pi[/tex]
Hence we can conclude that the area of the resulting surface is π units.
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John is 12 meters away from a cliff and looks up to the top of the cliff at an angle of 45. His eyes are 2 meters above the ground. How tall is the cliff?
Answer:
14m
Step-by-step explanation:
Please refer to the attached figure
B is the position where John is standing, His eyes are at point A, 2 meters from the ground
D is the base of the cliff and E is the top of the cliff
∠EAC is the angle at which John looks up to the cliff and is given as 45°
BD is the distance from the cliff given as 12m
So AC is also 12m
∠ACE is 90°
Therefore ∠AEC is 180-(45+90) = 45° since AEC forms a triangle and sum of angles in a triangle = 180°
In the ΔAEC, by the law of sines
12/sin(45) = EC/sin(45) . This means EC = 12 since the denominators cancel out
Since point C is 2 meters above ground(the base of the cliff) add 2 and we get the height of the cliff as 12+2 = 14m
Solve the system of equations by graphing.
2x^2 + 8y^2 = 50
x^2 + y^2 = 13
The solutions for the given system are (3,2), (3,-2), (-3,2) and (-3,-2).
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The solution of these equations represents the points at which the parabolas intersect.
2x²+8y²=50 (1)
x² + y²= 13 (2)
Multiplying the equation 2 by -2, you have:
2x²+8y²=50 (1)
-2x² -2 y²= -26(2)
Sum both equations, you have: 6y²= 24. Now, you can find y.
6y²= 24
y²=4
y=±2
If y=2, from equation 2, you have
x² + y²= 13
x² + 2²= 13
x² + 4= 13
x² =13-4
x² =9
x=±3
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Find the inverse of function f
f(x)9x+7
The inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9
How to determine the inverse of the function?The function is given as:
f(x) = 9x + 7
Express f(x) as y
y = 9x + 7
Swap the positions of x and y in the above equation
x = 9y + 7
Subtract 7 from both sides
9y = x - 7
Divide through by 9
y = x/9 - 7/9
Express as an inverse function
f-1(x) = x/9 - 7/9
Hence, the inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9
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Solve the compound inequality and graph the solution on a number line
5x + 9 ≤ 2 and x + 6 > 12
Answer:
First:
5x + 9 < 2
x= 9/5= 1,8 < 2
Second:
x + 6 < 12
x= 12/6= 2 < 12
(06.02) which of these is the algebraic expression for "seven more than the product of three and some number?" 7 3 x 3 10 ÷ x 3x 7 3 7x
Answer:
Step-by-step Explanation:
The correct option is C.
The algebraic expression for "seven more than the product of three and some number = 3x + 7 = 0
What is Algebraic Expression?An algebraic expression is one that is composed of variables, integer constants, and algebraic operations. An algebraic expression is, for instance, 3x² 2xy + c.
According to the given Information:we can search for the product of 3 and "some number",
Let the number be x.
So, the product of x is 3 times = 3x
And now
7 more then the Product .
we add the 7 to the product .
3x + 7 = 0
So the equation will be 3x + 7 = 0
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I understand that question you are looking for is:
Which of these is the algebraic expression for "seven more than the product of three and some number?"
A. 7 + 3 + x
B. 3 + 10 ÷ x
C. 3x + 7
D. 3 + 7x
Can anyone solve 12? ASAP FIND EACH LENGTH TO THE NEAREST TENTH
Answer:
no solution
Step-by-step explanation:
The Law of Sines tells you the relationship between sides and angles of a triangle.
Law of SinesThe Law of Sines tells you ...
sin(A)/a = sin(B)/b = sin(C)/c
Using the given information, this would tell us ...
sin(55°)/12 = sin(B)/b = sin(C)/27
Then angle C would be ...
sin(C) = (27/12)sin(55°) ≈ 1.843
There is no angle whose sine is greater than 1. The triangle we seek does not exist. (Side BC is too short relative to side AB.)
using a number line, find both the intersection and the union of following intervals: [1,5] and (0,8]
Please help what is the answer?
Answer:
C
Step-by-step explanation:
[tex]-15x+60\leq 105 \\ \\ -15x \leq 45 \\ \\ x \geq -3[/tex]
[tex]14x+11 \leq -31 \\ \\ 14x \leq -42 \\ \\ x \leq -3[/tex]
The intersection is x = 3.
marcel plugged in his work tablet and phone. the phone had a battery charge of 13% and started increasing by 2 percentage points every 3 minutes. the tablet had charge of 25% and started increasing by 1 percentage point every 3 minutes.
Let t represent the time, in minutes, since Marcel plugged in the phone and tablet.
Complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet
Answer:
t ≥ 36
Step-by-step explanation:
took a while but i had to try a lot of the numbers. hope it helped, mark me brainleist.
The inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.
We know that t is the time, in minutes, since Marcel plugged in the phone and the tablet.
For phone:-
Initial battery charge = 13%.
Rate of charging = 2% points in 3 minutes = 2/3 % in 1 minute.
Thus, the total charge on the phone after t minutes = 13% + t(2/3)%.
For tablet:-
Initial battery charge = 25%.
Rate of charging = 1% points in 3 minutes = 1/3 % in 1 minute.
Thus, the total charge on the tablet after t minutes = 25% + t(1/3)%.
We are asked to complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.
Since the phone is required to have at least as much battery charge as the tablet, we can show this as:
The total charge on the phone after t minutes ≥ The total charge on the tablet after t minutes,
or, 13% + t(2/3)% ≥ 25% + t(1/3)%,
or, t(2/3)% - t(1/3)% ≥ 25% - 13%,
or, t(1/3)% ≥ 12%,
or, t ≥ 12%/(1/3)%,
or, t ≥ 36.
Thus, the inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.
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What is 0.08 written as a fraction in simplest form?
Answer:
[tex]\frac{2}{25}[/tex]
Step-by-step explanation:
Each "place" in the decimal, can be represented with a base 10 in the numerator.
For example the "tenths" place can be represented as: [tex]\frac{a}{10^1}[/tex] where a=decimal.
The hundredths place can be represented as: [tex]\frac{a}{10^2}[/tex]
The thousandths place can be represented as: [tex]\frac{a}{10^3}[/tex]
and so on...
In this case, we have a decimal in the hundredths place which can be represented as: [tex]\frac{8}{10^2} = \frac{8}{100}[/tex]. Now to simplify this fraction, you simply divide both sides by 4 (greatest common factor of 8 and 100), or in other words multiply it by 0.25/0.25 which is just 1, so the value is the same. [tex]\frac{8}{100} * \frac{0.25}{0.25} = \frac{2}{25}[/tex]
Select the correct answer. what is this series written in sigma notation? 2.5 2.5(1.2) 2.5(1.2)2 ⋯ 2.5(1.2)87 a. ∑ k = 1 87 2.5 ( 1.2 ) k b. ∑ k = 1 87 2.5 ( 1.2 ) k − 1 c. ∑ k = 1 88 2.5 ( 1.2 ) k d.
∑ k = 1 88 2.5 ( 1.2 ) k is this series written in sigma notation.
What is the series written in sigma notation?
A series can be represented in a compact form, called summation or sigma notation. The Greek capital letter, ∑ , is used to represent the sum. The series 4+8+12+16+20+24 can be expressed as 6∑n=14n . The expression is read as the sum of 4n as n goes from 1 to 6 .Given:
2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87
If we look at the power it is always one less the term i.e., for first term the value of k=0.
So, the series in the form of summation can be written as
∑ k = 1 88 2.5 ( 1.2 ) k
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If a function has a positive average rate of change over
an interval, does that mean that the function must be increasing over that
interval? Explain.
Step-by-step explanation:
Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)
Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)
Therefore, the positive average rate of change over an interval must be increasing over that interval.
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A line contains the points R (-5, -3) S (-1, -1) and T (x, 3). Solve for x. Be sure to show and explain all work.
Answer:
x = 7
Step-by-step explanation:
since the points all lie on the same line then the slopes of adjacent points will have the same slope.
calculate the slope using R and S then equate to slope using R and T or S and T
calculate slope using slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = S (- 1, - 1 )
[tex]m_{RS}[/tex] = [tex]\frac{-1-(-3)}{-1-(-5)}[/tex] = [tex]\frac{-1+3}{-1+5}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = T (x, 3 )
[tex]m_{RT}[/tex] = [tex]\frac{3-(-3)}{x-(-5)}[/tex] = [tex]\frac{3+3}{x+5}[/tex] = [tex]\frac{6}{x+5 }[/tex]
equating [tex]m_{RS}[/tex] and [tex]m_{RT}[/tex]
[tex]\frac{6}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
x + 5 = 12 ( subtract 5 from both sides )
x = 7
How does changing the function from f(x) = -5 cos 2x to g(x) = -5 cos 2x-3 affect the range of the function?
Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).
Answer:
See below.
In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a
Step-by-step explanation:
Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1
If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a
An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.
But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.
Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2
Geometry: Write the theorem or postulate for each of the following, ASAP!!!
The theorems or postulates for the given pair of angles are as follows:
2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;
3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;
4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;
5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;
6. ∠4 ≅ ∠8 → Corresponding angles are congruent;
What are the types of pairs of angles?Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.
So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.
Based on their position, they are paired into different categories. Such as:
Interior angles: ∠3, ∠4, ∠5, ∠6
Exterior angles: ∠1, ∠2, ∠7, ∠8
'Alternate interior angles' are the pair of interior angles on the opposite side of the transversal 't'. I.e., (∠3, ∠5), (∠4, ∠6) are congruent.'Alternate exterior angles' are the pair of exterior angles which are on the opposite side of the transversal 't'. I.e., (∠2, ∠8), (∠1, ∠7) are congruent.'Consecutive interior angles' are the pair of interior angles which are on the same side of the transversal 't'. I.e., (∠3, ∠6), (∠4, ∠5). These are also called "Supplementary angles" which mean they add up to 180°.'Consecutive exterior angles' are the pair of exterior angles on the same side of the transversal 't'. I.e., (∠2, ∠7), (∠1, ∠8). These are also called "Supplementary angles" which mean they add up to 180°.'Vertically opposite angles' are the pair of angles that are opposite to each other at the point of intersection. I.e., (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), (∠6, ∠8)'Corresponding angles' are the pair of consecutive angles in which one of the angles is exterior and the other is interior. I.e., (∠1, ∠5), (∠2, ∠6), (∠4, ∠8), (∠3, ∠7)Theorems or postulates for the given pair of angles:Classifying the given pair of angles and their corresponding theorems:
2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.
Theorem - "The alternate exterior angles are congruent"
3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.
Theorem - "The verticle angles are congruent"
4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.
Theorem - "The alternate interior angles are congruent"
5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.
Theorem - " The supplementary angles add up to 180°"
6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.
Theorem - " The corresponding angles are congruent".
Learn more about the pair of angles here:
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pls help questions 5-7
Answer: 0.032, 18, 4224, 7.58
Step-by-step explanation:
5. 5 L = 5000 mL = 5000 [tex]cm^{3}[/tex]
5000/(6*6*6) = 23 r 32 so 5 L of water can fill up 23 cubic tanks length 6 cm and is left with 0.032 L
6. There is (13 - 11) x 20 x 10 = 400 [tex]cm^{3}[/tex] left unoccupied in the box
400/23 = 17.4 so it takes 18 balls to overflow the water
7. 1 mL = 1 [tex]cm^{3}[/tex]
(a) 22 x 12 x 16 = 4224 [tex]cm^{3}[/tex] = 4224 mL
(b) 2 L = 2000 mL = 2000 [tex]cm^{3}[/tex]
22 x 12 = 264
2000/264 = 7.58 cm
