Answer:
So, if you need to convert the fraction into a decimal, 3/4=0.75. So, I think it's 19-0.75 I'm not sure if I'm correct.
Step-by-step explanation:
A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? hint: look at the difference between number of people and cost to get cost per person and then cost without people
How much does each person cost?
Write an equation to show cost, c, of a bus with x number of people on it.
1) The base rate for the empty bus is $120.
2) The variable cost (slope) for each person on board the bus is $2.
3) An equation to show the cost, c, of a bus with x number of people on it is C = 120 + 2x.
How the base rate and slope for the equation are derived:The total charge for taking 30 people aboard = $180
The total charge for taking 50 people on board = $220
The differences in the number of people and charges are 20 and $40, respectively.
Let x = the number of people boarding the bus and n = the fixed rate per bus.
30x + n = 180 ... Equation 1
50x + n = $220 ... Equation 2
Subtract Equation 1 from Equation 2:
20x = $40
x = $2 ($40/20)
The variable cost per person = $2 ($40/20)
The base rate for the empty bus = 30(2) + n = $180, where n is the base rate or fixed cost per bus.
= 60 + n = $180
n = $120
OR:
50(2) + n = $220
100 + n = $220
n = $120
The equation for the cost, c, of a bus with x number of people:
C = 120 + 2x
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ANSWER AS MANY AS POSSIBLE
1. What is the area of a right triangle with a height of twelve and one-fourth feet and a base of 35 feet?
2.What is the horizontal distance between (16, –24) to (–3, –24)?
3.A dog food storage container is in the shape of a rectangular prism. If the dimensions of the container are 38 inches by 26 inches by 20 inches, what is the maximum amount of food that the container can hold?
4.Which of the following is the fourth vertex needed to create a rectangle with vertices located at (5, 6), (9, 6), and (5, 3)?
(5, –6)
(5, –3)
(9, –6)
(9, 3)
5. A family is building a sandbox for their yard that is shaped like a rectangular prism. They would like for the box to have a volume of 32,188.04 in3. If they already have the length measured at 59.3 inches and the width at 59 inches, what is the height needed to reach the desired volume?
6.
An office manager needs to cover the front face of a rectangular box with a label for shipping. The vertices of the face are (–6, 5), (6, 5), (–6, –4), and (6, –4). What is the area, in square inches, of the label needed to cover the face of the box?
The height of rectangular prism needed to reach the desired volume is 9 inches.
What is the volume of the rectangular prism?
The volume of a rectangular prism is the product of its three dimensions, that is volume = length × width × height.
V= l.w.h
l Length
w Width
h Height
Given :
volume of rectangular prism (v) 32,188.04 inches
length of rectangular prism(l) 59.3 inches
width of rectangular prism(w) 59 inches
Since , V= l.w.h
32,188.04 = 59.3 * 59 * h
or h = 32188.04/59.3 * 59
or h = 32188.04/3498.2
or h = 9.2
Hence , the height of rectangular prism needed to reach the desired volume is 9 inches.
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Which equation represents a nonlinear
Function
2y = 1/2x + 5
y = 1/2x - 5
3y = 1/2x + 5
4y = (1/2)^x -5
Answer:
4y = (1/2)^x -5
Step-by-step explanation:
The first three equations are lines. All the variables have a power of just one (power of one is a math number that is not written) They are actually all written in slope-intercept form even. Line equations are linear function. Yay the words match!
You get a curve (not linear) when you have exponents, square roots or variables in the denominator of a fraction. Or as here, a variable for an exponent!
Graph the line with y-intercept 6 and slope 1/3
Answer:
y = 1/3x + 6
Step-by-step explanation:
based on the graph how many tiles are im figure 0
For figure {0}, the number of tiles will be equal to 2.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph as shown in the image.
The line passes through point -
(3, 8) and (4, 10)
So, the slope of the line will be -
m = (10 - 8)/(4 - 3)
m = 2
y = 2x + c
For the point (3, 8), we can write -
8 = 6 + c
c = 2
For figure {0}, the number of tiles will be equal to 2.
Therefore, for figure {0}, the number of tiles will be equal to 2.
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(100 POINTS!)
Create a proportion using the form %/100= is/of to represent the following word problem:
15 is 1 1/2 % of what number?
Answer:
To create a proportion using the form %/100 = is/of, we can first write the given information in the form %/100 = is/of. In this case, we know that 1 1/2% represents 15, so we can write:
1 1/2%/100 = 15/of
Next, we need to solve for the "of" value, which is the number we are trying to find. To do this, we can multiply both sides of the equation by 100 and then divide both sides by 1 1/2% to get:
(1 1/2%/100) * 100 = (15/of) * 100
of = (15/1 1/2%) * 100
Finally, we can evaluate the right-hand side of the equation to find the value of "of". Since 1 1/2% is the same as 1.5%, we can substitute 1.5 for 1 1/2% in the equation to get:
of = (15/1.5%) * 100
of = (15/0.015) * 100
of = 1000
Therefore, the number we are trying to find is 1000.
In summary, the proportion that represents the given word problem is:
1 1/2%/100 = 15/1000
Answer:
[tex]\textsf{Proportion}: \quad \sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]
[tex]\textsf{Solution}: \quad \sf x=1000[/tex]
Step-by-step explanation:
Given proportion formula:
[tex]\sf \dfrac{\%}{100}=\dfrac{is}{of}[/tex]
Given word problem:
15 is 1¹/₂% of what number.Let the unknown number be x.
Therefore:
% = 1.5is = 15of = xSubstitute these into the proportion formula to create a proportion to represent the given word problem:
[tex]\sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]
To solve the proportion, cross multiply:
[tex]\implies \sf 1.5x=15 \cdot 100[/tex]
[tex]\implies \sf 1.5x=1500[/tex]
Divide both sides by 1.5:
[tex]\implies \sf \dfrac{1.5x}{1.5}=\dfrac{1500}{1.5}[/tex]
[tex]\implies \sf x=1000[/tex]
give a big-o estimate for each of these functions. for the function g in your estimate f (x) is o(g(x)), use a simple function g of smallest order. of(x)
The big-o estimate for each of these functions are:
nlog(n^2 + 1) = o (n^2 logn)
What is the big O notation?It is a commonly used notation in algorithms and data structures domain to get an approximate upper bound of the time the algorithm in question will take to run.
For example, if you want to find the maximum element in a list of n elements, the worst case scenario is that the maximum is the last number. Then we write O(n) .
How do you calculate big O notation for a function?If the function is not too unweildy, it's pretty easy to do.
Consider the function f(x) = 4x^3 + (7x^2)(log(x)) + 3x +8
Look for the highest order term - the term that grows faster than the other terms, as x gets larger. For this function, that term is 4x^3.
Now just get rid of the constant out front to get x^3.
Then put a Big O in front: O( x^3 ).
So we say that f(x) is O( x^3 ).
Since,
nlog(n^2 + 1 ) + n^2 logn is approximately equals to n^2logn
which implies,
nlog(n^2 + 1) + (n^2 logn) = O (n^2 logn)
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A circle with center w is shown in the figure below .
Step-by-step explanation:
(a). Radius = WX, WY or WT as they are all points going from the centre of the circle.
(b). Diameter = TX or XT as it goes through the circle points.
(c). Chord = UV or TX as it is two points that originate from the centre of the circle.
(d). The diameter is two times the radius, as the radius (WY = 3) we can find out that the diameter is 3 * 2 so 6.
Work out angle bcc give a reason for each angle you work out
Answer:
70 degrees
Step-by-step explanation:
Triangle XBC is an isosceles triangle.
From the question given, you already know that angle XBC = 55 degrees. This means that angle XCB = 55 degrees. This is because the two sides XB and XC are of equal length, which means that the angles are also equal to each other.
Using this info, we can calculate angle BXC:
The sum of a triangle adds up to 180, so call the unknown angle x:
55 + 55 + x = 180
110 + x = 180
x = 180 - 110 = 70 degrees
A four year lease agreement requires payments of 10000php at the begginning of every year if the interest is 6% compounded monythly what is cash value of the lease
Answer:
36647.36
Step-by-step explanation:
Lease payment =$1000
interest rate= 6%, compounded monthly
Time = 4 years
We have to calculate the present value
PV = 10000 + 10000/(1+ 0.06/12)^12 + 10000/(1+0.06/12)^24+ 10000(1+0.06/12)^36 = 36647.36
If you can, please give me a Brainliest. Thank you, and have a good day!
help me out in this que ....Thank you
see the attached solution
Answer:
[tex]\dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{2}{x+1}-\dfrac{2x}{x-1}+\dfrac{4}{x^2+1}[/tex]
The least common multiplier of the denominators is:
[tex](x+1)(x-1)(x^2+1)[/tex]
Adjust the fractions based on the least common multiplier:
[tex]\implies \dfrac{2(x-1)(x^2+1)}{(x+1)(x-1)(x^2+1)}-\dfrac{2x(x+1)(x^2+1)}{(x+1)(x-1)(x^2+1)}+\dfrac{4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]
[tex]\textsf{Apply the fraction rule}: \quad \dfrac{a}{c} \pm \dfrac{b}{c}=\dfrac{a \pm b}{c}:[/tex]
[tex]\implies \dfrac{2(x-1)(x^2+1)-2x(x+1)(x^2+1)+4(x+1)(x-1)}{(x+1)(x-1)(x^2+1)}[/tex]
Simplify:
[tex]\implies \dfrac{2(x^3-x^2+x-1)-2x(x^3+x^2+x+1)+4(x^2-1)}{(x+1)(x-1)(x^2+1)}[/tex]
[tex]\implies \dfrac{2x^3-2x^2+2x-2-2x^4-2x^3-2x^2-2x+4x^2-4}{(x+1)(x-1)(x^2+1)}[/tex]
[tex]\implies \dfrac{-2x^4+2x^3-2x^3-2x^2-2x^2+4x^2+2x-2x-2-4}{(x+1)(x-1)(x^2+1)}[/tex]
[tex]\implies \dfrac{-2x^4-6}{(x+1)(x-1)(x^2+1)}[/tex]
What are x and y if angle A is (2x), angle B is (y+x), and angle C is (y-x)?
Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).
Define angle.The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation. A geometrical shape called an angle is created by connecting two rays at their termini. In most cases, an angle is expressed in degrees. In geometry, there are several different kinds of angles. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.
Given
Angle A = 2x
Angle B = y + x
60 = y + x
y = 60 - x
Angle C = y - x
60 = y - x
60 + x = y
As we know, sum of triangle is 180
2x + 60 - x + 60 + x = 180
2x - x + x = 180 - 120
2x = 60
x - 30
For value of y, equating value of x in y = 60 - x
y = 60 - 30
y = 30
Value of x is 30 and y is 30, if angle A is (2x), angle B is (y+x), and angle C is (y-x).
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(a)write the integral formula for the remainder of the taylor expansion of order n of a cn 1(r) function f around x
When the sequence limn→∞ (1 n! ∫x t = a f(n+1)(t)(x−t)n d t) converges to zero, as seen on the left side equation the Taylor series will accurately converge to f(x). For the Taylor series of f, this side is known as the integral form of the remainder (x).
What is Taylor's formula with remainder?Rn(x) = f(n+1)(c) (n + 1); thus, (x a)n + Rn(x)! when there is a c between a and x, (x a)n+1. The Taylor formula is the name given to the second equation. The residual of order n or error term for the Pn(x) over I approximation of f is known as the function Rn(x) (x). To integrate a Taylor Series function, expand the Taylor Series as usual before integrating each term. There is a general expression for the new series. Prior to determining the generic phrase, it is essential to avoid simplification.
Assume that f(x) is a real or composite function and that f(x) is a differentiable function of a real or composite neighborhood number. The following power series is then described by the Taylor series: F (x) = F a F ′ a 1! (x−a)+f”(a)2!
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The question is in the picture
Answer: (3,-6) x=3 y=-6
Step-by-step explanation:
Bookwork code: A99
The table shows the hair colours of the
students in a sports team.
Hair colour
Black
Blonde
Brown
Frequency
1
< Back
a) What fraction of the students have brown
hair? Give your answer in its simplest form.
b) How many sections on this pie chart
would you shade to show the students with
brown hair?
4
2
Scroll down
Watch video
Answer >
A fraction of the students who have brown hair is equal to 1/7.
You should shade only one (1) section on the pie chart to show the number of students with brown hair.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;
Number of brown hair = 1 brown hair.
Number of blonde hair = 4 blonde hair.
Number of black hair = 2 black hair.
Therefore, the total number of hairs is equal to 7 hairs.
For the fraction of students with brown hair, we have;
Fraction = 1/7.
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Which function has a y-value of 6, if the x-value is 3?
Oy= 3 x
Oy=x-3
Oy=x+2
O y = 2 x
Option (d) i.e y = 2x is correct option as this function is satisfying given values of y and x.
What is a function in mathematics?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially offered the standard concept of function in 1837.
y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).
We need to check by substituting value of y in every equation to check correct option.
(a) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = 3x= 3×3=9
L.H.S≠R.H.S
So, it is not a correct option.
(b) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = x-3= 3-3=0
L.H.S≠R.H.S
So, it is not a correct option.
(c) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = x+2= 3+3=5
L.H.S≠R.H.S
So, it is not a correct option.
(d) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = 2x= 2×3=6
L.H.S=R.H.S
So, it is correct option.
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Levi takes a textbook to a pawnshop to borrow some money and is given $45.00. Levi must pay back the $45.00 in addition to a $15.25 fee in 5 months.
What simple interest rate is he being charged?
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Levi is being charged a simple interest rate of _______.
The simple interest rate that Levi is being charged, given that he will have to pay back $ 45 and $ 15. 25 in 5 months, is 81.3 %
How to find the simple interest rate ?The simple interest rate can first be found by finding the monthly amount that Levi has to pay in fees which is :
= 15. 25 / 5 months
= $ 3. 05 fee per month
The amount that the fee would have been in a year is :
= 3. 05 x 12
= $ 36. 60
The simple interest rate is therefore :
= 36. 60 / 45
= 81.3 %
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Give one pair of vertical angles and one pair of supplementary angles
One pair of vertical angles are 2 and 3.
One pair of supplementary angles are 1 and 3.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
Vertical angles are:
1 and 4
2 and 3
6 and 7
5 and 8
Supplementary angles are:
1 and 3.
2 and 4.
6 and 8.
5 and 7.
Thus,
Vertical angles are 2 and 3.
Supplementary angles are 1 and 3.
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PLEASE HELP ME SOMEONE!!!
A bank teller hourly wage will increase from $18 to $21.60. What percent increase does this represent?
The percentage increase is about 16.66%.
What is a percentage increase?
The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.
The initial amount was $18 and the final amount is $21.60.
By using the percentage increase formula, we can write
Percentage increase = (final value - initial value)/|Final value| * 100
= ((21.60 - 18)/21.60)*100
= 16.66%
Hence, the percentage increase is about 16.66%.
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Read the sentences. Choose the one that is informational.
The pancake rolled across the floor, thinking, “I must get out of here, or there’s a great chance I’m to be eaten!”
The world’s largest pancake griddle is located in Penn Yan, NY, and measures 27 feet from end to end.
Tamika’s favorite time of the week was Sunday morning, when she and her dad would make their weekly stop at the diner for Poppi’s famous pancakes.
Syrup drizzled onto the plate as I poured it on the fresh stack of pancakes.
How to find the value of a + b + c.
I know the answer but I do not know how to arrive at the answer:
[tex]answer = 9[/tex]
The attached picture is of a similar problem. But different radii.
Notice how you can form 2 equilateral triangles, and that there are 4 semi circles (at AC, AD, BC, BD).
This is because points C and D lie on the circumference of the circles. So distance from centres( A and b) to C and D are the radius
To get the area of your shaded section, you would just need to add up the areas of the 4 semi circles and 2 equi. triangles.
To get the area of a semi circle, work out the area of one of the sectors, i.e sector ABC, then subtract area of an equilateral triangle.
(Note, due to symmetry all semi circles have same area)
________________________________________________________
For example, for the picture below:
Area of equi triangle = absinC = 1*1*sin60 = √(3) --> (C is angle)
Area of sector = (angle/360) * πr² = (60/360) * π * (1)² = π/6
So area of 1 semi circle = Area of Sector - Area of equi triangle
= π/6 - √(3)
Now you would just add the areas of 4 semi circles, and 2 equi triangles, and compare coefficients to get a, b, c.
______________________________________
Now you would do the same for your question, except radius is now 6cm instead of 1cm.
Enola wants to invest $8,600.00 in a savings account that pays 5.1% simple interest.
How many years will it take for this investment to triple in value?
Round your answer to the nearest tenth of a year.
It will take ________ years for this investment to triple in value.
Step-by-step explanation:
To find the number of years it will take for Enola's investment to triple in value, we can use the formula for simple interest:
I = P * r * t
where I is the total interest earned, P is the principal (the initial amount invested), r is the interest rate, and t is the number of years.
Since the investment will triple in value, the total interest earned will be equal to two times the initial investment, or 2 * $8,600.00 = $17,200.00. Substituting these values into the formula and solving for t, we get:
$17,200.00 = $8,600.00 * 5.1% * t
t = $17,200.00 / ($8,600.00 * 5.1%) = 3.28 years
Rounding this value to the nearest tenth of a year, we get t = 3.3 years. Therefore, it will take approximately 3.3 years for Enola's investment to triple in value.
HELP ASAPPPPPP WILL MARK BRAINLIEST!!!!!
Answer:
ive did the math and its r= 4
Step-by-step explanation:
A 4-cylinder engine with 543 Cubic Centimeters volume per cylinder has what approximate displacement?
Answer:
you would times them both so 4x543 =2172
Step-by-step explanation:
543 cubic centimeters has 0.543 L approximate displacement.
What is Engine displacement?Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.
Basic formula to calculate engine displacement is =
V = π/4 x D² x H x N
Where :
D = Bore Diameter
H = Length of Stroke
N = Number of Cylinder
Since the question has already stated cubic centimeter, it has already shown the displacement. So, we can ignore above formula and the 4-cylinder engine information.
First, we state what is known. It is the displacement at cubic centimeter.
Cubic centimeter = 543 cc
Next, we change the unit of cubic centimeter (cc) into liter (L)
Displacement = cc / 1000 L
= 543 / 1000 L = 0.543 L
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Anyone explain please
The relation between variables is represented by an equation ; y = 2.5x+15
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Alexa joined a program at some coffee shop which offers her $15 per month, after which she will get her coffee at a discount rate which $2.5
We can represent the relationship as ;
y = 2.5x+15
Where, x (number of coffee) is an independent variable because it does not depend on any condition, and y (cost) is a dependent variable because it depends on the value of x.
Hence, the relation is described as y = 2.5x+15
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Help!!!!!! See image.
The shape of the graph of a function is the shape assumed by the graph of the function after the dataset generated by using the function is plotted on the coordinate plane. The shape in the graph of the question is a triangular shape.
What is a function?A function is a direction used to map the values of an input variable of the function to the output variables.
The points in the attaches graph which are connected by lines are;
(0, 1.5), and (4.5, 0)
The joining of the above points in the attached graph, and the origin forms a triangular shape.
Details about the shape of the graph of a function
The graph of a function such as f(x) = -x² + 2·x + 3, is obtained by finding the values of the output values of the function, f(x) for each input value of the function, x as follows;
x [tex]{}[/tex] f(x)
0 [tex]{}[/tex] 3
1 [tex]{}[/tex] 4
2 [tex]{}[/tex] 3
3 [tex]{}[/tex] 0
4 [tex]{}[/tex] -5
5 [tex]{}[/tex] -12
6 [tex]{}[/tex] -21
7 [tex]{}[/tex] -32
8 [tex]{}[/tex] -45
Please find attached the graph of the sample function created with MS Excel
The graph of the function f(x) = -x² + 2·x + 3 has the shape of a parabola, which is the shape of a quadratic function.
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I kinda get it and i kinda do pleas help
Answer:
Step-by-step explanation:
first things first go back in the lesson or your notes if you wrote down some and if not go right some down and in the notes there would be the answer between pages 1-5 or maybe 6 IDR ( i dont remember ) but look thru those pages and you will find the answer hope this helped. please mark me brainiest please.
Six stand up comics A,B,C ,D ,E and F are to perform on a single evening at a comedy club. The order of phrases of performance is determined by random selection.
a. Comic D wall perform fourth.
b. Comic F will perform first and Comic C will perform fourth.
e. The connections will perform in the following order, D, F, C, E, A, B.
d. Comic A or Comic B will perform third.
a.
b.
c.
d.
A) The Probability that comic D will perform fourth is; 1/6
B) The Probability that Comic F will perform first and Comic C will perform fourth is; 1/30
C) Probability that the comedians will perform in the following order, D, F, C, E, A, B is; 1/720
D) Probability that Comic A or Comic B will perform third is; 1/15
How to solve permutation and combination?A) Probability that comic D will perform fourth;
Number of ways that this will succeed = 1 * 5!
Number of possible outcomes normally = 6!
Thus;
P(D is 4th) = 5!/6! = 1/6
B) Probability that Comic F will perform first and Comic C will perform fourth.
Number of ways that this will succeed = 1 * 1 * 4!
Number of possible outcomes normally = 6!
Thus;
P(F is 1st and C is 4th) = 4!/6! = 1/30
C) Probability that the comedians will perform in the following order, D, F, C, E, A, B;
There is only 1 way and as such the probability = 1/6! = 1/720
D) Probability that Comic A or Comic B will perform third;
(2!*4!)/6! = 1/15
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Consider this diagram.
(6x+30)
(8x+10)
Given: m/CEA (8+10): m/AED
Prove: - 10
Statement
Part A
Mr. Avila asked his students to write either a two-column proof or a paragraph proof for the question shown.
Student A and Student B each made a mistake in their proof. Identify each student's mistake and the step in which they
made it.
Type your response in the box.
mZCRA
mZAED
838°
ZCEA and ZAED are a near
pair.
m/CEA + m/AED
8z + 10 + 6x + 30
14x + 40 180
14 140
-10
Student A's Proof
and
=
180°
L 180
(6m+30)
Reason
given
definition of linear pair
Linear pairs are
supplementary.
substitution
Like terms can be combined.
addition property of equality
division property of equality
Student B's Proof
We are given that mZCEA (8 + 10) and
m/AED = (6x +30) By the definition of vertical
angles, we know that ZCEA and ZAEDare vertical
angles. Vertical angles have equal measures, so
m/CEA m/AED substituting
m/CEA -
3x + 10and m/AED - 6x + 30 into
m/CEA
ZAED, we get
8+10= 6z+ 30. Using the subtraction property
of equality on the variable terms, this becomes
2z+10 30. Using the subtraction property of
equality on the constants, we get 2z - 20 By the
division property of equality, we prove that m 10
-
-
The angles m∠CEA and m∠AED are supplementary .hence the value of x will be 10 has been proved.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays known as the vertex—is referenced as an angle's sides.
We are Given that m∠CEA and m∠AED are only two angles on a straight line thus they will be supplementary.
Therefore, we have
m∠CEA + m∠AED = 180°
8x + 10 + 6x + 30 = 180
14x + 40 = 180
14x = 140
x = 10
Hence "The value of x will be 10 that proved the angles m∠CEA and m∠AEDare complementary".
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