I need help with these 2 questions.
A) Write and solve a proportion to determine the height of the cell phone tower. Please show your work.
B) What is the height of the tower in meters?
Answers
Part (A)
Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.
P/Q = R/S
where,
P = height of the personQ = horizontal distance person is from the left-most cornerR = height of the towerS = horizontal distance the tower is from the left-most cornerIn this case,
P = 1.8 metersQ = 6 metersR = unknown, we'll use variable hS = 60 metersTherefore, we go from this
P/Q = R/S
to this
(1.8)/6 = h/60
Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.
--------------
Answer: (1.8)/6 = h/60====================================================
Part (B)
Let's cross multiply and solve for h.
(1.8)/6 = h/60
1.8*60 = 6h
108 = 6h
6h = 108
h = 108/6
h = 18
--------------
Answer: 18 metersAnswer:
A). [tex]\frac{1.8}{6} = \frac{height}{60}[/tex]
B). 18 meters tall
Step-by-step explanation:
We see TWO right triangles in this problem:
the one with the man and the 6m and the one with the phone tower and the 60mThese triangles are proportional so we can make a ratio out of them
the height of the man over the side of the triangle (6m)
and the height of the tower over the length of its triangle (60m)
Set these equal to each other to complete part A
[tex]\frac{1.8}{6} = \frac{height}{60}[/tex]
And by using cross multiplication (which is what you do for ratios), solve for h!
For a quick example of cross multiplication, I've attached a picture.
Now let's do it!
1.8 × 60 = 6 × h
108 = 6h
108/6 = h
h = 18
The height of the cell phone tower is 18 meters.
Related Questions
Solve for x in the equation x2-14x+31-63-
Ox=-16 or x = 2
O x=-7±3-√√7
Ox=-2 or x = 16
Ox=7±3√√√7
Answers
Answer:Value of x are 16 and -2
Step-by-step explanation:
Solve for x in the equation:
Subtract 63 from both sides we have;
To factor this equation as:
⇒
Take (x-16) common we have;
⇒
By zero product property we have;
x-16 = 0 or x+2 = 0
⇒x = 16 or x = -2
Therefore, the value of x are: 16 and -2
The value of x in the equation are x = -2 or x = 16.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given is a quadratic equation,
x² - 14x + 31 = 63
We have to find the value of x.
x² - 14x + 31 - 63 = 0
x² - 14x - 32 = 0
Using the quadratic formula,
x = [14 ± [tex]\sqrt{(-14)^2-(4*1*-32)}[/tex]] / 2
= (14 ± √324) / 2
= (14 ± 18) / 2
x = 14 + 18 / 2 or x = 14 - 18 / 2
x = 16 or x = -2
Hence the value of x are x = 16 or x = -2.
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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
Answers
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!
(a)write the integral formula for the remainder of the taylor expansion of order n of a cn 1(r) function f around x
Answers
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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What are x and y if angle A is (2x), angle B is (y+x), and angle C is (y-x)?
Answers
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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Work out angle bcc give a reason for each angle you work out
Answers
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
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 _______.
Answers
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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calculate the volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution . express your answer using three significant figures.
Answers
The volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution is 1.176 ml.
Volume is a degree of the quantity of area that be counted occupies. Matter is described as a bodily substance that occupies area and has a mass. In bodily sciences like chemistry, the usual unit of extent is cubic metres (m3). From this, different gadgets are derived inclusive of litre (L) and millilitre (mL).
A correct region to begin is the balanced chemical equation for this neutralization: 2 H Br + Ba (OH)2 → Ba Br2 + 2 H2O The crucial aspect right here is that it takes moles of H Br to neutralize one mole of Ba(OH)2 . The variety of moles of Ba(OH)2 is 0.28x 0.210 =0.0588 moles. Thus 2 x .0.0588 = 1.176 moles of H Br are wished. The extent, V, of H Br answer wished may be computed from V) = 1.176 L.
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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?
Answers
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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The question is in the picture
Answers
Answer: (3,-6) x=3 y=-6
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $6,000.00 in the account in 389
days?
Assume the account earns 2-% simple interest.
You would need to deposit_____ in your account now.
Answers
Answer:
$5,851.88
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given values:
A = $6000r = 2³/₈% = 0.02375t = 389 days = ³⁸⁹/₃₆₅ yearsSubstitute the given values into the formula and solve for P:
[tex]\implies 6000=P\left(1+0.02375 \times \dfrac{389}{365}\right)[/tex]
[tex]\implies P=\dfrac{6000}{1+0.02375 \times \dfrac{389}{365}}[/tex]
[tex]\implies P=\dfrac{6000}{1+0.0253116438...}[/tex]
[tex]\implies P=\dfrac{6000}{1.0253116438...}[/tex]
[tex]\implies P=5851.87931....[/tex]
Therefore, you would need to deposit $5,851.88 in your account now.
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)
Answers
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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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.
Answers
During the year, Salaries Payable decreased by $12,000. Using the direct method of reporting cash flows from operating activities, if Salaries Expense amounted to $450,000 for the year, the cash paid to employees (including deductions from gross pay) is
Answers
If during the year, Salaries Payable decreased by $12,000. Using the direct method of reporting cash flows from operating activities, if Salaries Expense amounted to $450,000 for the year, the cash paid to employees is $462,000.
What is cash paid?Cash paid can be defined can be defined as the amount that is payable to an employee by an employer.
Using this formula to find the cash paid to employees
Cash paid to employees = Salaries payable decreased + Salaries Expense
Where:
Salaries payable decreased = $12,000
Salaries expense = $450,000
Let plug in the formula
Cash paid to employees = $450,000 + $12,000
Cash paid to employees = $462,000
Therefore the Cash paid to employees is the amount of $462,000.
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G(X)=-3x+2 find g(2)
Answers
Answer:
-4
Step-by-step explanation:
[tex]-3*2 + 2=-4[/tex]
In ΔQRS, m∠Q = 11° and m∠R = 40°. Which list has the sides of ΔQRS in order from shortest to longest?
PLEASE HELP!!
Answers
Answer:
RS, SQ, QR
Step-by-step explanation:
The three angles in a triangle add up to 180° Two angles are given, so we can find the third angle.
11 + 40 + S = 180
51 + S = 180
subtract 51
S = 129°
S is the biggest angle, so the biggest side will be opposite from S. QR is the biggest side.
AngleQ is 11°, the smallest angle. The smallest side will be opposite from the smallest angle. The smallest side is RS.
The 40° angle, AngleR is in the middle. The medium length side is opposite from the medium size angle. SQ is the medium length side.
From small to big:
RS, SQ, QR
Answer:
The 4th answer down
RS, SQ, RQ
Step-by-step explanation:
There is a relationship between the angle measurement and the length of the side opposite of the angle. The side opposite of the largest angle measurement has the longest side opposite to that angle, the same is true for the middle angle and the smallest angle.
Which equation represents a nonlinear
Function
2y = 1/2x + 5
y = 1/2x - 5
3y = 1/2x + 5
4y = (1/2)^x -5
Answers
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!
HELP ASAPPPPPP WILL MARK BRAINLIEST!!!!!
Answers
Answer:
ive did the math and its r= 4
Step-by-step explanation:
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.
Answers
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.
solve each of the following quadratic inequalities using any Convenient
method :
A)
[tex]x(10x + 19) \leqslant 15[/tex]
[tex](x + 2)^{2} > (3x + 1)^{2} [/tex]
Answers
Answer:
-2.5 ≤ x ≤ 0.6-0.75 < x < 0.5Step-by-step explanation:
You want the solutions to the following inequalities by any convenient method:
x(10x +19) ≤ 15(x +2)² > (3x +1)²ComparisonWe choose to rewrite these inequalities to be comparisons to zero. This is because our graphing calculator easily identifies the x-intercepts of a graph. We can look a the graph to tell where the function is above or below the x-axis.
f(x) = x(10x +19) -15; f(x) ≤ 0g(x) = (x +2)² -(3x +1)²; g(x) > 0GraphThe attached graph shows the solutions to be ...
f(x) ≤ 0 for -2.5 ≤ x ≤ 0.6g(x) > 0 for -0.75 < x < 0.5The values obtained for the first equation will be x ≤ 3/5 and x ≤ -5/2 and the values obtained for the second equation will be x < 1/2 and x < -3/4.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given inequalities in the question,
1.
x(10x + 19) ≤ 15
Firstly, simplify it to the simpler form,
10x² + 19x - 15 ≤ 0
Solve the quadratic equation,
D = b² - 4ac
= 19² - 4(10)(-15).
D = 961
Now, use the formula,
(-b±√D)/2a
√D = √961 = 31
(-19 ± 31)/2(10)
So, the roots are:
1.
(-19 + 31)/20 = 12/20 = 3/5
Or, x ≤ 3/5
2.
(-19 - 31)/20 = -50/20 = -5/2
Or, x ≤ -5/2
2.
(x + 2)² > (3x + 1)²
Simplify the equation first.
x² + 4x + 4 > 9x² + 6x + 1
x² - 9x² + 4x - 6x + 4 - 1 > 0
-8x² - 2x + 3 >
8x² + 2x - 3 < 0
Now, find the roots for the equation,
D = b² - 4ac
D = 4 + 96
D = 100
Now, use the formula,
(-b ± √D)/2a
(-2 ± 10)/16
So, the roots are:
1. (-2 + 10)/16 = 1/2
Or, x < 1/2
2. (-2 - 10)/16 = -12/16 = -3/4
Or, x < -3/4
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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]
Answers
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.
 patrick takes a textbook to a pawnshop to borrow some money and is given $30.00. Patrick must pay back the $30.00 in addition to a $12.50 fee in 6 months.
What simple interest rate is he being charged?
Answers
Answer:
here,
simple interest (S)=12.50$
Principal(p)=30.00$
time(t)=0.5 year
Now,
S=PTR/100
or,12.50=30×0.5×R/100
or,1250=15R
or,1250/15=R
:.R=83.33% per annum
Give one pair of vertical angles and one pair of supplementary angles
Answers
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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A circle with center w is shown in the figure below .
Answers
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.
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.
Answers
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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Time to think about your New Year's Resolution for the new year. Nora decided she needed more
exercise. She decided that starting with the first full week in 2023, she will do a 45-minute workout
four times a week ( four days during every seven-day week.) This means she will exercise four of the
days during the week of Jan, 1 through Jan. 7 and will do the same during the week from Jan. 8
through Jan. 14, etc. If Nora sticks to her resolution, what is the first possible date on which she will
complete 25 hours of exercise for the year?
Answers
The first possible date on which she will complete 25 hours of exercise for the year is on March 1.
How to calculate date?In general, dates can refer to a specific day on the calendar, such as January 1 or December 31. Dates can also refer to a specific point in time, such as a specific hour, minute, or second. In some cases, dates can also refer to a specific period of time, such as a year, month, or week.
Since Nora plans to do a 45-minute workout four times a week,
she will exercise for a total of 4 * 45 minutes = 180 minutes per week.
This means that each week, she will exercise for a total of 180 / 60 = 3 hours.
To complete 25 hours of exercise for the year,
Nora will need to exercise for a total of 25 / 3 = 8.3 weeks.
The first possible date on which she will complete 25 hours of exercise is therefore 8.3 weeks after Jan 1,
Which is approximately 8.3 * 7 = 58 days after Jan 1.
Therefore, the first possible date on which Nora will complete 25 hours of exercise is 58 days after Jan 1, which is on March 1.
Overall, if Nora sticks to her New Year's resolution to exercise four times a week, the first possible date on which she will complete 25 hours of exercise for the year is on March 1.
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Construct a geometric mean between a and c.
Answers
Geometric mean will be a line segment with length x such that x² = a × c.
What is Geometric Mean?Geometric mean of two line segments p and q is a line x such that it satisfies the formula x² = a × b or x/a = b/x.
To construct geometric mean, first simply draw a line segment and mark a point P anywhere on this line.
Mark the length of the line segment 'a' from the point P and mark the endpoint of 'a' as A. Now, in the same line, from the point P, mark the length of the given line 'c' and mark its endpoint as C.
Now, draw a perpendicular bisector of the resulting line PC. Then we get the midpoint of PC. Let this point be O.
Draw a semicircle with center O and the endpoints P and C.
Now draw a vertical perpendicular line from the point A until it cuts the semicircle. Let N be the point where this line touches the semicircle.
Now join P with N.
The line PN will be the geometric mean x such that a × c = x².
Hence the line segment PN is the geometric mean with length x.
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Answers
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
-
-
Answers
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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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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help me out in this que ....Thank you
Answers
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]