The Solution:
Required:
To use the three theorems of similarity:
There are 3 theorems for proving triangle similarity:
AA Theorem
SAS Theorem
SSS Theorem
SAS Theorem
What happens if we only have side measurements, and the angle measures for each triangle are unknown? If we can show that all three sides of one triangle are proportional to the three sides of another triangle, then it follows logically that the angle measurements must also be the same.
SSS Theorem
Or what if we can demonstrate that two pairs of sides of one triangle are proportional to two pairs of sides of another triangle, and their included angles are congruent?
AA Theorem
As we saw with the AA similarity postulate, it’s not necessary for us to check every single angle and side in order to tell if two triangles are similar. Thanks to the triangle sum theorem, all we have to show is that two angles of one triangle are congruent to two angles of another triangle to show similar triangles.
In a triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle. find the measure of all 3 angles. Hint: the angles of a triangle add up to 180.
The three angles of the triangle are 22.5, 67.5 and 90 degrees.
How to find the angles of a triangle?A triangle is a polygon with three sides.
The sum of angles in a triangle is 180 degrees.
Therefore, the angles of the triangle can be found as follows;
In the triangle one angle is three times the smallest angle and the third angle is 45 more than twice the smallest angle.
Therefore,
let the smallest angle = x
Therefore, the three angles are as follows;
x3x45 + 2xTherefore,
x + 3x + 45 + 2x = 180
6x + 45 = 180
6x = 180 - 45
6x = 135
divide both sides by 6
x = 135 / 6
x = 22.5
Therefore, the three angles are as follows;
22.5 degrees22.5 × 3 = 67.5 degrees45 + 22.5(2) = 90 degreeslearn more on triangle here: https://brainly.com/question/15386380
#SPJ1
If 5 books of equal weight, weigh 1.755 kilograms, how many books will weigh 1.404 kilograms?
If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books
The 5 books are equal weights
The weight of 5 books = 1.755 kilograms
Then the weight of one book = The weight of 5 books / 5
Substitute the values in the equation
The weight of one book = 1.755/5
= 0.351 kilograms
To find the number of books we have to use division again
The number of books will weight 1.404 kilograms = 1.404 / The weight of one book
=1.404/0.351
= 4 books
Hence, If 5 books of equal weight, weigh 1.755 kilograms, then the number of books will weight 1.404 kilogram is 4 books
Learn more about division here
brainly.com/question/21416852
#SPJ1
What is the measure of ZABD? What is the reason?60° , isosceles triangle theorem48°, equilateral triangle theoremCO 48°, isosceles triangle theorem60° , equilateral triangle theoremB66°DA
Consider the traingle ABD,
The side AB and A are equal means that angle A is equal to angle D.
Determine the angle B of traingle ABD by using angle sum property of triangle.
[tex]\begin{gathered} \angle A+\angle B+\angle D=180^{\circ} \\ 66^{\circ}+66^{\circ}+\angle B=180^{\circ} \\ \angle D=48^{\circ} \end{gathered}[/tex]So angle D is of 48 degree and two sides are equal so isoceles traingle theorem is used for angle measurement. Option C is correct.
please help!!! only 20 mins left
The rule of (x, y) → (-x, y), which is reflection over y-axis.
Given that, ΔABC maps to triangle ΔA'B'C'.
What is the reflection on y-axis?When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).
Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.
Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.
From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.
Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.
To learn more about the reflection over y-axis visit:
https://brainly.com/question/15175017.
#SPJ1
Borrowed $30000 four year loan at 7% what’s monthly payment? And what’s the intrest I will pay on loan?
given:
There are given that the Borrowed is $30000.
Explanation:
To find the monthly amount, we need to use the formula:
[tex]R=\frac{P}{1-(i+1)^{-n}}[/tex]Where,
[tex]\begin{gathered} P=30000 \\ r=0.07 \\ m=12\text{ Thenn} \end{gathered}[/tex][tex]\begin{gathered} i=\frac{r}{m}=\frac{0.07}{12} \\ =0.0058 \end{gathered}[/tex]Ans,
[tex]\begin{gathered} n=mt=12(4) \\ =48 \end{gathered}[/tex]Then,
From the formula:
[tex]\begin{gathered} R=\frac{Pi}{1-(1+i)^{-n}} \\ R=\frac{30000(0.0058)}{1-(1+0.0058)^{-48}} \\ R=\frac{30,000(0.0058)}{1-(1.0058)^{-48}} \\ R=\frac{30000(0.0058)}{0.24} \\ R=725 \end{gathered}[/tex][tex]\begin{gathered} S.I=\frac{P\times r\times t}{100} \\ =\frac{30000\times7\times4}{100} \\ =4800 \end{gathered}[/tex]Final answer:
Hence, the monthly payment is $725 and the interest will be: $4800
HELP!
Do units affect significant figures? For example, I know that the number 5600 has two significant figures. But if I wrote it as 5600 L, would the unit "L" count as a sig fig? Please help me!!
Round 18,792 to the nearest thousand is the answer 18,790 or 00019 or 00018 or 18800 please due today please give brainiest.
Answer:
The answer is 19,000
Step-by-step explanation:
18,792 you round to the thousand which is 8 and the number after is 7 which is above 5 so the 8 turns into a 9
Answer:
19000
Step-by-step explanation:
18,792
Rounding to the nearest thousand
The 8 is in the thousands place
We look at the number in the hundreds place, 7
It is 5 or higher so we will round the 8 up to 9 and everything else to the right will become zeros
18,792 becomes 19000
If g(x) = 5x, h(x) = √x , find the composition. (g . h)(0)
The composition (g . h)(0) has a value of 0
How to evaluate the composite function?The definitions of the functions are given as
g(x) = 5x and h(x) = √x
To find the composition (g . h)(o), we make use of
(g . f)(x) = g(x) * h(x)
This can also be expressed as
(g . f)(x) = h(x) * g(x)
Substitute g(x) = 5x and h(x) = √x
So, we have
(g . f)(x) = 5x * √x
Substitute 0 for x
So, we have the following equation
(g . f)(0) = 5 x 0 * √0
Evaluate the product
So, we have the following equation
(g . f)(0) = 0
Hence, the value of the composition is 0
Read more about composite functions at
https://brainly.com/question/10687170
#SPJ4
In desperate need of help with my college algebra problem
To find the nth degree of polynomial function f(x) = x^4 - 4x^3 + 27x^2 -46x +60
What is Function?
Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
For polynomial with real coefficients, the complex zeros come with conjugates so 2+4i must come with 2-4i , then for 4th degree polynomial
f(x) =a (x+1)(x-3)(x-2-4i)(x-2+4i). With given f(1)=-68
a(1+1)(1-3)(1-2-4i)(1-2+4i)= -68.
By this we can find a
a (2)(-2)(-1-4i)(-1+4i) = -68
a(-4)(1+4i-4i-16i^2) = -68
a(-4)(1+16) = -68
a(-4)(17) = -68
a(-68) = -68
a = 1
Now, solving
f(x) =(x+1)(x-3)(x-2-4i)(x-2+4i)
f(x) = (x+1)(x-3)(x^2 - 2x + 20)
f(x) = (x^2 - 2x - 3)(x^2 - 2x + 20)
f(x) = x^4 - 2x^3 + 20x^2 - 2x^3 + 4x^2 - 40x + 3x - 6x + 60
f(x) = x^4 - 4x^3 + 27x^2 -46x +60
Hence, the for 4th degree polynomial is f(x) = x^4 - 4x^3 + 27x^2 -46x +60
To learn more about Function click on the link
https://brainly.com/question/10439235
#SPJ9
please quick I need this
Answer:
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
Step-by-step explanation:
Step 1: Do long division
To divide these expressions, we will have to make use of long division, which is shown in the picture.
Step 2: Identifying the remainder and quotient
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
Show all work for full credit.
Sketch the following curves, indicating all relative extreme points and inflection points. (10 pts)
a. y= x^3-6x^2+9x+3
For the given function, it is found that:
The extreme points are given by: (3,3) and (1,7).The inflection point is: (1,7).What are the extreme points of a function?The extreme points of a function happen at the values for x for which the first derivative is zero, that is:
y' = 0.
In this problem, the function is:
y = x³ - 6x² + 9x.
Hence the first derivative is:
3x² - 12x + 9.
The extreme values of x are:
3x² - 12x + 9 = 0.
3(x² - 4x + 3) = 0
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0.
Then:
x - 3 = 0 -> x = 3.x - 1 = 0 -> x = 1.The numeric value of the function at these points is:
x = 3: y = 3³ - 6(3)² + 9(3) + 3 = 3.x = 1: y = 1³ - 6(1)² + 9(1) + 3 = 7.Hence the points are:
(3,3) and (1,7).
What are the inflection points of a function?The extreme points of a function happen at the values for x for which the second derivative is zero, that is:
y'' = 0.
For this problem, the second derivative is given by:
y'' = 6x - 12.
Hence the x-coordinate of the inflection point is:
6x - 12 = 0
6x = 12
x = 2.
The numeric value at x = 2 is:
2³ - 6(2)² + 9(2) + 3 = 5.
Then the inflection point is:
(2,5).
The graph with these points labeled is given at the end of the answer.
More can be learned about extreme and inflection points of a function at https://brainly.com/question/14338487
#SPJ1
The domain of a function f(x) is x< 4, and the range is y≤ 0. What are the
domain and range of its inverse function, f-¹ (x)?
A. Domain: x≤0
Range: y< 4
B. Domain: x<0
Range: y≤ 4
C. Domain: x24
Range: y> 0
D. Domain: x < 4
Range: y≤ 0
Answer:
Step-by-step explanation:
d
1. The number of fans produced by a manufacturer in a week can be no more than five times the number of lamps produced by the same manufacturer during the same week. If the number of fans produced this week by the manufacturer was 20, what is the minimum number of lamps produced by the manufacturer this week?
A) 4
B) 5
C) 15
D) 20
help
fast 20 point
please
Answer:
A. 2
Step-by-step explanation:
Hope this helps
Evaluate : limx→ tan2-sin2x x3
Given:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Solve:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Use l'hopital's rule:
[tex]\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}[/tex]Simplify:
[tex]\begin{gathered} =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \\ =\lim _{x\to0}\frac{2(-\cos (2x)+\tan ^2(2x)+1)}{3x^2} \end{gathered}[/tex]Apply the constant multiple rule:
[tex]\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}[/tex][tex]\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}[/tex]Similary :
[tex]\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}[/tex]Choose the figure that accurately represents the following relation on the Cartesian coordinate plane? {(-2,-2),(2,-3),(4,-1),(5,-6),(6,-8),(6,9)}
Recall that, in a point (a,b), the first entry represents the x-entry, and the second entry represents the y-entry, and its graph is as follows:
Therefore, the graph of the given relation is:
Answer:
The office floor is 250 ft. X 80 ft. The conference room floor is 50 ft. X 20 ft. , which covers __?__ of the office
The percentage of area covered by the conference room is 5%.
What is area?
A region's size on a flat or curved surface is expressed in terms of area, a unit of measurement. A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.
The quantity of unit squares necessary to completely encompass a form is its area. In order to express and measure it, square units are used.
Given, the dimension of office as
Length= 250 ft and breadth is 80 ft
Area of office = length ×breadth = 250 ×80 = 20,000
Length of conference room = 50 ft
Breadth of conference room = 20 ft
Area = 50 (20) = 1000
Percentage of office covered by conference room is given as:
1000/20000×100=5
Hence, 5% is occupied
To know more about area, visit:
https://brainly.com/question/27743815
#SPJ9
Selwyn wanted to place point V on the same number line to represent the opposite number of point W . Which instruction should he follow to place point V
Move ten units to the left of point W.
1) Counting the marks on the number line, we can tell that Selwyn placed point V 5 units to the right of zero.
2) Since we need to find the opposite number, we need to find the negative 5 ( -5). Hence, we need to:
Move ten units to the left of point W.
Because we need to remember that the reference is not zero but W.
If a 1/3 cup serving of cheese provides your fully daily value of calcium, then what percentage of your daily value of calcium is provided by 3/4 cup of the cheese?
If a 1/3 cup serving of cheese provides your full daily value of calcium, then 225% of your daily value of calcium is provided by ¾ cup of the cheese.
What are the ratios rules?Between amounts of the same sort, the ratio should exist. The units used to compare two items should be comparable.
Terms should be in a meaningful sequence. If two ratios are comparable to one another like fractions, they may be compared.
An easy ratio Is what?When both sides are whole numbers and cannot be split by another
whole number, a ratio is considered to be in its simplest form.
Think about full number ratios, such as 6:4. The fraction 64 can be used to represent it.
What proportion of your daily intake of calcium is delivered by 3/4 cup of the food if a serving of cheese that is 1/3 cup in size delivers your whole daily value of calcium?Daily value of calcium= (3/4)/(1/3) = 9/4
3/4 cup gives you 9/4 of your daily value of calcium.
We can convert fractions to percentages, we will get
9/4= 2.25
2.25*100=225%
Then the percentage of your daily value of calcium is 225%.
Learn more about the Ratio here:
https://brainly.com/question/2914376
#SPJ9.
An attic floor is shaped like a triangle with a height of n yd and a base of 6 yd.Which expression represents the area of the floor? 6n3nn + 63n2
In order to calculate the area, we can use the formula for the triangle area:
[tex]A=\frac{b\cdot h}{2}[/tex]Where b is the base length and h is the height relative to this base.
So, for b = 6 and h = n, we have:
[tex]\begin{gathered} A=\frac{6\cdot n}{2} \\ A=3n \end{gathered}[/tex]Therefore the correct option is the second one.
Please help me brainly!!!<3
The probability that an adult is actively looking for a job is 0.18. The probability of an adult being unemployed and actively looking for a job is 0.04. What is the probability of an adult being unemployed given that they are actively looking for a job?
The probability of an adult being unemployed given that they are actively looking for a job is 0.22.
How to calculate the probability?It should be noted that probability gas to do with the likelihood that something will occur.
Remember the multiplication rule for conditional probability:
P(B AND A)=P(B|A)P(A)
Rearranging, we see thatP(B|A)=P(B AND A)P(A)
So if we think of A as being the event that an adult is actively looking for a job and B as the event that an adult is unemployed, then we can plug in the known information to find
P(B|A)=0.04 + 0.18
≈0.22
Learn more about probability on
https://brainly.com/question/25870256
#SPJ1
Mr. Connor's physics class has 105 students, classified by academic year and gender, as illustrated in the table. Mr. Connor randomly chooses one student to collect yesterday's work
Academic Year male female
Junior 8 11
senior 19 19
freshman 9 12
sophomore 19 8
The probability that he selects a Mel given that he chooses randomly from only the Juniors is 0.076.
How to calculate the probability?It should be noted that the probability is the likelihood that something will happen. The table shows that Connor's physics class has 105 students, classified by academic year and gender.
The probability will be:
Fraction of males that are junior / Fraction if Junior
= 8/105 / 19/105
= 0.076
The probability is 0.076.
The complete question is written below.
Learn more about probability on:
brainly.com/question/25870256
#SPJ1
What is the probability that he selects a Mel given that he chooses randomly from only the Juniors.
Gourmet in Italy has a policy of automatically adding an 18% tip to a restaurant bill. How much would a restaurant bill be if it had a tip of $3.20 added to it?
The restaurant charger a tip of the 18% of the bill
So the total amount charged is the money spent + 18%
The bill had a tip of $3.20 this is the 18% of the amount spent.
Using cross multiplication you can calculate the amount of the bill as:
Bill without tip: 100%
Tip: 18%
Total amount (bill + tip): 118%
If 18% ____ $3.20
Then 118%___$x
[tex]undefined[/tex]
How could you correctly rewrite the equation 6(11-3) = 4(7 + 5) using the distributive property?
66-3 = 28 +35
Answer:
The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c );
Step-by-step explanation:
6(11-3) = 4(7 + 5)
(6×11)-(6×3)=(4×7)+(4×5)
66 - 18 = 28 + 20
PLEASEE I NEED HELP!!
Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. Which statement describes a possible sequence of transformations that transforms figure 1 into figure 3?
A. a rotation 180 degrees clockwise about the origin, followed by translation 2 units to the left.
B. a rotation 90 degrees clockwise about the origin, followed by a reflection across the x-axis.
C. a rotation 180 degrees clockwise about the origin, followed by a reflection across the y-axis.
D. a rotation 90 degrees clockwise about the origin, followed by a translation 3 units to the right.
the correct answer is A. Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To transform figure 1 into figure 3, we need to apply two transformations. We can eliminate option B because a rotation of 90 degrees followed by a reflection across the x-axis would transform figure 1 into a mirror image of figure 2, not figure 3.
Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left. This would transform figure 1 into figure 3, so option A is a possible sequence of transformations.
Option C describes a rotation of 180 degrees clockwise followed by a reflection across the y-axis. This would transform figure 1 into a mirror image of figure 2, not figure 3.
Option D describes a rotation of 90 degrees clockwise followed by a translation of 3 units to the right. This would transform figure 1 into a position that is similar to figure 3, but the orientation of the triangle would be different.
Therefore, the correct answer is A.
To learn more about triangle from the given link:
https://brainly.com/question/2773823
#SPJ1
f(x)=x^2+6x+7
f(x+h)=?
f(x+h)-f(x)=?
f(x+h)-f(x)/h=?
The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The value of the function is;
f (x) = x² + 6x + 7
Now, Find the given values of f (x + h) , f (x + h) - f (x) and f (x + h) - f (x) / h by substitution method.
The value of the function is;
f (x) = x² + 6x + 7
Substitute x = x + h;
The value of the function is;
f (x + h) = (x + h)² + 6(x + h) + 7
= x² + 2xh + h² + 6x + 6h + 7
Thus, The value of f (x + h) = x² + 2xh + h² + 6x + 6h + 7.
Now,
f (x + h) - f (x) = (x² + 2xh + h² + 6x + 6h + 7) - (x² + 6x + 7)
= x² + 2xh + h² + 6x + 6h + 7 - x² - 6x - 7
= h² + 2xh + 6h
Thus, The value of f (x + h) - f (x) = h² + 2xh + 6h.
Now,
f (x + h) - f (x) / h = h² + 2xh + 6h / h
= h (h + 2x + 6) / h
= h + 2x + 6
Thus, The value of f (x + h) - f (x) / h = h + 2x + 6.
Therefore, The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
Learn more about the substitution method visit:
https://brainly.com/question/19256999
#SPJ1
The measures of the angles of a triangle are shown in the figure below. Solve for x.
50°
(6x-18)°
70°
Answer:
x=13
Step-by-step explanation:
We add all the numbers together, and all the variables
6x-78
We move all terms containing x to the left, and all other terms to the right
6x=78
x=78/6
which should equal 13
What’s the correct answer answer asap i need help can somebody answer this question?
il give you brainlist
Answer: A
Step-by-step explanation:
A DVD is available at a store for $16.99. The list price of this DVD was $18.75. What was the percent discount? % (Round to the nearest tenth as needed.)
The cost of DVD = $16.99
The list price of this DVD was $18.75
So, the discount =
[tex]18.75-16.99=1.76[/tex]And the percent discount =
[tex]\frac{1.76}{18.75}\cdot100=9.3866\%[/tex]Rounding the answer to the nearest tenth
So, the answer will be : the percent discount = 9.4%