Regard triangleTRI and the following facts:
Segment IR || Segment NA
TA= 12 cm, RA= 3 cm, NT= 18 cm, AN= 22
(a)What theorem or postulate proves Triangle ANT similar to RIT?(b)Solve for NI by using the Side-Splitting Theorem.Show all work.(c)What is the scale factor for similar triangles ANT and RIT?
(d)Calculate RI. Show your work.
(e)What is the ratio of the areas of the two triangles? Show your work.
Answers
B) NI = 4.5
C) 4:5
D) RI = 27.5
E) 16:25
Explanation
We will set up a proportion for b:
AT/RT = NI/TI
12/15 = 18/x
Cross multiply:
12*x = 18*15
12x = 270
Divide both sides by 12:
12x/12 = 270/12
x = 22.5
Since TI = TN + NI, we have
22.5 = 18 + NI
-18 -18
4.5 = NI
C) The ratio of the sides of the smaller triangle to the larger rectangle are given by the ratio AT/RT, or 12/15 = 4/5.
D) Setting up a proportion we have
AN/RI = AT/RT
22/RI = 12/15
Cross multiply:
22*15 = RI*12
330 = 12RI
Divide both sides by 12:
330/12 = 12RI/12
RI = 27.5
E) The ratio of the areas will be the square of the ratio of the side lengths, since area is a square measurement:
(4/5)² = 4²/5² = 16/25
Related Questions
Using complete sentences, explain the key features of the graph of the sine function.
Answers
how do i graph and shade this linear inequality?
4x + 5y < 20
x - 2y <6
Answers
y<-4/5x+4
y>1/2x-3
Select the following series as arithmetic, geometric, or neither. 1 + 2 + 3 + 4 + . . . + 10
Answers
The progression has a common difference of 1. You can tell because it involves a plus sign, which is indicative of an arithmetic progression,
A geometric progression would include multiplying the numbers by a certain amount. For example:
1, 3, 9, 27 ... 243
In this series, you multiply the numbers by three to get your answer.
The following series is an arithmetic series. Because the progressive term has a difference of 1.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
The given equation is;
1 + 2 + 3 + 4 + . . . + 10
The series is arithmetic in nature. The typical difference in the progression is 1. Because it has a plus sign, which indicates an arithmetic progression.
Hence, the following series is an arithmetic series.
Learn more about the sequence here:
brainly.com/question/21961097
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A cone shaped cup has a radius of 4 inches and a height of 6 inches. Which measurement is the closest to the volume in cubic inches for the cup? Use 3.14 for π.
25.12 in³
12.28 in³
100.48 in³
6.14 in³
Answers
Substituting into the formula: V = [tex] \frac{ \pi 4^{2} 6}{3} [/tex] = 32(3.14) = 100.48
A regular decagon is mapped onto itsslf everytime it is rotated by how many degrees
Answers
Answer:
36° is correct.
Step-by-step explanation:
The degree of rotational symmetry is equal to 360° divided by the number of sides of a regular polygon
360° ÷ 10 = 36°
Answer:
A regular decagon is mapped onto itself every time it is rotated by 36°
Step-by-step explanation:
A regular decagon means a polygon with 10 sides and all sides are equal.
Refer the given figure, if we rotate by 36° we will get same decagon.
So a regular decagon is mapped onto itself every time it is rotated by 36°
What is the value of z in the equation 11 + z = 6?
66
5
−5
1
Answers
Answer:
z = -5
Step-by-step explanation:
To find the value of z in the equation 11 + z = 6
we will simply subtract 11 from both-side of the equation. That is;
11 + z = 6
Subtract 11 from both-side of the equation
11 - 11 + z = 6 - 11
(On the left-hand side of the equation 11 will be subtracted from 11 which gives zero, thereby leaving us with just z while on the right-hand side of the equation 11 will be subtracted from 6 which will give negative 5)
z = -5
divide. and simplify 4/7÷8/3
Answers
Choose the graph of 3x + y = –2.
Answers
[tex] \left[\begin{array}{ccc}\boxed{\boxed{Slope: \ -3 ; \ Y-intersect: \ -2} }\end{array}\right] [/tex]
Your correct answer would be the second picture, this fit in with what we considered with the slope and all.
I hope this helps you!
HELLO
could anyone PLEASE help me??
Id appreciate it!!!!!
Answers
How to solve it:
Okay. So first off, lets subtract 424 from both sides. 424 - 424 cancels out. 1,000 - 424 is 576. That makes 9x = 576. Now, divide each side by 9 to isolate the c. 9x/9 cancels out. 576/9 is 64. There. x = 64. The team will need to score an average of 64 points in their remaining games in order to reach their goal.
Yulia estimates college tuition and fees, room and board, books, and other charges total $15,350. She will receive a $1500 scholarship. If she has 4 years to save, how much should Yulia save per month to cover the costs of college (minus the scholarship)? A. $288.54 B. $319.79 C. $3462.50 D. $3837.50
Answers
Now to find how much she will need to save each month, we are going to divide the total cost of her college education by 48 months:
[tex] \frac{13850}{48} =288.54[/tex]
We can conclude that Yulia will have to save $288.54 per month to cover the costs of her college education. Therefore, the correct answer is: A. $288.54
The solution to the equation x + 4.5 = 9.2 is x = 4.7.
True or false
Solve the equation. b + 2.9 = 8.7
b = 3
b = -5.8
b = 11.6
b = 5.8
Solve the equation. 2.5 + a = 8.7
a = 6.2
a = .2
a = -6.2
a = 3.48
Answers
The First One Is True Then The Next One Is A.B=3 And The Last One Is D.A=3.48
Hope It Helps And PLEASE MARK ME THE BRAINLYEST
What is the value of x?
sin(x+22)°=cos(2x−7)°
Remember to show all of you work for credit!
Given cosx=1213 and sinx=513 .
What is ratio for tan x ?
leave answer as a fraction in simplest form
Remember to show all of you work for credit!
Answers
Q1: Given sin(x+22)° = cos(2x−7)°
Using the concept of Right triangles and Trigonometric ratios, we can use a formula given as follows :-
If, sin(A) = cos(B). Then we must have A + B = 90 degrees.
We have sin(x+22)° = cos(2x−7)°
Then it must be true that (x+22)° + (2x−7)° = 90 degrees.
(x + 22) + (2x - 7) = 90
3x + 15 = 90
3x + 15 - 15 = 90 - 15
3x = 75
[tex] \frac{3x}{3} =\frac{75}{3} \\\\x = 25 \;degrees [/tex]
Hence, x = 25 degrees is the final answer.
Q2: Given cos(x) = 1213 and sin(x) = 513.
It says to find ratio of tan(x).
Using the concepts of Trigonometric ratios, We can the formula that relates all three functions i.e. sin(x), cos(x), and tan(x).
tan(x) = [tex] \frac{sin(x)}{cos(x)} [/tex]
We can plug the given values in the formula.
[tex] tan(x) = \frac{513}{1213} [/tex] is the final answer.
You have a camera with a 16 mp resolution. how many pixels are represented by that resolution? 16 16 million 16,000 16 billion
Answers
ANSWER: 16 million
Hope this helps! :)
The right triangle ABC shown below is inscribed inside a parabola. Point B is also the maximum point of the parabola (vertex) and point C is the x intercept of the parabola. If the equation of the parabola is given by y = -x2 + 4x + C, find C so that the area of the triangle ABC is equal to 32 square units.
Answers
Which property is demonstrated below
Answers
An 80 ft guy wire is attached to a pole. The angle of elevation from the wire to the top of the pole is 48. How tall is the pole?
Answers
height = 59.45 feet Round answer as needed.
7. Simplify the product using the distributive property.
(5h - 3)(3h + 7)
(A). 15h^2 - 44h + 21
(B). 15h^2 - 26h - 21
(C). 15h^2 + 44h + 21
(D). 15h^2 + 26h - 21
8. Simplify the product using a table. ***I will add a picture of the table***
(5h + 4)(3h + 6)
(A). 15h^2 + 42h + 24
(B). 15h^2 - 42h + 24
(C). 15h^2 + 18h - 24
(D). 15h^2 - 18h - 24
9. Simplify using a table. ***I will also add a picture of this table***
(-4m + 6)(3m + 2)
(A). -12m^2 + 10m + 12
(B). -12m^2 - 10m - 12
(C). -12m^2 + 26m + 12
(D). -12m^2 - 26m - 12
10. Simplify the product using FOIL.
(4x - 4)(3x - 4)
(A). 12x^2 - 28x + 16
(B). 12x^2 - 4x - 16
(C). 12x^2 + 4x - 16
(D). 12x^2 + 28x + 16
11. A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form best describes the total volume of the cylinder? Use the formula V= πr^2h for the volume of a cylinder.
(A). 80πx^3 + 144πx^2 + 84πx + 16π
(B). 20πx^2 + 26πx + 8π
(C). 80πx^3 + 144πx^2 + 84πx - 16π
(D). 400πx^4 + 1040πx^3 + 996πx^2 + 416πx + 64π
12. A sphere had a radius of 2x + 5. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S= 4πr^2 for surface area of a sphere.
(A). 16πx^2 + 80πx + 100π
(B). 16πx^2 + 40πx + 100π
(C). 100πx^2 + 80πx + 16π
(D). 100πx^2 + 100π
Answers
15h² + 35h - 9h - 21
15h² + 26h -21
D
8.) A (see picture)
9.) A (see picture)
10.) (4x-4)(3x-4)
12x² - 16x - 12x +16
12x² - 28x +16
A
11.) π(4x+2)²(5x+4)
π(16x² + 16x + 4)(5x+4)
π(80x³ + 64x² + 80x² + 64x +20x +16)
π(80x³ +144x² + 84x + 16)
80πx³ +144πx² + 84πx + 16π
A
12.) 4π(2x+5)²
4π(4x² + 20x + 25)
16πx² + 80πx +100π
A
Describe one way that concepts about similarity could be used in real life
Answers
2. Cars. Suppose you like a specific type of brand car. Then there are many cars of this brand. You want to buy one of that car, so you decide to go to a concessionaire. One concessionaire has that car and its cost is $2000. Another one has the same car, it is a similar one, same color, same year, but at a price of $1900, so obviously you choose the less expensive.
Answer with explanation:
Uses of Similarity in Real Life:
1. When you will look,at the technology, personal Computers or Laptops produced by the same company,they all appear Similar.
2. When you will look at the bricks,which are used on the walls,on the roads, whether it is in the shape of a cube, Three dimensional Pentagon,or Hexagon,all of them are Similar.
→Similarity is also used for creating Electrical equipment ,Bulbs,Tube light,fans of different kinds.
So, There are Thousand of places on earth in which Concept of Similarity is used by Humans.Just Wrote few of them.
write 4bc/16b in simplest form
Answers
ILL GIVE BRAINLIST TO FIRST PERSON!!! Which of these is a primary economic activity? A) tourism B) farming C) healthcare D) construction
Answers
Lindsey’s college will cost her a total of $6,000 a year for the next four years. She is also
foregoing making $26,000 a year at the local mall. However, she will be able to make
about $8,000 a year while going to school. What is her total investment in education?
$24,000
$26,000
$72,000
$96,000
Karam anticipates spending $8,400 a year for the next five years on his college education. He will also forgo making $12,000 a year during this time. How much will he invest in his education?
$42,000
$102,000
$60,000
$12,000
Answers
2. 42000 bc 8400*5
Her total investment in education is $96,000, the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Total= $6,000
At local mall=$26,000
Now,
To find the total investment in education, we need to consider both the direct costs and the opportunity costs of going to college. The direct costs are the expenses that Lindsey has to pay for her education, such as tuition, fees, books, etc. The opportunity costs are the income that Lindsey could have earned if she did not go to college, such as working at the local mall.
The direct costs of going to college are $6,000 a year for four years, which is $24,000 in total.
The opportunity costs of going to college are $26,000 a year minus $8,000 a year for four years, which is $18,000 a year or $72,000 in total. This is because Lindsey could have earned $26,000 a year at the mall, but she is only earning $8,000 a year while going to school.
The total investment in education is the sum of the direct costs and the opportunity costs, which is
$24,000 + $72,000
= $96,000.
Therefore, by algebra the answer will be $96,000.
More about the Algebra link is given below.
brainly.com/question/953809
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What is the product of 5the square root of 3. • 4the square root of 15.? Simplify if possible. 60the square root of 5. 20the square root of 5. 60the square root of 15. 20the square root of 15.
Answers
We are to find:
[tex]5 \sqrt{3} *4 \sqrt{15} [/tex]
Multiplying and simplifying the radicals, we get:
[tex]20 \sqrt{45} \\ \\ =20 \sqrt{9*5} \\ \\ =20*3 \sqrt{5} \\ \\ =60 \sqrt{5} [/tex]
In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
112√ in.
211−−√ in.
11−−√ in.
1111−−√ in
What is the exact value of sin 45° ?
Enter your answer, as a simplified fraction, in the box.
$$
What is the area of a regular hexagon with a side length of 4 m?
Enter your answer in the box.
Round only your final answer to the nearest hundredth.
m²
In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
Enter your answer in the box.
cm
Answers
we know that
cos 45°=√2/2
[he length of the hypotenuse]=11/cos 45-----------> 11/(√2/2)----> (11*2)/√2
=22/√2-------> 11√2 in
the answer Part A) is 11√2 in
Part B) What is the exact value of sin 45° ?
we know that
sin 45°=11/(11√2)-------> 1/√2---------> (1/√2)*(√2/√2)-----> √2/2
the answer part b) is √2/2
Part C)
What is the area of a regular hexagon with a side length of 4 m?
we know that
In case of a regular hexagon each of the six triangles that are formed by connecting its center with all six vertices is an equilateral triangle with a side equaled to 4 m.
The area of this hexagon is six times greater than the area of such a triangle
In an equilateral triangle with a side d
the altitude h can be calculate from the Pythagorean Theorem as
h²=d²−(d/2)²=(3/4)d²
Therefore,
h=d√3/2
Area of such a triangle is
A=d*h/2------------> d²*√3/4
From this the area of the regular hexagon with a side d is
S=6*A----------> d²3√3/2
for d=4 m
S=4²3√3/2------> 24√3 m²------------> 41.57 m²
the answer Part C) is 41.57 m²
Part D) In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?
[he length of the hypotenuse]=5/sin 30--------> 5/(1/2)---------> 10 cm
the answer part D) is 10 cm
Answer:
In a 45°-45°-90° triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
I took the test and this is the correct answer:
11√ 2 inches
Step-by-step explanation:
SOLVE FOR X PLEASE :D
Answers
[tex] \dfrac{10x-2}{8x} = \dfrac{5x+3}{7x} \\\\ x \neq 0\\\\ \dfrac{10x-2}{8} = \dfrac{5x+3}{7} \\\\ 70x-14=40x+24\\\\ 30x=38\\\\ x= \dfrac{19}{15} [/tex]
A sphere is dilated by a scale factor of 1.5 to create a new sphere. How does the volume of the new sphere compare with the volume of the original sphere?
A)
The volume of the new sphere is 1.5 times the volume of the original sphere.
B)
The volume of the new sphere is 3.0 times the volume of the original sphere.
C)
The volume of the new sphere is 1.52 times the volume of the original sphere.
D)
The volume of the new sphere is 1.53 times the volume of the original sphere.
Answers
Answer: D
Step-by-step explanation:
What law does static electricity illustrate?
A. Ohm's law
B. Law of Conservation of Motion
C. Law of Conservation of Energy
D. Law of Conservation of Charge
Would this be D?
I know its not math...>:P
Answers
Static electricity illustrates or mostly related to the Law of Conservation of Charge. This law states that the charge of matter is constant and it will only change if there is the entrance of new charge or there is a removal of charge. This is the same with static electricity since charge of static electricity is constant.
Find a positive angle less than one revolution around the unit circle that is co-terminal with the given angle: 52pi/5
Answers
x=52/5π-5*2π=2/5π
the positive angle less than one revolution around the unit circle that os co-terminal with angle of 52/5π is 2/5π
Express 18.48 ( 48 bar) in the form of p/q where p and q are integers and q is not equal to 0.
Answers
100x=1848.48. (1)
x=18.48. (2)
subtract 2 from 1
99x=1830.00
x=1830/99
We have to express [tex] 18.\bar{48} [/tex] in the form of [tex] \frac{p}{q} [/tex] where p and q are integers and q is not equal to zero.
Let x = [tex] 18.\bar{48} [/tex]
Multiplying the given equation by 100, we get
[tex] 100x = 1848.48484848... [/tex]
[tex] 100x = 1830+ 18.48484848... [/tex]
[tex] 100x = 1830+ 18.\bar{48} [/tex]
[tex] 100x = 1830+ x [/tex]
[tex] 99x=1830 [/tex]
[tex] x=\frac{1830}{99} [/tex]
Therefore, [tex] 18.\bar{48} [/tex] is represented as [tex] x=\frac{1830}{99} [/tex] in the form of [tex] \frac{p}{q} [/tex]
Miss Monett gave 1 cup of red paint to each of her 20 students how many quarts of red paint does she give out
Answers
So, 2 cups are in a pint.
So, 16 cups in a gallon
4 cups for each quart.
Your answer is 5 quarts.
Hope that helped! :D
~Izzy~
Answer: 5 Quarts
Hope this helped :>
1. Ki’von has a sink that is shaped like a half-sphere. The sink has a diameter of 20 inches. One day, his sink clogged. He has to use one of two different cups to scoop the water out of the sink. The sink is completely full when Ki’von begins scooping. (a) What is the exact volume of the sink? Show your work. (3 points) (b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points) (c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it? Round the number of scoops to the nearest whole number. Show your work. (6 points)
Answers
Find the volume of a sink
Volume sink=(4/6)*pi*r³ (half-sphere)
Diameter=20 in--------------> r=D/2-----------> r=10 in
Volume sink=(4/6)*pi*10³---------> (2000/3)*pi in³ --------> 2093.33 in³
(a) What is the exact volume of the sink?
the answer part a) is (2000/3)*pi in³ (2093.33 in³)
(b) One conical cup has a diameter of 8 in. and a height of 6 in. How many cups of water must Ki’von scoop out of the sink with this cup to empty it?
volume of a conical cup=pi*r²*h/3
diameter=8 in--------------> r=4 in
h=6 in
volume of a conical cup=pi*4²*6/3-----------> 32*pi in³
if one cup---------------------> 32*pi in³
X---------------------------> (2000/3)*pi in³
X=(2000/3)*pi/(32*pi)------------> 20.83----------> 21 cups
the answer part b) is 21 cups
(c) One cylindrical cup has a diameter of 4 in. and a height of 6 in. How many cups of water must he scoop out of the sink with this cup to empty it?
volume of a cylindrical cup=pi*r²*h
diameter=4 in--------------> r=2 in
h=6 in
volume of a cylindrical cup=pi*2²*6-----------> 24*pi in³
if one cup---------------------> 24*pi in³
X---------------------------> (2000/3)*pi in³
X=(2000/3)*pi/(24*pi)------------> 27.77----------> 28 cups
the answer part c) is 28 cups