Stacy drew a triangle to explain the relationship between the angles of a triangle and an exterior angle. She labeled the interior angles 1, 2, and 3. She labeled as 4 the exterior angle that is adjacent to angle 2. Triangle with angles labeled 1, 2, 3, & exterior angle at angle 2 is labeled 4. What should Stacy do to explain the relationship between an exterior angle and the interior angles in a triangle?

Answers

Answer 1

9514 1404 393

Explanation:

Stacy can write two equations showing the relationships of the angles:

  ∠1 +∠2 +∠3 = 180° . . . . . . . sum of angles in a triangle

  ∠2 +∠4 = 180° . . . . . . . . . . angles of a linear pair are supplementary

__

Subtracting the second equation from the first gives ...

  (∠1 +∠2 +∠3) -(∠2 +∠4) = (180°) -(180°)

  ∠1 +∠3 -∠4 = 0

Adding ∠4 to both sides gives the relationship Stacy is looking for:

  ∠1 +∠3 = ∠4

_____

Alternative approach

Stacy could subtract ∠2 from both equations to give ...

  ∠1 +∠3 = 180° -∠2

  ∠4 = 180° -∠2

Then she could equate the two expressions for 180° -∠2:

  ∠1 +∠3 = ∠4


Related Questions

write three ratios equivalent to the given ration 7/2

Answers

Answer:

(7*2 / 2*2) = 14/4 = 3.5

(7*3 / 2*3) = 21/6  = 3.5

(7*4 / 2*4) = 28/8 = 3.5

Step-by-step explanation:

just multiply or divide both number by the same quantity and you will maintain the ratio

Favorite Sport Use the table to identify the labels for the segmented bar graph. Favorite Sport Male Female Football 10 2 Relative Frequency 100 90 80 70 60 50 40 30 20 OB OA Soccer 8 9 Basketball 7 6 Label A is 10 Label B is 0 Label C is < С C D E Label D is Sport Label E is < Intro Done​

Answers

The labels for the segmented bar graph include:

Label A is MaleLabel B Is FemaleLabel C is FootballLabel D Is SoccerLabel E Is Basketball

What is a bar graph?

A bar graph is a graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.

Here, the identification of the labels for the segmented bar graph has been depicted based on the information.

Learn more about bar graph on:

https://brainly.com/question/24741444

#SPJ1

1. What is the discriminant of the equation 5x2 - 20x + 20 = 0?

Answers

Answer:

0

Step-by-step explanation:

D = 20²-4(5)(20) = 400-400 = 0

Which of the following triangles have three sides of different length? A. acute B. scalene C.equilateral D. right​

Answers

Answer:

scalene

hope this helps

have a good day :)

Step-by-step explanation:

Multiply each term number below by 5 to form a sequence​

Answers

Answer:

Multiply the numbers by 5

Step-by-step explanation:

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Find the area

76 sq meters
60 sq meters
30.5 sq meters
65 sq meters

Answers

Step-by-step explanation:

2*10+((4+10)x8)/2

=20+14*8/2

=76 sq meters

The sales tax for an item was $6.40 and it cost $320 before tax.
Find the sales tax rate. Write your answer as a percentage.

Answers

Answer:

2%

Step-by-step explanation:

Find the sales tax rate by dividing the amount of sales tax by the original cost:

6.40/320

= 0.02

So, the sales tax rate is 2%

1.Ramu deposited Rs. 10,000 in a bank where interest is compounded
half yearly. If the rate of interest is 10% annually. How much amount he
will get after a year?
3​

Answers

Answer:

Future value, A = $10,500

Step-by-step explanation:

Given the following data;

Principal = Rs. 10,000

Interest rate compounded half yearly = 10% = 10/2 = 5%

Time = 1 year

To find the future value, we would use the compound interest formula;

[tex] A = P(1 + \frac{r}{100})^{t}[/tex]

Where;

A is the future value. P is the principal or starting amount. r is annual interest rate. n is the number of times the interest is compounded in a year. t is the number of years for the compound interest.

Substituting into the equation, we have;

[tex] A = 10000(1 + \frac{5}{100})^{1}[/tex]

[tex] A = 10000(1 + 0.05)[/tex]

[tex] A = 10000(1.05)[/tex]

Future value, A = $10,500

What is the quotient when (-12x9 + 3x7 + 24x6) is divided by 6x?

Answers

-2x^8+.5x^6+4x^5 is the quotient.

verify that A(3, 1), B(0, 5), and C(-1, -1) are the vertices of a right triangle.

Answers

No, not a right triangle

Need help ASAP NO LINKS

Answers

Answer:

9

Step-by-step explanation:

5(n-2)=35

5n-10=35

5n=35+10

5n=45

n=45/5

n=9

Please mark me as brainliest

hope this helps! feel free to clarify

What is the greatest prime you must consider to test whether 4295 is​ prime?

Answers

Answer:

5

Step-by-step explanation:

4295/5 = 859

4295 is divisible by the prime number 5

no need to test any higher priime

The measure of _A is 18° greater than the measure of _B. The two angles are complementary. Find the
measure of each angle.
The m_A is
1° m
and m_B is

Answers

Answer:

angle A=54 degree

angle B =36 degree

Step-by-step explanation:

let angle B be x

angle A=x+18

since they are complementary angles sum of these two angles will be 90 degree

x+x+18=90

2x=90-18

2x=72

x=72/2

x=36 degree

substitute the value of x to find angle A and angle B

for angle A

x+18

36+18

54 degree

for angle B

angle B =x

=36 degree

Mia cut a piece of felt into 3 equal
sections. She used 1 section for an art project. What fraction of the felt did Mia use for the art
project?
(1 Point)

Answers

Answer:

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

Mia used One Third of the felt for her art project. 3/3 would be the whole felt together. Since one part of three sections was used up then this means that 1/3 was used.

The graph of g(x) resembles the graph of f(x) = x2, but it has been changed.
Which of these is the equation of g(x)?

Answers

Answer:

B. g(x)=x²-3 b is my answer

What is the equivalent recursive definition for an = 12+ (n - 1)3?
A. a1 = 3, An = An-1 + 12
B. a1 = 12, An = 30n-1
C. a1 = 12, Un = On-1 +3
D. a1 = n, an= 1201-1+3

Answers

Answer:

[tex]A_1 = 12[/tex]

[tex]A_n = A_{n-1} + 3[/tex]

Step-by-step explanation:

Given

[tex]A_n =12+(n-1)3[/tex]

Required

Write as recursive

We have:

[tex]A_n =12+(n-1)3[/tex]

Open bracket

[tex]A_n =12+3n-3[/tex]

[tex]A_n =12-3+3n[/tex]

[tex]A_n =9+3n[/tex]

Calculate few terms

[tex]A_1 =9+3*1 = 9 + 3 = 12[/tex]

[tex]A_2 =9+3*2 = 9 + 6 = 15[/tex]

[tex]A_3 =9+3*3 = 9 + 9 = 18[/tex]

The above shows that the rule is to add 3.

So, we have:

[tex]A_1 = 12[/tex]

[tex]A_n = A_{n-1} + 3[/tex]

Now that we know that 2π is about 6.28, π2 is about 9.86, and 58−−√ is between 7 and 8, which choice represents the correct order of these expressions from least to greatest: 58−−√, 2π, π2, 8?

Answers

Answer:

use miss r sir hope I helped you

plllzzz im new and i neeed help

find the volume of the following composite object. enter your answer as an integer in the box


Answers

Answer:

4082

Step-by-step explanation:

Given

The composite object

Required

The volume

The object is a mix of a cone and a hemisphere

Such that:

Cone

[tex]r = 10cm[/tex] ---- radius (r = 20/2)

[tex]h = 19cm[/tex]

Hemisphere

[tex]r=10cm[/tex]

The volume of the cone is:

[tex]V_1 = \frac{1}{3}\pi r^2h[/tex]

[tex]V_1 = \frac{1}{3}\pi * 10^2 * 19[/tex]

[tex]V_1 = \frac{1900}{3}\pi[/tex]

The volume of the hemisphere is:

[tex]V_2 = \frac{2}{3}\pi r^3[/tex]

[tex]V_2 = \frac{2}{3}\pi 10^3[/tex]

[tex]V_2 = \frac{2000}{3}\pi[/tex]

So, the volume of the object is:

[tex]V = V_1 + V_2[/tex]

[tex]V = \frac{1900}{3}\pi + \frac{2000}{3}\pi[/tex]

[tex]V = \frac{3900}{3}\pi[/tex]

[tex]V = 1300\pi[/tex]

[tex]V = 1300 * 3.14[/tex]

[tex]V = 4082[/tex]

Help again pleaseeeee

Answers

It’s D
Hope it helps :)

The radius of a circle is 9in. Find it’s circumference in terms of

Answers

[tex]{ \bf{ \underbrace{Given :}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 9 in.

[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]

The circumference of the circle.

[tex]{ \bf{ \underbrace{Solution :}}}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]

[tex] = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in[/tex]

Therefore, the circumference of the circle is 56.52 in.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

What is the value of a?
A. 12
B. 15
C. 17.25
D. 21.25

Answers

Answer:

the answer is a.12

i think

Answer:

17.25

Step-by-step explanation:

please helppppppppp me​

Answers

So there was a total of 28 games played and the Houston Tigers only scored above 53 points 4 times. Now the fraction would be 4/28 but we have to reduce so the real answer is actually 1/7

Lisa played two rounds of
miniature golf. Her score was –3 in the
first round and +2 in the second round.
What was Lisa's score after two
rounds?

Answers

Answer:

-1 I think so.....

n please rate this

Lisa’s score after two rounds is -1
Explanation:
1st round: -3
2nd round: 2
-3 + 2 = -1

I really hope this helps!
Glad to help, I also want to know if my answer was right.

A six-character license plate can be any three letters of the alphabet, followed by any three numerical digits. How many different license plates are possible?

Answers

Answer:

17,576,000 different license plates are possible.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

In this question:

For each letter, there are 26 possible outcomes.

For each digit, 10 possible outcomes.

So

L - L - L - D - D - D

Number of possible outcomes:

26 - 26 - 26 - 10 - 10 - 10

Each character of the license plate is independent, so, by the fundamental counting principle:

26*26*26*10*10*10 = 17,576,000

17,576,000 different license plates are possible.

The concentration of a pollutant in a lake is 85 parts per million (ppm) and is increasing at a rate of 4.6% each year. A possible formula for the concentration C as a function of year tis:
(a) C 85 +4.6t
(b) C-85-4.6t .
(c) C-85 +0.046t
(d) C-85 -0.046
(e) C = 85 (0.046)
(f) C-85 (0.954)
(g) C = 85 (1.046)
(h) C-85(1.46)
(i) C85(0.46)
(j) C-4.6 (0.85)

Answers

Answer:

[tex]C(t) = 85(1.046)^t[/tex], and the correct answer is given by option g.

Step-by-step explanation:

Equation for an concentration increasing exponentially:

The concentration after t years, considering that it increases exponentially, is given by the following equation:

[tex]C(t) = C(0)(1 + r)^t[/tex]

In which C(0) is the initial concentration and r is the growth rate, as a decimal.

The concentration of a pollutant in a lake is 85 parts per million (ppm) and is increasing at a rate of 4.6% each year.

This means that [tex]A(0) = 85, r = 0.046[/tex]. Thus

[tex]C(t) = C(0)(1 + r)^t[/tex]

[tex]C(t) = 85(1 + 0.046)^t[/tex]

[tex]C(t) = 85(1.046)^t[/tex], and the correct answer is given by option g.

Will mark Brainlest help plsssss​

Answers

Answer:

45 is answer I guess cuz my teacher taught me just like that


Find the surface area of the regular pyramid

Answers

Answer:

surface are of the pyramid =(1/2×6×5.2)+(3×1/2×6×10) =15.6+90 =105.6 yd²

3. (a) Find the elasticity of the demand function p2 + 2p +
4 = 49 at p = 6.

(b) How will a price increase affect total revenue?​

Answers

Answer:

6^2+12+4=49

36+16=49

52=49

therefore.3

[12÷(9-6)]+4×6
please help ​

Answers

The answer is 28 ez.

Answer:

the answer is 28

Step-by-step explanation:

HELP ME PLEASEEEEEEEEEEEEEEEEEE

Answers

Answer:

y = 3/2x + 15

Step-by-step explanation:

change f(x) to 'y='

interchange 'x' and 'y' then solve for 'y':

y = 2/3x - 10

x = 2/3y - 10

x+10 = 2/3y

multiply each side by 3/2 to get:

y = 3/2x + 15

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