Name the theorem or postulate that can be used to prove that these triangles are similar

Answer:

ΔASA ≅ ΔASA

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

15/3=5

Answer: Water in the container = 87.75 cu.inches.

Step-by-step explanation:

Formula: Volume of rectangular prism = Base area x height

Base area = [tex]19\dfrac12[/tex] sq. inches    Height = [tex]4\dfrac12[/tex] inches

So,

Volume of container = [tex]19\dfrac12\times4\dfrac12\text{ cu.inches}[/tex]

[tex]=\dfrac{39}{2}\times\dfrac{9}{2}\text{ cu.inches}[/tex]

[tex]=\dfrac{351}{4}\text{ cu.inches}[/tex]

[tex]=87.75\text{ cu. inches}[/tex]

Hence, Water in the container = 87.75 cu.inches.

Answer:

Equivalent

Step-by-step explanation:

2/3 times 2=4/6

4/6 divided by 2=2/3

(hope this helps :P)

Answer:

780

Step-by-step explanation:

65% of 1,200 is 780 :)

Answer:

780

Step-by-step explanation:

65% x 1,200 = 780

Answer:

The two rules we need to use are:

Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)

cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)

And we also know that:

sin^2(a) + cos^2(a) = 1

To solve the relations, we start with the left side and try to construct the right side.

a) Sin(3*A) = sin (2*A + A) = sin(2*A)*cos(A) + sin(A)*cos(2*A)

sin(A + A)*cos(A) + sin(A)*cos(A + A)

(sin(A)*cos(A) + sin(A)*cos(A))*cos(A) + sin(A)*(cos(A)*cos(A) - sin(A)*sin(A))

sin(A)*cos^2(A) + sin(A)*cos^2(A) + sin(A)*cos^2(A) - sin^3(A)

3*sin(A)*cos^2(A) - sin(A)*sin^2(A)

sin(A)*(3*cos^2(A) - sin^2(A))

Now we can add and subtract 4*sin^3(A)

sin(A)*(3*cos^2(A) - sin^2(A)) + 4*sin^3(A) -  4*sin^3(A)

sin(A)*(3*cos^2(A) + 3*sin^2(A)) - 4*sin^3(A)

sin(A)*3*(cos^2(A) + sin^2(A)) - 4*sin^3(A)

3*sin(A) - 4*sin^3(A)

b) Here we do the same as before:

cos(3*A) = 4*cos^3(A) - 3*cos(A)

We start with:

Cos(2*A + A) =  cos(2*A)*cos(A) - sin(2*A)*sin(A)

= cos(A + A)*cos(A) - sin(A + A)*sin(A)

= (cos(A)*cos(A) - sin(A)*sin(A))*cos(A) - ( sin(A)*cos(A) + sin(A)*cos(A))*sin(A)

= (cos^2(A) - sin^2(A))*cos(A) - sin^2(A)*cos(A) - sin^2(A)*cos(A)

= cos^3(A) - 3*sin^2(A)*cos(A)

=  cos(A)*(cos^2(A) - 3*sin^2(A))

now we subtract and add 4*cos^3(A)

= cos(A)*(cos^2(A) - 3*sin^2(A)) + 4*cos^3(A) - 4*cos^3(A)

= cos(A)*(-3*cos^2(A) - 3*sin^2(A)) + 4*cos^3(A)

= cos(A)*(-3)*(cos^2(A) + sin^2(A)) + 4*cos^3(A)

= -3*cos(A) + 4*cos^3(A)

Answer:

55 is the answer I think so

Answer: 55

Step-by-step explanation:

Step One: Add: 2 + 3 = 5

Step Two: Multiple: 11 * the result of step No. 1 = 11 * 5 = 55

Answer:

-5/6

Step-by-step explanation:

Using the slope formula we can easily find the slope

m=(y2-y1)/(x2-x1)

m=(-1-4)/(10-4)

m=-5/6

Answer:

slope = - 2, point on line = (- 1, 3 )

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = - 2(x + 1) ← is in point- slope form

with slope m = - 2 and (a, b ) = (- 1, 3 )

The slope of equation y−3=−2(x+1) is -2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

y−3=−2(x+1)

Using Slope- Intercept form

y= mx + b

So, the slope for the equation is -2.

Hence, the slope is -2.

Learn more about slope here:

https://brainly.com/question/3605446

#SPJ2

Answer:

a) 3, 6, 9, 12, 15,...,[tex]3\cdot n[/tex], b) 4, 7, 10, 13, 16,...,[tex]3\cdot n +1[/tex], c) Both sequences are arithmetic.

Step-by-step explanation:

a) The sequence of natural numbers which are multiplied by 3 are represented by the function [tex]f(n) = 3\cdot n[/tex], [tex]n\in \mathbb{N}[/tex]. Let see the first five elements of the sequence: 3, 6, 9, 12, 15,...

b) The sequence of natural numbers which are multiplied by 3 and added to 1 is represented by the function [tex]f(n) = 3\cdot n + 1[/tex], [tex]n\in \mathbb{N}[/tex]. Let see the first five elements of the sequence: 4, 7, 10, 13, 16,...

c) Both sequences since differences between consecutive elements is constant. Let prove this statement:

(i) [tex]f(n) = 3\cdot n[/tex]

[tex]\Delta f = f(n+1) -f(n)[/tex]

[tex]\Delta f = 3\cdot (n+1) -3\cdot n[/tex]

[tex]\Delta f = 3[/tex]

(ii) [tex]f(n) = 3\cdot n +1[/tex]

[tex]\Delta f = f(n+1)-f(n)[/tex]

[tex]\Delta f = [3\cdot (n+1)+1]-(3\cdot n+1)[/tex]

[tex]\Delta f = 3[/tex]

Both sequences are arithmetic.

9514 1404 393

Answer:

  62°

Step-by-step explanation:

The measure of the external angle where the secants meet is half the difference of the arcs they subtend.

  ∠A = (DE - BC)/2

  2×∠A = DE -BC

  DE = BC + 2×∠A

  DE = 38° +2(12°)

  arc DE = 62°

Answer:

Terry had £780 initially and Faye had £1300

Step-by-step explanation:

System of Equations

We'll call the following variables:

x = Terry's balance in his bank account

y = Faye's balance in her bank account

The initial relation between them is:

[tex]\frac{x}{y}=\frac{3}{5}[/tex]

Cross-multiplying:

5x = 3y        [1]

If Terry put £220 in his account he had x+220 and if Faye withdrew £300 from her account, she had y-300. Both quantities are equal, thus

x + 220 = y - 300

Subtracting 220:

x = y - 520         [2]

Substituting in [1]

5(y - 520) = 3y

Multiplying:

5y - 2600 = 3y

Adding 2600 and subtracting 3y:

2y = 2600

Dividing by 2:

y = 1300

From [2]:

x = 1300 - 520

x = 780

Terry had £780 initially and Faye had £1300

Answer:

(a+9)(a-9)

Step-by-step explanation:

Both terms are perfect squares, use the difference of squares formula

a^2-b^2=(a+b)(a-b) where a=a and b=9

Answer:

D half a barrel an hour

Step-by-step explanation:

hope it helps

Answer:

x² + y² is equal to = (4 / 81)(845m² + 78m + 18)

Step-by-step explanation:

We first need to get the values of x and y, which can be done using a system of equations, substituting one of the two functions into the other:

Given:

y = 2x + 2

3x + 3y = 26m

Then:

3x + 3(2x + 2) = 26m

3x + 6x + 6 = 26m

9x + 6 = 26m

9x = 26m - 6

x = (26m - 6) / 9

Now we can solve for y:

y = 2x + 2

y = 2(26m - 6) / 9 + 2

y = 2(26m - 6) / 9 + 18 / 9

y = (52m - 12 + 18) / 9

y = (52m + 6) / 9

Now we can sum up their squares:

x² + y²

= ((26m - 6) / 9)² + ((52m + 6) / 9)²

= (676m² - 312m + 36) / 81 + (2704m² + 624m + 36) / 81

= (3380m² + 312m + 72) / 81

= (4 / 81)(845m² + 78m + 18)

Answer:

5400

Step-by-step explanation:

you would measure the length and width. Multiply the length by the width to get the area, and add twice the length to twice the width to get the perimeter

Answer:

164 degrees

Step-by-step explanation:

The measure of the individual internal angle in a polygon is;

(n-2)180/n

n = 22

So we have;

(22-2)180/22

= (20 * 180)/22

= 163.64 degrees

To the nearest whole number, this is 164

Answer: Its gameshop its being sold for only 4 dollars each

Step-by-step explanation:

you divide each sum of money by the amount of games and that tells you X the price per game

Answer:

4 liters

Step-by-step explanation:

simplify 2/6 = 1/3

Multiply 1/3 times the 12 bottles

1/3 * 12

12/3

Simplify

4

Answer:

4 liters of soda.

Step-by-step explanation:

2/6⋅12=24/6

24/6=4

Therefore, your answer is 4 liters.

Answer:

B) [tex]\displaystyle \frac{1}{45}\:of\:a\:pound[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{1}{9} \times \frac{1}{5} = \frac{1}{45}[/tex]

I am joyous to assist you at any time.

Answer:

its B

Step-by-step explanation:

simple just b

Answer:

Step-by-step explanation:

a + c = 321

6a + 4c = 1590

c = 321 - a

6a + 1284 - 4a = 1590

2a = 306

a = 153

c = 168

Answer:

Step-by-step explanation:

From the given graph the line is straight ,so it means that the relation between x and y is directly proportional

(or) you can also say that at each point the slope of the line is same

slope =y/x ,  slope= 26/2  = 65/2 = 117/9 =13

hence slope is same that's why relation between x and y is direct relation

y∝ x

y=k*x

k=y/x

putt any point one the line to find the value of constant of proportionality,

i putt (2,26)

Answer:

Step-by-step explanation:

.........

this ones confusing, i wish i could help sorry.

Answer:

Commision may be defined as a percentage cut which an employee, broker, vendor, retailer or other persons within a sale chain receive from an employer or production firm for selling a good or offering a successful service based on agreed terms by both parties. ;

$18700

Step-by-step explanation:

Given :

Commision pattern :

5% on first $200,000

6% on remaining amount

Amount of commission on $345000

0.05 * 200000 = 10,000

0.06 * (345000 - 200000) = 8700

Total commission :

10,000 + 8700 = 18,700

Answer:

y=4/5x-1 is the answer (A)

Step-by-step explanation:

Answer: Step-by-step explanation:

the first one would be your answer (y= 4/5x -1)

because the y intercept is -1 and the rise if 4 and run is 5 and that would be your slope.

Answer:

y = -8x - 8

Step-by-step explanation:

Add -8x on both sides to get -y = 8x + 8 and flip the y sign on the left to get your slope function which is y = - 8x - 8.

To graph the function, you would need to put (0, -8) as your y-intercept, and each unit will go down 8 units when you add 1.

Answer:

y=8x+8

Step-by-step explanation:

Just rewrite the problem so it's in y=mx+b format then it's easy to graph

Remember the y intercept is 8 because when x=0  y=8 and the slope is 8 so go up 8 and right 1

Answer:

Step-by-step explanation:

11