solve similar triangles (advanced)

Answer:

the angles are 89.2°, 34.5°, 56.3° and the sides are √26units, √8units, √18units respectively

Step-by-step explanation:

Distance between points (2,5) and (-1,2)

Using the formula, √(X2 - X1)² + (Y2 - Y1)²

= √(-1-2)²+(2-5)²

=√(-3)²+(-3)²

=√9+9

=√18 or 3√2

Distance between points (-1,2) and (4,3)

=√[4-(-1)]²+(3-2)²

= √5²+1²

=√25+1

=√26

Distance between points (2,5) and (4,3)

=√(4-2)²+(3-5)²

=√2²+(-2)²

=√4+4

=√8

Using Cosine rule/formula, C²= A²+B²-2abcosc

Let C be √18, A be √26 and B be √8

√18²=√26²+√8² - 2√26.√8cosc

18= 26+8 - 2√208cosc

18= 34 -2√208cosc

2√208cosc= 34-18

Cosc = 16/2√208

Cosc= 0.5546

c= Cos`¹(0.5547)

c= 56.3°

Using sine rule/formula

Sinc/C= Sina/A=Sinb/B

Sin56.3/√18= Sina/√26

Sina= (0.8320 × √26)/ √18

Sina= 0.9999

a= Sin`¹(0.9999)

a= 89.2

56.3+89.2+b= 180°( sum of angles in a triangle)

145.5 + b =180

b=180-145.5

b= 34.5

Answer:

14 sq units

Step-by-step explanation:

square - 4

triangle - 4

secong triangle - 6

4+4+6 = 14 sq units

Answer:

A = 10 sq. units

Step-by-step explanation:

Area of a trapezium is the average of the bases times the height.

Base 1 is 8 units

Base 2 is two units

Average is (8 + 2)/2 = 5 units

A = 5(2) = 10 sq. units

Answer:

  4.6 ft

Step-by-step explanation:

The formula for the area of a triangle is ...

  A = 1/2bh

Fill in the given values and solve for the base.

  5.52 = 1/2b(2.4)

  5.52/1.2 = b = 4.6 . . . . divide by the coefficient of b

The base is 4.6 feet.

Answer:

Rate of change = 3 gallons/minute

Starting volume = 30 gallons

Step-by-step explanation:

A graph of the pool's water level would be useful.  The slope of the line would represent the rate of change for filling the pool.  It will also help us determine the amount of water that was in the pool to start.  Although it is tempting to say the rate of fill is 45gallons/5 minutes, or 9 gallons/minute, it is not correct.  The pool already started with an unknown volume of water.  The rate of change after 5 minutes, however, can be used.  The problem states it is being added at a constant rate.  Let's find an equation for a line, in the format of y=mx+b, where m is the slope (rate of change) and b is the y-intercept.

We'll let y represent the volume of water in the pool, and x will be the time in minutes.  The y-intercept will give us the amount of water in the pool at the start (x = 0).

The slope can be determined between the two given points:

(5,45) and (30,120):

Slope = Rise/Run [The change in y divided by the change in x].

Rise = (120 - 45) = 75

Run = (30-5) = 25

Slope = 75/25 or 3

The line, so far, becomes y=3x + b

The slope of 3 has units of gallons/minute.  It is the rate at which the pool is being filled.

We can find b, the starting volume of water, by using one of the two points in the equation and solving for b:

y=3x + b   [I'll use (5,45)]

45 = 3*(5) + b

b = 30 gallons

The pool had 30 gallons to start (at x = 0(minutes))

See the graph of the line, attached.

Answer:

the answer is 5.9 since both sides are the same and on the other side its 5.9

Hope This Helps!!!

Therefore, the total cost of the patio is $352.

Hoped this helped!

[tex]BrainiacUser1357[/tex]

Answer:

49 hot dogs, 77 sodas

Step-by-step explanation:

2.25h + 1.5s = 225.75

h + s = 126, so s = 126 - h. Substitute that into the first equation.

2.25h + 1.5(126 - h) = 225.75

Solve for h

2.25h + 189 - 1.5h = 225.75

0.75h = 36.75

h = 49  So they sold 49 hot dogs

h + s = 126, so 49 + s = 126, s = 77

Answer:

Yes, it is a rotation!

Step-by-step explanation:

You know this because the shape rotated. It did not flip, change size, or remain the same.

I hope this helps!

Answer:

11n

Step-by-step explanation:

7+4 =11

so then 7n+4n=11n

Answer:

1.5

Step-by-step explanation:

6/4

Answer:

it's C. 1.5

Step-by-step explanation:

I did the test

The total cost during a school year to attend a given number of daces is a

linear function of the number of dances attended.

The correct responses are;

Reasons:

The given parameter are;

Admission price per person = $4

The annual fees members pay = $50

A. The function that can be used to determine c is a linear function, with a y-intercept (initial value) of 50 and a rate (slope) of 4

The total cost to attend n dances a year, c = 50 + 4·n

B. If a member attends 15 dances a year, we have;

n = 15

Therefore;

The total cost, c = 50 + 4 × 15 = 110

The total cost for 15 dances a year, c = $110

1. As the number of dances attended increase, the total cost increase, and the cost when no dance is attended by a member during the year is $50.

2. The essential information that can be used to find the solution are;

3. Part A; c = 50 + 4·n

Part B; c = $110

Learn more about linear functions here:

https://brainly.com/question/20478559

Answer:

Step-by-step explanation:

Given - This is the start of the proof. Use this for the information given from the start.

Addition property of equality - Use this when adding terms on both sides of an equation.

Division property of equality - Use this when dividing terms on both sides of an equation.

Answer:

THANK U!

FOR THE TIP.

HAVE A GREAT DAY!

Answer:

c on edge YW

Step-by-step explanation:

The value of ∛4 × √3 is 2.75 or  [tex]\sqrt[6]{432}[/tex].

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given;

Expression,

product 3 sqrt 4 times sqrt 3.

In numerator form:

As per the given expression,

∛4 × √3

Simplifying,

∛4 × √3

= [tex]4^{1/3}[/tex] x [tex]3^{1/2}[/tex]

= [tex]4^{2/6}[/tex] x [tex]3^{3/6}[/tex]

= [tex]\sqrt[6]{16 + 27}[/tex]

= [tex]\sqrt[6]{432}[/tex]

= 2.749

= 2.75

Therefore, the product is 2.75 or  [tex]\sqrt[6]{432}[/tex].

To learn more about the multiplication;

https://brainly.com/question/19634536

#SPJ5

Answer:

11

Step-by-step explanation:

It's clearly 11

1 + 1 = 11

just put the 2 numbers together

Answer:

Second option = TB - L > D

Step-by-step explanation:

[Given] T > [tex]\frac{L +D}{B}[/tex]

[Multiply both sides by B] TB > L + D

[Subtract L from both sides] TB - L > D

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

For finding the inflection points you'll have to put the first derivative equal to zero and solve for x. After you've done that, you can plug in the x you've just found into the original function and find also the y, so you'll find the ordered pair (x,y) of the inflection point(s).

Answer:

Double-entry bookkeeping,in accounting, is a system of bookkeeping where every entry to an account requires a corresponding and opposite entry to a different account. The double-entry system has two equal and corresponding sides known as debit and credit.

The given question can be solve using quadratic formula.

The correct option is (c) [tex]3x^2 +8x -10=-8[/tex].

Given:

The given equation is,

[tex]x=\dfrac{-8\pm\sqrt{8^2-4(3)(-1)}} {2(3)}[/tex]---------------------------(1)

Write the general quadratic equation.

[tex]ax^2 + bx +c=0[/tex]

Write the quadratic formula.

[tex]x =\dfrac {-b \pm \sqrt{(b^2 - 4ac)} } {2a}[/tex]------------------------------- (2)

Compare equation (1) and (2).

[tex]a=3\\b=8\\c=-2[/tex]

Substitute the value of [tex]a[/tex], [tex]b[/tex] and [tex]c[/tex] in general quadratic.

[tex]3x^2 +8x -2=0[/tex]

Subtract [tex]8[/tex] from each side of above equation.

[tex]3x^2 +8x -2 -8=0-8\\3x^2 +8x -10=-8[/tex]

Thus, the correct option is (c) [tex]3x^2 +8x -10=-8[/tex].

Learn more about quadratic equation here:

https://brainly.com/question/17177510

Answer:

w < -7

Step-by-step explanation:

Do -42 divided by 6 and keep the sign the same.

You get w < -7.

Hope this helps! :)

Answer:

22 +22 - 8=0

=

-2 +6

=

2

-2 +4+32

2.

=

= = =

I = -4; = 2

x = -13

TI

-2 = 36

2

-2 +(2) – 4(1)(-8)

2 (1)

2

= r = -1 -3: x = -1 +3 = sin   \theta  

Step-by-step explanation:

Answer:

-53 /14

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

first you do 11 + 11 =22

23+45=68

now im postitive you add 68 and 22 and get you final answer which is ...

90

Answer:

1 23/45

Step-by-step explanation:

Start by multiplying numerators and denominators to get the LCD in all fraction denominators

=11×45/11×45+23×11/45×11

Then rewriting the equation with the equivalent fractions

=495/495+253/495

With like denominators we can operate on just the numerators

=495+253/495

=748/495

Simplifying the answer

=68/45

=68/45

=1 23/45

Answers:

===============================================

Explanation:

The domain consists of the set of x coordinates of each point. In this case, we only have one x value listed. The domain is {15}. Use curly braces even if there's only one item. This tells the reader we have a set.

The range is {0,-2} to indicate the y coordinates of the two points.

We don't have a function because x = 15 repeats itself. The input x = 15 leads to multiple outputs at the same time, which isn't allowed if you want a function. You can use the vertical line test as a visual way to see that we don't have a function.

Answer:

4,500 hope this help

Step-by-step explanation:

x = 5.25

since there is a scale factor of 1.75, you multiply 3 * 1.75 and get 5.25

hope this is helpful!

Answer:

Sale price is [tex]15.2\$[/tex]

Step-by-step explanation:

Price is reduced by 80% from the original price.

Here original price is $76

Sale price is

[tex]=76-76\times\frac{80}{100}\\\\=0.2\times76\\\\=15.2\$[/tex]