Which two triangles are congruent by the SAS Theorem?

9514 1404 393

Answer:

  (8.49; 225°)

Step-by-step explanation:

The angle is a 3rd-quadrant angle. The reference angle will be ...

  arctan(-6/-6) = 45°

In the 3rd quadrant, the angle is 45° +180° = 225°.

The magnitude of the vector to the point is its distance from the origin:

  √((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49

The polar coordinates can be written as (8.49; 225°).

_____

Additional comment

My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.

Answer:

Sale tax rate = 21.46%

Step-by-step explanation:

Sale Tax % = ( Amount after sale tax - Original  cost) ÷ original × 100

Sale Tax % = ( $9.96 - $8.20) ÷ $8.20 × 100

Sale Tax % = $1.76 ÷ $8.20 × 100

Sale Tax % = .2146341463 × 100

 Sale Tax % = 21.46

Coding the given algorithm in python 3, the greatest common divisor of the values (124 and 244) and (4424 and 2111) are 4 and 1 respectively.

The program implementation goes thus :

def gcd(a, b):

#initialize a function named gcd which takes in two parameters

if a>b:

#checks if a is greater than b

return gcd (b, a)

#if true interchange the Parameters and Recall the function

elif a == 0:

return b

elif a == 1:

return 1

elif((a%2 == 0)and(b%2==0)):

#even numbers leave no remainder when divided by 2, checks if a and b are even

return 2 * gcd(a/2, b/2)

elif((a%2 !=0) and (b%2==0)):

#checks if a is odd and B is even

return gcd(a, b/2)

else :

return gcd(a, b-a)

A sample run if the program on the values given :

print(gcd(124, 244))

print()

#leaves a space after the first output

print(gcd(4424, 2111))

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Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -17x its coefficient is -17 .

The last term, "the constant", is +60

Step-1 : Multiply the coefficient of the first term by the constant 1 • 60 = 60

Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .

-60 + -1 = -61

-30 + -2 = -32

-20 + -3 = -23

-15 + -4 = -19

-12 + -5 = -17 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5

x2 - 12x - 5x - 60

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-12)

Add up the last 2 terms, pulling out common factors :

5 • (x-12)

Step-5 : Add up the four terms of step 4 :

(x-5) • (x-12)

Which is the desired factorization

Equation at the end of step

1

:

(x - 5) • (x - 12) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

2.2 Solve : x-5 = 0

Add 5 to both sides of the equation :

x = 5

Solving a Single Variable Equation:

2.3 Solve : x-12 = 0

Add 12 to both sides of the equation :

x = 12

Supplement : Solving Quadratic Equation Directly

Solving x2-17x+60 = 0 directly

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

3.1 Find the Vertex of y = x2-17x+60

For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 8.5000

Plugging into the parabola formula 8.5000 for x we can calculate the y -coordinate :

y = 1.0 * 8.50 * 8.50 - 17.0 * 8.50 + 60.0

or y = -12.250

Parabola, Graphing Vertex and X-Intercepts :

Root plot for : y = x2-17x+60

Axis of Symmetry (dashed) {x}={ 8.50}

Vertex at {x,y} = { 8.50,-12.25}

x -Intercepts (Roots) :

Root 1 at {x,y} = { 5.00, 0.00}

Root 2 at {x,y} = {12.00, 0.00}

Solve Quadratic Equation by Completing The Square

3.2 Solving x2-17x+60 = 0 by Completing The Square .

Subtract 60 from both side of the equation :

x2-17x = -60

Now the clever bit: Take the coefficient of x , which is 17 , divide by two, giving 17/2 , and finally square it giving 289/4

Add 289/4 to both sides of the equation :

On the right hand side we have :

-60 + 289/4 or, (-60/1)+(289/4)

The common denominator of the two fractions is 4 Adding (-240/4)+(289/4) gives 49/4

So adding to both sides we finally get :

x2-17x+(289/4) = 49/4

Adding 289/4 has completed the left hand side into a perfect square :

x2-17x+(289/4) =

(x-(17/2)) • (x-(17/2)) =

(x-(17/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-17x+(289/4) = 49/4 and

x2-17x+(289/4) = (x-(17/2))2

then, according to the law of transitivity,

(x-(17/2))2 = 49/4

We'll refer to this Equation as Eq. #3.2.1

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

(x-(17/2))2 is

(x-(17/2))2/2 =

(x-(17/2))1 =

x-(17/2)

Now, applying the Square Root Principle to Eq. #3.2.1 we get:

x-(17/2) = √ 49/4

Add 17/2 to both sides to obtain:

x = 17/2 + √ 49/4

Since a square root has two values, one positive and the other negative

x2 - 17x + 60 = 0

has two solutions:

x = 17/2 + √ 49/4

or

x = 17/2 - √ 49/4

Note that √ 49/4 can be written as

√ 49 / √ 4 which is 7 / 2

Solve Quadratic Equation using the Quadratic Formula

3.3 Solving x2-17x+60 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -17

C = 60

Accordingly, B2 - 4AC =

289 - 240 =

49

Applying the quadratic formula :

17 ± √ 49

x = —————

2

Can √ 49 be simplified ?

Yes! The prime factorization of 49 is

7•7

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 49 = √ 7•7 =

± 7 • √ 1 =

± 7

So now we are looking at:

x = ( 17 ± 7) / 2

Two real solutions:

x =(17+√49)/2=(17+7)/2= 12.000

or:

x =(17-√49)/2=(17-7)/2= 5.000

Two solutions were found :

x = 12

x = 5

Step-by-step explanation:

please mark my answer in brainlist

Multiply the amount per week by the number of weeks (x) and add that to the starting amount they had. Set those to equal each other and solve for x:

222 + 10x = 148 + 12x

Subtract 10x from both sides:

222 = 148 + 2x

Subtract 148 from both sides

74 = 2x

Divide both sides by 2

X = 37

Answer: 37 weeks

Step-by-step explanation:

given points,

(0,-5) and (2,5)

we know,

slope = y2 - y1 / x2 - x1

→ 5 - (-5) / 2 - 0

→ 5+5/2 = 10/2

→ 5

therefore, slope of the line is 5.

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Answer:

circle, triangle, rectangle

Answer:

the first cross section would make a circle (option 2, the second would make a triangle (option 6), and the last one would make a rectangle (option 1). hope this helps!

Answer:

3 dollars per can

Step-by-step explanation:

divide 6 by 2

Answer:

107 adults 16 children

Step-by-step explanation:

can i get brainlest

Answer:

5a+2b+b-2a

5a-2a+2b+b

3a+3b

Answer:

the building is aged and unique.

Answer:

  both ends tend toward negative infinity

Step-by-step explanation:

The ends of an even-degree polynomial go in the same direction. The sign of that direction matches the sign of the leading coefficient.

Here, the leading coefficient is negative, so ...

  y → -∞   when   x → ±∞

I believe it is a because I had a question just like that in 8th grade

Answer:

2195

Step-by-step explanation:

filler filler filler lol

Answer: 2,195

Step-by-step explanation:

439x5

9x5=45

3x5+4=19

4x5+1=21

2195

Answer:

  y = 5

Step-by-step explanation:

The base angles of this isosceles triangle are congruent, so the angle at A is ...

  A = 180° -2(75°) = 30°

  (4y +10)° = 30° . . . . . substitute the given expression for angle A

  4y = 20 . . . . . . . . . . divide by °, subtract 10

  y = 5 . . . . . . . . . divide by 4

_____

Additional comment

The value of x is 25.

x is found from 3x=75, by dividing both sides of this equation by 3.

Answer:

4 2/3

Step-by-step explanation:

Answer:

3b

Step-by-step explanation:

[tex]3\sqrt{b^{2} }[/tex]

= 3b

Answer:y=2.5x+5 i thank

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

Step-by-step explanation:

The dog is 75 pounds

1 pound requires 4 mg

75 pounds requires 4*75 = 300 mg

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 1.25\%\to \frac{1.25}{100}\dotfill &0.0125\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (500)(0.0125)(3)\implies \boxed{I = 18.75}[/tex]

Answer:

D

Step-by-step explanation:

-1.25 is less than -1.02 and 1.4.

> -1.25 + 1.02 = -0.23

1.4 is a greater amount because it is a positive number

So, if you put it this way, -1.25 is lesser, -1.02 is the 2nd least, & 1.4 is the greatest.

Which means your overall answer should be -1.25 < -1.02 < 1.4

Answer:

The answer is slope: -32 y-intercept:480

Step-by-step explanation:

I took the test

Answer: slope -32 y-intercept 480

Step-by-step explanation:

Took the k12 test

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As we know,

and

now, let's add them as shown ~

Answer: C

Step-by-step explanation: