How To Solve The Congruency Of Triangle MNO And Triangle XYZ Using A Reflection Across The Line Bisecting (2024)

Answer:Let, one leg be x units.

since the other leg is 9.0 units shorter than the other,

the measure of the other leg =x-9

hypotenuse =13.0 units

According to Pythagorean theorem, the square of the hypotenuse is equal to the sum of squares of the other two sides.

x^2 +(x-9)^2 =13^2

x^2 + x^2 -18x +81 = 169

2x^2-18x-88=0

Divide the whole equation by 2

x^2 - 9x -44 =0

Let's use the quadratic formula to find the roots.

formula: x= [-b ± sqrt(b^2-4*a*c)]/2*a

a=1 b=-9 c=-44

x= [9±sqrt(81+176)]/2

=[9±sqrt(257)]/2

=[9±16.03]/2

=25.03/2 or -7.03/2

length of a triangle cannot be negative,

Therefore, x=25.03/2 =12.52

one leg =12.5 units

other leg =12.52-9 =3.5 units

Step-by-step explanation:

A statement that best explains the paradox that occurs to Alexia at the end of the passage is she realizes that the reward is not worth the cost. The Option A is correct.

The Excerpt from the Passage of "Virtual Reality":

“Hey, Sis,” Eric answered after two rings, shouting over loud music in the background. “Where’ve you been? Why didn’t you return my calls?”

“Sorry, Eric,” Alexia bit her lip guiltily. “I’ve been really busy.”

“Well, I’m sorry too,” Eric replied, “because my old band just asked me to sit in on their weekend shows and I won’t be able to see you at all now.”

Alexia’s heart plummeted. “Oh, Eric, can’t I come see you?”

“No, we’re traveling around the state,” Eric said. “I won’t be back home from school again until spring. I hope whatever was keeping you so busy was worth it. I miss you, Lex.”

As Alexia said goodbye, she noticed that her likes had topped 5,000. She had won, but somehow, she didn’t feel victorious at all.

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Therefore , the solution of the given problem of linear equation comes out to be x= 2 and y=0.

How a linear equation is defined ?

A model of linear regression is one that applies the formula y=mx+b. B is the slope, and m is the y-intercept. Despite the fact because both y and x are distinct components, the previous sentence is frequently referred to it as a "mathematical formula with two variables." Bivariate linear equations only have two variables. The application domains of linear equations have zero solutions in all cases. The equation for a solitary linear equation is Y=mx+b, where m stands for the elevation and b for the y-intercept. Y=mx+b, where m stands for slopes and b for the y-intercept, is how the equation is expressed.

Here,

Given :

=> y = 4x -8

=> 4y=4x−8 ​ or y = x -2

So,

=> y =4x-8

Thus,

=> 4x -8 = x-2

=> 3x =6

=> x =2

and

=> y = 8-8 =0

Therefore , the solution of the given problem of equation comes out to be x= 2 and y=0.

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Each type of commercial spray is needed to get the desired mixture is,

⇒ spray x: 10,

⇒ spray y: 5,

⇒ spray z: 12

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now,

Let, a - number of gallons of chemical A

b - number of gallons of chemical B

c - number of gallons of chemical C

x - number of gallons of spray x

y - number of gallons of spray y

z - number of gallons of spray z

So, We can formulate;

CHEMICAL SPRAY X SPRAY Y SPRAY Z

a = 6 = 1/5x + 0y + 1/3z

b = 8 = 2/5x + 0y + 1/3z

c = 13 = 2/5x + y + 1/3z

So:

1/5x + 1/3z = 6

2/5x + 1/3z = 8

2/5x + y + 1/3z = 13

Multiply the first equation by (-1) and add it to the second equation;

⇒ - 1/5x - 1/3z = - 6

2/5x + 1/3z = 8

____________

1/5x = 2

x = 2 × 5

x = 10

From here:

1/5x + 1/3z = 6

Put x = 10;

1/5 × 10 + 1/3z = 6

2 + 1/3z = 6

1/3z = 4

z = 4 × 3

z = 12

⇒ 2/5x + y + 1/3z = 13

Put, x = 10, z = 12

2/5 × 10 + y + 1/3 × 12 = 13

4 + y + 4 = 13

8 + y = 13

y = 13 - 8

y = 5

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Step-by-step explanation:

Let's call the width of the rectangle "w".

The length of the rectangle is 7w - 16.

The perimeter of the rectangle is 48, so:

2w + 2(7w - 16) = 48

Expanding the second term:

2w + 14w - 32 = 48

Combining like terms:

16w = 80

Dividing both sides by 16:

w = 5

So the width is 5 inches.

To find the length, use the formula for the length:

7w - 16 = 7 * 5 - 16 = 24 - 16 = 8

The length is 8 inches.

Therefore, the answer is:

B. 8 inches.

To calculate the state income tax owed on a $50,000 per year salary, we need to apply the progressive tax rate based on the income range.

What does money interest mean?

You pay interest on any loans or borrowings of money. the portion of the loan's value that lenders use to calculate interest. Consumers can earn interest by lending money (via a bond or certificate of deposit, for example), or by putting money into an interest-bearing bank account.

The first $10,000 of the salary will be taxed at 3%, the next $40,000 (from $10,001 to $50,000) will be taxed at 5%, and the remaining $0 will be taxed at 5.5%

Tax on first $10,000 = $10,000 x 3% = $300

Tax on next $40,000 = $40,000 x 5% = $2,000

Tax on remaining $0 = $0 x 5.5% = $0

Total tax owed = $300 + $2,000 + $0 = $2,300

Therefore, the state income tax owed on a $50,000 per year salary is $2,300.

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Diagram C does not depict a function, according to the idea of function.

What is meant by function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x.

Therefore,

Each input value of a function can be connected to a single output value.Only one line can exit the diagram from each value entered in the input.Diagrams A, B, and D are functions since each input value has a single corresponding value on the output for each of these three diagrams.Diagram C's input 7 is mapped to outputs 8 and 12, i.e., one input is mapped to two outputs, indicating that the diagram is not a function.

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The length of EF is 10.63 units.

What is Distance Formula?

The formula to find the distance between the two points is usually given by d=√((c – a)² + (d– b)²).

This formula is used to find the distance between any two points on a coordinate plane or x-y plane.

Given:

From the graph the coordinates of E( -3, -4) and F(4, 4).

Using Distance Formula

EF = √ (4 - (-3))² + ( 4 -(-4))²

EF = √ (4+ 3)² + (4+4)²

EF = √ 7² + 8²

EF = √ 49 + 64

EF = √113

EF = 10.63 units

Hence, the length of EF = 10.63 units

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By subtracting 42 in both sides of the equation, we will get:

k = -45

Thus the correct option is B.

What inverse operation should be used to solve the equation for k?

We want to solve the following equation:

42 + k = -3

To solve this equation, we need to isolate the variable k in that equation.

To do so, we can just subtract 42 in both sides of the equation, then we will get:

42 + k - 42 = -3 - 42

(42 - 42) + k = -3 - 42

k = -45

That is the equation solved, we can see that the correct option is B.

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Answer:

B

Step-by-step explanation:

Answer:

a₆ = -13

Step-by-step explanation:

A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence. Therefore, when giving a recursive rule, we need to define the first term of the sequence, as it is not part of the formula.

Given recursive rule:

[tex]\begin{cases}a_1=7\\a_n=a_{n-1}-4\end{cases}[/tex]

To find the value of a₆, use the recursive formula to find the first 6 terms of the sequence:

[tex]a_1=7[/tex]

[tex]a_2=a_1-4=7-4=3[/tex]

[tex]a_3=a_2-4=3-4=-1[/tex]

[tex]a_4=a_3-4=-1-4=-5[/tex]

[tex]a_5=a_4-4=-5-4=-9[/tex]

[tex]a_6=a_5-4=-9-4=-13[/tex]

Therefore, the value of a₆ is -13.

The lateral surface area and total surface area of the given triangular prism are 252cm² and 348 cm² respectively.

What is lateral surface?

The entirety of an object's sides, excluding its base and top, are referred to as the lateral surface. The size of the lateral surface is referred to as the lateral surface area. The total surface area, which includes the lateral surface area as well as the areas at the base and top, should be distinguished from this.

Total surface area of this prism = 3 × l × b + 2 × h × b

= 3 × 14 × 6 + 2 × 8 × 6

= 348 cm²

And lateral surface area = 3 × l × b

= 3 × 14 × 6

= 252cm²

Thus, the lateral surface area and total surface area of the given triangular prism are 252cm² and 348 cm² respectively.

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The required solution to the given equation is x = 20. The correct answer would be an option (C).

What is the equation?

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

2(2x - 4) = 3(x + 4)

Apply the distributive property of multiplication,

4x - 8 = 3x + 12

Rearrange the likewise terms and apply the arithmetics operation,

4x - 3x = 12 + 8

x = 20

Thus, the required solution is x = 20.

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Answer:

Step-by-step explanation:

The domain of the function f(x) = 7^x is all real numbers.

A function's domain is the set of all input values (x-values) for which the function returns a valid result (y-value). The input value x for the function f(x) = 7x can be any real number. This is because the equation 7x is a real number and an acceptable output value for any real number x. As a result, the domain of f(x) = 7x is defined as (-infinity, +infinity).

It is worth noting that when x is a negative number, 7x is a fraction. In addition, when x is 0, 7x equals 1. And if x is positive, 7x will be bigger than zero.

In conclusion, the domain of f(x) = 7x is all real numbers since the function may take any real integer as input and output a valid result.

Appreciation is an increase in the value of an asset over time. The term is widely used in several disciplines, including economics, finance, and accounting.

How do you determine a house’s appreciation rate?

The easiest technique to calculate home appreciation is to divide the increase in value by the starting cost and multiply by 100 to get the difference as a percentage.

Final value minus initial value equals monetary change.

(Value change / initial investment) 100 represents the appreciation %.

1.0 N rate of appreciation)

2.0 N years equals the appreciation factor.

Appreciation value after N years = (appreciation factor)(current value).

The appreciation rate is the rate at which the value of an asset rises. An increase in the value of financial assets such as stocks is referred to as capital appreciation.

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Let x be the first number and y be the second number. We know from the given information that:

3x + 2y = 22

We also know that the sum of the two numbers is 9, so:

x + y = 9

To find the values of x and y, we can use a method such as substitution. We can solve one equation for one variable, and then substitute that expression into the other equation.

We can solve the first equation for y:

y = (22 - 3x)/2

Then substitute this expression for y into the second equation:

x + (22 - 3x)/2 = 9

Simplifying and solving for x, we get:

2x + 22 = 18

x = -2

Now that we know x = -2, we can substitute it back into the first equation to find y:

3(-2) + 2y = 22

y = 4

So the two numbers are x = -2, y = 4.

Answer: -0.333 repeating

Step-by-step explanation:

5/9 x -3/5 = -0.3 repeating decimal

Your answer for this would be -0.333 repeating decimal, which converts to ~-1/3 ! I hope this helps lol :)

An ordered pair which best represents the location of point R′ include the following: B. (−3n, −5n).

What is dilation?

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage (Triangle TRW) by using a scale factor of n centered at the origin as follows:

Ordered pair T (-3, 5) → Ordered pair T' (-3 × n, 5 × n) = Ordered pair T' (-3n, 5n).

Ordered pair R (-3, -5) → Ordered pair R' (-3 × n, -5 × n) = Ordered pair R' (-3n, -5n).

Ordered pair W (4, -5) → Ordered pair W' (4 × n, -5 × n) = Ordered pair W' (4n, -5n).

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Complete Question:

Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R′?

answer choices

(-3/n, -5/n)

(−3n, −5n)

(−3+n,−5+n)

(−3−n,−5−n)

Answer:

0.36km/

Step-by-step explanation:

speed= distance/time

14.4km/40min

= 0.36km/min

1/3 cup does not exceed 1/2 cup. While a half cup is equivalent to 8 tablespoons, a third cup is equivalent to 4 tablespoons. So, 1/3 cup is exactly 1/2 of a 1/2 cup. 1 / 5 < 1 / 3 < 1 / 2 .

Which is the bigger fraction 1 3 or 1 5?

The fact that 1/3 covers a larger portion of the whole than 1/5 is also extremely obvious. Therefore, 1/3 is greater than 1/5. No, a third of a cup does not equal a full cup. In comparison to a half cup, which is equal to 8 tablespoons, a third cup is equivalent to four. As a result, 1/3 cup is precisely 1/2 of a 1/2 cup. Half is bigger than thirds, hence one half is bigger than one third.

In strictly US volumetric culinary measurement terms, a third of a cup plus two tablespoons and two teaspoons equals exactly one cup. 1/3 cup plus 2 tablespoons and 2 teaspoons equals 1/2 cup in smaller proportions. It is possible to compare fractions with the same denominator by examining their numerators.

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Answer: 4,5, and 6

Step-by-step explanation:

Step-by-step explanation:

5f = 160+9c

f = {160+9c} ÷ 5

Answer:

r=8/3q-3/p

Step-by-step explanation:

9/p=8q-3r

9/p+3r=8q

3r=8q-9/p

3r/3=8q/3-(9/p)/3

r=8q/3-3/p

Answer:

after 42 months he has $2,696 in interest

compound quarterly is equivalent to annual rate of 4.835%

Part b

after 42 months he has $2,713 compound continuously

the diffrence is $17

15000 + 4.75% · 42 compound quarterly is $2,696

15000 + 4.75% · 42 compound continuously is $2,696

Answer:

Step-by-step explanation:

Stop posting FLVS questions on this website. It is illegal, and you can be expelled from the program. :)

The surface area of the cylinder with diameter 3 cm is 8.4 π cm²

What is a Cylinder?

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the first cylinder be A

Let the second cylinder be B

Now , the radius of first cylinder r₁ = 8/2 = 4 cm

The radius of second cylinder r₂ = 3/2 = 1.5 cm

Since the two cylinders are similar ,

Area of cylinder 1 / Area of cylinder 2 = ( r₁ / r₂ )²

Substituting the values in the equation , we get

60π / B = ( 4/1.5 )²

On simplifying the equation , we get

60π / B = 7.111

Multiply by B on both sides of the equation , we get

B = 60π / 7.11111

B = 8.4375 π cm²

Hence , the area of second cylinder B = 8.4 π cm²

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Answer:

About $1.45

hope this helps and I accept venmo

The statement " The sum of a negative and a positive number is a negative number " is false sometimes.

What is an integer?

A full number, not a fraction, that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer). Integer examples include: -5, 1, 5, 8

The statement " The sum of a negative and a positive number is a negative number " is false sometimes.

When positive number is bigger than the smaller one, sum can be positive

Example:

-4+3 = -1 ( statement is true, 3 is smaller )

but,

-4 + 6 = 2 ( statement is false, 6 is bigger)

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Answer:

[tex]AB=\sqrt{53}[/tex]

[tex]BC=\sqrt{265}[/tex]

[tex]CD=\sqrt{265}[/tex]

[tex]DA=\sqrt{53}[/tex]

ABCD is a kite.

Step-by-step explanation:

Given vertices of quadrilateral ABCD:

A = (4, 5)B = (-3, 3)C = (-6, -13)D = (6, -2)

To find the exact lengths of the sides of the quadrilateral, use the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}AB&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(-3-4)^2+(3-5)^2}\\&=\sqrt{(-7)^2+(-2)^2}\\&=\sqrt{49+4}\\&=\sqrt{53}\\\end{aligned}[/tex]

[tex]\begin{aligned}BC&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-6-(-3))^2+(-13-3)^2}\\&=\sqrt{(-3)^2+(-16)^2}\\&=\sqrt{9+256}\\&=\sqrt{265}\\\end{aligned}[/tex]

[tex]\begin{aligned}CD&=\sqrt{(x_D-x_C)^2+(y_D-y_C)^2}\\&=\sqrt{(6-(-6))^2+(-2-(-13))^2}\\&=\sqrt{(12)^2+(11)^2}\\&=\sqrt{144+121}\\&=\sqrt{265}\\\end{aligned}[/tex]

[tex]\begin{aligned}DA&=\sqrt{(x_A-x_D)^2+(y_A-y_D)^2}\\&=\sqrt{(4-6)^2+(5-(-2))^2}\\&=\sqrt{(-2)^2+(7)^2}\\&=\sqrt{4+49}\\&=\sqrt{53}\\\end{aligned}[/tex]

A kite has two pairs of adjacent equal sides.

Therefore, quadrilateral ABCD is a kite as:

AB is adjacent to DA and AB = DA.BC is adjacent to CD and BC = CD.

Answer:

4

Step-by-step explanation:

x is equals to 4

..........