If PQRS ~ WXYD, find the value of x.
(If possible, show step-to-step)

Five different ways to prove the given triangles are similar is given by :

SAS, SSS, ASA, AA, and RHS.

Five different ways to prove triangles are similar is given by:

1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.

2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle

3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.

4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.

5.  RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.

Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.

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Answer:

1st and 3rd 4th

graph of f(x) = x² - 12x-45 has an x-intercept at x = -3

-3 is a zero of the function f(x) = x²-12x- 45

x + 3 is a factor of x² - 12x-45

Steps:

other solution is (x - 15) or x = 15

x² - 12x-45

2 numbers that when multiplied give -45 & when added give -12 are -15 & 3

(x-15) (x+3)

"zero" is a fancy way for asking for the answer or root

imaginary number is i which is √-1 so

if you have √-9 = √9 * √-1 = 3i

if you have √-20 = √4 * √-1 * √5 = 2i√5

.

The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.

An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.

The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Let the length is given as, l = √24 and,

The width is given as, w = √10

Use the formula of area of rectangle,

A = lw

A = √24 × √10

A = 4.89 × 3.16

A = 15.45 ≈ 15 square units.

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In Parallelogram: Area = base x height(perpendicular distance).

In rectangle: Area = base x height.

Parallelogram:

A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.

Area = base x height(perpendicular distance)

Rectangle:

Area = base(length) x height(width).

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Answer:

9.6

Step-by-step explanation:

What is the mean of the following data set 4 8 11 12 13?

Mean: is the average of values so:

(4 + 8 + 11 + 12 + 13) / 5 = 9.6

The equation of the quadratic function is (c) f(x) = 3(x - 1)² - 2

From the question, we have the table of values that can be used in our computation:

A quadratic equation is represented as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have the vertex to be

(h, k) = (1, -2)

Substitute (h, k) = (1, -2) in f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 1)² - 2

Also, from the graph, we have the point (0, 1)

This means that

a(0 - 1)² - 2 = 1

So, we have

a(1) = 3

Divide both sides by 1

a = 3

Substitute a = 3 in f(x) = a(x - 1)² - 2

f(x) = 3(x - 1)² - 2

Hence, the equation is f(x) = 3(x - 1)² - 2

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Answer:

11111111111111111111

The median is the exact middle number in a sequence or set of numbers.

Steps to find the median is given below:

Finding the Median in an Odd Set of Numbers:

Step 1: Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.

Step 2: Find the number that is exactly in the middle. This means that the median number has the same amount of numbers in front of it as it does behind it.

Finding the Median in an Even Set of Numbers

Step 1: Sort out your set of numbers from least to greatest. An even set of numbers is going to have two numbers exactly in the middle.

Step 2: Find the average of the two numbers in the middle. If 2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.

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Answer:

first one and second one

Step-by-step explanation:

x + y is lesser or equal to 20

20 being the max amount of hours he can work in one week and x and y being hours he works

second one because they can earn at least 300 dollars, not less than, but x+Y must still be less than 20 though

D.

The line never increases, so we can cancel out A and C.

The line starts off straight, so it's not B.

So, the answer is D. since it starts off constant and then decreases sharply.

We need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

We u can move, flip, twist, and turn these triangles to produce the same effect.

When relocated, they are parallel to one another.

Two triangles are deemed similar by the SSS test for triangle resemblance if their third sides are proportionate to one another.

Therefore, we need to draw all sides of the triangle equal in order to make a SSS triangle because we know that the SSS triangle has all 3 sides equal.

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Step-by-step explanation:

A triangle AAA does not satisfy congruence theorem. Triangle denoted by AAA refers a triangle having three equal side lengths and three equal angles.

Congruence theorem is developed based on two triangles which have equal corresponding side lengths and equal corresponding angles.

there are four criteria in where one or more criteria needed to satisfy. if two triangles have all three equal side lengths and equal corresponding angles then they satisfy congruence theorem. if two triangles have 2 equal side lengths and angle between sides are equal, they satisfy congruence theorem. If two triangles have equal two angles along

with equal similar side length, they satisfy congruence theorem.

hence, the triangle mentioned in the question is not congruent.

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Answer:

FALSE

Step-by-step explanation:

The angles can be the same, but the lengths of the sides can differ.

Answer:

Step-by-step explanation

In the first equation

x=17-4y

In the second equation

We clear "x"

y=x-2

x=y+2

We ecuate "x"

x=17-4y=y+2

17-4y=y+2

15=5y

y=3

we substitute to find "x"

x=17-4y=17-4(3)=5

Yes , the equation 3x² + 11x + 10 = 0 is a quadratic equation and the roots are x = -5/3 and x = -2

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c = 0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

3x² + 11x + 10 = 0   be equation (1)

Now , the equation is of the form ax² + bx + c = 0 , where the value of a = 3 , b = 11 and c = 10

So , the coefficient a is has the variable x² and equation 3x² + 11x + 10 = 0 is a quadratic equation

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -11 ± √ ( ( 11 )² - 4 ( 3 ) ( 10 ) ) ] / 2 ( 3 )

On simplifying the equation , we get

x = [ -11 ± √ ( 121 - 120 ) ] / 6

x = ( -11 ± 1 ) / 6

So , the two roots of the equations are

x = ( -11 - 1 ) / 6 and

x = ( -11 + 1 ) / 6

x = -2 and

x = -5/3

Therefore , the values of x are -5/3 and -2

Hence , the roots of the quadratic equations are -5/3 and -2

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Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.

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Hence, the standard deviation of the given data is 7 .

10 28 13 18 29 30 22 23 25 32

Here is the total number of observations n are 10

total= 10 +28+ 13+ 18+ 29+ 30+ 22+ 23+ 25+ 32 = 230

mean  (μ) = total/n

         = 230/10

         = 23

         Xi                 Xi-μ                    (Xi-μ)²

         10           10-23=-13                   169

         28           28-23=5                      25

          13           13-23=-10                   100

          18           18-23=-5                      25

          29           29-23=6                      36

          30          30-23=7                       49

           22         22-23=-1                         1

            23         23-23=0                        0

           25          25-23=2                         4

            32          32-23=9                       81

Use the formula to calculate the standard deviation.

√1/n*∑   (Xi-μ)² =√1/10*490

                        = √49

                         =7

Hence, the standard deviation of the given data is 7 .

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Negative infinity is a concept that has no direction and function. It is the lowest possible number and is represented by the symbol "-∞".

Negative infinity is the lowest possible number, meaning there is no lower number than negative infinity. It is a concept that has no direction, meaning it is not a specific point on a number line. It is represented by the symbol "-∞", which can be thought of as a point before the beginning of the number line. Negative infinity is an abstract concept, but it is still used in mathematical operations. For example, if you have a set of numbers that contains negative infinity, then the sum of all the numbers in the set will be negative infinity. This is because negative infinity is the lowest possible number, so no matter how large the other numbers in the set are, the sum will always be lower than all of them.Negative infinity can also be used to represent undefined limits. For example, if you are looking at a graph of a function, and the y-axis goes to negative infinity, then the limit of the function at that point is undefined. This is because there is no lower number than negative infinity, so the limit cannot be determined.Negative infinity is a concept that can be confusing, but it is an important part of mathematics. It is used to represent the lowest possible number, as well as undefined limits. It is represented by the symbol "-∞" and has no direction.

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The x and y intercept of y=3x-15 is X intercept  is 5, Y interceptis -15

To find X intercept substitute y=0

y=0

0=3x-15

3x=15

x=15/3

x=5

X intercept  is 5 line cuts at (5,0)

To find Y intercept substitute x=0

y=3(0)-15

y=-15

Y interceptis -15 line cuts at  (0,-15)

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Yes, 5 is the high standard deviation which is considered very good.

85 persons responded to my survey about their capacity to carry out specific duties.

The responses are rated on a Likert scale of 1 to 5:

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898 integers in that range excluding 100 and 999

There are 900 integers between 100 and 999, inclusive.

Numbers between 999 and 100 inclusive:  999 - 99 = 900

If you want to know the number of integers between 100 and 999, but not including either 100 or 999, then there are 898 integers in that range.

What is an integers number:

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. Integers include things like -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that consists of the following:

Positive Numbers: If a number is greater than zero, it is considered positive. For instance, 1, 2, 3, etc.

Negative numbers are those that are less than zero. For instance: 1, 2, 3, etc.

Zero is described as being neither a positive nor a negative number. A whole number, that is.

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The length of the guy wire, to the nearest foot, is 201 ft.

Refer to the diagram attached below for the given information

We have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 4 ft

BD = 32 ft

Length of the guy wire (AE)

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

Plug in the values:

AB/11 = (32 + 4)/2

AB/11 = 36/2

Cross multiply:

AB = (36 × 11)/2

AB = 198 ft

Apply Pythagorean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(198² + 36²)

AE = 201 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is 201 ft.

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We have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 4 ft

BD = 32 ft

Length of the guy wire (AE)

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

AB/11 = (32 + 4)/2

AB/11 = 36/2

AB = (36 × 11)/2

AB = 198 ft

AE = √(AB² + BE²)

AE = √(198² + 36²)

AE = 201 ft (nearest foot)

A- The maximum vertical distance from the water surface to the diver’s

shoulders are 12.061 meters.

B- The time that the diver’s shoulders enter the water is 1.936 seconds.

C- The total distance traveled by the diver’s shoulders from the time

she leaps from the platform until the time her shoulders enter the water is 12.946 meters.

D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.

A-  

[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]

The maximum vertical distance from the water surface to the diver’s

shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.

B-

[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]

when A= 1.936 seconds.

C-

[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]

At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]

D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]

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Answer:

I think 11 trips to New York because it's a popular tourist attraction.

Answer:

Step-by-step explanation:

you can use the zero-product property to find the roots of a factored equation. After you factor a polynomial into its different pieces, you can set each piece equal to zero to solve for the roots with the zero-product property.

Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons

The data of the sugar solutions are;

The volume of 5% sugar solution Kate has = 3 quarts

The volume of the 12% sugar solution = X

Let 'Y' represent the volume of the 8% sugar solution, we have;

The volume of the resultant solution, Z = X + Y + 3

The concentration of the resultant solution = 10%

0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)

Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, we have;

X = (2 × 2 + 15)/2 = 9.5 Quartz

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Answer: slope= change in y-intercept and x-intercept

Step-by-step explanation:

1-9=-8

-8- -9=1

-8/1=-8

The factors of the quadratic equation 3x² -4x -4 are (3x + 2)(x - 2)    .

The process of factoring the quadratic equation means expressing the given equation as the product of two linear factors.

The quadratic expression is given as 3x² -4x -4 ;

it can be written as ⇒ 3x² -6x +2x -4    ,...by using split the middle term method .

⇒ 3x(x - 2) + 2(x - 2) ..taking 3x common from first two terms and 2 common from the last two terms .

⇒ (3x + 2)(x - 2)

Therefore , the factors are (3x + 2)(x - 2)  .

The given question is incomplete , the complete question is

What are the factors of the quadratic equation 3x² -4x -4 ?

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five plus eight times nine

Answer:

x=12

Step-by-step explanation:

3x+7 = 5x-17

-2x=-24

x=12

Hope this helps you can thank me if this helps and 5 star if you dont mind :)

Answer:

x=12

Step-by-step explanation:

The two sides must be equal in length

3x+7 = 5x-17

Subtract 3x from each side

3x-3x+7 = 5x-3x-17

7 = 2x-17

Add 17 to each side

7+17 = 2x-17+17

24 = 2x

Divide each side by 2

24/2 = 2x/2

12 =x