What is the first step in a 2 step equation?

The short leg of a 30-60-90 triangle is 1/2 the length of the hypotenuse. 30-60-90 triangle is the half of an equilateral triangle.

Right triangles with 30-60-90 interior angles are called special right triangles.

A 30-60-90-degree triangle is a special right triangle and its side lengths are always consistent with each other. The ratio of the sides follows the 30-60-90 triangle ratio: 1: 2: [tex]\sqrt{3}[/tex] .

Short side (opposite the 30° angle) = x

Hypotenuse (opposite the 90° angle) = 2x

Long side (opposite the 60° angle) = x√3

30-60-90 Triangle Theorem:

These three properties can be examined by the 30-60-90 triangle theorem and are unique to these special right triangles:

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that usually means that word has a definition that will be given at the bottom of the page or in the glossary depending on what type of book or excerpt of text you have.

hope this helps!

if n is a positive integer: 1²+ 2² + 3² + ... +n² = 1/6n(n+1)(2n+1)​ IS 1

P(n) :

1²+ 2² + 3² + … +n² = 1/6n(n+1)(2n+1)​

P(1) :

[tex]1^2=\frac{1(1+1)(2(1)+1)}{6}[/tex]

[tex]1=\frac{6}{6}=1[/tex]

∴ LHS = RHS

Assume P(k) is true

P(k):

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Answer:

-1 - 3/(5 - 2x)

Step-by-step explanation:

f/g (x) =

f(x) / g(x) =

(2x − 3) / (5 - 2x) =  ==> plugin 5 - 2x for g(x) and 2x − 3 for f(x)

              -1 - 3/(-2x + 5)

-2x + 5 | 2x - 3

        + (-2x)

               0 - 3

Answer: -1 - 3/(5 - 2x)

Consequently, the solution of the given question of probability comes out to be  P(x<5.67 = 0.63

Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Here,

we use the z-score algorithm to answer this query.

Score Z = x - 40/5

x = the raw score

 population mean= μ 

Population standard deviation is σ

Hence,

x = 40  μ = 5.67, σ =5

Z = 5.67 - 40/5

z=0.37

Probability based on the Z-Table:

P(x<5.67 = 0.63

Consequently, the solution of the given question of probability comes out to be  P(x<5.67 = 0.63 .

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The equation of the parabola after the translation is:

g(x) = (x - 7)^2

We know that we start with a parabola of the form:

y = x^2

Now we know that the parabola has been translated 7 units to the left.

Remember tht for a general function y = f(x), a horizontal translation of N units is written as:

g(x) = f(x + N)

So a translation of 7 units to the left is written as:

g(x) =f(x - 7)

g(x) = (x - 7)^2

That is the equation of the parabola after the translation.

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The linear equation for jj is ($7.46 - $2.66) / 5 and the cost of each bottle of juice is $0.96.

What in mathematics is a linear equation?

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 step to take in order to determine jj, is to determine the total cost of the  5-pack of juice bottles.

Cost of the  5-pack of juice bottles = Total cost before tax - cost of the bag of oranges

Cost of the  5-pack of juice bottles = $7.46 - $2.66 = $4.80

The second step is to determine the cost of each bottle of juice

The cost of each bottle of juice = Cost of the  5-pack of juice bottles / total number of bottles

$4.80 / 5

= $0.96

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She can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter

In the given question, Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter.

We have to find how many pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter.

The radius of a ball of yarn six inches in diameter is

r = 6/2 = 3 inches

The radius of a ball of yarn twelve inches in diameter is

r = 12/2 = 6 inches

Now, the volume of the six inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]

The volume of the six inches yarn = [tex]\frac{4}{3} \pi (3)^3[/tex]

The volume of the six inches yarn = 36π

Now, the volume of the twelve inches yarn = [tex]\frac{4}{3} \pi r^3[/tex]

The volume of the twelve inches yarn = [tex]\frac{4}{3} \pi (6)^3[/tex]

The volume of the twelve inches yarn = 288π

Now we finding the numbers of pairs of identical mittens she can knit with a ball of yarn twelve inches in diameter

= 288π/36π

= 8

Hence, she can knit total 8 pairs of identical mittens with a ball of yarn twelve inches in diameter.

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Answer: There are 30 cubes in each layer and 3 layers. (Up to down.)

Explanation: You can multiply the x and y axis for one layer, and then count how many layers there are. There are 90 cubes in all.

I hope this helps, have a good day!

y = 4 is a horizontal line.

The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

Now, According to the question:

Let's know:

What is Horizontal lines?

If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.

The equation is y = 4.

The graph of the equation y=4 is a horizontal line. It is function since each x is mapped to one y or each element of the domain is mapped to only one element of the range. It also passes the vertical line test.

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The complete question is this :

Is y = 4  a vertical line?

Answer:

-65

Step-by-step explanation:

Median = middle number

-76, -74, -67, -65, -63, -58, -48

out of the numbers I am shown, from the photo, I would say "-65" is the answer, but if there is another number I'm missing, add it to the row of numbers above and add the two numbers together and divide by 2

I hope this helps!

Answer:

The fourth one could not represent the three sides of a triangle

Step-by-step explanation:

because the two sides of the triangle must be larger together than the third side and 7+16=23<24, so the fourth one could not represent the three sides of a triangle.

Answer:

C

Step-by-step explanation: The third one down. There are two ways you know this.

1. If you had two boards that where 6 cm and 20 cm and tried to make a triangle with the third side = 27, the two little boards would lie flat on the 27 cm board.

2. The other three answers all make the smaller two sides larger than the third larger side.

A value of 20 would fit the best in the table's empty cell to imply that there is no proof of a link between the variable and the outcome.

Option c is accurate.

The pattern between the supplied series must be found in order to determine the missing number. Verify that the series only shows increases, decreases, or both. The difference between two numbers should then be checked; this will help you discover the pattern.

To locate the missing numbers, the candidate must first identify the pattern or relationship between these numbers and then apply it.

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The required value of x is 17 for the given equation 11 = x - 6.

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:

11 = x - 6

We can determine the value of x by adding 6 to both sides of the equation.

As per the question, we have

⇒ 11 = x - 6

⇒ 11 + 6 = x - 6 + 6

⇒ x = 11 + 6

Apply the addition operation, and we get

⇒ x = 17

Therefore, the required value of x is 17.

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The classification of the transformations based on the properties are presented as follows;

[tex]\begin{array}{|c|c|c|} & \mathbf{Preserves \ length} & \mathbf{Does \ not \ preserve \ lengths} \\\mathbf{Preserves \ angle \ measure} & Reflection\ Rotation &Translation \ followed \ by \ dilation \\&&Dilation \ with \ K > 1\\\mathbf{Does \ not \ preserve \ angle \ meas} & & \\\end{matrix}[/tex]

The transformations that preserves the lengths of the original figure or pre-image and also preserves the angle measure is a rigid transformation.

Rigid transformations includes; Reflections, rotations, and translations

Transformations that preserves the angle of measure but in which the lengths of the preimage is not preserved are non-rigid transformations

Non rigid transformations includes; Dilation with a scale factor

Transformations that does not preserve the angle measure includes; Shear transformation

A translation and a dilation transformation does not preserve the lengths of the original figure.

The classification of the transformations based on their properties are therefore presented as follows;

[tex]{}[/tex]                               Preserves lengths      Does not preserve lengths

Preserves               Reflection              [tex]{}[/tex]    Translation followed by dilation

angle measure       Rotation                   [tex]{}[/tex]  with k > 1

                                                          [tex]{}[/tex]        Dilation with k > 1

Does not              

Preserve angle

measure

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For the provide inquilty problem,

a) The feasible region lies in between the following equations,

b) The extreme points of feasible region are (2,5) , (6,1) ,(0,0),(6,0),(0,5).

Let consider, x = A and y = B, this changes your inequalities and equations as follows: Maximize x + 2y, such that:

x ≤ 6

y ≤ 5

2x + 2y = 14

x,y ≥ 0

We use graphical method, for getting the solution of problem. So, first change the Inequalities into equality equations.

we would then find the region of feasibility by looking at the areas on the graph that satisfy the inequalities and equations,

x ≤ 6

y ≤ 5

2x + 2y = 14 (this is an equation)

x ≥0

y ≥ 0

a) The graph will look like as present above : we can see that the feasible region is the area on the graph that is:

on or below the line y = 5

on or to the left of the line x = 6

on or above the line y-axis , y = 0

on or to the right of the x-axis, x = 0

on the line 2x + 2y = 14

This says is that your solution has to be on the line of 2x + 2y = 14, have an x-coordinate that is greater than or equal to 0 and less than or equal to 5 and have a y-coordinate that is greater than or equal to 0 and less than or equal to 5. The maximum or minimum value should be at the corner points of the feasible region.

b) The corner points would be at (x,y) = (2,5) and (x,y) = (6,1). Also, plotted some other points on the line just to show the max/min value of function on the corner points of the feasible region.

(2,5) = 12

(4,3)= 10

(3,4) = 11

(6,1) = 8

the maximum solution is at the coordinate of (2,5) and all of your constraints have to be satisfied at the this point. The solution is that the maximum value is when x = 2 and y = 5, that is one of the corner points of the feasible region.

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Complete question:

Consider the following linear program:

Max. 1A+2B , s.t.

1A ≤6

1B≤5

2A+2B=14

A,B>0

a. Show the feasible region.

b. What are the extreme points of the feasible region?

probability of landing on heads - 49 %

Answer:

49%

Step-by-step explanation:

Check the picture below.

No, an isosceles triangle is not always 60 degrees. The angles of an isosceles triangle must be equal, but the overall measure of the angles can be any value greater than 0 degrees.

A triangle having two equal sides and two equal angles is known as an isosceles triangle.. The equal sides create two equal angles that are opposite each other. The two equal angles are the only two angles that define an isosceles triangle. There is no specific measure for the angles of an isosceles triangle, so the angles do not necessarily have to be 60 degrees and The angles can be any value greater than 0 degrees. The two equal angles, however, must be equal in measure to make the triangle an isosceles triangle. Therefore, an isosceles triangle is not always 60 degrees.

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The equation and the answer of this question is 1.20 + 3.25x = 40.20, x = 12

According to the information that has been provided to us, the cost that the taxi company charged was $1.20, in addition to $3.25 per mile, for a total fare of $40.20.

Therefore, the equation would be:

1.20 + 3.25X = 40.20

To find the distance from Zoey’s house to the airport we need to calculate the value of X

1.20 + 3.25X = 40.20

3.25X = 39

X = 39 : 3.25

X = 12 miles

As a result, the distance from the house to the airport would be around 12 miles.

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Answer: o.7619

Step-by-step explanation: i used the standard algorithm i am sorry i cant do a more in depth just hard to do with words ;)

Answer: 0.7619

:)

Step-by-step explanation:

0.01 is not the way of expressing the relationship because it does not represent the correct ratio between 10 square and 100 square

A ratio tells the relationship between two or more quantities by comparing their relative sizes.It is typically written as two or more numbers separated by a colon (:), such as 2:4, or expressed as a fraction, such as 2/4. The numbers in a ratio represent the relative amounts of the quantities being compared. A ratio can be used to compare any type of quantity, such as length, weight, or time.

A) 10 square is 1/10th of the area of 100 square. It can be represented as a fraction, where the numerator is the area of the smaller square (10) and the denominator is the area of the larger square (100). The fraction would be 1/10.

B) Another way of expressing the relationship is as a percentage, where the smaller area (10) is divided by the larger area (100), and the result is multiplied by 100 to get the percentage. So 10 square is 10% of 100 square.

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To solve the equation 5 = v + 29, you can subtract 29 from both sides of the equation. This will isolate the variable on one side of the equation and allow you to find its value.

The given equation is

5 = v + 29

Subtract 29 from both sides:

5 - 29 = v + 29 - 29

-24 = v

So the solution is v = -24.

So, we subtract 29 from both sides of the equation, this operation cancels out the addition of 29 from the variable v, and we get -24 = v. This means that -24 is the value that makes the equation true.

--The question is incomplete, answering to the question below--

"How do you solve 5 = v + 29?"

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Answer: N= x24 over 3

Step-by-step explanation:

Answer:

Bonjour is the bonjour of qui

Step-by-step explanation:

Points points

The value of the other leg of the right triangle will be 13 units. Then the correct option is C.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

A right triangle with hypotenuse 85 and legs 84 and y. Then by the Pythagoras theorem, the value of the variable 'y' is calculated as,

85² = y² + 84²

Simplify the equation, then we have

85² = y² + 84²

7225 = y² + 2056

y² = 7225 - 2056

y² = 169

y = 13

The value of the other leg of the right triangle will be 13 units. Then the correct option is C.

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On solving the provided question, we can say that by having the equation 15 attendees were at the party

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x = number of attendees

[tex]2x[/tex] + 20 = number of slices 5(x-5) = [tex]2x[/tex] - 20

[tex]5x[/tex] - 25 = [tex]2x[/tex] + 20

[tex]3x[/tex] = 45

[tex]x[/tex] = 15

[tex]2x[/tex] + 20 = 50 slices

15 attendees

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The slope of the line is 40 if the points are joined.

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:

Take two points from the graph as (2, 80) and (4, 160)

Then, the slope of line is

slope, m = ( 160- 80) / ( 4- 2)

slope, m = 80 /2

slope , m = 40

Hence, the slope is 40.

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Answer: 215

Step-by-step explanation: