Olving ytem of linear equation in two variable
1. 4x8y=24 2. 2xy=19 3. 3x2y=15
4x2y=12 x-y=11 x2y=10

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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The total distance traveled from 0 ≤ t ≤ 7, considering the position function x(t) = t³ - 6t² - 29, is given as follows:

288.75 units.

The position function for this problem is defined as follows:

x(t) = t³ - 6t² - 29.

The total distance traveled over an interval [a,b] is given by the definite integral of the function x(t) over the interval from x = a to x = b.

The definite integral in this problem is calculated as follows:

I = 0.25t^4 - 2t³ - 29t, from t = 0 to t = 7.

Applying the Fundamental Theorem of Calculus, the total distance is calculated as follows:

I = 0.25(7)^4 - 2(7)³ - 29(7) - (0.25(0)^4 - 2(0)³ - 29(0))

I = 288.75 units.

(which is the absolute value of the result of the definite integral).

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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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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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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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Marissa velocity while skateboarding is 162 meters per minute

An equation is used to show the relationship between numbers and variables.

Velocity is the ratio of displacement to time taken. It is a vector quantity (has magnitude and direction) and it is given by:

Velocity = displacement / time

Marissa travels 486 meters in 3 minutes, hence:

Velocity = displacement / time

Velocity = 486 m / 3 min = 162 meters per minute

The velocity is 162 meters per minute

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Answer: The correct answer is 2.7m/s

Step-by-step explanation:

I took the test

The volume of the cone is 50π cubic units .

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.

A cone has a circular base.

A cone has no edges, one face, and one vertex.

The length of the line segment from a cone's apex to any point around the circle of the cone's base is known as the slant height of the cone.

A right circular cone is a cone with its apex perpendicular to the base of the cone and directly above it.

An oblique cone is one that doesn't have its apex precisely over the base's circle.

Radius of the cone = 5

Height of the cone is 6

Volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] = [tex]\frac{1}{3}\pi *5^{2}* 6 = 50\pi[/tex] cubic units.

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer: The slope is 2.

Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.

We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.

Let me know if this is right! :)

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:

-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)

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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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?

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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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: 907.46 inches squared

Step-by-step explanation:

The formula for the area of the circle is:

[tex]A = \pi r^{2}[/tex]

In this question, pi is 3.14. The radius of a circle is half of its diameter. So:

[tex]\frac{34}{2} =17[/tex]

Plug these values into the equation:

[tex]A = (3.14)(17)^2[/tex]

Simplify:

[tex]A = 907.46[/tex]

The area of the circle is 907.46 inches squared.

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!

Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it

According to our question-

x is the quantity of oranges.

y is the quantity of apples.

Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.

Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.

0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).

x + y = 15

0.5x + 0.65y = 9.00

As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).

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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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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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When reflected in the y-axis, the image of the point (2/3) is (-2/3).

The sign of the x coordinate changes when a point is mirrored on the y-axis.

When a figure is built around a single point known as the point of reflection or the figure's centre, a reflection point results. There is an exact opposite point on the other side of each point in the figure. The shape and dimensions of the figure remain unchanged underneath the point of reflection.

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

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To find the mass of an object, one can use the formula (Force x Distance) / Gravitational Constant (FG). This formula involves multiplying the force applied to an object by the distance it moves, and then dividing the result by the gravitational constant (FG). The resulting number is the mass of the object in kilograms.

Mass can be found by using the formula (Force x Distance) / Gravitational Constant (FG).

For example, if a force of 10N is applied to an object that is moving 2 meters, the mass of the object can be calculated as follows:

Mass = (10 N x 2 m) / FG

Mass = 20 / 9.8

Mass = 2.04 kg

Finding mass using the force-distance formula (FG) is a simple process. To use it, one needs to know the force applied to an object, the distance it moves, and the gravitational constant (FG). The force and distance values can be measured or calculated depending on the situation. The gravitational constant is a fixed number and is equal to 9.8 m/s2. To calculate the mass, one needs to take the force multiplied by the distance and then divide it by the gravitational constant (FG). The resulting number is the mass of the object in kilograms. This formula is useful for calculating the mass of objects in a variety of situations. It is also useful for verifying the mass of an object that has already been measured.

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The number of coins of nickels and quarters will be 27 and 13, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters.

Let 'x' be the number of nickels and 'y' be the number of quarters. Then the equations are given as,

x = y + 14                               ....1

0.05x + 0.25y = 4.60             ....2

From equations 1 and 2, then we have

0.05(y + 14) + 0.25y = 1

0.05y + 0.70 + 0.25y = 4.60

0.30y = 3.9

y = 13

Then the value of 'x' is given as,

x = 13 + 14

x = 27

The number of coins of nickels and quarters will be 27 and 13, respectively.

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Answer: N= x24 over 3

Step-by-step explanation:

Answer:

He scored an average of 4.8 points per minute.

something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.

The inequality is x ≤ 35, where x represents the amount of gas in gallons.

This question means by the statement that we have been given that the number of gallons cannot exceed 35 so it actually means that they are either 35 or less than 35. so will use < = sign to come up with this equation.

You can have up to 35 gallons of gas at a time at the gas station. The inequality x ≤ 35 represents the fact that x (the amount of gas in gallons) is less than or equal to 35.

This means that the equation will be x≤35

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Blank space 1: 3

Blank space 2: 4.242

Blank space 3: 6

Blank space 4: 6

Blank space 5: 3

This can be solved using triangle theorem.

Given that,

Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal.

The bigger square = 36 sq. in.

Then the side of the bigger square = √36 inch = 6 inch

Next, The side of the bigger square = Diagonal of the smaller square

Let the side of the smaller square = a (let)

Diagonal (smaller square): a√2 = 6 inch

so, a = 3√2 inch

Thus,  a = 3 x 1.414 = 4.242

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The complete question is as follows:

The weight of the baby after five months is 15 Kg.

Step 1:

Given:

New-born baby weight = 5kg

Monthly average weight gained = 2kg

To find:

The weight of the baby after 5 months.

Average Weight of Baby:

Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).

Step 2:

Represent the unknown.

Let x-the number of months .

Let y-weight of the baby after 5 months.

Step 3:

Formulate the equation.

The mathematical equation is:

5+2x = y

Step 4:

Solve the equation.

5+2x = y

5+2(5) = y

5+10 = y

y = 15

Thus, the baby weight is 15kg after 5 months.

Step 5:

Using the equation 5+2x=y.

5+2x = y

5+2(5) = 15

5+10 = 15

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Answer:

16 and 18

16 + 18 = 34 .......... .....