Your rectangular claroom rug ha an area of 110. 5 quare feet. What i the perimeter of the rug?

The substance having half-life of 6 seconds and quantity of 50 gm initially will remain 1.5625gm after 30seconds.

What is half-life of a substance?

When we talk about half life, we are talking about the time taken for exactly half of the mass of the radioactive mass in question to have disintegrated.

More like, the amount of time it takes for the radioactive mass to have lost exactly half of its mass.

Now,

Since it is just 5 half lives, we can proceed manually

In the first, we shall have 25g left

in the second, we shall have 12.5g left

In the third, we shall have 6.25g left

In fourth, we shall have have 3.125g left

and finally, in the fifth, we shall have 1.5625g.

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The ellipse's equation is [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex] and  [-3, 3] is the ellipse's domain.

The ellipse's equation is (Part A) [tex]$\frac{x^2}{3^2}+\frac{y^2}{4^2}=1$[/tex] , The hyperbola's equation is shown in Part B as [tex]$ \frac{x^2}{(-4)^2}-\frac{y^2}{(-7)^2}=1$[/tex]

Part C: [-3, 3] is the ellipse's domain.

The hyperbola's domain lies between [-, -4].

The ellipse and hyperbola's domains do not intersect, hence the system of equations cannot be solved. The origin is the location of the ellipse's centre;8 units make up the vertical main axis. The minor axis equals six units.

Here is a general representation of the ellipse equation:;[tex]$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$[/tex]

a= The semi-major axis, where 8/2 = 4.

The semi-minor axis, b= 6/2 = 3.

Therefore, the ellipse's equation is

[tex]${\frac{-x^2}{3^2}+\frac{y^2}{4^2}=1}$[/tex]

The negative vertex and the domain of the hyperbola are equal.

∴ The hyperbola's domain is [x -4] = [-, -4]

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The equation of line is y = 2x + 8 and the slope of the line is m = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be represented as P ( -2 , 4 )

y = 2x + 7   be equation (1)

On simplifying the equation , we get

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line is m = 2

Since , the lines are parallel the slopes of the lines will be equal

So , m = 2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = 2 ( x - ( -2 ) )

On simplifying the equation , we get

y - 4 = 2 ( x + 2 )

y - 4 = 2x + 4

Adding 4 on both sides of the equation , we get

y = 2x + 8

Hence , the equation of line is y = 2x + 8

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The parallel sides are 24 units and 25 units, and the distance between them is 10 units (the height of the trapezoid) the area of the shape is 245 square units.

what is trapezoid?

A trapezoid is a geometric shape with four sides, where two of the sides are parallel to each other, but the other two sides are not. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The height of the trapezoid is the perpendicular distance between the two bases.

The shape in the image is a trapezoid, which has a formula for its area:

Area = (1/2) x (sum of parallel sides) x (distance between parallel sides)

In this case, the parallel sides are 24 units and 25 units, and the distance between them is 10 units (the height of the trapezoid).

Plugging these values into the formula, we get:

Area = (1/2) x (24 + 25) x 10

Area = (1/2) x 49 x 10

Area = 245 units²

Therefore, the area of the shape is 245 square units.

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Answer:the answer is wrong I did this and i got it wrong

Step-by-step explanation:

Answer:

Simon's age is 18.

Step-by-step explanation:

Let Simons age be s and the age of each twin be t.

s + 2t = 48

s - t = 3

Subtract the second equation from the first:

s - s + 2t - (-t) = 45

2t + t = 45

3t = 45

t = 45/3 = 15.

Now we find Simon's age by plugging t = 15 in the second equation:

s - t = 3

s - 15 = 3

s = 3 + 15 = 18.

The value of x for the equation 2x-3=7 is x=5

Given the equation:

2x-3=7

Here, we have to determine the value of  

For that, transposition method should be used.

Now, transpose 3 to the right hand side of the above equation.

2x=7+3

Now, add the terms on the right side of the above equation, we get

2x=10

Now, we have to divide both sides by 2 we get

[tex]\[\frac{{2x}}{2} = \frac{{10}}{2}\][/tex]

Simplify further, we get

x=5

Thus, the required solution is x=5

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The derivation of the surface area of the cuboid,

A  =  2(ab² + bc² + ca²)

The surface area is a total outer layer of the three-dimensional figure. It is defined only for three dimensional shapes.

Suppose,

The length of  sides of the cuboid  are

a,

b,

c

Cuboid has 6 faces, and each face is like a rectangle,

So, If area of each face is calculated,

Then, the sum of area of each face will be equal to surface area of cuboid.

Surface Area =  A₁ + A₂ + A₃ + A₄ + A₅ + A₆

                      =  ab + bc + ca + ab + bc + ca

                      = 2( ab + bc + ca )

Hence, the surface of a cuboid is 2( ab + bc + ca )

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A triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex.

There are three angles in a triangle ABC. A triangle is a three-sided polygon and it has three angles. Each angle is formed by the intersection of two sides of the triangle.

In a triangle, the angle between two sides is measured in degrees and these angles are formed by the intersection of the two lines that represent the sides of the triangle. The three angles in a triangle are labeled with the corresponding vertex, for example, angle A, angle B, and angle C.

In a triangle, the sum of the three angles is always 180 degrees. This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

Therefore, In short, a triangle is a three-sided polygon with three angles, each angle is formed by the intersection of two sides of the triangle and these angles are labeled with the corresponding vertex. The sum of the three angles in a triangle is always 180 degrees.

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No, 6x and 6xy are not like terms; that is, they are two different terms due to different variables.

Like terms can be defined as terms containing the same variable raised to the same power. Only the numerical coefficients differ. We are the only ones who can combine the same terms in expressions. Combining similar terms shortens and simplifies algebraic expressions to make them easier to work with. Consider example 2xy², 12xy², 7xy²and xy²/2, here also all four terms are like terms because xy ² is the common variable. We have, 6xy and 6x terms. First term 6xy, has a varible xy and in second term 6x, only x is a varible i.e., both varibles are different. Therefore, these terms do not have the same set of variables so they are not like terms. Algebraic expressions can be made simpler by combining like words, which makes advantage of some fundamental real number features. The distribution of multiplication over addition is the most frequent use of the distributive property.

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Correct options are B, E. The point (0, -5) lies on the graph. The function is undefined for x = 1.

The core concept of mathematics' calculus is functions. The unique varieties of relations are the functions. In mathematics, a function is represented as a rule that produces a distinct result for each input x.

In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The range is made up of all values that the function's output can take.

Given,

the function is y = 2x + 5 / x - 1

⇒ The value of x ≠ -1, as function can become undefined.

⇒ Horizontal Asymptote is 2

the value of y for x = 0,

y = 2x + 5 / x - 1

y = 2(0) + 5 / 0 - 1

y = -5

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Answer:

8kg:800g:4000g

1kg=1000g

8kg=8000g

8000:800:4000

80:8:40

10:1:5

The normal written form of the number given as in the task content is; 0.000101.

It follows from the task content that the normal representation of the given number as in the task content is to be determined.

On this note, since the given number is; 1.01 × 10-⁴, it follows that the given normal representation of the number requires shifting the decimal point 4 spaces to the left so that we have;

= 0.000101.

Ultimately, the required normal representation of the number is; 0.000101.

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By drawing every diagonal from one vertex in a convex, n-sided polygon, the polygon can be decomposed into n - 2 triangles.

The sum of a the internal angle measures of a polygon of n sides is given by the equation presented as follows:

S(n) = 180(n - 2).

Hence the sum of the internal angle measures of a triangle, composed of three sides, is given as follows:

180.

Thus the number of triangles on a polygon of n sides is given as follows:

180(n - 2)/180 = n - 2.

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The domain of a logarithm function is the set of all input values (x) for which the logarithm function is defined.

For the natural logarithm function, ln(x), the domain is all positive real numbers, x > 0. This is because the natural logarithm function is defined for input values greater than zero, as the logarithm of any non-positive number is not a real number.

For a logarithm function with a base other than e, such as log_a(x) or logb(x), the domain is also all positive real numbers x > 0. This is because the logarithm function is only defined for input values greater than zero for the same reason as the natural logarithm function.

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Answer:

h

Step-by-step explanation:

uwuwuwuuwu2u2u2uuwuwuwuwuwuwuwuwu

The Z-score of both numbers is equal so both types of grades are better.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

here, z = x - μ / σ

where, μ = mean and σ = standard daviation,

Here,
A. 78 on a test whose mean is 72 and the standard deviation of 6.5,

z = 78 - 72 / 6.5
z = 0.92

B 83 on a test whose mean is 77 and the standard deviation is 8.4

z = 83 - 77 / 8.5
z = 0.92

Thus, the Z score of both numbers is equal so both types of grades are better.

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Answer:

I am positive it is B guys!

Step-by-step explanation:

took da quiz

The range of data is calculated by subtracting the lowest value from the highest value.

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Range, which shows statistical dispersion, is the size of the smallest interval in descriptive statistics that encompasses all the data. It is best suited to capturing the dispersion of tiny data sets because it only depends on two observations.

Data is a group of discrete values used to represent information. These discrete values can describe amount, quality, fact, statistics, or other fundamental units of meaning. They can also just be a series of symbols that can be further understood.

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a) To find the domain of the equation 3x = 12, we need to solve for x, i.e. x = 4

b) x = 2.83

Divide both sides by 3:

3x/3 = 12/3

x = 4

The domain of this equation will be all real numbers.

b) To find the domain of the equation 1.06x = 3, we need to solve for x.

Divide both sides by 1.06:

x = 3 / 1.06

x = 2.830188679245283

The domain of this equation will be all real numbers.

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The inequality of p is p < 10

From the question, we have the following parameters that can be used in our computation:

Total amount = $140

Coupon = $20

Number of people = 12

The inequality of p is then represented as

p < (Total amount - Coupon)/Number of people

Substitute the known values in the above equation, so, we have the following representation

p < (140 -20)/12

Evaluate

p < 10

Hence, the inequality is p < 10

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After addition, 3/5 + 2/7 can be expressed as a fraction as 31/35.

Math is not complete without fractions. The same fundamental procedures that may be applied to integers also apply to fractions. To solve the given problem, we need to add the given fractions using the common denominator property of fractions.

The Least Common Multiple (LCM) of 5 and 7 is 35. Hence, the common denominator is 35.

So, 3/5 + 2/7 = (3 × 7) / (5 × 7)  + (2 × 5) / (7 × 5)

                    = 21/35 + 10/35

                    = 31/35.

Hence, 3/5 + 2/7 can be represented as 31/35 as a fraction after addition.

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You can add the same amount to each side, take the same amount away from each side, multiply or divide each side by the same positive amount, and so on when resolving an inequality.

The inequality symbol must be turned around if either side is multiplied or divided by a negative number.

Run the show 1. The imbalance image remains the same whether the same amount is included or subtracted from both sides of an disparity. Run the show 2. The imbalance image remains unaltered when both sides are duplicated or isolated by a positive number.

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The property of circumcircle is that the circumcircle always passes through all three vertices of a triangle.

A circumcircle is a circle that traverses a triangle's three vertices. It is also known as a "circumscribed circle." Every triangle's three vertices fall within the circumcircle.

The object's Center is defined as the point at where all of the triangle's perpendicular bisectors intersect. The circumcenter is the name of this Centre. The triangle's triangle might have its  Centre within or outside the circle. The radius of the circumcircle is also known as the triangle's circumradius. In a right triangle, the Centre is located precisely at the midpoint of the hypotenuse, and the hypotenuse is a diameter of the circumcircle.

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The expression a² - 2ab - 36b², can be factorize as: (a - 6b)^2.

The polynomial expression a² - 2ab - 36b² can be factored as shown below:

This is done by finding two numbers that multiply to -36 and add to -2ab. The numbers are -6b and 6b, and the expression can be written as:

(a - 6b)(a - 6b), which can be simplified to (a - 6b)^2.

Therefore, given the polynomial expression, a² - 2ab - 36b², when factorized, we would get (a - 6b)².

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The gradient of the line y = x - 10 is 1

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x).

Given the equation of a line is y = x - 10.

The general equation of the line is y = mx + c.

We now get the equation y = x – 10. This will give us the following results when we compare it to the previous line: m = 1 and c = -10.

As a result, the supplied line has a slope of 1.

We must now locate the intercepts. In order to get the y-intercept, let's first enter x = 0 in the equation y = x - 10.

Adding x = 0 to y = x – 10 results in y = – 10.

Therefore, the provided line's y-intercept is equal to -10.

Let's now enter y = 0 to determine the x-intercept in the equation y = x - 10.

By substituting y = 0 for y = x - 10, we obtain x - 10 = 0.

The result of adding 10 from one side to the other is x = 10.

Therefore, the provided line's x-intercept is 10.

∴ m = 1

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Answer:

BDE

Step-by-step explanation:

congruent triangles have corresponding sides and angles congruent.

from B → A → C along  sides BA → AC →CB

now BD ≅ BA , DE ≅ AC ,  EB ≅ CB , that is

BD → DE → EB

then

BAC ≅ BDE

Answer: -3/2

Step-by-step explanation:

To find the slope of the line perpendicular to the given one, we first need to change the equation to y=mx+b to find the original slope.

[tex]6x-9y=216[/tex]             [subtract both sides by -6x]
[tex]-9y=-6x+216[/tex]        [divide both sides by -9]
[tex]y=\frac{2}{3} x-24[/tex]

Now we know slope is 2/3. The slope of the perpendicular line is the opposite sign and reciprocal of the slope.

Opposite would make it -2/3.

Reciprocal would be -3/2.
So the slope is -3/2.

Answer:

(A) 22

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the answer is 24 according to therom 3

We can see here that the factor pairs of 16 are:

(1, 16), (2, 8), (4, 4).

The different ways Kevin and his friends could divide into groups are:

(1, 15), (2, 8), (4, 4).

Factors are numbers that can be divided into a larger number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12 because each of these numbers can be divided into 12 with no remainder. Factors are used in mathematics to simplify or evaluate expressions and to find common denominators in fractions.

16 is an odd number of factors because it is a square number.

A square number is a number that can be written as the product of an integer multiplied by itself.

For example, 16 can be written as 4 x 4. Every square number has an odd number of factors because it has one more factor than its square root, which is an integer (e.g 4 in this case). So, 4 x 4 = 16 has 5 factors (1, 4, 2, 8, 16) which is an odd number.

Yes, you can stop checking for factor pairs when you find a pair that repeats. This is because when you find a pair that repeats, you have reached the square root of the number, so you have already found all the factors.

For example, in the case of 16, the square root is 4, so when you find the pair (4, 4), you can stop looking because you have already found all of the factors.

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Answer:

The equation y=-1.5x+5.5 forms a straight line with a slope of -1.5 and a y-intercept of 5.5. Graphically, the solution can be estimated to be around (3.3, -1.05).