The length of the base of an isosceles triangle is x. The length of a leg is 5x -2. The perimeter of the triangle is 106. Find x. X =​

The easiest way to solve linear equations is to use the elimination method.

A linear equation is an equation that has two variables and when it is graphed it gives a straight line. Linear equations can be graphed according to their slope and y-intercept. The standard equation for a line is y = mx + b, where b is the y-intercept and m is the slope.

To solve linear equations in the easiest and simplest way use the elimination method. In this method, you either add or subtract the equations to obtain an equation in one variable. When the coefficients of one variable are opposites, you add the equations to eliminate a variable and when the coefficients of one variable are equal, you subtract the equations to eliminate a variable.

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Answer:

You can represent "the opposite of Shana's temperature is equal to Pearl's" as follows:

(-20 C) + (-x) = x

Where x represents Pearl's temperature.

Alternatively, you can also write it as:

20 C - x = x

Both of these equations are equivalent and mean the same thing: the opposite of Shana's temperature is equal to Pearl's temperature.

Step-by-step explanation:

20 degrees Celsius

The temperature in Pennsylvania is the opposite of the temperature in Canada, therefore -20⁰ Celsius in Canada would then be 20⁰ Celsius in Pennsylvania.

The number of times which the two computers back up at the same time in twenty four hours as required is; 144.

It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.

On this note, the least common multiple of both backup times represents when the two computers back up at the same time.

Hence, since the LCM of 5 and 2 is; 10.

It follows that the two computers back up at the same time after every ten minutes.

Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;

= ( 24 × 60 ) / 10

= 24 × 6

= 144 times.

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The volume of the prism in the attached figure is calculated to be

672 m³

In the given problem, the formula used for volume of prism is

= area of base * height

Assuming a triangular base

area of triangular base = 1/2 * base * height

where

base = 12 m

height = 14 m

area of triangular base = 1/2 * 12 * 14

area of triangular base = 84 m²

The volume of the prism with a triangular base

volume of the prism = area of triangular base * height

where

area of triangular base = 84 m²

height = 8 m

volume of the prism = 84 * 8

volume of the prism = 672 m³

The volume of the prism is solved to be 672 m³

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A value calculator is a tool used to help assess the worth of an asset or investment.

The value calculator is designed to help individuals and businesses determine whether an asset or investment is a good value. The calculator takes into account various types of data, such as the current market value, expected future value, and any associated risk factors.

This data is then used to calculate the present value, which is the amount of money an asset or investment is worth today. The calculator also takes into account inflation and other factors that could affect the current value of the asset or investment.

The value calculator can be used to help individuals and businesses make informed decisions about their financial investments.

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Answer:

4444/1000

You take the number of decimal points and turn them into zeros for the denominator

The expression which represents the value of the area could be the six times the circumference of the circle.

What is area of circle ?

area of circle can be defined as the product of pi(3.14) and square of radius of the circle.

Given,

helicopter pad which is in the shape of a circle has a circumference 72.48

and the diameter of 24 feet.

radius = diameter/2

radius = 24/2

radius = 12

circumference of circle = 72.48

area of circle =  π*r*r

area of circle = 22/7 * 12 * 12

area of circle = 452.5

area of circle is approximately 6 times the circumference of circle.

Hence , The expression which represents the value of the area could be the six times the circumference of the circle.

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Answer:

n= 6

Step-by-step explanation:

7^9/7^6 is the same as 7^9 - 7^6/ 7^9-6 but it gives you 7^3

The height of the cone is 24.6cm and the volume of the cone is 1/3 * pi * 4^2 * 24.6 = 268.08cm^3

We can start by using the formulas for the surface area of a sphere and the curved surface area of a cone. The surface area of a sphere is given by 4 * pi * r^2, where r is the radius of the sphere. The curved surface area of a cone is given by pi * r * l, where r is the radius of the base of the cone and l is the slant height of the cone.

Given that the surface area of the sphere is five times the area of the curved surface of the cone, we can write the following equation:

4 * pi * (5^2) = 5 * pi * r * l

We can then solve for the slant height l of the cone:

l = (4*5^2) / r

Given that the radius of the cone is 4 cm, we can substitute this into the equation and solve for l:

l = 100/4 = 25cm

The volume of the cone is 1/3 * pi * r^2 * h, where r is the radius of the base and h is the height of the cone.

As we know the slant height and radius of the cone, we can use the Pythagorean theorem to find the height of the cone:

h = sqrt(l^2 - r^2) = sqrt(25^2 - 4^2) = sqrt(625 - 16) = sqrt(609) = 24.6cm

Therefore, the height of the cone is 24.6cm and the volume of the cone is 1/3 * pi * 4^2 * 24.6 = 268.08cm^3

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If the Cylinder's height equals to the diameter of its base , then the fraction of the total surface area of the cylinder to the total surface area of the two bases is 1/3 .

The curved surface area of the cylinder with height "h" and radius "r" is written as ⇒ [tex]2\pi rh[/tex] ;

the area of the top and bottom of the cylinder is ⇒ [tex]\pi r^{2} + \pi r^{2}[/tex] = [tex]2\pi r^{2}[/tex] ;

the total surface area of the cylinder will be ⇒ [tex]2\pi rh[/tex] [tex]+2\pi r^{2}[/tex]  ....equation(1)

it is given that the height of cylinder is equal to the diameter of the base ,

that means ; [tex]h = 2r[/tex]

Substituting the value [tex]h = 2r[/tex] in the equation(1) ,

we get ,

total surface area of cylinder = [tex]4\pi r^{2} +2\pi r^{2}[/tex] = [tex]6\pi r^{2}[/tex]

So , the required fraction is = [tex]\frac{2\pi r^{2} }{6\pi r^{2} }[/tex] ,

On simplifying ,

we get ,

= [tex]\frac{1}{3}[/tex]  .

Therefore , the fraction of two bases to the total surface area is [tex]\frac{1}{3}[/tex] .

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Answer:

142%

Step-by-step explanation:

How I got this solution is made it as a ratio, "82.86:195.82".

I then simplified the balance by dividing 82.86 into both sides.

It then equaled around 0.42 (or 42%). Including itself, it got a markup percentage of 142%

Answer: He received $3.51 in change.

Step-by-step explanation:

To get the answer we can subtract the amount Felix paid ($20) by the cost of the dinner ($16.49).

It will look like this:

$20.00 - $16.49 = $3.51

Answer:3 dollars and 51 cents

Step-by-step explanation:

The graph from the function is a linear graph

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

g(x)=(x+2)(x−1)−x 2

Express properly

So, we have the following representation

g(x) = (x + 2)(x − 1) − x²

Next, we set x = 0, 1, 2 and 3 to determine the table of values

g(0) = (0 + 2)(0 − 1) − (0)² = -2

g(1) = (1 + 2)(1 − 1) − (1)² = -1

g(2) = (2 + 2)(2 − 1) − (2)² = 0

g(3) = (3 + 2)(3 − 1) − (3)² = 1

So, the table is

x        0         1        2        3

g(x)     -2      -1        0        1

From the table above, we can see that as x increases by 1, y constantly increase by 1

This means that the function is a linear function

See attachment for the graph

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By using the fact that the two images are similar, we can write and solve a linear equation to get x = 3/2.

We know that the two figures are similar, then, if we take the quotient between the adjacent sides for both figures, these quotients should give the same value.

Thus, we can write the equation:

14/10 = (x + 9)/(x + 6)

Now we can solve that equation for x, if we multiply both sides by (x + 6) we will get:

(14/10)*(x + 6) = x + 9

Now we can multiply both sides by 10 to get:

14*(x + 6) = 10*(x + 9)

14x + 84 = 10x + 90

Now we can solve this linear equation for x.

14x - 10x = 90 - 84

4x = 6

x = 6/4

x = 3/2

That is the value of x.

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Mama bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) fraction.

The fraction is expressed in the form a/b, where an is referred to as the numerator and b is referred to as the denominator. The fraction is a rational number that only divides two integers.

Let the pie's largest portion be a.

Half of the pie was consumed by Papa Bear.

Papa Bear then consumed = (1/2)a.

Rest of the pie is equal to a- (1/2).

a= (1/2)a

Mama bear consumed (half) of the remaining pie.

Mother bear consumed (1/2)(1/2).

pie portion a= (1/4) pie portion after mom bear has eaten = (1/2)

a- (1/4)a= (1/4)a

Baby bear afterwards consumed (half) of the remaining pie.

Baby bear ate (1/2)(1/4), thus. After the young bear has finished eating, the remaining pie is equal to (1/4) a- (1/8)a= (1/8)

The remainder of the component was given to GoldLiocks.

As a result, mom bear only ate (1/4) of the pie, leaving Goldilocks with the remaining (1/8) portion.

The complete question is Papa Bear ate 1/2 of a pie. Mama Benr ate 1/2 of what was left Baby Bear ate 1/2 of what

was left after Mama Bear finished.

3) What fractional part of the pie did Mama Bear eat?

4) What fractional part of the pie was left for Goldilocks?

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Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.

Absolute Value Function:

An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values ​​of x and find some ordered pairs.

In mathematics, the absolute value or modulus of the real number x, represented as.

|x| is the non-negative value of x, regardless of sign.

x is positive and |xI =-x}.  For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.

Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.

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A linear system has infinite solutions if it consists of exactly the same equations.

The 3  possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

Example:

3x + 2y = -4  ..... (equation 1)

6x = -4y - 8   ..... (equation 2)

Add 4y to both sides of equation 2:

6x + 4y = -8

Divide both sides by 3:

3x + 2y = -4

Hence, equation 2 is exactly the same as equation 1. If we plot their graphs, they will share the same graph. Any solution of equation 1 is also solution of equation 2. Therefore, this linear system has infinite solutions.

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Answer:

Lauren will finish the race faster 7 seconds faster, and 14 meters ahead.

Step-by-step explanation:

To answer this question, I will use the strategy of finding the slope of each of the proportional relationships (y = 8x for Lauren's run and y = ?x for Amani's run). The slope represents the rate at which the distance changes for each unit of time, so the person with the greater slope will finish the race faster.

To find the slope of Amani's run, I will use the tool of point-slope form, which is y - y1 = m(x - x1). I will plug in the coordinates for the second point listed in the table for Amani's run (5 seconds and 30 meters) to get y - 30 = m(5 - x1). Since I don't know the value of x1, I will solve for it in terms of m. I get x1 = 5 - (30/m).

Next, I will plug in the coordinates for the first point listed in the table for Amani's run (3 seconds and 18 meters) into the equation y - 30 = m(5 - (30/m)). I get 18 - 30 = m(5 - (30/m)). Solving for m, I find that Amani's run has a slope of m = -6.

Since Lauren's run has a slope of 8 and Amani's run has a slope of -6, Lauren will finish the race faster. To find out by how much, I will use the tool of proportional reasoning. Since the slope represents the rate at which the distance changes for each unit of time, the difference in the slopes (8 - (-6)) represents the difference in the rate at which the distance changes for each unit of time between the two runs. The difference is 14, so Lauren will finish the race 14 meters ahead of Amani for each second that they run. Since the race is 100 meters long, Lauren will finish the race approximately 7 seconds faster than Amani.

The fractions of the numbers are found as follows:

To divide a number by the nth power of 10, the decimal digit in the number is moved n units to the right.

The fraction that represents 10% of a number is given as follows:

10/100 = 1/10.

Meaning that the number is divided by 10, which is the first power of 10, and thus the decimal digit is moved one unit right in the number.

The fraction that represents 1% of a number is given as follows:

1/100.

Meaning that the number is divided by 100, which is the second power of 10, and thus the decimal digit is moved two units right in the number.

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The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints of the segment and the ratio of the desired point from the first endpoint.

The formula is:

Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1))

Where x1 and y1 are the coordinates of the first endpoint, x2 and y2 are the coordinates of the second endpoint, and r is the ratio of the desired point from the first endpoint.

The segment partition formula is used to calculate the coordinates of a point on a line segment, given the coordinates of the two endpoints and the ratio of the desired point from the first endpoint. The formula is given in the form of Point = (x1 + r * (x2 - x1), y1 + r * (y2 - y1)).

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On solving the provided question, we can say that the e slope of the linear regression prediction equation if a person with 12 years of schooling is 1.

When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.

the e slope of the linear regression prediction equation if a person with 12 years of schooling

a. 1(correct)

b. 12

c. 13

d. 1,500

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The correct answer to the given question is 49. To solve the given problem following steps are followed :

Step 1: 7 power 2 means 7 multiplied by itself 2 times.

Step 2: 7 times 7 is 49.

Step 3: So, the answer is 49.

Comparing two quantities that generate the same result when one is multiplied by a certain amount is known as a multiplicative comparison. Sam, for instance, has twice as many balloons as Sid does. Sid's got three balloons. Sam has two times Sid's amount of balloons. Sam has a total of 6 balloons, which is equal to 2 + 3 + 1.

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From the equation (2-3 x 2⁹ = 2n), the value of n is -767.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.

The word equation and its cognates in various languages may have slightly different meanings. In mathematics, an equation is a formula that uses the equals sign to denote the equality of two expressions.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Given data :

2-3 x 2⁹ = 2n

= 2n = 2 - 3 .

= 3 .   = 1536

= 2n = 2 - 1536

= 2n = -1534

Divide both sides by 2

= 2n/2

= -1534/2

n = -767

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Answer:

answer is below

Step-by-step explanation:

1.

Two lines from right angles.

The lines are perpendicular

2.

x + 20 = 32

x =12

3.

You are a third year high school student.

You are a junior high school student.

4.

An angle measures 20°.

The angle is acute.

5.

A figure is square.

The figure is quadrilateral.

Here the exact values of circle is not given.so in general .Area of Circle = πr² or πd2/4 in square units, where (Pi) π = 22/7 or 3.14.

The space a circle takes up in a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. A = r2, where r is the circle's radius, is the formula for c

Area of Circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of circumference to diameter of any circle. It is a special mathematical constant.

Area of Circle:

[tex]\pi[/tex]×r²

Where [tex]\pi[/tex]=3.14

But Here we need correct values to find the area of the circle.

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Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.

Here,

Given:

Mean = 2

Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.

We can determine that at least

100 (1-1k2)% = 100 (1-1/4)% = 75%

is within 2 standard deviations of the mean using Chebyshev's Rule with

k = 2.

The percentage times the sample size yields the equivalent number of households:

=> 75% x 40 = 30

Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

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The value of the given expression is -32w⁵.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

The given expression is (-2w)⁵.

Here, (-2w)⁵=(-2)⁵×w⁵

= -32w⁵

Therefore, the value of the given expression is -32w⁵.

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The side length of the triangle are

A triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is

= a + b + c

where

a, b, and c are the dimensions of the side length of the triangle:

Using the values given in the problem we have

let the ratio be a multiple of x such that

154 = 3x + 5x + 6x

154 = 14x

x = 11

a = 3 * 11 = 33 feet

b = 5 * 11 = 55 feet

c = 6 * 11= 66 feet

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