How do you know how many solutions a system of linear equations has?

Using linear regression to calculate the line of best fit is ŷ = 25.91429X + 553.13333

A line of best fit is a straight line that is used to describe the relationship between two variables in a scatter plot. The line of best fit is also known as the "trend line" or "regression line" and is used to make predictions about the values of one variable based on the values of the other variable.

Linear regression is a statistical method used to find the line of best fit for a set of data. Linear regression analysis is used to determine the linear relationship between two variables.

In the given data;

Sum of X = 21

Sum of Y = 3863

Mean X = 3.5

Mean Y = 643.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = 453.5

Regression Equation = ŷ = bX + a

b = SP/SSX = 453.5/17.5 = 25.91429

a = MY - bMX = 643.83 - (25.91*3.5) = 553.13333

ŷ = 25.91429X + 553.13333

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The value of x is 13.74 units.

Consider the following figure.

In this question we have been given a right triangle with the length of hypotenuse = 47 units.

From figure we can observe that the dotted line segments are parallel to the legs of right triangle.

So, the vertical side of right triangle = x units

And the angle opposite to side 'x' would be 17°  as they are the alternate angles formed by parallel lines and transversal.

Consider the cosider the sine of angle 17°

sin(17°) = x/47

0.2924 × 47 = x

x =  13.74 units

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The value of x is 2 and NM = OL = 7

Now, According to the question:

What is a parallelogram?

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, LMNO is a parallelogram and NM = x + 5 and OL = 2x + 3,

Since, we know that, opposite sides of a parallelogram are equal,

Therefore,

NM = OL

x+5 = 2x+3

x = 2

Therefore, NM = OL = 7

Hence, the value of x is 2 and NM = OL = 7

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The equation for the horizontal asymptote of the function f is y=Lim x→∞ f(x).

In algebra and calculus, a horizontal asymptote is a horizontal line that the graph of a function approaches as the x-values or input values increase or decrease without bound.

The equation for the horizontal asymptote of a function f is:

Lim f(x) → ∞ = c

Where c is the horizontal asymptote.

Example:

f(x) = x2 + 3x + 2

Horizontal Asymptote:

Lim f(x) → ∞ = ∞

numeric value in equation

For example, if x = 5:

f(5) = 5^2 + 3*5 + 2 = 32

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$1897  she has in the account after 10 years.

Use the formula for calculating compound interest

Compound interest can be regarded as the addition of interest on the loan to the principal sum of the deposit.

where A(t) is the account balance, P0 is the principal, r is the yearly interest rate (in decimal form), n is the frequency of compounding interest, and t is the time (in years).

P=$1,100, r=0.037, n=1, and t=15 are all given to us.

Using a calculator to calculate the result after entering the variables into the formula, we discover

A(t)=P(1+rn)n⋅t=$1,100(1+0.0371)(15)(1)≈$1,897.03

So the final answer is $1,897

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Answer:

Step-by-step explanation:

using the rise over run method:

1 up and three to the right

the slope is 1/3
m = 1/3

y = -5x - 23, is the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3).

What is the slope intercept?

The slope-intercept form of a line is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To find the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3), we can use the point-slope form of a line which is y - y1 = m(x - x1), where m is the slope of the line, (x1,y1) is a point on the line.

We know the slope of the line is -5 and the point is (-4,3), so we can substitute these values into the point-slope form to get:

y - 3 = -5(x + 4)

Simplifying this equation gives:

y = -5x - 23

Hence, y = -5x - 23, is the slope-intercept form of the line that has a slope of -5 and passes through the point (-4,3).

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Answer:

192.5 miles

Step-by-step explanation:

let h be number of hours Anne takes to drive to her friend's house

[tex](55mph)(h) = (35mph)(h+2)[/tex]

Both sides of this equation represent the miles to her friend's home. (speed * time = distance)

We add 2 to h on the right side because the way back takes 2 hours longer than the way to her friend's home.

Now we can solve.

[tex](55)(h) = (35)(h+2)\\55h = 35h+70\\20h = 70\\h = \frac{7}{2} = 3.5[/tex]

Now that we have how long the trip to her friend's house takes, we can solve for the distance to her friend's house by using either side of our equation. I will use the left side because it is simpler.

[tex](55)(h)\\(55)(3.5)\\\boxed{192.5}[/tex]

That is the answer

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The correct value of "x" is equal to 4

Step-by-step solution:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem.

These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.

When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Using Pythagoras's Theorem:-

[tex](Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}[/tex]

[tex](x+1)^{2} -x^{2} =3^{2}[/tex]

[tex](x+1)^{2} -x^{2} =3^{2}[/tex]

[tex](x+1+x)(x+1-x) =3^{2}[/tex]

[tex](2x+1)(1) =3^{2}[/tex]

[tex](2x+1)(1) =9[/tex]

[tex](2x+1) =9\\2x=9-1\\2x=8\\x=4\\[/tex]

Therefore, the value of "x" is: x=4

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The rational expression is

[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]

for x ∈ R - {1}

The ratio of two polynomials is a rational expression. If an expression is rational, it may be expressed in the form p/q, where p and q are polynomials.

When the numerator and denominator of an equation are both polynomials, the expression is said to be rational. The lowest form of the numerator and denominator is used to simplify rational formulas. An algebraic fraction is another name for a rational expression.

The value of a logical statement is diminished to its simplest form or lowest terms when it is simplified. Similar to how we simplify fractions, we can simplify a rational equation. In fractions, a rational number is said to be in its simplified form if its numerator and denominator share no factors other than 1. The only distinction is that when simplifying rational expressions, the same strategy also applies because the fraction contains polynomials.

The expression is

[tex]\frac{(x+1)}{(x-1)(x+1)} = \frac{1}{(x-1)}[/tex]

for x ∈ R - {1}

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Answer:

3

Step-by-step explanation:

x = the third side

x² + ([tex]\sqrt{55}[/tex])²= 8²

x² = 64 - 55 = 9

x = [tex]\sqrt{9}[/tex] = 3

The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.

To determine the domain of a function, look at the equation defining the function and identify any restrictions on the input values. For example, if the function is a square root, the input (x) value can not be negative.

To determine the range of a function, you can use the equation of the function and test several input values to find the corresponding output values. You can also use the graph of the function to identify the range. If the function is continuous, you can use the graph to see the range of the function.

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The length of arc COD is approximately 12.56 units.

To find the radius of the circle, we can use the area of sector COD and the angle COD.

We know that the area of a sector is (angle/360) * pi * r^2, and we know that the area of sector COD is 50.24 square units. We also know that the angle COD is 90 degrees.

So we can set up the following equation:

50.24 = (90/360) * 3.14 * r^2

Solving for r, we get:

r = sqrt(50.24 / (90/360) * 3.14) = sqrt(50.24 / (0.25 * 3.14)) = sqrt(50.24 / 0.785) = sqrt(64.28) = 8 (approximately)

So the radius of the circle is approximately 8 units.

To find the length of the arc, we can use the formula of arc length which is Arc Length = (Angle/360) * 2πr

So the length of the arc COD is (90/360) * 23.148 = 4*3.14 = 12.56 (approximately).

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Refer to the attached images.

The L angle is used for measuring the area of the rectangle.

A right angle is one that is 90 degrees in length. It is the most frequently encountered angle in our daily lives. It can be noticed in room corners, box edges, mobile phone screens, and so on.

A square's and a rectangle's sides always make a right angle with each other. It is represented in radians as /2.

The angle formed by two lines that are perpendicular to each other is called a right angle. A right angle is equal to 90° and is in the shape of the letter "L". In the following figure, ray AB and BC form a right angle ABC.

Thus, the L angle is used for measuring the area of the rectangle.

Complete question: What measurement is L angle used for?

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There are two types of classifications for triangles, Classification according to internal angles and Classification according to the length of its sides.

A geometrical shape with three vertices, angles and sides, whose sum of internal angles is 180° is considered as a triangle.

Classification of triangles :-

There are two ways to classify triangles,

1) Based on the Angle :-

a) Acute Angled Triangle :- A triangle that has all three angles less than 90° is an acute angle triangle.

b) Right-Angled Triangle :- A triangle that has one angle that measures exactly 90° is a right-angle triangle.

c) Oblique Angled Triangle :- A triangle that has one angle that measures more than 90° is an obtuse angle triangle.

2) Based on the Sides :-

a) Scalene Angled Triangle :- A triangle that has all three sides of different lengths is a scalene triangle.

b) Isosceles Angled Triangle :- A triangle that has two sides of the same length and the third side of a different length is an isosceles triangle.

c) Equilateral Angled triangle :- A triangle that has all three sides of the same length is an equilateral triangle.

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Use the section formula to get the coordinates of a point that separates a line segment outside or internally in a specific ratio.

By building two right triangles and applying AA similarity, the section formula can be obtained. After determining the ratio of the triangle's side lengths in terms of the supplied ratios, we may solve for x and y to determine the coordinates of the point that divides the line segment.

To determine the coordinates of a point that splits a line segment externally or internally in a certain ratio, apply the section formula. A line segment's midpoint can be determined using this technique as well.

By section formula, we have, if (x, y) divides the line segments joining [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] internally in the ratio m: n then,

[tex]$x=\frac{m x_2+n x_1}{m+n}$[/tex] and [tex]$y=\frac{m y_2+n y_1}{m+n}$[/tex]

Here,

[tex]\left(x_1, y_1\right)=(8,-1) \\\\ \left(x_2, y_2\right)=(2,5) \\\\ (x, y)=(4, 3) \\[/tex]

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The value of y after solving the given equation is -8.

We can calculate the value of y through the following method,

We have been provided with an exponential equation [tex]8^{y} = 16^{y+2}[/tex]

As we know, an exponential equation is an equation whose exponent or part of the exponent is a variable.

For solving an exponential equation, we need to use logarithms and their properties.

We can write [tex]8^{y}[/tex] also as [tex]2^{3y}[/tex] since we know that 2³ = 8

Similarly, we can write [tex]16^{y+2}[/tex] also as [tex]2^{4(y+2)}[/tex] since we know that [tex]2^{4}[/tex] = 16

Therefore we get the new equation as,

[tex]2^{3y}[/tex] = [tex]2^{4(y+2)}[/tex]

Now we will add log with base 10 on both the sides

Therefore the equation will become,

log₁₀ [tex]2^{3y}[/tex] = log₁₀ [tex]2^{4(y+2)}[/tex]

Since, according to the property of logarithm,

log₁₀ aᵇ = b log₁₀ a

Therefore,

3y log₁₀ 2 = 4(y + 2) log₁₀ 2

We can cancel out log₁₀ 2 on both sides

We get the equation as,

3y = 4(y + 2)

3y = 4y + 8

y = -8

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A perpendicular bisector of a triangle is a segment that is perpendicular to the side of a triangle at its midpoint. So option A is the correct answer.

Specifically, it is a line which passes through the midpoint of a side of the triangle, and is perpendicular to that side. It crosses the side at a 90 degree angle, and divides the side into two equal parts.

It can also be thought of as a line which connects the vertex and the opposite side at 90 degrees. In order for a triangle to be equilateral, the three perpendicular bisectors must all intersect at the same point, which is the center of the triangle.

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Answer:

Below

Step-by-step explanation:

It is just the angles that are next to GHI  

  this would be IHJ   and  FHG  

Note that where there's a moderate positive correlation between the length of a child's hair and the amount of time it takes for the child to run 100 meters, then the statement that is TRUE is: "The correlation is most likely due to a lurking variable." (Option B).

A correlation does not imply causation, and a moderate positive correlation is not enough to establish a causal relationship between two variables.

It is possible that the correlation is due to an underlying factor (lurking variable) that affects both the length of the child's hair and the time it takes for the child to run 100 meters. To establish causality, other methods such as experimental design and statistical analysis are necessary.

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Answer:

The diameter of the circle is 7/2.

Step-by-step explanation:

⭐What is the radius of a circle?

⭐What is the diameter of a circle?

Thus, the diameter of said circle is twice the radius of said circle.

diameter = 2(radius)

diameter = 2(7/4)                   . . . . substitute known values

diameter = 14/4                      . . . . multiply the numerator & denominator

diameter = 7/2                       . . . . simplify

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In the given expression, 7^x=28, as there is variable in one side while in other side there is constant, also there is no logarithmic value, so it is not possible to  solve the equation by changing the base of both sides

The basic formula has been changed to logb b a = [logc c a] / [logc c b]. It simply implies that to alter the base of a logarithm logb b a, we divide [log a] / [log b], where these logarithms might have any (same) positive number as a basis.

The change of base formula gives you the answer of a log with a different base by utilizing only log computations with a base of 10. The formula instructs you to divide the log of the number in parentheses by the log of your base.

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No matter how far they reach, parallel lines are those that do not have a shared meeting point in the same plane.

If two lines cannot collide when extended in both directions to infinity, they are said to be parallel in a plane. Throughout the entire length, there remains a constant gap between two lines.

|| is the symbol used to represent the parallel lines. Assuming that lines "a" and "b" are parallel to one another, we may indicate this using the symbol "a||b," which means "a is parallel to b."

We need a ruler and a compass to create a line parallel to the other line starting from an outside point. The diagram of parallel line is given below:

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The result of dividing 2x^3 + x^2 - 2x + 8 by x + 2 is:

Quotient: 2x^2 - 3x + 4

Remainder: 0

The given polynomial is 2x^3 + x^2 - 2x + 8.

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.

(x)(2x^2) = 2x^3

Thus, we multiply the divisor (x + 2) by 2x^2 which gives 2x^3 + 4x^2.

Now we subtract this from the polynomial which gives -3x^2 - 2x +8.

Next we multiply the divisor by -3x which gives -3x^2 - 6x. Again we subtract the same from the remaining polynomial -3x^2 - 2x +8 and get 4x + 8.

Repeating the same we multiply the divisor by 4 which gives 4x + 8. Subtracting the same from the remaining polynomial 4x + 8 we get the remainder 0.

Thus, the quotient is 2x^2 - 3x + 4.

The question is incomplete, the complete question is:

What is the result of dividing 2x^3 + x^2 - 2x + 8 by x+2?

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Formula used to calculate the y-intercept when coordinates of two points are given is as follow: y = mx + c where 'm' represents the slope and 'c' represents the y-intercept.

As given in the question,

Let us consider points of two coordinates be equal to

( x₁ , y₁ ) =  ( 2, 3 )

( x₂ , y₂ ) = ( 4, 7 )

Equation of the line is equal to :

( y - y₁ ) / ( x - x₁ )  = ( y₂ - y₁ ) / ( x₂ - x₁ )

⇒ ( y - 3 ) / ( x - 2 ) = ( 7 - 3 ) / ( 4 - 2 )

⇒ ( y - 3 ) / ( x - 2 ) = 2

⇒ y - 3 = 2x - 4

⇒ y = 2x - 1

Same as y = mx + c

Here c = -1

Here y-intercept is equal to -1 by substituting x = 0 we can get                 y - intercept.

Therefore, the value of y-intercept can be calculated with the coordinates of the given points using formula given by :

y = mx + c where 'c' represent y-intercept.

The given question is incomplete, I answer the question in general according to my knowledge:

If you're given coordinates of 2 points, how do you find the y-intercept?

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The inverse meaning in math is a function or operation which reverses the order or operation of another function or operation.

Let us take an inverse math example, The inverse operation of addition is subtraction, and the inverse operation of multiplication is division.

For example, The multiplication of two numbers 3 and 6 is 3 × 6 = 18. The inverse operation of this is a division which is as follows: 18/6 = 3.

The Inverse of a Number

Consider a number y where y is not equal to zero. Then the inverse of a number y is the reciprocal of the number that is 1/y.

For example, The inverse of the number 200 is 1/200, and the inverse of the number 32 is 1/32.

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