y equals 5x proportional or non-proportional

The equation will have only one root.

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.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation.

Given equation:

2x + 3 = 4x + 2

On solving

2x - 4x = 2-3

-2x = -1

x= -1/(-2)

x= 1/2

Also, the equation as only one variable of degree one which implies that it will have only one solution.

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2x+12-7x=-2

-5x+12=-2

-5x=-14

x=14/5

Final answer:

The equation of the line passing through the points (7, -7) and (6, -5) is determined by finding the slope, which is -2, and then using the point-slope formula. However, the correct equation y = -2x + 21 is not listed among the student's provided options.

Explanation:

The student's question asks for the equation of a line that passes through two given points: (7, -7) and (6, -5). To find the equation of the line, we first need to determine its slope.

We use the formula for slope which is (change in y) / (change in x), often written as (y2 - y1) / (x2 - x1)

Slope = (-5 - (-7)) / (6 - 7) = 2 / -1 = -2. Therefore, the slope (m) is -2.

With the slope known, the next step is to use the point-slope form of the line equation, which is y - y1 = m(x - x1). Substituting one of the points and the slope, we get y - (-7) = -2(x - 7). Simplifying this gives us y = -2x + 14 + 7, which simplifies further to y = -2x + 21.

Therefore, among the options provided by the student, none of the equations match precisely, which means either there is a mistake in the question's options or in the calculation. However, the closest match, by the slope, would be option y = -2x - 7, considering only the slope and not the intercept.

The term 'mean square within' (MSwithin) refers to the sample variance in a set of data, which is computed by dividing the sum of squares within (SSwithin) by its degrees of freedom. This term is used in ANOVA to estimate how much variation within the sample data is due to chance.

The term mean square within (MSwithin) is another term for the variance of the sample data. MSwithin represents the variance within groups.

To calculate this variance, the sum of squares within (SSwithin), which represents the variation within samples that is due to chance, is divided by its respective degrees of freedom.

The variance is a measure of how much the data points in a sample differ from the sample mean.

Variance is calculated by taking the mean of the squared deviations from the mean.

This calculation is often used to determine how spread out the values in a data set are.

In the context of an analysis of variance (ANOVA), the MSwithin is used in conjunction with mean square between (MSbetween), which represents the variance between groups, to calculate the F ratio used for testing the null hypothesis.

Answer:

1 meter = 100 centimeter

Step-by-step explanation:

A conversion factor is a numerical value that we use to change one set of unit to another set by performing actions like multiplication or division. When we are converting something, we must use the appropriate conversion factor of an equal value. Few conversions are :

1 meter = 100 centimeter

1 kilometer = 1000 meter

1 foot = 12 inches

1 gallon = 4.54 liters

We want the conversion factor for converting meters to centimeters. this is 1 m = 100 cm.

Final answer:

The number 15 belongs to several sets of numbers: it is a rational number, an integer, a whole number, and a natural number. Therefore, the correct answer to which sets contain the number 15 is D. Rational numbers, integers, natural numbers, and whole numbers.

Explanation:

Number sets form a hierarchy where certain numbers fit into multiple categories based on their characteristics. Starting from the broadest categories, we have complex numbers, which include all numbers with a real and imaginary part. However, the number 15 does not have an imaginary part, so we look to smaller sets.

The real numbers include all the values that can be found on the number line, which includes rational numbers (like fractions), irrational numbers (like √2), integers, whole numbers, and natural numbers. The number 15 is a real number because it can be found on the number line, but it is also specifically a rational number, an integer, a whole number, and a natural number because:

Therefore, the correct answer to the question is D. Rational numbers, integers, natural numbers, and whole numbers all contain the number 15.

The statements that are true are: v+2u+1 is written as a sum of three terms, and 1 is a constant.

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The formulae for resistance R is R = V/I

What is Ohm's Law ?

Providing that all physical conditions and temperatures are constant, Ohm's law says that the voltage across a conductor is directly proportional to the current flowing through it.

Ohm's law is given as :

V = IR

Now to find the value of R we divide both side by current I :

[tex]\begin{aligned}V&=IR\\R&=\frac{V}{I}\end{aligned}[/tex]

Therefore, the formulae for resistance R is R = V/I

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Answer:

[tex]2\times 2\times 2\times 2\times 2\times 5[/tex]

Step-by-step explanation:

We have been given that a computer code is based on the prime factorization of 160. We are asked to find prime factorization of 160.

We know that prime factorization of a number is writing the prime factors of a number such that their product gives the original number.

To find prime factors of 160, we will divide 160 by 2 for 5 times and then divide by 5.

Prime factorization of 160: [tex]2\times 2\times 2\times 2\times 2\times 5[/tex].

Therefore, the prime factorization of 160 is [tex]2\times 2\times 2\times 2\times 2\times 5[/tex].

The value of ∠Q in the figure is 146⁰.

How to determine the value of The value of ∠Q in the figure.

From the figure

Given

∠P = 2x + 10

∠R = 6x - 4

In ∆PQR

∠P + ∠Q + ∠R = 180⁰(sum of angles in triangle)

Substitute

2x + 10 + ∠Q + 6x - 4 = 180

8x + 6 + ∠Q = 180

But m∠P = m ∠R(base angles of issoceles triangle)

2x + 10 = 6x -4

-4x = -14

x = 7/2

Substitute into 8x + 6 + ∠Q = 180

8(7/2) + 6 + ∠Q = 180

28 + 6 + ∠Q = 180

34 + ∠Q = 180

∠Q = 180 - 34

= 146⁰

The value of ∠Q is 146⁰

Answer:

Step-by-step explanation:

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The solution for this problem is:

One way to solve is to using the "stars and bars" approach, but this could be the other one:

x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = 20 

then use  (20+10-1) C(10-1), this will result to 29C9.

Then find the way to distribute x 

as a result, (20-10+10-1) C (10-1) = 19C9

Thus, the probability is 19C9/29C9 or 0.0093

Final answer:

Using the Pythagorean theorem, the length of the longest side of right-angled triangle CDE, which is the hypotenuse DE, is found to be 39 units.

Explanation:

In triangle CDE, angle C is given as 90 degrees, making this a right-angled triangle. According to the information provided, side CD is 15 units long, and side DE is 3 units more than side CE. We are asked to find the length of the longest side, which would be the hypotenuse in a right-angled triangle. To find the hypotenuse, which we'll designate as side DE, we must first establish the relationship between the sides. Let's call CE 'x'; therefore, DE will be 'x + 3'. Since we've established that the triangle is right-angled at C, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

So, the equation becomes CD² + CE² = DE², or 15² + x² = (x + 3)². If we solve for 'x' we have:

As a result, CE = 36 units and DE, the longest side, equals 36 + 3, which is 39 units.

By applying the Pythagorean theorem correctly, we've found that the length of the longest side of triangle CDE is 39 units.

Answer with Step-by-step explanation:

The solution of system of equations is all those values of x and y which satisfy both the inequalities or the points which lie in the region common between both the inequalities.

N=100x+40y

The optimal solution will be find from the points which lie on the extreme end of the region common between the inequalities i.e. (2,6), (0,8) or (5,0)

(x,y)=(2,6)

N=100×2+40×6

N= 200+240

N=440

(x,y)=(0,8)

N=100×0+40×8

N= 0+320

N=320

(x,y)=(5,0)

N=100×5+40×0

N= 500+0

N=500

Hence, optimal solution is:

(5,0)

Final answer:

The slope of a line parallel to the line 4x - 7y = -14 is determined by converting the equation to slope-intercept form, revealing that the slope is 4/7. Thus, any line parallel to it will have the same slope of 4/7.

Explanation:

The slope of a line parallel to the line 4x - 7y = -14 is first determined by rewriting the given line in slope-intercept form (y = mx + b), where m represents the slope. For the line 4x - 7y = -14, we can solve for y to find the slope:

Add 7y to both sides: 4x = 7y - 14.

Then add 14 to both sides: 4x + 14 = 7y.

Finally, divide every term by 7 to solve for y: (4/7)x + 2 = y.

The slope of the line is 4/7. Since parallel lines have equal slopes, any line parallel to the given line will also have a slope of 4/7.

Final answer:

The expression 8(xy + 8) + 1 simplifies to 8xy + 65 by applying the distributive property and combining like terms.

Explanation:

The question asks to simplify the expression 8(xy + 8) + 1.

To simplify this expression, we need to apply the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Hence, we distribute the 8 across the terms inside the parentheses:

After distributing we combine the like terms:

8xy + 64 + 1

Then we combine the numerical terms:

8xy + 65

So, the expression simplifies to 8xy + 65. This is the final simplified form of the given expression.

The solutions of the quadratic equation are 3 ± √3.

Quadratic equations are defined as the polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given quadratic equation is x² - 6x + 6 = 0.

The solutions of a quadratic equation ax² + bx + c = 0 can be found using the quadratic formula,

x = [-b ± [tex]\sqrt{b^2-4ac}[/tex] ] / 2a

From the given equation,

a = 1, b = -6 and c = 6

Substituting in the quadratic formula,

x = [-(-6) ± [tex]\sqrt{(-6)^2-(4*1*6)}[/tex] ] / [2 × 1]

  = [6 ± [tex]\sqrt{36-24}[/tex]] / 2

  = [6 ± [tex]\sqrt{12}[/tex]] / 2

  = [6 ± 2√3] / 2

  = 3 ± √3

Hence the solutions of the given quadratic equation are 3 + √3 and 3 - √3.

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