Write the slope intercept equation for line AB

Answer:

a = 10

Step-by-step explanation:

9a + 10 = 60a - 500

51 a = 510

a = 10

The solution of the expression is,

⇒ a = 10

An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called mathematical expression.

Given that;

The expression is,

⇒ 3/4a + 5/6 = 5a - 125/3

Now,

We can solve the expression as;

⇒ 3/4a + 5/6 = 5a - 125/3

⇒ 5/6 + 125/3 = 5a - 3/4a

⇒ 5/6 + 250/6 = (20a - 3a) / 4

⇒ 255/6 = 17a/ 4

⇒ 255 × 4 / 6 = 17a

⇒ 17a = 170

⇒ a = 10

Thus, The solution of the expression is,

⇒ a = 10

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The expression that is not a variation of the Pythagorean identity is the third option.

The Pythagorean identity can be written as:

\(sin^2(x) + cos^2(x) = 1\)

For example, if we subtract cos^2(x) on both sides we get the second option:

\(sin^2(x) = 1 - cos^2(x)\)

Which is a variation.

Now, let's divide both sides by cos^2(x).

\(sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1\)

Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.

Concluding, the correct option is the third one.

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The equation that represents the total number of miles the car has been driven after the number of days that Clarence works is m = 1050 + 90d

Number of miles driven = 1050 miles

Miles drove by Clarence = 90

Number of days = d

Based on the information given, the equation to use will be:

= 1050 + (90 × d)

= 1050 + 90d

Therefore, the number of miles is 1050 + 90d.

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The graph of the linear equation, y = -7x - 1, is shown in the image below.

Given the linear equation, y = -7x - 1, in slope-intercept form, the slope (m) is -7, and the y-intercept, which is where the line intercepts is b = -1, we ca find three points on the line, plot them on a graph, then connect the points by a straight line in other to graph the equation, y = -7x - 1.

The coordinate of the y-intercept is, (0, -1).

To find two other points, substitute x = 1 and x = 2 into y = -7x - 1 respectively:

For x = 1:

y = -7(1) - 1

y = -8

For x = 2:

y = -7(2) - 1

y = -15

The points to plot are (0, -1), (1, -8), and (2, -15).

The graph of y = -7x - 1 is shown below.

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The answer would be C, (The measure of ZY is the greatest of the three angles.)

YX=3, ZY=5, ZX= 4

(YX)≤(ZX)≤(ZY)

or

3≤4≤5

Answer:

A)  The measure of ∠X is the greatest of the three angles.

Step-by-step explanation:

In a triangle:

Therefore, in triangle XYZ, where XY = 3, YZ = 5 and XZ = 4:

The measure of the all the angles cannot be the same since the three side lengths are different.

The average (mean) of the data is approximately 16.89 to two decimal places.

To calculate the average (mean) of the given data, you need to sum all the values and divide by the total number of values.

Sum of the data: 25.3 + 27.9 + 16.1 + 6 + 6.8 + 7.7 + 28.4 = 118.2

Total number of values: 7

Average (mean) = Sum of the data / Total number of values

Average = 118.2 / 7

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The points  (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)

The Cartesian coordinate system on a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates.

These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.

A graph having one x-axis and one y-axis is referred to as a cartesian plane (also known as an X-Y graph).

The orientation of these two axes is perpendicular.

The graph's exact center is marked by the origin (O).

So, we have the points:

(4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5)

Now, the graph is as follows:

(Refer to the graph attached below)

Therefore, the points  (4.5,1.5), (0.5, – 1.5), and (1.5, – 2.5) have been graphed on the coordinate plane (Refer to the graph attached below.)

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The denominator of the formula for the variance of a sample is given as follows:

N - 1.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

The formula for the variance of a sample is given as follows:

\(s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}\)

Hence the denominator is the bottom term, which is of N - 1.

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Answer: 86

Step-by-step explanation:

Mean Value Theorem and its application to given functions on the interval [a, b].

The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that the derivative of the function at c (f'(c)) is equal to the average rate of change of the function over the interval [a, b]. Mathematically, it can be represented as:

f'(c) = (f(b) - f(a)) / (b - a)

To determine whether the Mean Value Theorem applies to a given function on the interval [a, b], you need to check two conditions:

1. The function must be continuous on the closed interval [a, b].
2. The function must be differentiable on the open interval (a, b).

If both conditions are met, then the Mean Value Theorem applies, and there exists a point c in the open interval (a, b) that satisfies the theorem.

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The random variables x and y are defined as x = 1 if the die comes up 3, and x = 0 otherwise, and y = 1 if the die comes up 5, and y = 0 otherwise. The variable z is the product of x and y, which is 1 only when both x and y are 1. The probability that z is 1 is 1/36.

When we toss a fair six-sided die, there are six possible outcomes that are equally likely. The values of x and y depend on the outcome of the die. The variable x is equal to 1 if the die comes up 3, and x is equal to 0 otherwise. Similarly, the variable y is equal to 1 if the die comes up 5, and y is equal to 0 otherwise.

Therefore, x and y are both binary variables, taking on values of 0 or 1. The probability that x is 1 is 1/6, since there is only one way to get a 3 out of six possible outcomes. The probability that y is 1 is also 1/6, since there is only one way to get a 5 out of six possible outcomes.

The variable z is defined as the product of x and y, which is 1 only when both x and y are 1. Therefore, z is also a binary variable that takes on values of 0 or 1. The probability that z is 1 is the probability that both x and y are 1, which is equal to the probability of getting a 3 and a 5 on the same roll of the die.

Since the outcomes of the die are independent, the probability of getting both a 3 and a 5 on the same roll is the product of the probabilities of getting a 3 and a 5 separately, which is equal to (1/6) × (1/6) = 1/36. Therefore, the probability that z is 1 is 1/36.

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Answer:

f(x)

Step-by-step explanation:

f(x) changes at a constant rate   when x changes from 1 to 2 the change in y = 7      when x changes from 2 to 3 the change in y = 7   etc

the others do not change at a constant rate when x changes by one

The data represented by table number one is showing the linear relation.

A linear relationship (or linear association) is a statistical term that describes a two-variable relationship that follows a straight line.

The momentum of a variable is represented by the rate of change, which is used to mathematically describe the percentage change in value over a defined period of time. If the rate of change is constant then the relationship will be linear.

For table number one the data is,

x    F(x)

1     12

2    19

3    26

4    33

The rate of change will be,

R₁ = ( 19 - 12 ) / ( 2 - 1 )  = 7

R₂ = ( 26 - 19 ) / ( 3 - 1 ) = 7

R₃ = ( 33 - 26 ) / ( 4 - 3 )= 7

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Answer:

I cannot solve it step-by-step because like I'm helping other people cuz I'm busy with my homework so just I'm going to direct you the question you're supposed to solve simultaneous equation by any method example elimination method substitution method then you get the answer if you get stuck you can inform me

Answer:

When p = -5 the answer is 45

Step-by-step explanation:

First, since p = -5, you have to plug -5 in as p into the equation

5(-5) + 2(-5)^2 +20          now we do pemdas, so we must fullfill the exponent

5(-5) +2 (25) + 20             now we multiply

-25 + 50 +20                       now we add / subtract

25 + 20                       and we continue adding

45

Answer:

45

Step-by-step explanation:

Substitute p = - 5 into the expression

5(- 5) + 2(- 5)² + 20

= - 25 + 2(25) + 20

= - 25 + 50 + 20

= - 25 + 70

= 45

The equation of the tangent line to f(x)=ln(x) at x=2 is given by y = 1/2x - ln(2).

To find the formula for the tangent line to f(x)=ln(x) at x=2, we first need to take the derivative of the function:

f'(x) = 1/x

At x=2, the derivative is:

f'(2) = 1/2

The equation of the tangent line at x=2 is given by:

y - f(2) = f'(2)(x - 2)

Substituting the values of f(2) and f'(2) gives:

y - ln(2) = 1/2(x - 2)

Simplifying this equation gives us the equation of the tangent line:

y = 1/2x - ln(2) + ln(2)

Therefore, the equation of the tangent line to f(x)=ln(x) at x=2 is given by y = 1/2x - ln(2).

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Answer:

The answer is 852 I think. Please tell me if this is correct.

Step-by-step explanation:

The 4 steps to solve an equation:

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Answer:

x = 80

Step-by-step explanation:

x + .1x = 88

or

x(1+.1) = 88

which ever makes more sense to you

1.1 x = 88

x = 88/1.1

x = 80

The given homogeneous system of equations can be represented as a matrix equation Ax = 0, where A is the coefficient matrix and x is the vector of variables.

To find the solution set in parametric vector form, we can perform row operations on the augmented matrix [A|0] and express the variables in terms of free parameters.

The augmented matrix for the given system is:

[3 3 6 | 0]

[-9 -9 -18 | 0]

[0 -7 -7 | 0]

Using row operations, we can transform this matrix to row-echelon form:

[3 3 6 | 0]

[0 -6 -12 | 0]

[0 0 -7 | 0]

Now, we can express the variables in terms of free parameters. Let x2 = t and x3 = s, where t and s are arbitrary parameters. Solving for x1 in the first row, we get x1 = -2t - 2s.

Therefore, the solution set in parametric vector form is:

x = [-2t - 2s, t, s], where t and s are arbitrary parameters.

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The meaning of the slope of the linear model is,

A.) There are 30 additional grams of sugar for every additional calorie in a menu item.

We have,

Katie uses the equation y= 30x + 70 to model the data.

Here, In graph,

x - axis represent sugar in grams and y - axis represent calories.

Here, The equation is,

y = 30x + 70

Slope = 30

Which represent 30 additional grams of sugar for every additional calorie in a menu item.

Therefore, The meaning of the slope of the linear model is,

A.) There are 30 additional grams of sugar for every additional calorie in a menu item.

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Step-by-step explanation:

x =7-y

subs x in eqn 2

3(7-y)+y=15

21-3y+y=15

21-2y=15

21-15=2y

6=2y

y=6/2

y=3

No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.

We have the information:

P(A)= 0.48  

P(B) = 0.42

P(A∩B) = 0.38

To find out if watching a movie and buying a popcorn are independent,

The formula is used:

P(A|B) = P(A∩B)/P(A)

Plug all the values in above formula:

P(A|B) = 0.38/0.48 = 0.79166

P(A|B) = 0.79

From the deductions above;

Hence, the answer is

No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

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For complete question, to see the attachment

Answer:

$3,400,000

Step-by-step explanation:

170,000/ 5% for the increase

170,000/ 5% = $3,400,000

Answer:

The Slope is -1/3

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest

Answer:

Str (Texture aspect ratio) Str is a measure of uniformity of the surface texture

Step-by-step explanation:

Answer:

D(300

Step-by-step explanation:

It in edu 2021

Answer:

The instantaneous rate of change of \(y\) with respect to \(x\) at the value \(x = 3\) is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of \(y\) with respect to \(x\) over the interval by definition of secant line:

\(r = \frac{y(b) -y(a)}{b-a}\) (1)

Where:

\(a\), \(b\) - Lower and upper bounds of the interval.

\(y(a)\), \(y(b)\) - Function exaluated at lower and upper bounds of the interval.

If we know that \(y = 3\cdot x^{2}\), \(a = 3\) and \(b = 6\), then the average rate of change of \(y\) with respect to \(x\) over the interval is:

\(r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}\)

\(r = 27\)

The average rate of change of \(y\) with respect to \(x\) over the interval \([3,6]\) is 27.

b) The instantaneous rate of change can be determined by the following definition:

\(y' = \lim_{h \to 0}\frac{y(x+h)-y(x)}{h}\) (2)

Where:

\(h\) - Change rate.

\(y(x)\), \(y(x+h)\) - Function evaluated at \(x\) and \(x+h\).

If we know that \(x = 3\) and \(y = 3\cdot x^{2}\), then the instantaneous rate of change of \(y\) with respect to \(x\) is:

\(y' = \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}\)

\(y' = 3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}\)

\(y' = 3\cdot \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}\)

\(y' = 6\cdot \lim_{h \to 0} x +3\cdot \lim_{h \to 0} h\)

\(y' = 6\cdot x\)

\(y' = 6\cdot (3)\)

\(y' = 18\)

The instantaneous rate of change of \(y\) with respect to \(x\) at the value \(x = 3\) is 18.

The matrix A is not invertible.

A matrix is invertible if and only if it is square and its determinant is non-zero. In the given case, matrix A is a 5 × 5 matrix and can be written as A = BC, where B is a 5 × 4 matrix and C is a 4 × 5 matrix.

Since B is a 5 × 4 matrix and C is a 4 × 5 matrix, the product BC will be a 5 × 5 matrix, which is the same size as A. However, the rank of the product BC cannot be greater than the smaller of the ranks of B and C. Since B is a 5 × 4 matrix, its rank cannot be greater than 4, and similarly, the rank of C cannot be greater than 4. Therefore, the rank of the product BC cannot be greater than 4.

Since the rank of A is the same as the rank of BC, the rank of A cannot be greater than 4. However, for a 5 × 5 matrix to be invertible, its rank must be 5.

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Answer:

m1: 35
m2: 77
m3:49
m4:77
m5:62
m6: 28

Step-by-step explanation:

So basically u can figure out that the angle opposite the 103deg thing is also 103. 360-2(103) = 154. Then 154/2 = 77 and u can work out the rest from there. good luck with the rest of the problems.