Write the slope-intercept equation of a line that passes through the points (-2,5) and (6,-4)

Given parameters:

Midpoint of AB =  M(3, -1)

Coordinates of A = (5,1)

Unknown:

Coordinates of B = ?

Solution:

To find the mid point of any line, we use the expression below;

              \(x_{m} = \frac{x_{1} + x_{2} }{2}\)    and \(y_{m} = \frac{y_{1} + y_{2} }{2}\)

where \(x_{m}\)  and \(y_{m}\) = coordinates of the mid points = 3 and -1

   x₁  = 5 and y₁ = 1

  x₂ = ?  and y₂ = ?

Now let us input the variables and solve,

            3  = \(\frac{5 + x_{2} }{2}\)           and     -1 = \(\frac{1 + y_{2} }{2}\)

    5 +  x₂  = 6                          -2 = 1  + y₂

            x₂ = 1                             y₂ = -2 -1 = -3

The coordinates of B = 1, -3

Answer:

760 in^2

Step-by-step explanation:

2(22*10)+2(22*5)+2(5*10) = 760in^2

Answer:  -21

Step-by-step explanation:

11-32

The slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3 is -1/2.

To find the slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3, we need to first find the derivative of r with respect to θ, and then evaluate it at θ = π/3.

Differentiating both sides of the polar equation with respect to θ, we get:

dr/dθ = d/dθ(2 - sinθ)

dr/dθ = -cosθ

So, the derivative of r with respect to θ is -cosθ.

Evaluating this derivative at θ = π/3, we get:

dr/dθ|θ=π/3 = -cos(π/3) = -1/2

Therefore, the slope of the tangent line to the polar curve r = 2 - sin(θ) at the point specified by θ = π/3 is -1/2.

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Answer:

n•√n

here is an accurate representation

Answer:

600⁰00000000000000000

============================================

Work Shown:

3 & 1/2 = 3 + 1/2 = 3 + 0.5 = 3.5

3.5% = 3.5/100 = 0.035

r = 0.035 is the decimal form of \(3\frac{1}{2}\%\) which is used along with

to get the following

A = P*(1+r/n)^(nt)

A = 500*(1+0.035/12)^(12*0.5)

A = 508.81405074594

A = 508.81

Extra info: Gabe earned A-P = 508.81 - 500 = 8.81 dollars in interest.

The value of j is j = 103 - k = 115 - f.

A collection of equations for which we searched for common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.

Consider the two equations,

f + j = 115                                                                    ----------------------(1)

j + k = 103                                                                   ----------------------(2)

Consider equation (2),

j + k = 103

Subtracting k from each side of the equation.

j + k - k = 103 - k

j = 103 - k

Consider equation (1),

f + j = 115

Subtraction f from each side of the equation,

f + j - f = 115 - f

j = 115 - f

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Answer:

50 Fahrenheit (F) 10 Celsius (C)

1 F = -17.222 C 1 C = 33.800 F

Answer:

50 Fahrenheit (F) 10 Celsius (C)

1 F = -17.222 C 1 C = 33.800 F

Answer:

Step-by-step explanation:

Given line:

Perpendicular lines have negative-reciprocal slopes:

Since m₁ = 3, we can find m₂:

Given choices:

Correct choice is the first one

Since you have basic knowledge of computer hardware, an action which you should take as an ethical employee include the following: A. Initiate help by offering to check the computer.

A computer hardware can be defined as a physical component of a computer system or an information technology (IT) that can be seen, touched and replaced.

In Computer technology, there are various examples of a computer hardware and these include the following:

Based on ethical principles, we can reasonably infer and logically conclude that an ethical employee should initiate help by offering to help check the colleague’s computer since he or she has basic knowledge of computer hardware.

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Answer:

Distance = 17.5 miles

Step-by-step explanation:

Note.

Given question is not complete

Given:

Speed upstream = x

Time taken in upstream = 3.5 hour

Speed in return trip = (x+2)

Time taken in return trip = 2.5 hour

Computation:

Distance = speed × time

Distance = x (3.5)

Distance = 2.5 (x+2)

Distance = 2.5x + 5

So,

2.5x + 5 = 3.5 x

1.5 x = 5

x = 5 miles/hour

Distance = x (3.5)

Distance = 5 (3.5)

Distance = 17.5 miles

Given:

Bella bought packs of stickers to give to her friends.

Cost of each pack of stickers = $4

Total amount spent on packs of stickers = $12

To find:

The equation for the given statement.

Solution:

Let s be the number of packs of stickers.

Cost of one pack of stickers = $4

Cost of s packs of stickers = $4s

Total amount spent on packs of stickers is $12. So,

\(4s=12\)

Therefore, the correct option is B.

Answer:10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

8 + (9- 1) ÷ 4

Use PEMDAS to determine order of operations in a mathematical expression

The order of operations is

P = parentheses
E = exponent

M = multiplication

D == division

A = addition

S = subtraction

Note that multiplication and division have the same priority and we go from left to right that case. Because it does not affect the answer.

So 12 ÷ 4 x 6 = 12 x 6 ÷ 4
Same for addition and subtraction - same priority

Using PEMDAS

(9 - 1) is executed first giving 8

The expression becomes 8 + 8 ÷ 4

Next division is performed so 8 ÷ 4 is executed giving 2 as the answer

Finally 8 + 2 is executed giving 10

The percentage of women that have heights between 64 and 66 inches is 42.06%

The third quartile is 65.1875 inches

Part a

Given: mean=63.5 inches

std. deviation=2.5 inches

To find percentage: we calculate probability and convert to percentage

P(64<X<66) would mean

Z statistic=64-63.5/2.5=0.2

                 =66-63.5/2.5=1

From Z table, we find corresponding probability values.

Therefore, P(64<X<66)=P(0.2<Z<1)=0.84134-0.42074

                                                                     =0.4206

Thus percentage=0.4206*100

                           =42.06%

Part b

Finding the third quartile, Q3

Q3=mean+(0.675)*std. dev

Q3=63.5+(0.675*2.5)

=65.1875 inches

Hence, the third quartile is 65.1875 inches  

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Answer: 6.44 square meters

Step-by-step explanation:

The area of a rectangle is given by the formula: A = L x W, where L is the length and W is the width.

Substituting the given values, we get:

A = 2.8 x 2.3 = 6.44 square meters

Therefore, the area of Ana's garden is 6.44 square meters.

Answer:

It's A. The points all lie very close to the line of fit, and the line is decreasing.

Step-by-step explanation:

The points all lie very close to the line of fit, and the line is decreasing option (A) is correct.

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

\(\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}\)

It is given that:

The value of the correlation coefficient r = -0.97

As we know,

If the value of the correlation coefficient is positive it represents the line of best-fit increasing.

If the value of the correlation coefficient is negative it represents the line of best fit decreasing.

If the value of r is close to 1 then we can say that the correlation between the two variables is very strong.

Thus, the points all lie very close to the line of fit, and the line is decreasing option (A) is correct.

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Answer: Z<4

Step-by-step explanation:

Rearrange the equation

-3(z-6) - (2z-2)>0

-3z+18-2z+2>0

-5z +20>0

-5(z-4)>0

divide  both side by -5

z-4<0

z<4

Answer:

Step-by-step explanation:

Given the price of 10packs as $41.50, we can express it as;

10 packs = $41.50

To get the equivalent price of 1 pack, we will say;

1 pack = $x

Solving both equalities for x;

10 packs = $41.50

1 pack = $x

cross multiply

10 * x =  1 * 41.50

10x = 41.50

Divide both sides by 10

10x/10 = 41.50/10

x = 4.150

Hence the price for each pack is $4.150

FALSE. The number of degrees of freedom in cross-tabulation data is calculated by subtracting 1 from the product of the number of rows and columns.

Therefore, in this case, the number of degrees of freedom would be (3-1) x (4-1) = 6.

Degrees of freedom refer to the number of independent pieces of information in a data set, which can be used to calculate statistical significance and test hypotheses.

In cross-tabulation, degrees of freedom indicate the number of cells in the contingency table that are not predetermined by the row and column totals.

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Answer:

Lots of "ifs" here.

A=bh/2 is the formula for the area of a triangle.

A=bh is the formula for the area of a rectangle or a parallelogram.

If the 6 & 4 area the base & height of a rectangle, then (6)(4) = 24 in^2

If the 6 & 10 are the base and height of a triangle, then 1/2(6)(10) = 30 in^2

Step-by-step explanation:

Using 1 balls and bins, n balls are thrown into m bins; m and n are positive numbers. the probability of any given bin containing one ball is n/m n * (1 - (1 - 1/m)^n) / m^2

Given that n is the number of balls and m is the number of bins, the probability of any given bin containing one ball is n/m. Therefore, the variance of x is equal to the variance of a binomial random variable with n trials and probability of success p = n/m.

By the formula for the variance of a binomial random variable, the variance of x is equal to n * (1 - (1 - 1/m)^n) / m^2.

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By performing these elementary row operations, we can transform matrix A into matrix B. To turn A=[00 10] into B=[01 00], we need to perform the following elementary row operations .

Swap the first and second rows: R1 ↔ R2 Multiply the first row by -1/2: -1/2 * R1 Add the first row to the second row: R2 + R1 To turn A=[4 -1 3 0] into B=[0 1 1 1], we need to perform the following elementary row operations .

Divide the first row by 4: (1/4) * R1 Multiply the second row by -1/5: -1/5 * R2 Subtract 3 times the first row from the third row: R3 - 3R1 Subtract 4 times the first row from the fourth row: R4 - 4R1 Swap the second and third rows: R2 ↔ R3

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Answer:

$448.50

General Formulas and Concepts:

Pre-Algebra

Statistics

Simple Interest Rate Formula: A = P(1 + rt)

Step-by-step explanation:

Step 1: Define variables

P = 390

r = 0.03

t = 5

Step 2: Find A

And we have our final answer!

Answer:

The Answer Is: 448.50 Just did the question

Step-by-step explanation:

A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

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Answer:

1 2/3

Step-by-step explanation:

she will need 1 and 2/3rds cups of of flour

Answer:

1 2/3

Step-by-step explanation:

1/3 for 1 pie

1/3 x 5 for 5 pies = 1 2/3

Answer:

5

Step-by-step explanation:

y2-y1/x2-x1

-6- -16 = 10

10-8=2

10/2=5

The unit rate for the given case is 8 shirts per hour.

The ratio of two numbers a and b can be written as a : b = a/b. The ratio of two quantities is the unit rate of one quantity with respect to the other.

The total number of shirts are 32.

And, the time for sale is 4 hours.

Now, the unit rate can be calculated by taking the ratio of shirts and time as below,

Unit rate = Number of shirts ÷ Time

⇒ 32 ÷ 4 = 8

Hence, the unit rate of the sale is 8 shirts per hour.

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This given figure carries onto themself at 360, 180, and 60 degrees respectively.

If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.

Given three figures those figures have rotational symmetry from their center point.  The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.

for figure 1

figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.

for figure 2

figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.

for figure 3

figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.

therefore, the given figures have 1, 2, and 6 rotational symmetry.

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