find the equation of a line perpendicular to 2y=6-2x that passes through point (6,-7)

The value of e (exponential) is approximately equal to 2.718281 which is rounded to 6 digits. The exponential constant frequently happens in mathematics every time the exponential functions are involved.

Log mention to a logarithm to the base 10. Ln mentions a logarithm to the base e. This is also known as a common logarithm. This is also known as a natural logarithm.

The first common log is represented as log 10 (x) The second natural log is represented as log e (x) The exponent form of the common logarithm is 10 x =y.

An exponential function is a function in which a number or data is raised to the power of another number or a variable.

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Answer:

Step-by-step explanation:

from the figure we kown the speed is 9/3=15/5=21/7=3 km per minute

the distance in 8 minute is 3 ×8=24 km

201.06 square units (rounded to 2 decimal places) is the area of the given circle.

The formula for the area A of a circle is A = πr², where r is the radius of the circle and π is the famous, well-known irrational number pi equal to 3.14159 (rounded to 5 decimal places).

Given that the circle's diameter is 16, and that a circle's radius is equal to half its diameter, the following conclusions can be drawn:

r = d/2

= 16/2

= 8

A=πr2

AND HALF THE DIAMETER IS THE RADIUS (r)

r=8

A= πr2 = π (8) squared = 64 * π = 200.96

or,

Now, substituting the values of r and π into the formula for the area of a circle, we get

A = πr²

= (3.14159)(8²)

= (3.14159)(64)

= 201.06 square units (rounded to 2 decimal places) is the area of the given circle.

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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² = [tex](10 \sqrt{34})^2 \\[/tex]

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

When two or more lines in a plane cross one another, they are referred to as intersecting lines. The common point shared by all intersecting lines is the point of intersection, which can be found on all of them.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² =

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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Answer:

The answer is $4.50.

Step-by-step explanation:

To solve this problem, divide the result ($6.75) by the percentage (150%). This gives you the original number which was multiplied by the percentage. So,

$6.75 / 150% = $4.50.

Answer:

$4.50

Step-by-step explanation:

150% × □ = $6.75

First, we can rewrite 150% as the fraction 3/2.

[tex]\dfrac{3}{2} \times \square = \$ 6.75[/tex]

Then, we can also rewrite 6.75 as the fraction 27/4.

[tex]\dfrac{3}{2} \times \square = \$ \, \dfrac{27}{4}[/tex]

Next, we can isolate the unknown by multiplying both sides by 2/3 (the reciprocal of 3/2).

[tex]\left(\dfrac{2}{3} \right)\left(\dfrac{3}{2} \times \square \right) = \left(\$ \, \dfrac{27}{4}\right)\left(\dfrac{2}{3} \right)[/tex]

After that, simplify by multiplying out the numerators and denominators on the right side of the equation.

[tex]\square = \$ \, \dfrac{27 \times 2}{4 \times 3}[/tex]

[tex]\square = \$ \, \dfrac{54}{12}[/tex]

Finally, simplify the expression on the right side to a decimal form.

[tex]\square = \$ \, \dfrac{54 \div 2}{12 \div 2}[/tex]

[tex]\square = \$ \, \dfrac{27 \div 3}{6 \div 3}[/tex]

[tex]\square = \$ \, \dfrac{9}{2}[/tex]

[tex]\square = \$ 4.50[/tex]

The sample size needed for a margin of error of 1%, for a confidence level of 90%, is of:

6,766.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error of the interval is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.

We have no prior estimate, hence the proportion is given as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of M = 0.01, the needed sample size n is obtained as follows:

[tex]0.01 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.645 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.645 \times 0.5}{0.01}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 0.5}{0.01}\right)^2[/tex]

n = 6,766.

(rounding up, as for a sample size of 6,765 the margin of error would be slightly above 0.01).

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 The value of h'(2) = 50.

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. In other word, it is a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

here we are given a function h(x)

here h(x) = - 5f(g(x)) ------(i)

and we are given the value of

g(2) =3   ;   f(2) = 1     ;     g'(2) = -2

f(3) = 4   ;    f'(3) = 5    ;    f'(2) = 6.

and we need to find the value of h'(2).

here f(x), g(x) and h(x) are the function of x and f'(x), g'(x) and h'(x) denotes the derivative of f(x), g(x) and h(x) respectively.

so we are given ,

h(x) = - 5f(g(x))

differentiating with respect to x both side

h'(x) = -5 f'(g(x).g'(x).

at x =2,

h'(2) = [tex]-5*f'(g(2))*g'(2)[/tex]

and we know  g(2) = 3 and g'(2) = -2.

so,

h'(2) = [tex]-5*f'(3)*-2[/tex]

h'(2) = [tex]-5*5*-2\\[/tex]       ( as f'(3) = 5 )

h'(2) = 50

so Option C is correct, the value of h'(2) = 50.

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The function which has greater slope is Function 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Function 1:

y = -2x + 10

and Function 2:

Slope = (5-10)/( 2-0) = -5/2

So, the Equation of line

(y - 10) = -5/2 (x -0)

y - 10 = -5/2x

y = -5/2x + 10

y= -2.5x +10

So, the slope of Function 1 is greater than slope of function 2.

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The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Now, According to the question:

Solving Two Step Equations:

Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:

Step 1: Addition and subtraction to isolate the variable.

Step 2: Multiplication or division to determine the value of the variable.

Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:

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For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

discriminant : [tex]b^2-4ac[/tex]

if [tex]b^2-4ac[/tex] is positive, Both solutions are real.

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Answer:

d ≈ 7.07 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )

d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]

  = [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]

  = [tex]\sqrt{7^2+1}[/tex]

  = [tex]\sqrt{49+1}[/tex]

  = [tex]\sqrt{50}[/tex]

  ≈ 7.07 units ( to 2 decimal places )

Answer:

$8

Step-by-step explanation:

Let x be the coefficient of y^2 in the expression 2x^2y+15xy^2-7y. So x=0.

What is co-efficient?

A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves.

Write an example of co-efficient.

As an illustration, 6z stands for 6 times z. Since z is a variable, 6 is a coefficient. For variables without a value, the coefficient is 1.

The given algebraic expression is 2yx^2+15xy^2-7y.

The terms are xy^2, yx^2 any y^2

So the co-efficient of y^2 is 0

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Answer:

46

Step-by-step explanation:

You multiply 23×2 and that is how I got my answer.

Answer:

  9 cm

Step-by-step explanation:

You want the radius of the sphere that has a surface area of 324π cm².

The area of a sphere is given by the formula ...

  A = 4πr²

Filling in the given values, we can solve for r:

  324π = 4πr²

  81 = r² . . . . . . . . . divide by 4π

  9 = r . . . . . . . . . . . take the square root

The radius of the sphere is 9 cm.

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Answer: To find the height of the goalpost, we can use the information provided in the problem and the concept of similar triangles. Since Violet is looking down at the mirror, the line of sight from her eyes to the top of the goalpost forms a right angle with the ground. This right angle creates two similar triangles, one between her eyes, the ground, and the top of the goalpost, and the other one between the mirror on the ground, the goalpost, and a point on the ground that is the same distance from the mirror as the top of the goalpost is from Violet's eyes.

Since similar triangles have the same angle measures, we can set up the following proportion:

(distance from mirror to point on the ground) / (distance from mirror to top of goalpost) = (distance from Violet's eyes to ground) / (height of goalpost)

We can now use the information provided in the problem to solve for the height of the goalpost.

(6.65+4.25)/x = 1.75 / H

x = (6.65+4.25) * (1.75/H)

Where x is the distance from mirror to top of the goalpost.

Substitute the known values and solve for H

H = 1.75*(6.65+4.25) / x = 1.75*10.9 / x

We know that x = 4.25, so

H = 1.75*10.9 / 4.25 = 4.093 m

The height of the football goalp

Step-by-step explanation:

Answer:

The independent variable in this scenario is the number of meals Gabe and Bridgette prepare (m), because this is the variable that they can control and manipulate. The dependent variable is the number of people they will be able to serve (p), because this is the variable that depends on the number of meals they prepare.

Step-by-step explanation:

In other words, the number of people they can serve is affected by the number of meals they prepare, but the number of meals they prepare is not affected by the number of people they can serve.

Answer:

independent variable = m

dependent variable = p

Step-by-step explanation:

The number of people they are able to serve depends on the number of meals they prepare.

A table of equivalent ratios for the number of treasure chests and hours that Hannah recovered is as follows:

Treasure chests      Hours

8                                  4

12                                 6

10                                 5

In order to have a proportional relationship and equivalent ratios, the variables x and y must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 4/8

Constant of proportionality (k) = 0.5.

When hours y = 6, the number of treasure chests x is given by:

x = y/k

x = 6/0.5

x = 12.

When treasure chests x = 10, the number of hours y is given by:

y = kx

y = 0.5(10)

y = 5.

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Complete Question:

Hanna is recovering hundreds of treasure chests from an ancient shipwreck. She is able to recover 8 chests every 4 hours.

Complete the table using equivalent ratios. Select all the answers that will fill the table.

The range and the IQR of the weights are 3.3 pounds and 0.95 pounds respectivly.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, there are different processes to take when calculating the median.

The term "standard deviation" (or "[tex]\sigma[/tex]") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

a) the range is the difference between the highest and lowest value:

range =7.5-4.15 =3.3 pounds

the IQR is the difference between the third and first quartile

IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds

b) Skewed because the mean and median are not the same value.

c) All values will be multiplied by 16

Mean: 96 ounce

Standard deviation: 10.4 ounce

Quartiles: 89.6 ounce and 104.8 ounce

Median:99.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

d) The mean,quartiles and median increase by 30,the result remain unchanged:

Mean: 126 ounce

Standard deviation: 10.4 ounce

Quartiles: 119.6 ounce and 134.8 ounce

Median:129.2 ounce

IQR: 15.2 ounce

Range: 52.8 ounce

e)  The median, quartiles and IQR might not changed,because they are unaffected by an outlier.

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Answer: 256b

Step-by-step explanation: So, first we need to find the square root of 16b.

That'd be 4b, because a square root is when a number can be divided by a number, such as 4 can go into 16 4 times, and like 5 can go into 25 5 times. So, we got 4b

So, 4 to the power of 4 (ignore the b right now) is the same as 4 x 4 x 4 x 4.

So simplified, that'd be 16 x 4 (64). So, 64 x 4 = 256.

So, I'd be 256b

The decimal that is represented by the shaded portion of the model is 0.45

Suppose that the number is abcd.efg and belongs to the decimal numerical system.

Remember one thing that the place on the left of decimal point is called ones. Move one-one places to right, and divide by 10 and 10 more and more.

Move one-one places to left, and multiply (un-divide) by 10 and 10 more and more.

We are given In the model, a hundreds grid represents 1 whole.

Since 45 out of the 100 squares are shaded,

This means the fraction would be 45/100

45/100 = 0.45.

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The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.

The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.

What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters

we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,

then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters

the ladder touches the build at 4.53 meters vertical distance from the ground.

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Answer:

when x=10 & y=6

10-6=4 so,

x=8

y=4

After solving, the height in feet of the sixth bounce is 1.892 feet.

In the given question, we ave to find the height, in feet, of the sixth bounce.

From the given question,

Height on the first bounce = 6.7

Subsequent bounce reaches a height of the previous bounce = 81%

Suppose the height is h.

So according to the question:

h(6) = height on the first bounce*(subsequent bounce reaches a height of the previous bounce)^6

h(6) = 6.7*(81%)^6

h(6) = 1.892 feet

So the height of sixth bounce is 1.892 feet.

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Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.

An equation is an expression that shows the relationship between two or more numbers.

From the line plot shown:

Total number of students = 3 + 4 + 2 + 2 + 8 + 4 + 6 + 9 = 38

Students who ran more than 3 laps = 2 + 8 + 4 + 6 + 9 = 29

Students who ran more than 2 1/2 laps = 2 + 2 + 8 + 4 + 6 + 9 = 31

Students who ran more than 3 1/2 laps = 2 + 8 + 4 + 6 + 9 = 29

Hence:

Most of the students ran more than 3 laps and Most of the students ran 2 1/2 laps.

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Answer:

See picture below

Step-by-step explanation:

The value of x would be 32.

What are a congruent quadrilaterals?

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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By analyzing the figure, The value of x would be 32.

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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Answer:

The numbers are being divided by 2 each time.

240/2 = 120

120/2 = 60

So the next set of numbers would be:

30, 15 because

60/2 = 30

30/2 = 15

Step-by-step explanation:

Hope it helps!