What type of conic section is formed when a right, circular cone is intersected by a plane that is parallel to the base of the cone?

The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

First, we determine the slope of the line.

Given the two points are (-7, -3) and (1, 2)

We can find the slope of the line by using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values, we get:

m = (2 - (-3)) / (1 - (-7))

m = 5/8

Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.

Let's use the point (-7, -3:

y - y₁ = m(x - x₁)

[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]

Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].

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An equation for this linear function that describes how height varies with age is y = 1/5(x) + 2.

The predicted height at 9 is 3.8 feet.

The predicted height at 31 is 8.2 feet.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Conversion:

1 feet = 12 inches

24 inches = 24/12 = 2 feet.

Next, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 - 2)/(10 - 0)

Slope (m) = 2/10

Slope (m) = 1/5

At data point (0, 2) and a slope of 1/5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 1/5(x - 0)  

y = 1/5(x) + 2

When x = 9, the predicted height is given by;

y = 1/5(9) + 2

y = 3.8 feet.

When x = 31, the predicted height is given by;

y = 1/5(31) + 2

y = 8.2 feet.

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Answer:

Step-by-step explanation:

4x - 5 = 7

4x = 7 + 5

4x = 12

x = 12/4

x = 3

When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)

First, we shall determine the value of A. Details below:

Quadratic equation is expressed as:

x² - (sum of root)x + product of root

Comparing the above with x² - 11x + 30, we have

x² - 11x + 30 = x² - (sumof root)x + product of root

Product of roots = 30

Thus,

A = 30

Next, we shall determine the value of B. details below:

f(x) = x² + 5

f(2) = 2² + 5

f(2) = 9

Thus,

B = 9

Next, we shall determine the value of C. Details below:

Let

x + 4 = 0

Thus,

x = -4

Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:

Remainder = x² - 2x - 24

Remainder = (-4)² - 2(-4) - 24

Remainder = 0

Thus,

C = 0

Finally, we shall determine value of A/5 + √(B - C). Details below:

A/5 + √(B - C) = 30/5 + √(9 - 0)

A/5 + √(B - C) = 6 + √(9

A/5 + √(B - C) = 6 + 3

A/5 + √(B - C) = 9

Thus, the value of A/5 + √(B - C) is 9 (option B)

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The number for which the theoretical probability matches the experimental probability is 2.

Experimental probability and theoretical probability are two different ways to determine the likelihood of an event occurring.

Experimental probability is determined by performing an experiment or conducting observations and collecting data to see how often an event occurs. This method involves counting the number of times an event occurs and dividing that number by the total number of trials or observations.

Theoretical probability, on the other hand, is determined by using mathematical principles and calculations to determine the likelihood of an event occurring. It is based on the assumption that all outcomes are equally likely.

In the given table;

For theoretical, P(2) = 1/4

For experimental, P(7) = 7/28 = 1/4

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The [tex]f^{-1}[/tex] inverse of f  of each

1) (x + 1)/2

2) [tex]\sqrt{\frac{x+1}{4} } \\[/tex]

3) 3 - 4x

4) [tex](x+5)^{1/3}[/tex]

5) [tex]\sqrt{x + 4}[/tex]

1) function f(x) = 3x + 1

let f(x) = y

y = 3x + 1

y - 1 = 3x

(y - 1)/3 = x

x obtained is [tex]f^{-1}[/tex]

and y will be x

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

2) equation f(x) = 4x² - 1

let f(x) = y

y = 4x² - 1

y + 1  = 4x²

(y + 1 )/4 = x²

x = [tex]\sqrt{\frac{x + 1}{4} }[/tex]

x obtained is [tex]f^{-1}[/tex]

and y will be x

[tex]f^{-1}[/tex] =  [tex]\sqrt{\frac{x + 1}{4} }[/tex]

similarly,

3) f(x) = 3-x/4

y = 3-x/4

4y = 3 - x

x = 3 - 4x

[tex]f^{-1}[/tex] =  3- 4x

4) y = x³ - 5

y + 5 = x³

x = [tex](y + 5)^{1/3}[/tex]

[tex]f^{-1}[/tex] = [tex](x+5)^{1/3}[/tex]

5) y = x² - 4

y + 4 = x²

x = √y + 4

[tex]f^{-1} = \sqrt{x + 4}[/tex]

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The length of AB is 27.3m and AD is 113 m.

Using Trigonometry in Triangle ABC

tan 50. 8 = P / B

tan 50.8 = AB / 22.3

1.2261 = AB/ 22.3

AB =  27.34 m

Now, again using Trigonometry

tan 25.4 = P / B

tan 50.8 = AD / 27.34

0.474 = AD/ 27.34

AD =  12.95916 m

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I can't see the chart...

The equation of the line passing through the given points is y = 6x

Given that are the values of x and y coordinates we need to find the equation of the line using them,

So, considering the points (4, 24) and (5, 30),

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (4, 24) and (5, 30),

Therefore, the required equation is =

y-24 = 30-24/5-4 (x-4)

y-24 = 6(x-4)

y-24 = 6x-24

y = 6x

Hence, the equation of the line passing through the given points is y = 6x

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Answesar:

Step-by-step explanation:

SA = 10(5)² = 250cm²

Volume² = 2 (5)³ = 250cm³

They are not equal.

Surface area is in square cm and volume is in cm³.

A. Using the formula for area of rectangle, the length of the rectangular space is: 2x - 3

B. The expression to prove this is: (2x - 3) * 4x = 8x² - 12x

To find the area of a rectangle, multiply the width and the length together. This means: Area = length * width.

Part A: We are given that area of the rectangular space is expressed as 8x² - 12x, if the width is 4x, then:

Length of the rectangular space = (8x² - 12x) / 4x = 4x(2x - 3)/4x

Length = 2x - 3

Part B: To prove this, we have:

length * width = 8x² - 12x

Substitute:

(2x - 3) * 4x = 8x² - 12x

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Therefore , the solution of the given problem of unitary method comes out to be 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).

The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.

Here,

The circumference of the circle the bike tyre forms is equal to the distance travelled in one rotation of the tyre. The following formula determines a circle's circumference:

=> C = 2πr

where the mathematical constant is roughly equivalent to 3.14159 and r is the circle's radius.

Your bicycle tyre's radius in this instance is 12 inches. The tyre's circumference is as follows:

=> C = 2π(12) = 24π inches

You may easily calculate how far you will travel after 50 spins by multiplying the tyre's circumference by the number of turns:

=> Covered distance:  50 × 24π ≈ 376.99 inches

As a result, after 50 tyre rotations, you will have covered around 376.99 inches (or about 31.41 feet).

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The required maximum area of the rectangle is 17.5m

The perimeter of a rectangle is = 70m.

We have to find The maximum area of rectangle .

A rectangle will have the maximum possible area for a given perimeter when all the sides are the same length. Since every rectangle has four sides, if you know the perimeter, divide it by four.

Maximum area of rectangle is = 70 / 4

                                                   = 17.5

The required value of maximum area of the rectangle is 17.5m.

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the perimeter of a rectangle is 70m. What are the dimensions that will produce the maximum area of such a rectangle

Answer:

[tex]y = -x/5 -4.[/tex]

Step-by-step explanation:

To simplify the line x + 5y = 20 into y = mx + b form:

x + 5y = 20.

5y = -x + 20.

y = -x/5 + 4.

The line parallel to the line y = -x/5 + 4 will have the same slope of -1/5.

We get the equation:

y = -x/5 + b.

To find b, we plug in the point (5, -5).

-5 = -5/5 + b.

-5 = -1 + b.

b = -4.

[tex]y = -x/5 -4.[/tex]

The calculated value of the surface area of the cylinder is 138π square inches

From the question, we have the following parameters that can be used in our computation:

Height, h = 5 1/2 inches

Diameter, d = 12 inches

Using the above as a guide, we have the following:

SA = 2πr(r + h)

Where

Radius, r = d/2

r = 12/2

r = 6

Substitute the known values in the above equation, so, we have the following representation

SA = 2 * π * 6(6 + 5 1/2)

Evaluate

SA = 138π

Hence, the surface area of the cylinder is 138π square inches

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Answer: 12

Step-by-step explanation:

We have to find h so the first step is to subtract the 11 from the 20

3/4h=9

Then to move the 3/4 over to the other side, you must multiply it by it's reciprocal, 4/3.

h= 4/3 x 9

This equals 12.

Answer:

36 °

Step-by-step explanation:

The markings imply equal sides*

So both of the angles are 27° there

To find angle a we do 180 - (27+27) and obtain 126°

Then to find angle y, we do 180-angle a which is 180-126 and we get 54°

We now have reached the triangle where you're supposed to find x right?

So x is equal to 180 - both other angles, which is 180 - (90 and angle y) = 180- (90+54) = 180 - 144 = 36 which is your final answer

Shawn's phone is 36 cubic cm larger than Ellie's phone.

To get difference in volume between the two phones, we must calculate  volume of each phone and subtract the volume of Ellie's phone from the volume of Shawn's phone.

The volume of a rectangular prism is: length*width* height. The height of both phones is 3/4 centimeters.

The volume of Ellie's phone is:

= length x width x height

= 12 cm x 6 cm x (3/4) cm

= 54 cubic centimeters

The volume of Shawn's phone is:

= length x width x height

= 15 cm x 8 cm x (3/4) cm

= 90 cubic centimeters

The difference in volume is:

= Volume of Shawn's phone - Volume of Ellie's phone

= 90 cubic centimeters - 54 cubic centimeters

= 36 cubic centimeters

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The area of a shape is calculated by calculating the amount of space on the shape

By definitinon, the area of a shape is the amount of space on the shape

using the above as a guide, we have the following:

There are several formulas to calculate area

The formula to use is dependent on the shape whose area is being calculated

This means that the area of trapezoid cannot be calculated using the area of parallelogram

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The result of the row 1 multiplication by 1/4 is determined as  [¹/₂  0 ].

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [2 0]

To multiply row by 1/4, we will multiply each entity by 1/4 as shown below;

[2 0] x 1/4 = 1/4(2 0)

= [¹/₂  0 ]

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, that is 2, and 0 by 1/4.

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the equation for the curve C as n approaches infinity     is           y = x This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

what is diagonal line ?

A diagonal line is a straight line that runs obliquely (at an angle) between two opposite corners of a geometric shape, such as a rectangle or a square. It is called "diagonal" because it connects two non-adjacent vertices of the shape, forming a diagonal across the interior of the shape.

In the given question,

As n increases, the process described in the question creates a set of line segments that connect the equally spaced points on the x-axis to the equally spaced points on the y-axis. The resulting curve is a piecewise linear function that converges to a continuous curve as n approaches infinity.

To derive an equation for this curve, we can start by considering the line segment connecting the first mark on the x-axis to the last mark on the y-axis. Let's call this point (0, 1) and the nth mark on the x-axis (1, 0). The slope of the line connecting these two points is given by:

m = (0 - 1) / (1 - nth mark) = (1 - nth mark)^(-1)

where the nth mark on the x-axis is given by:

nth mark = 1 - (1/n)

Substituting this expression for nth mark into the equation for m, we get:

m = (n/(n-1))

The y-intercept of the line is given by:

b = 1 - m = 1 - (n/(n-1)) = 1/(n-1)

Therefore, the equation for the line segment connecting the first mark on the x-axis to the last mark on the y-axis is:

y = (n/(n-1))x + 1/(n-1)

Similarly, the equation for the line segment connecting the second mark on the x-axis to the second last on the y-axis is:

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

Continuing this process for all n line segments, we get:

y = (n/(n-k))x + 1/(n-k)

where k = 1, 2, ..., n.

To get the equation for the curve C, we need to take the limit as n approaches infinity. As n goes to infinity, the value of k becomes insignificant compared to n, and we can approximate the equation for the curve as:

y = x

Therefore, the equation for the curve C as n approaches infinity is:

y = x

This is the equation of the diagonal line that passes through the points (0, 0) and (1, 1).

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The interest rate if Ted made $56 in interest for 1 year on a principle of $700 will be 8%.

Given, the interest amount is $56.

The principal amount is $700.

The time period of investment is 1 year.

Now, we have to find the interest rate.

The formula to find the simple interest is,

  S.I = PTR/100.

Now, we need to substitute the values in the above formula.

S.I = PTR/100

56 = 700×1×R / 100

56 = 700R/100

5600 = 700R

R = 5600/700

R = 8

Therefore, the interest rate is 8%.

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Answer:

what arecrosses on line 2

Answer:

Step-by-step explanation:

In a circle, the measure of an inscribed angle is equal to half the measure of its intercepted arc. In this case, the inscribed angle is ∠WVX and its intercepted arc is ⌢WX.

Since the length of ⌢WX is (9/2)π, its measure in degrees is (9/2)π * (180/π) = 810/2 = 405 degrees.

Therefore, the measure of ∠WVX is half the measure of its intercepted arc, which is 405/2 = 202.5 degrees.

Answer:

(r, y)=(10,-2)

Step-by-step explanation: Hope this helps :)

False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.

The tax incidence (the division of the burden of a tax between buyers and sellers) does not depend on which side of the market the tax is levied on, but rather on the relative elasticities of supply and demand. In this case, we don't have information about the elasticities of supply and demand, so we cannot determine the tax incidence. However, we can infer that the tax on consumers did reduce the quantity sold (from 30 million liters to 25 million liters), so it's unlikely that a tax on producers would have had a larger effect.

Therefore, False. The effect of the tax on the quantity sold would not have been larger if the tax had been levied on producers.

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If a turtle lives in a garden and a hedgehog lives in the woods. The distance between the garden and the woods is 450m.

Let d represent the distance between the turtle's garden and the hedgehog's wood

Let h represent the  speed of the hedgehog

Let the  turtle's speed = h-10

Le the time it takes for the hedgehog to walk from the woods to the meeting point= t

Set up two equations

d = (h-10)(t+4.5) + ht (Equation 1)

d - 150 = ht (Equation 2)

Solve for d by substituting equation 2 into equation 1:

ht + (h-10)(t+4.5) = ht + 150

(h-10)t + 45h = 150

t = (150 - 45h) / (h-10)

Substitute t into equation 2:

d = ht + 150 - (h-10)(t+4.5)

d = h(150 - 45h)/(h-10) + 150 - (h-10)(45h/(h-10) + 4.5)

d = 2250/(h-10) (distance between the garden and the woods)

Since the turtle and hedgehog meet in 5 hours

Thus,

d = ( h-10 ) (5) + h( 5- 4.5 )

d = 5h - 25

Substitute

5h - 25 = 2250/(h-10)

Multiplying both sides by h-10

5h² - 75h + 250 = 0

Dividing both sides by 5

h²- 15h + 50 = 0

Using the quadratic formula

h = (15 ± sqrt(15^2 - 4(1)(50))) / (2*1)

h = (15 ± 5) / 2

So,

h = 10 or h = 5

Distance between the garden and the woods :

d = 2250/(h-10)

d= 2250/(5-10)

= 450 meters

Therefore the distance is 450m.

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Answer: A) Let's first calculate how far the van would have traveled in the half hour before the car started. The van's speed is 50 km/h, which means in half an hour it would have traveled 50/2 = 25 km.

Now let's consider the time it takes for the car to catch up to the van. We can represent this using the formula:

distance = rate × time

Let's call the time it takes for the car to catch up "t". We know that during this time, the van is also traveling. In fact, it has been traveling for t + 0.5 hours (the half hour before the car started plus the time it takes for the car to catch up). So the distance the van has traveled is:

distance van = 50 × (t + 0.5)

The distance the car has traveled is:

distance car = 60t

When the car catches up to the van, they will have traveled the same distance. So we can set the two distances equal to each other:

50(t + 0.5) = 60t

Simplifying this equation:

50t + 25 = 60t

Subtracting 50t from both sides:

25 = 10t

So t = 2.5 hours.

But we're not done yet! We need to add the 0.5 hours that the van traveled before the car started to get the total time it took for the car to catch up:

t + 0.5 = 2.5 + 0.5 = 3 hours

So the car catches up to the van 3 hours after the van started, or at 12:15 pm.

B) We can use the formula:

distance = rate × time

to find the distance between the two towns. We know the car traveled for 6 hours (from 9:45 am to 3:45 pm) and its speed was 60 km/h. So the distance it traveled is:

distance car = 60 × 6 = 360 km

We also know that the van traveled for 6.5 hours (from 9:15 am to 3:45 pm) and its speed was 50 km/h. So the distance it traveled is:

distance van = 50 × 6.5 = 325 km

The distance between the two towns is the difference between these two distances:

distance = distance car - distance van = 360 - 325 = 35 km

So the distance between the two towns is 35 km.

The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.

To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula

x = (-b ± √(b²-4ac)) / 2a

Substituting the values, we get

x = (-2 ± √(2²-4(-2)(1))) / 2(-2)

Simplifying the expression inside the square root

x = (-2 ± √(4+8)) / (-4)

x = (-2 ± √12) / (-4)

Simplifying the radical

x = (-2 ± 2√3) / (-4)

Reducing the fraction

x = (1 ± √3/2)

Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).

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A linear function would be the best fit for the given data because as x increase the y-values change linearly.

Rounded to the .5 the slope of the function is approximately 32.5

A linear relation means that any increase of 1 unit in the independent variable (x) has always the same impact in the other variable (y).

In this particular case, the increases in the y-value are:

56 - 24 = 32

88 - 56 = 32

122 - 88 = 34

The mean of that, rounded to .5, is (32 + 32 + 34)/3 = 32.5

So the change is almost the same one, then this seems to be a linear relation.

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