How to get the centre of the circle when the circumference is not given

Answers

Answer 1

To find the center of a circle when the circumference is not given, you still find it.

1. Determine the coordinates of at least three non-collinear points on the circle. Non-collinear points are points that do not lie on a straight line.
2. Using these points, create two line segments that are chords of the circle. A chord is a line segment connecting two points on the circle.
3. Find the midpoints of each chord. The midpoint formula is given as: Midpoint (M) = ((x1 + x2) / 2, (y1 + y2) / 2).
4. Calculate the slope of each chord using the slope formula: Slope (m) = (y2 - y1) / (x2 - x1).
5. Calculate the slope of the perpendicular bisectors of each chord. Since these lines are perpendicular to the chords, their slopes are the negative reciprocal of the chord slopes: m_perpendicular = -1 / m_chord.
6. Write the equation of each perpendicular bisector using the point-slope formula: y - y_midpoint = m_perpendicular * (x - x_midpoint).
7. Solve the system of equations formed by the two perpendicular bisectors. The solution is the coordinates of the center of the circle.

By following these steps, you can find the center of the circle even when the circumference is not given.

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Related Questions

I NEED HELP ON THIS ASAP!! PLEASE, IT'S DUE TODAY!!!! I WILL GIVE BRAINLIEST!

Answers

Step-by-step explanation:

A, 7^(x+3) = 823, 543

7^(x+3) = 823, 543

7^(x+3) = 7^7 ....... write in the power form which it's base must be 7 in order to equalify the power

x+3 = 7

x = 4

B, 4^ -4x = 4^-8

4 ^ -4x = 1/65, 536

4^ -4x = 1/4^8 ........ write in the power form

4^ -4x = 4^-8

-4x = -8 ..... write equality among the power cause it's base is same

x=2

C, 1/(6^(x-5) ) = 1296

1/(6^(x-5) ) = 1296

6^-(x-5) = 1296

6^-(x-5) = 6^4........ write in the power form

-(x-5) = 4

-x + 5 = 4

-x = -11

x = 1

D, 1/3^x+7 = 1/243

1/3^x+7 = 1/243

3 ^ -(x+7) = 3^-5 .... write in the power form

-(x+7) = -5

-x-7 = -5

-x = 2

x= -2

At a large university, 15% of students are left-handed. A psychology professor selects a random sample of 10 students and records L = the number of left-handed students in the sample. Starting on line 1 of the random-number table, how many left-handed students occur in the first trial of the simulation if we let 00-14 represent left-handed students?

Answers

The number of left-handed students in the first trial of the simulation can be found by following the above steps and counting the occurrences of two-digit numbers within the 00-14 range on line 1 of the random-number table.

To find out how many left-handed students occur in the first trial of the simulation, you'll need to follow these steps,
1. Identify the probability range for left-handed students, which is 00-14 as you've mentioned.
2. Start on line 1 of the random-number table.
3. Read each two-digit number on the line and check if it falls within the range 00-14.
4. Count the number of times a number within the 00-14 range appears in the first 10 two-digit numbers (since you're selecting a random sample of 10 students).
5. The count of numbers within the 00-14 range represents the number of left-handed students in the first trial of the simulation.

By doing the aforementioned processes and counting the occurrences of two-digit numbers between the ranges of 00 and 14 on line 1 of the random-number table, it is possible to determine the number of left-handed pupils in the simulation's first trial.

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Evaluate the limit using L'Hospital's rule
lim (e^x + 2x - 1)/2x

Answers

To evaluate the limit using L'Hospital's rule, we need to take the derivative of both the numerator and denominator separately until we get a determinate form. We have:

lim (e^x + 2x - 1) / (2x)

Taking the derivative of the numerator:

lim (e^x + 2) / 2

Taking the derivative of the denominator:

lim 2

Since we now have a determinate form, we can evaluate the limit by plugging in the value of x. We get:

(e^x + 2) / 2

As x approaches infinity, e^x also approaches infinity, so the limit diverges to positive infinity. Therefore, the limit does not exist.

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What is the probability that a randomly selected participant dreams in black and white or color?

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The evaluated probability of randomly choosing a  participant dreams in black and white or color is 0.13, under the condition that the given Students are passing from psychology surveyed 200 of their fellow students regarding their dreams.

Probability means the possible chances of an event occurring in a particular time frame. It is a considered a branch of mathematics that deals with the occurrence of a random event.

The value is presented from zero to one. Probability has been induced in math to predict how prone are the events going to occur. The meaning of probability is basically the express  something that is likely to happen.

Black Probability = 4/200=0.02

White Probability = 12/200=0.06

Probability of all other color = 10/200=0.05

So, probability of randomly choosing a participant dreams in black and white or color =0.02+0.06+0.05=0.13

Therefore, the probability of randomly selecting participant dreams in black and white or color = 0.13

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The complete question is

Students majoring in psychology surveyed 200 of their fellow students about their dreams. The results of the survey are shown in the Venn diagram. Let B be the event that the participant dreams in black and white and let C be the event that the participant dreams in color.

What is the probability that a randomly selected participant dreams in black and white or color?

Use the expression 1/2 x 12 divided by 2 - 2 + 11 to create an expression that includes a set of parentheses so that the value of the expression is 13.

Answers

The expression (1/2 x 12 / (2 - 2 + 11) + 10) will give a value of 13.

We have,

One possible way to use parentheses to make the value of the expression equal to 13 is:

1/2 x (12 / (2 - 2 + 11))

Here's how the expression evaluates step by step:

- The expression inside the parentheses (2 - 2 + 11) evaluates to 11.

- The expression inside the innermost parentheses (12 / 11) evaluates to approximately 1.090909...

- The expression outside the parentheses (1/2) multiplied by 1.090909... evaluates to approximately 0.5454545...

- Finally, the subtraction of 2 and the addition of 11 to 0.5454545... gives a value of approximately 9.5454545...

However, this value is not 13.

So, we need to modify the expression further.

One way to do this is to add a constant inside the outermost parentheses to adjust the value of the expression.

For example:

(1/2 x 12 / (2 - 2 + 11) + 10)

Therefore,

The expression (1/2 x 12 / (2 - 2 + 11) + 10) will give a value of 13.

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Find the direction angles of the vector. (Round your answers to one decimal place.)
u = (-1, 9, -6)

Answers

The direction angles of the vector u = (-1, 9, -6) are approximately -6.1°, 64.8°, and -75.2° for the x, y, and z axes, respectively.

The direction angles of a vector are the angles that the vector makes with the positive x, y, and z axes. To find the direction angles of the vector u = (-1, 9, -6), we can use the formulas:

cosθx = u_x/||u||, cosθy = u_y/||u||, and cosθz = u_z/||u||

where θx, θy, and θz are the angles that u makes with the x, y, and z axes, respectively, and ||u|| is the magnitude of u, given by:

||u|| = √(u_x² + u_y² + u_z²)

Substituting the values of u, we have:

||u|| = √((-1)² + 9² + (-6)²) = √118

cosθx = -1/√118 ≈ -0.183, cosθy = 9/√118 ≈ 0.551, and cosθz = -6/√118 ≈ -0.366

Taking the inverse cosine of each of these values, we get:

θx ≈ -6.1°, θy ≈ 64.8°, and θz ≈ -75.2°

Therefore, the direction angles of the vector u are approximately -6.1°, 64.8°, and -75.2° for the x, y, and z axes, respectively.

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I Need help with this problem

Answers

It’s can be 240 or 5,278

This graph represents a quadratic function. The graph shows a downward parabola vertex at (0, 9) and passes through (minus 4, minus 7), (minus 3, 0), (3, 0), and (4, minus 7). What is the value of a in this function’s equation? A. 2 B. 1 C. -1 D. -2

Answers

Answer:

Based on the given information, we can conclude that the graph represents a quadratic function. The vertex of the parabola is located at (0, 9) and the function passes through several points including (-4, -7), (-3, 0), (3, 0), and (4, -7).

To find the equation of the function, we need to determine the value of "a" in the equation f(x) = ax^2 + bx + c. Since the vertex is located at (0, 9), we know that the x-coordinate of the vertex is 0. Therefore, we can use the vertex form of the equation, which is f(x) = a(x - 0)^2 + 9, or simply f(x) = ax^2 + 9.

Next, we can use one of the given points to solve for "a". Let's use the point (-3, 0).

0 = a(-3)^2 + 9

0 = 9a - 9

9 = 9a

a = 1

Therefore, the value of "a" in the equation of the function is B. 1.

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1.2.1 determine this family's annual medical aid tax credit,
(3)
1.2.2 this amount is deducted from annual tax payable. calculate this
family's monthly income tax after this tax credit
determine the zulu family's actual percentage tax paid of their monthly
.
taxable income.
(3)
[18]
2:
value added tax (vat)
15% vat is payable on all goods and services, except for sanitary pads, fresh
produce and a few other staple food items. we will assume that 1.0% of​

Answers

To determine this family's annual medical aid tax credit, we need to consider their medical aid expenses for the year. Medical aid expenses are expenses related to medical services that are not covered by the government or medical insurance.

This family can claim a tax credit of up to R310 per month for the main member and the first dependent, and R209 per month for each additional dependent. This tax credit is only applicable to registered medical schemes and is deducted from the tax payable.

In addition to medical aid expenses, this family will also need to consider the 15% VAT payable on all goods and services, except for sanitary pads, fresh produce, and a few other staple food items. This means that if this family spends R10,000 on goods and services, they will need to pay an additional R1,500 in VAT.

However, the good news is that they won't have to pay VAT on their fresh produce and staple food items. This will help to reduce their overall expenditure on food, which is an essential expense for every family.

In conclusion, while this family will need to pay VAT on most goods and services, they can claim a tax credit for their medical aid expenses. Additionally, they won't have to pay VAT on fresh produce and staple food items, which will help to reduce their overall food expenditure.

By carefully managing their expenses and taking advantage of tax credits and exemptions, this family can ensure that they are able to provide for their essential needs while also managing their financial obligations.

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Mr. Vara is designing post caps in the shape of a square pyramid for a fence that he just built in his backyard. The caps are solid wood and each one has a volume of 94. 5 cubic centimeters

Answers

The height of the wooden post cap is approximately 11.34 centimeters.

To find the height of the wooden post cap, we need to use the formula for the volume of a square pyramid which is V = (1/3) Bh, where B is the area of the base and h is the height. Since we know that each post cap has a volume of 94.5 cubic centimeters, we can plug this into the formula to get:

94.5 = (1/3) B h

We also know that the base of the pyramid is a square, so the area of the base is equal to s², where s is the length of one side. Since we don't know the length of the side or the height of the pyramid, we need to use another piece of information. Let's assume that the fence posts are all the same height and that the caps fit snugly on top of them. If we measure the height of the fence post, we can use this to find the height of the cap.

Let's say that the height of the fence post is 10 centimeters. We can use this to find the area of the base:

B = s² = (10/2)² = 25 square centimeters

Now we can plug this into the formula:

94.5 = (1/3) (25) h

Simplifying this equation, we get:

h = (94.5 * 3) / 25 = 11.34 centimeters

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The equation m= 35g gives the distance in miles, m, that a car can travel using g


gallons of gas.


Q4. 1) If the car has gone 210 miles, how much gas was used?


A4. 1) Write the amount of gas that was used to travel 210 miles here.


Q4. 2) Write an equation that represents the inverse function: the gallons of gas as a


function of distance in miles.


A4. 2) Write the equation of the inverse function here.


Q4. 3) The equation m=hg gives the distance in miles, m, that a car can


travel using g gallons of gas, if it travels h miles per gallon.


Write an equation that represents the inverse function: the gallons of gas as


function of distance in miles for this new equation.


A4. 3) Write the equation of the inverse function here.

Answers

6 gallons of gas were used to travel 210 miles.

If the car can travel a distance of 210 miles using gallons of gas, what is the value of h in the equation m=hg?

A4. 1) To find the amount of gas used to travel 210 miles, we can rearrange the given equation m=35g to solve for g:

g = m/35

Substituting m=210, we get:

g = 210/35 = 6

6 gallons of gas were used to travel 210 miles.

A4. 2) To find the inverse function, we need to solve the given equation for g in terms of m:

m = 35g

Divide both sides by 35:

g = m/35

So the inverse function is:

g(m) = m/35

A4. 3) Similar to A4.2, we need to solve the given equation m=hg for g in terms of m:

m = hg

Divide both sides by h:

g = m/h

Now, we can write the inverse function as:

g(m) = m/h\

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Can someone help me with this question and show the steps please

Answers

answer: W 3/5

Apply the rule
x m/n=^n√x^m
to rewrite the exponentiation as a radical.
5√x3

The target to the right is in your backyard. What is the probability of hitting the bulls eye (center circle) when you shoot an arrow? The radius of the bulls eye is 2ft and the radius of the target is 6ft. (Use 3. 14 for pi)

Answers

The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.

Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.

The area of the bull's eye can be calculated as follows:

Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet

The area of the entire target can be calculated as follows:

Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet

Therefore, the probability of hitting the bull's eye can be calculated as:

Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%

So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.

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find the surface area of the prism 6m 5m 8m

Answers

The surface area of the rectangular prism in the image above is determined as:

236 square meters.

What is the Surface Area of a Prism?

The prism given above in the image is a rectangular prism. The formula for finding the surface area of the prism is given as:

surface area of the prism = 2(lh + lw + hw), where:

h is the height

w is the width

l is the length of the prism.

Given the following:

length (l) = 6 m

width (w) = 5 m

height (h) = 8 m

Plug in the values:

Surface area of the prism = 2·(5·6 + 8·6 + 8·5) = 236 square meters.

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Sam and jeremy have ages that are consecutive odd interferes. The product of their ages is 783. Which equation could be used to find Jeremy’s age, j, if he is the younger man?

Answers

So, the equation we could use to find Jeremy's age, j, if he is the younger man, is: j = x + 2, where x satisfies the equation x(x + 2) = 783.

What is equation?

An equation is a mathematical statement that asserts the equality of two expressions. In an equation, an expression is written on the left side of an equals sign (=), and another expression is written on the right side of the equals sign. The equals sign indicates that the two expressions have the same value.

Here,

Let's use algebra to solve this problem. We can start by representing Sam's age as x and Jeremy's age as x + 2, since they are consecutive odd integers. We know that the product of their ages is 783, so we can set up the following equation:

x(x + 2) = 783

We can simplify this equation by multiplying out the left side:

x² + 2x = 783

Now we have a quadratic equation in standard form. We can solve for x by using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 2, and c = -783, so we can substitute these values into the formula:

x = (-2 ± √(2² - 4(1)(-783))) / 2(1)

Simplifying the expression under the square root, we get:

x = (-2 ± √(3136)) / 2

x = (-2 ± 56) / 2

So, we have two possible values for x:

x = 27 or x = -29

We can reject the negative value, since it does not make sense in the context of the problem. Therefore, we have:

x = 27

Now we can use this value to find Jeremy's age, which is x + 2:

j = x + 2

= 27 + 2

= 29

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A positive integer is 40 more than 29 times another. Their product is 10116 . Find the two integers.

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A positive integer is 40 more than 29 times another. Their product is 10116 these two integers are 19 and 571.

In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers can be used to represent quantities such as counting numbers, temperatures, or scores in a game.

How to determine the two integers?

Let's call the two integers x and y, where x is the larger integer and y is the smaller integer.

From the problem, we know that:

x = 29y + 40 (equation 1)

xy = 10116 (equation 2)

We can substitute equation 1 into equation 2 to get:

(29y + 40)y = 10116

Expanding and simplifying:

29[tex]y^{2}[/tex]+ 40y - 10116 = 0

We can use the quadratic formula to solve for y:

y = (-40 ± √([tex]40^{2}[/tex] - 429(-10116))) / (2×29)

y = (-40 ± √308576) / 58

y ≈ 18.95 or y ≈ -12.3

Since y is a positive integer, we can round up to 19.

Now we can use equation 1 to find x:

x = 29y + 40

x = 29(19) + 40

x = 571

Therefore, the two integers are 19 and 571.

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PLEASEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

Step-by-step explanation:

AngleSideSide because it's bad

but also, if you had an angle, a side and a side

For your example: let's say CD≅AS

You could change the angle of S or D and the parameters of the triangle would still be true.   Because you can change something and still have AngleSideSide be true, would make them not congruent any more.

Jaleesa deposited $4,000 in an account that pays 4% interest compounded annually. Which expression can be used to find the value of her investment at the end of 6 years?


4,000. Times 1. 4. Times 6.



4,000. Times. 0. 4. To the sixth power.



4,000. Times. 1. 4. To the sixth power.



4,000. Plus. 4,000. Times 0. 4. Times. 6

Answers

The correct expression is 4,000 times. 1. 4 to the sixth power.

The formula for the future value of an investment with annual compounding interest is:

A = P(1 + r)ⁿ

A = future value

P = principal amount

r = annual interest rate expressed as a decimal

n = number of years.

In this case, Jaleesa deposited $4,000 at an annual interest rate of 4% (0.04 as a decimal) and the investment is compounded annually for 6 years. So the expression that can be used to find the value of her investment at the end of 6 years is:

A = 4,000(1 + 0.04)⁶

Simplifying the expression, we get:

A = 4,000(1.04)⁶

Therefore, the correct expression is 4,000 times. 1. 4 to the sixth power.

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HELP (100 POINTS AND BRAINLIEST)

Answers

Answer:

Using the Distance Formula:

EG =√((-a - b)^2) + (0 - c)^2)

=√((a + b)^2 + c^2)

FH =√((-b - a)^2 + (c - 0)^2)

=√((a + b)^2 + c^2)

So EG = FH.

11. April shoots an arrow upward at a speed


of 80 feet per second from a platform 25


feet high. The pathway of the arrow can


be represented by the equation h =-


16t2 + 80t + 25, where h is the height


and t is the time in seconds. What is the


maximum height of the arrow? [3]

Answers

The maximum height of the arrow is 105 feet. To find the maximum height of the arrow, we need to determine the vertex of the quadratic function h = -16[tex]t^{2}[/tex] + 80t + 25.

The vertex is the highest point on the graph of the function, which represents the maximum height of the arrow.

To find the t-value at the vertex, we use the formula t = -b/2a, where a = -16 and b = 80. Plugging these values into the formula gives us t = -80/(2(-16)) = 2.5 seconds.

To find the maximum height, we plug t = 2.5 into the equation to get h = -16[tex](2.5)^{2}[/tex] + 80(2.5) + 25 = 105 feet. Therefore, the maximum height of the arrow is 105 feet.

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In δmno, m = 540 inches, n = 330 inches and o=600 inches. find the measure of ∠o to the nearest 10th of a degree

Answers

The measure of ∠O in ΔMNO is approximately 41.5°.

To find the measure of ∠O, we can use the Law of Cosines in ΔMNO, with sides M = 540 inches, N = 330 inches, and O = 600 inches. The Law of Cosines states:

O² = M² + N² - 2MN * cos(∠O)

Rearrange the equation to solve for cos(∠O):

cos(∠O) = (M² + N² - O²) / (2MN)

Substitute the values:

cos(∠O) = (540² + 330² - 600²) / (2 * 540 * 330)

cos(∠O) ≈ -0.7944

Now, find the angle using the inverse cosine function:

∠O ≈ arccos(-0.7944) ≈ 141.5°

Since ∠O is an obtuse angle, we need to find its supplement to the nearest 10th:

180° - 141.5° ≈ 38.5°

Thus, the measure of ∠O is approximately 38.5°.

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Find the volume of the largest right cylinder that fits in a sphere of radius 4

Answers

The volume of the largest right cylinder that fits in a sphere of radius 4 is 128π cubic units.

How to find the volume?

To find the volume, we need to understand that the cylinder that fits inside a sphere will have its height (h) equal to the diameter of the sphere (2r), and the cylinder's radius (r') will also be equal to the sphere's radius (r).

We can use the formula for the volume of a cylinder: V = π[tex]r^2^h[/tex], where π is pi (approximately 3.14), r is the radius, and h is the height.

Since the cylinder's height is equal to the sphere's diameter, which is 2r, the height of the cylinder is 2r. Therefore, we can write the volume of the cylinder as:

V = πr²(2r)

Simplifying this expression, we get:

V = 2π[tex]r^3[/tex]

To find the maximum volume of the cylinder that fits inside a sphere of radius 4, we need to maximize the volume by finding the maximum value of r. Since the radius of the cylinder is equal to the radius of the sphere, we have:

r = 4

Substituting this value into the formula for the volume of the cylinder, we get:

V = 2π[tex](4)^3[/tex]

V = 128π

Therefore, the volume of the largest right cylinder that fits in a sphere of radius 4 is 128π cubic units.

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What kind of triangle is this?

Answers

The triangle is a right triangle.

What is a right triangle?

Any given triangle in which one of its internal angles measures 90^o is said to be a right angle. Thus there is a common relations among the three sides of the triangle which is shown by the Pythagorean theorem.

The Pythagorean theorem states that;

For a right triangle, this relation holds among its three sides;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given diagram, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

             = 4^2 + 3^2

             = 16 + 9

             = 25

so that;

Hyp = 25^1/2

       = 5

Therefore the given triangle is a right triangle.

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Lori went to the grocery store and bought 7 1/2 of a pounds of vegetables. Kale made up 1⁄5 of Lori's vegetables. How many pounds of kale did Lori buy?

Answers

The amount in pounds of kale Lori bought is 1 1/2 pounds.

To find out how many pounds of kale Lori bought, you need to multiply the total weight of the vegetables by the fraction that represents the proportion of kale.

In this case, you can calculate the amount of kale as follows:

(7 1/2) * (1/5)

First, convert the mixed number 7 1/2 to an improper fraction:

(7 * 2 + 1) / 2 = 15/2

Now multiply the two fractions:

(15/2) * (1/5)

Multiply the numerators together and the denominators together:

(15 * 1) / (2 * 5) = 15 / 10

Now, simplify the fraction:

15 ÷ 5 / 10 ÷ 5 = 3 / 2

So, Lori bought 3/2 or 1 1/2 pounds of kale from the grocery store. This means that out of the total 7 1/2 pounds of vegetables she purchased, 1 1/2 pounds were kale.

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a = 10 m, b = 6 m and c = 9 m for the triangle shown below.

Work out the value of x rounded to 1 d.p.

Answers

In the given diagram, the value of x in the right triangle is approximately 14.7

Solving right triangles: Calculating the value of x

From the question, we are to calculate the value of x in the given diagram.

In the given diagram, we have two right triangles.

First, we will calculate the value of the side joining the two triangles.

Let the side joining the two triangles be d

Thus,

From the Pythagorean theorem, we can write that

d² = a² + b²

d² = 10² + 6²

d² = 100 + 36

d² = 136

Now, in the other triangle

Also, using the Pythagorean theorem, we can write that

x² = c² + d²

x² = 9² + 136

x² = 81 + 136

x² = 217

x = √217

x = 14.7309

x ≈ 14.7

Hence, the value of x is approximately 14.7

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If jones use online banking and averages 40 transactions monthly how much would he save in 2 months if he choose texas bank rather than lone star bank

Answers

Jones would save $20 over 2 months by choosing Texas Bank over Lone Star Bank for his online banking needs.

What are the fees and charges associated with online banking?

To answer this question, we need to know the fees and charges associated with online banking at Texas Bank and Lone Star Bank. Without this information, it's impossible to accurately calculate how much Jones would save by choosing one bank over the other.

Assuming we have this information, we can use the following steps to calculate Jones' potential savings:

Calculate the fees and charges associated with 40 transactions per month at each bank.

Subtract the total fees and charges at Texas Bank from the total fees and charges at Lone Star Bank to determine the difference.

Multiply the difference by 2 to determine how much Jones would save in 2 months by choosing Texas Bank over Lone Star Bank.

For example, let's say that the fees and charges at Lone Star Bank for 40 transactions per month total $20, while the fees and charges at Texas Bank for the same number of transactions total $10. In this case, the difference would be $10 per month.

To calculate Jones' potential savings over 2 months, we would multiply $10 by 2, giving us a total potential savings of $20.

So, in this hypothetical scenario, Jones would save $20 over 2 months by choosing Texas Bank over Lone Star Bank for his online banking needs.

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HELP ME UNDERSTAND THIS

Answers

The estimated areas of each curve are listed below:

Case 1: A = 12.75

Case 2: A = 12.5

How to estimate the area of the function by use of rectangles and triangles

In this problem we must estimate the area above the x-axis and under a curve by using sums of rectangles and triangles according to the following expression:

A = {∑ [MIN (f(xₙ₋₁), f(xₙ))] + 0.5 · ∑ [MAX (f(xₙ₋₁), f(xₙ)) - MIN (f(xₙ₋₁), f(xₙ))]} · Δx, for n = {1, 2, 3, ..., N}

Where:

A - AreaN - Number of blocks.

Case 1

A = (3.5 + 3.5 + 1.5) · 1 + 0.5 · (3.5 + 0.75 + 0.75 + 2 + 1.5) · 1

A = 8.5 + 0.5 · 8.5

A = 12.75

Case 2

A = (1 + 3 + 4) · 1 + 0.5 · (1 + 2 + 1.5 + 0.5 + 4) · 1

A = 8 + 4.5

A = 12.5

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Q4 (6 points) Use Mean value theorem to prove va + 3 1. Using methods other than the Mean Value Theorem will yield no marks. (Show all reasoning). Hint: Choose a > 1 and apply MVT to f(x) = V6x +3 - x - 2 on the interval [1.a) +

Answers

Using the Mean Value Theorem, we have proven that √(6a+3) < a + 2 for all a > 1.

To prove √(6a+3) <a + 2 for all a > 1 using the Mean Value Theorem, we will begin by defining a function f(x) as:

f(x) = √(6x+3)

We can see that f(x) is a continuous and differentiable function for all x > -1/2.

Now, let's choose two values of a, such that a > 1 and b = a + h, where h is a positive number. By the Mean Value Theorem, there exists a value c between a and b such that

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

where f'(c) is the derivative of f(x) evaluated at c.

Now, let's evaluate the derivative of f(x) as:

f'(x) = 3/(√(6x+3))

Thus, we can write

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

√(6(a+h)+3) - √(6a+3) = f'(c)h

Dividing both sides by h and taking the limit as h → 0, we get

lim h→0 (√(6(a+h)+3) - √(6a+3))/h = f'(a)

Now, we can evaluate the limit on the left-hand side using L'Hopital's rule

lim h→0 (√(6(a+h)+3) - √(6a+3))/h = lim h→0 [3/(√(6(a+h)+3)) - 3/(√(6a+3))] = 3/(2√(6a+3))

Therefore, we have

f'(a) = 3/(2√(6a+3))

Now, we can use this value to rewrite the inequality as

√(6a+3) - (a + 2) < 0

Multiplying both sides by 2√(6a+3) and simplifying, we get

3 < 4a + 2√(6a+3)

Subtracting 4a from both sides and squaring, we get

9 < 16a^2 + 16a + 24a + 12

Simplifying, we get

0 < 16a^2 + 40a + 3

This inequality holds for all a > 1, so we have proved that

√(6a+3) < a + 2 for all a > 1.

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The given question is incomplete, the complete question is:

Use Mean value theorem to prove √(6a+3) <a + 2 for all a > 1. Using methods other than the Mean Value Theorem will yield

Ben is 140 cm tall. Fareed is 1090 mm tall. Who is taller? How much taller?

Answers

Answer:

Ben is 31 cm taller

Step-by-step explanation:

1090mm is 109 cm

Subtract Fareeds height from Bens:

140-109=31

Hope this helps!

Kenny decides he wants to buy Christmas presents for his mom and dad. He went to the mall with $150. At the mall, he bought his mom a watch for $68. 99 and arrows for his dad for $38. 99. He then bought himself lunch for $8. 99. Kenny wants to buy his parents one more gift for the both of them to share. Using an inequality, show how much money Kenny could spend on his last gift. What range of costs could he spend on his last gift?

Answers

The range of costs that Kenny could spend on his last gift would be any amount less than or equal to $33.03. So the range would be: $0 ≤ x ≤ $33.03

To determine the range of costs Kenny could spend on the last gift, we'll first calculate the total amount he has spent so far and subtract that from the $150 he started with.

Kenny has spent $68.99 (watch) + $38.99 (arrows) + $8.99 (lunch) = $116.97.

Now, let x represent the cost of the last gift. The inequality to represent the situation is:

116.97 + x ≤ 150

To find the range of costs for the last gift, subtract 116.97 from both sides of the inequality:

x ≤ 150 - 116.97
x ≤ 33.03

So, the range of costs Kenny could spend on the last gift is $0 to $33.03.

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