Use a ruler and pair of compasses to make an accurate drawing of line
AB and its perpendicular bisector, as shown. You must show all of your
construction lines.
Mark point C on your drawing.
Measure the length of AC in your drawing to 1 d.p.

The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

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the possible dimensions of the rectangular prism are:

1 unit by 12 units by 10 units

2 units by 6 units by 10 units

3 units by 4 units by 10 units

Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:

V = l × w × 10

We are also given that the prism requires 120 unit cubes to fill completely, which means:

V = l × w × 10 = 120

Dividing both sides by 10, we get:

l × w = 12

Now we need to find pairs of positive integers l and w that multiply to 12. These are:

1 × 12

2 × 6

3 × 4

Therefore, the possible dimensions of the rectangular prism are:

1 unit by 12 units by 10 units

2 units by 6 units by 10 units

3 units by 4 units by 10 units

Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.

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Answer:

x=5/4 or x=5/9

pls mark me brainliest

Answer:

x=5/4 (for the first x),x=5/9 (for the second x)

Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

Answer:

4 apples

Step-by-step explanation:

We know

John had 3 apples, then Dropped 2, found 4, then gave 1 to his friend.

How many apples does he have now​?

3 - 2 + 4 - 1 = 4 apples

So, he has 4 apples now.

Answer:

4 apples

Step-by-step explanation:

We know that John had 3 apples

but then he had dropped 2 of them

he then found 4

then he gave 1 to his friend

3-2=1

1+4=5

5-1=4

The answer is 4

Hope this helps!

The number of students that are in the sixth grade is given as follows:

250 students.

The number of students is obtained applying the proportions in the context of the problem.

We know that all students in the sixth grade either purchased their lunch or brought their lunch from home on Monday, and 24% of the students purchased their lunch, hence 76% of the students brought their lunch from home.

190 students brought their lunch from home, which is equivalent to 76% of the number of students, hence the number of students is given as follows:

0.76n = 190

n = 190/0.76

n = 250 students.

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We need 144 men to build the house in 12 days working 13 hours a day.

Let M be the number of men needed to build the house in 12 days working 13 hours a day.

140 x 10 x 16 = M x 13 x 12

Simplifying the equation, we get:

22400 = 156M

Dividing both sides by 156, we get:

M = 144.1

An equation in mathematics is a statement that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). The expressions on either side can be numbers, variables, or combinations of both. The equation expresses that the values of the expressions on both sides are equivalent.

Equations play a fundamental role in many areas of mathematics and are used to model various real-world situations, such as physics, engineering, and finance. They can be solved using various techniques, such as substitution, elimination, or graphing, to find the values of the variables that satisfy the equation.

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The instantaneous velocity of the object at t = 6 is 2.

Suppose that s is the position function of an object, given as s(t) = 2t - 7. We compute the instantaneous velocity of the object at t = 6 as follows. Use exact values. First we compute and simplify (6 + h). s(6 + h) = 2(6 + h) - 7 = 12 + 2h - 7 = 2h + 5Then we compute and simplify the average velocity of the object between t = 6 and t = 6 + h.8(6+h) - s(6) h = 8(6 + h) - (2(6) - 7) h= 8h + 56

Then, to rationalize the numerator in the average velocity. (If it applies, simplify again.)$(6 + h) - $(6) h(h(h) + 56)/(h(h)) = (8h + 56)/h The instantaneous velocity of the object att = 6 is the limit of the average velocity as h approaches zero.s(6 + h) – $(6) v(6) lim h -0s(6 + h) – s(6) v(6) lim h -0Using the above calculation, we get:s(6 + h) – s(6) / h lim h -0s(6 + h) = 2(6 + h) - 7 = 2h + 5So,s(6 + h) – s(6) / h lim h -0(2h + 5 - (2(6) - 7)) / h= (2h + 5 - 5) / h = (2h / h) = 2

Therefore, the instantaneous velocity of the object at t = 6 is 2.

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Answer: 41666666669 / 50000000003

Step-by-step explanation:

Answer:

16 feet

Step-by-step explanation:

Area of triangle = 1/2(a x b)

A = 1/2(6.4 x 5)

A = 32/2

A = 16 feet

Answer:

Let's use the formula for the volume of a right circular cone to solve this problem:

V = (1/3)πr^2h

We are given that the radius is increasing at a rate of 1.4 in/s and the height is decreasing at a rate of 2.6 in/s. We want to find the rate at which the volume is changing when the radius is 144 in. and the height is 138 in. In other words, we want to find dV/dt when r = 144 and h = 138.

Using the chain rule of differentiation, we can express the rate of change of the volume as follows:

dV/dt = (dV/dr) (dr/dt) + (dV/dh) (dh/dt)

To find dV/dr and dV/dh, we differentiate the formula for the volume with respect to r and h, respectively:

dV/dr = (2/3)πrh

dV/dh = (1/3)πr^2

Substituting the given values and their rates of change, we have:

dV/dt = (2/3)π(144)(138)(1.4) + (1/3)π(144)^2(-2.6)

dV/dt = 55,742.4 - 1,994,598.4

dV/dt = -1,938,856 in^3/s

Therefore, when the radius is 144 in. and the height is 138 in., the volume of the cone is decreasing at a rate of approximately 1,938,856 cubic inches per second.

Step-by-step explanation:

Answer:

it will take approximately 5.88 months for Don to pay off the remaining amount of $R = $85t = $85(5.88) = $499.80

Step-by-step explanation:

Don paid $500 upfront and will make monthly payments of $85 for the remaining amount. Let's assume the remaining amount he needs to pay is $R. The total cost of the furniture is the sum of the amount paid upfront and the remaining amount:

Total Cost = $500 + $R

Since he will be paying $85 per month, we can set up an equation to determine the time it will take to pay off the remaining amount:

$R = $85t

where t is the number of months it will take to pay off the remaining amount.

Substituting $R = $85t in the total cost equation, we get:

Total Cost = $500 + $85t

Since we want to find the time it will take to pay off the furniture, we need to solve for t. We can equate the total cost to the amount Don will pay at the end of the payment period, which is:

Total Cost = Amount Paid

$500 + $85t = $500 + $85t + $R

$85t = $R

$500 + $85t = $500 + $85t + $85t

$500 + $170t = $500 + $R

$170t = $R

Substituting $R = $85t, we get:

$170t = $85t

t = $500/$85

t = 5.88 (rounded to two decimal places)

Answer:$2.60

Step-by-step explanation:40*0.065

Answer:42.06

Step-by-step explanation:

The gradient of the chord PQ is 2h + 8

Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.

Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).

Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).

The gradient of the chord PQ is given by:

(m) = Δy /Δx

(m) = (2h^2+8h+9 - 9) / (2+h - 2)

(m) = (2h^2+8h) / (h)

(m) = 2h + 8

As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.

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a) Measurement of arcCD is 40°

b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD

We know the formula for external angle as per given diagram,

∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]

50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]

Simplify, arcCD = 140° - 100° = 40°

Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW

We know the formula for external angle as per given diagram,

∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]

36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]

Simplify, arcVW = 72° + 62° = 134°

Therefore, measurement of arcVW is 134°

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According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

a) Given that, ∠CED=∠AEC =50°  arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°

b) Given that, ∠VYW =36°  arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°

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After 6 days, the probability that the stock has its original price is 5/16.

There are two possible scenarios that can take place when the stock price fluctuates from one day to the next. Either the price goes up by 1/8th of a point with probability 1/3 or it goes down by 1/8th of a point with probability 2/3.

The price of the stock after six days can be denoted as S6. The price of the stock after the first day can be represented as S0.

Since the price fluctuates either up or down by 1/8th of a point on each day, the price after six days can be represented as follows:S6 = S0 + (up, up, up, up, up, up), (up, up, up, up, up, down), (up, up, up, up, down, up), ... , (down, down, down, down, down, down)

In order to return to the original price, the stock must go up and down by the same amount. As a result, there must be an equal number of ups and downs in the six-day period.

As a result, we must calculate the probability of obtaining an equal number of ups and downs over six days.

Let's represent an increase in the stock price as 'U' and a decrease as 'D.'

The total number of ways in which the stock can go up and down over six days is [tex]2^6 = 64[/tex].

The total number of ways in which the stock can return to its original price can be calculated as follows: [tex]N(UUUDDD) = 6! / (3! * 3!) = 20[/tex]

The probability of the stock returning to its original price after six days can be calculated as:

[tex]P = N(UUUDDD) / 64 = 20 / 64 = 5 / 16[/tex]

Therefore, the probability that after 6 days the stock has its original price is 5/16.

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The value of X is 42.5 and Y is 90.98.

How to solve equations?

To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:

Simplify both sides of the equation by combining like terms and following the order of operations.

Add or subtract the same value from both sides of the equation to isolate the variable term.

Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.

Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.

Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:

[tex]10x/10 = 425/10[/tex]

Simplifying the left side of the equation gives:

[tex]x = 42.5[/tex]

Therefore, X is 42.5.

To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:

[tex]81729 = 898.12 \times Y[/tex]

Simplifying the right side of the equation gives:

[tex]Y = 81729 / 898.12[/tex]

[tex]Y = 90.98[/tex]

Therefore, Y is 90.98.

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Answer:

The value of t = 18

Step-by-step explanation:

202 = 2t + 5 + t + 3t - 2 + 5t +1  Combine like terms

202 = 11t + 4  Subtract 4 from both sides

198 = 11[tex]\frac{11x}{11}[/tex]x  Divide both sides by 11

[tex]\frac{198}{11}[/tex] = 18

Is the question the value of t or the length of each side?

Each side

2t + 5

2(18) + 5

41

T

18

3T - 2

3(18) - 2

52

5T + 1

5(18) + 1

91

91 + 52 + 18 + 41 = 2002

Helping in the name of Jesus.

     |-----|-----|-----|----|-----|-----|--│--|-----|----|-----|

    -5   -4   -3   -2   -1    0    1   │  2    3    4    5

                                            1 1/2

On this number line, the tick mark labeled "1 1/2" is located halfway between the integer values of 1 and 2.

To represent the number 1 1/2 on a number line, we need to draw a horizontal line with evenly spaced tick marks. Each tick mark represents a specific value on the number line. Since 1 1/2 is a mixed number that includes a whole number (1) and a fraction (1/2), we need to locate it between the integer values of 1 and 2. The tick mark for 1 1/2 should be halfway between these two integers, which means it would be located at the midpoint of the line segment that connects the tick marks for 1 and 2. By placing the tick mark for 1 1/2 in the correct position on the number line, we can accurately represent this number visually.

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Answer:

do you have the graph to solve it?

the answer to the problem that you need to is 1024

By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

To simplify the expression,

[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]

Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.

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Answer:

Step-by-step explanation:

see diagram

Answer:

$109.99

Step-by-step explanation:

The original price of each tire is [tex]\[/tex][tex]109.99[/tex]

Take the amount saved and divide by 4 to find the amount saved on each tire

[tex]96.16\div4 =24.04[/tex]

Add that to the sale price of each tire to find the original price

[tex]85.95+24.04 =109.99[/tex]

Therefore, The original price is $109.99.

Answer:

y = - 2x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (3, - 2 ) into the partial equation

- 2 = - 2(3) + c = - 6 + c ( add 6 to both sides )

4 = c

y = - 2x + 4 ← equation of perpendicular line

The values in the interval [0, 2π) for which the two points would intersect as required is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

Recall from the task content; the given functions are;

f (x) = 2cos2θ and g(x) = −1 − 4cos θ − 2cos2θ

Therefore, for intersection; f (θ) and g(θ):

2 cos²θ = −1 − 4cos θ − 2cos²θ

4cos²θ + 4cosθ + 1 = 0

let cos θ = y;

4y² + 4y + 1 = 0

y = -1/2

Therefore; -1/2 = cos θ

θ = cos-¹ (-1/2)

θ = 2π/3, 4π/3.

Ultimately, the correct answer choice is; Choice C; theta equals 2 times pi over 3 comma 4 times pi over 3.

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Answer: 0.96

Step-by-step explanation:

To round 0.956 to one decimal place, we need to look at the second decimal place (the hundredths place), which is 5. Since 5 is greater than or equal to 5, we need to round up the first decimal place (the tenths place), which is 9. Therefore, the rounded number to one decimal place is:

0.956 rounded to one decimal place = 0.96

The value of y when x=36 is 31/3.

According to the question,

x varies directly with 3y+5

Thus,

[tex]x = k(3y+5)[/tex]

where K is any positive integer.

Now, from the question,

y=5/3 when x=10

Thus,

[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]

Now we can use k to find the value of y when x=36:

[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]

In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.

Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.

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Complete Question:

If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36

Answer:

x=1.9

Step-by-step explanation:

[tex]\frac{x}{4.6} =\frac{4.6}{11}[/tex]

[tex]11x=21.16[/tex]

[tex]X=1.9[/tex]

Hi!
Let's write this out.
Her limit is $900, and she's used $450. So, we subtract 450 from 900.
900-450 = 450.

So, she has $450 available credit left.
Hope this helps!
~~~PicklePoppers~~~

Answer: your credit utilization ratio on that card would be 50% but the answer is 450

Step-by-step explanation:

900-450 = 450