P is a point 22m due east of a fixed point O and Q is a point 14m due south of O. A particle A starts at P and moves towards O at a speed of 4m/s while a particle B starts at Q at the same time as A and moves towards O at a speed of 3m/s. Express the distance between A and B t seconds after the start. Hence find the value of t when the distance between A and B is a minimum and find this minimum distance.

To rewrite the quadratic function y = -9(x-1)²-6 in standard form, we need to expand the squared term and simplify the expression. Here are the steps:

Distribute the negative sign to the squared term: y = -9(x² - 2x + 1) - 6

Multiply -9 by each term inside the parentheses: y = -9x² + 18x - 9 - 6

Combine the constants: y = -9x² + 18x - 15

Therefore, the standard form of the quadratic function y = -9(x-1)²-6 is y = -9x² + 18x - 15.

Answer:

y = -9x[tex]x^{2}[/tex]  + 18x - 15

Step-by-step explanation:

We need to convert both quantities to the same units before we can compare them.

24 ounces is equal to 1.5 pounds (since there are 16 ounces in 1 pound).

So the ratio of 24 ounces to 12 pounds can be written as:

1.5 pounds : 12 pounds

Simplifying this ratio by dividing both sides by 12, we get:

0.125 : 1

Therefore, the ratio that compares the relative sizes of 24 ounces to 12 pounds is 0.125 : 1.

The value of x on the first image is 5 and in the second image is 17.

Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees which is called interior angles.

According to the given information:

In fig 1, by midsegment theorem,

[tex]x+8 = \frac{1}{2} (3x+11)[/tex]

on simplifying

[tex]2x+16=3x+11\\3x-2x = 16-11\\x = 5[/tex]

In fig 1, by midsegment theorem,[tex]x+5=\frac{1}{2} (3x-7)[/tex]

on simplifying

[tex]2x+10 = 3x-7\\3x-2x = 10+7\\x = 17[/tex]

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The two streets that are the legs of the Triangle are Streets A and B.

The length of C street can be found to be 3. 61 miles.

If Dan can bike 4 miles in half an hour, then he can make the trip to Sarah's house in 30 minutes.

The length of C street can be found using the Pythagorean Theorem which is:

Length C ² = Leg A ² + Leg B²

This means the length of C street is:

Length C ² = 2 ² + 3 ²

Length C ² = 13

Length C = √ 13

= 3. 61 miles

This means that Dan can get to Sarah's house in 30 minutes if he is going at 4 miles per half hour.

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Answer:     3.25

Step-by-step explanation:

To round 3.254 to the nearest hundredth, we need to look at the digit in the thousandth place, which is 4. Since 4 is less than 5, we do not need to round up the hundredth digit (5) to the next higher number. Therefore, the rounded number to the nearest hundredth is:

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Answer:

The area of the trapezoid is 165.06mi.

Step-by-step explanation:

We can find the area of a trapezoid by the following formula:

[tex]\boxed{A_T = \frac{(B + b) \cdot h}{2} }[/tex]

Note: Base are the parallel sides of the trapezium.

Now, let's change the values in the previous formula:

[tex]A_T = \frac{(B + b) \cdot h}{2}\\\\A_T = \frac{(6.7 + 18.5) \cdot 13.1}{2}\\\\A_T = \frac{25.2 \cdot 13.1}{2}\\\\A_T = \frac{330.12}{2}\\\\A_T = 165.06[/tex]

Therefore, the area of this trapezoid is 165.06 mi.

I hope I've helped.

Happy studying! =D

Answer:

518

Step-by-step explanation:

Since you are rounding to the nearest whole number.

518.1 would need to be 518.5 or higher to be 519 so anything below that would just round up the 518

The correct equation would be:

0b. A = 240 - 4h

Explanation:

If Clayton can plow 4 acres per hour, the number of acres he can plow in 'h' hours would be 4h.

Therefore, the number of acres left to plow would be the total number of acres (240) minus the number of acres he has already plowed (4h).

Hence, the equation that represents the number of acres left to plow would be A = 240 - 4h.

The total cost is the same for both locations when there are 10 guests.

To determine the number of guests for which the total cost is the same at each location, we need to set up an equation and solve for the number of guests (let's call it x).

Roller rink cost: 5x + 55

Laser tag cost: 8x + 25

Now, set the two costs equal to each other and solve for x:

5x + 55 = 8x + 25

Subtract 5x from both sides:

55 = 3x + 25

Subtract 25 from both sides:

30 = 3x

Divide by 3:

x = 10

So, the total cost is the same for both locations when there are 10 guests.

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Answer: The answer is (B) 16.5%.

Step-by-step explanation:

The value of P and Q is 35.

Let's first understand the given information:

Charles has two six-sided dice, one fair and one biased. The fair die has equal probabilities for each side (1/6). The biased die has a 2/3 probability for rolling a six and 1/15 probability for each of the other five sides. Charles chooses a die randomly and rolls it three times.

Given that the first two rolls are sixes, we are asked to find the probability that the third roll will also be a six, expressed as a simplified fraction p/q.

We can solve this problem using conditional probability. Let A be the event that Charles chooses the biased die, and B be the event that he rolls three sixes in a row. We want to find the probability of B given A.

P(B|A) = P(A ∩ B) / P(A)

Since Charles chooses the die randomly, P(A) = 1/2. To find P(A ∩ B), we need to find the probability that Charles chooses the biased die and rolls three sixes in a row. This can be calculated as:

P(A ∩ B) = P(A) * P(rolling three sixes with the biased die) = (1/2) * (2/3)^3

Now we can find P(B|A):

P(B|A) = P(A ∩ B) / P(A) = ((1/2) * (2/3)^3) / (1/2) = (2/3)^3 = 8/27

Thus, the probability that the third roll will also be a six, given that the first two rolls are sixes, is 8/27, so the answer is p + q = 8 + 27 = 35.

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The required total cost of the tablet computer is $625.87.

let computer that is on sale at 15% off?

A sales discount, also referred to as a "discount," gives customers of a company a discount on one or more of the offered goods or services. Limits can be applied to almost any industry or business offering deals of an item or administration.

The discounted price of the tablet computer is:

[tex]$\begin{align*}708 \times 0.85 &= 601.80\end{align*}[/tex]

The sales tax on the tablet computer is:

[tex]$\begin{align*}601.80 \times 0.04 &= 24.072\end{align*}[/tex]

Therefore, the total cost of the tablet computer, including sales tax, is:

[tex]$\begin{align*}601.80 + 24.072 &= 625.87\end{align*}[/tex]

Therefore, the total cost of the tablet computer is $625.87.

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The circumference of the base of a circular flower pot with a diameter of 16.2 is 50.92.

Circumference of the circle or perimeter of the circle is the measurement of the boundary across any two-dimensional

circular shape including circle.

The circumference of a circle is the distance around its boundary.

If d is the diameter of the circle, then the circumference is given by:

Circumference = π × d

Circumference = π × 16.2

Using π ≈ 3.1415926,

we can calculate the circumference:

Circumference ≈ 3.1415926 × 16.2

Circumference ≈ 50.92

Therefore, the circumference of the base of a circular flower pot with a diameter of 16.2 is approximately 50.92.

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Answer: C.5

Step-by-step explanation:

Answer: 185.64 inches

The surface area of the box is 185.64 square inches.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

To find the surface area of the box, we need to calculate the area of each face and then add them up.

The four faces are rectangles with dimensions 8.8 inches by 4.3 inches, so their area is 4(8.8)(4.3) = 151.36 square inches.

The other area can be described as 2(4.3)(4.3) =36.98 square inches.

Finally, we need to account for the rectangular tear on one of the sides, which has dimensions of 0.5 inches by 5.4 inches. This tear creates an additional face with area (0.5)(5.4) = 2.7 square inches.

Therefore, the total surface area of the tissue box is:

151.36 + 36.98 - 2.7 =  185.64 square inches.

Hence, the surface area of the box is 185.64 square inches.

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Answer: No, it’s not a statistical question

Step-by-step explanation:this question only pertains to one person and it not something that can be represented as a statistic.

The graph of the function is in the image at the end, there we can see that the range is  (-3, ∞)

Remember that the range of a function is the set of the possible outputs of a function.

Here we have the function:

f(x) = (1/2)ˣ - 3

The graph of the function is in the image at the end.

There we need to look at the vertical axis to identify the range, here we can see that the function goes from y = -3 upwards (asymptothically), then the range is (-3, ∞)

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Given two similar triangles

The corresponding sides are proportions

So,

[tex]\dfrac{x}{y} =\dfrac{20}{90} =\dfrac{2}{9}[/tex]

So, the relation between x and y will be:

[tex]x=\dfrac{2}{9} y[/tex]

The area of the smaller triangle = 45 cm²

So, area =

[tex]\dfrac{1}{2} x\times y=45[/tex]

Substitute with x into the equation of the area to find the value of y

         [tex]\dfrac{1}{2} \times\dfrac{2}{9} y\times y=45[/tex]

[tex]y^2=\dfrac{45\times1\times9}{2} =\dfrac{405}{2}=202.5[/tex]

                [tex]y=\sqrt{202.5}[/tex]

Substitute with y into x

[tex]x=\dfrac{2}{9} \times\sqrt{202.5} =\frac{2\sqrt{202.5} }{9}[/tex]

So, the answer will be:

[tex]x=\frac{2\sqrt{202.5} }{9}[/tex]

[tex]y=\sqrt{202.5}[/tex]

Thw solution to the given system of equations as required to be determined in the task content is; (-1, 0).

It follows from the task content that the solution to the given system of equations is to be determined as required.

since the given equations are;

y = -3x - 3 and y = 4x + 4

Since; y = y

-3x - 3 = 4x + 4

7x = -7

x = -7 / 7

x = -1.

and y = -3 (-1) - 3; y = 0.

Ultimately, the solution (x, y) to the given system of equations as required to be determined is; (-1, 0).

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Jamie will therefore need five days to complete the book as a result, P – 90 pages equals 3/8 of the book.

A mathematical strategy for resolving proportionality issues is the unitary method. Finding the price of one unit is the first step, and utilizing that value to determine the value of yet another quantity with a different quantity is the second. Consider being told, for instance, that an automobile drives 300 kilometres in 5 hours. You are able to employ the unitary technique as shown below to determine how far the car drives in eight hours. For example, 1 hour is equal to 300/5, or 60 miles. To calculate the value of eight hours, use this value: Since 8 hours are equal to 8/1 units, 480 miles are covered in 8 hours.

given

Let P represent the book's total number of pages.

Jessica reads 30 pages per day, which translates to 330 pages after 3 days, or 90 pages total.

5/8 of the book is still to be read, which indicates that 3/8 of it has already been. As a result, P – 90 pages equals 3/8 of the book.

Divide both sides by 5, and you get:

P = 144

The book thus has 144 pages.

Regarding the second query:

She reads 45 pages per 225 pages, or 1/5 of the book.

We divide the total number of pages by the average number of pages Jamie reads each day to determine the number of days Jamie will need to finish the book.

Jamie will therefore need five days to complete the book as a result, P – 90 pages equals 3/8 of the book.

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The surface area of the given figure is 90sq inches which include 3 rectangular faces and two triangular faces.

Area of 1 rectangular face is 6.5x5=32.5.
Area of 2 rectangular face is 5x6=30
Area of 3 rectangular face is 2.5x5=12.5
Area of the two triangluar faces= 2.5x6x0.5x2=15

Total area is 90 sq inches.

To find the surface area of a joined figure, we need to add up the surface areas of all the individual components of the figure.

For example, if we have a figure made up of a rectangular prism and a pyramid attached to the top, we can find the surface area by first calculating the surface area of the rectangular prism:

Surface area of the rectangular prism = 2lw + 2lh + 2wh

Surface area of the pyramid = (1/2)3.14 + B

Finally, we add the surface area of the rectangular prism to the surface area of the pyramid to get the total surface area of the joined figure.

Total surface area = Surface area of the rectangular prism + Surface area of the pyramid

This method can be applied to any joined figure made up of multiple components. We just need to find the surface area of each individual component and then add them up.

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Answer:

  table 1

Step-by-step explanation:

You want to know which of the four given tables represents a linear function.

The x-values increase by 2; y-values decrease by 2/3. The rate of change is constant. This is a linear function.

The x-values increase by 2; y-values decrease, then increase again. The rate of change is not constant. This is not a linear function.

The x-values increase by 2; y-values increase by changing amounts. The rate of change is not constant. This is not a linear function.

The x-values repeat. This is not a function.

Answer:

I'm sorry, but your request is unclear. Can you please provide more context or information so that I can better understand and assist you? Thank you.

Answer:

I'm assuming that 1 is actually a point with coordinates (1, something) and you meant the point H(25,-16).

To find the equation of the line passing through two points (x1,y1) and (x2,y2), we can use the point-slope form:

y - y1 = m(x - x1)

where m is the slope of the line, which can be calculated as:

m = (y2 - y1) / (x2 - x1)

Using the points H(25, -16) and 1(-2.5, y), we have:

m = (-16 - y) / (25 - (-2.5)) = (-16 - y) / 27.5

Multiplying both sides by 27.5, we get:

-16 - y = -0.58x + b

where x is the x-coordinate and b is the y-intercept of the line. To find b, we plug in one of the points (let's use H) and solve for b:

-16 - (-16) = -0.58(25) + b

b = -16 - (-14.5) = -1.5

Therefore, the equation of the line passing through H(25, -16) and 1(-2.5, y) is:

y + 1.5 = -0.58(x + 2.5)

or:

y = -0.58x - 4.25

Note: I assumed that you meant H(25,-16) and I used -2.5 as the x-coordinate for point 1 because you didn't specify what it was.

Ms. Switer will need approximately 2981.388 square feet of sod for her front lawn.

Area is the measure of the amount of space inside a two-dimensional (2D) flat surface or shape, such as a rectangle, circle, or triangle. It is typically measured in square units, such as square meters or square feet. The formula for finding the area of a shape varies depending on the shape itself.

To find out how many square feet of sod Ms. Switer will need, we need to find the area of the lawn. The formula for the area of a rectangle is length x width. Therefore, the area of Ms. Switer's lawn is:

Area = Length x Width

Area = (36 2/3 ft) x (45 1/6 ft)

Area = (110/3 ft) x (271/6 ft)

Area = 2981.388... square feet (rounded to three decimal places)

Therefore, Ms. Switer will need approximately 2981.388 square feet of sod for her front lawn.

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Answer: The answer is B, or 32 m.

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Based on the given information, the angle is C. 22.1° an  A. 20.4°.

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The basic trigonometric functions are:

Sine (sin): the ratio of the length of the side opposite an angle to the length of the hypotenuse of the triangle.

Cosine (cos): the ratio of the length of the side adjacent to an angle to the length of the hypotenuse of the triangle.

Tangent (tan): the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle.

We can use the trigonometric function tangent to find angle R in the right triangle:

tan(R) = opposite/adjacent = PQ/QR

tan(R) = 5.2/13.4

R = tan⁻¹(5.2/13.4)

R ≈ 22.1°

Therefore, the answer is C. 22.1° rounded to one decimal place.

Using the Pythagorean theorem, we can find the length of side AB:

AB = √(AC² - BC²)

= √(25² - 10²)

= √(575)

Now we can use the sine function to find the measure of angle C:

sin(C) = BC/AB

C = sin⁻¹(BC/AB)

= sin⁻¹(10/√(575))

≈ 20.4°

Therefore, the answer is A) 20.4°.

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