The difference of -10 and the product of p and q

Answer:

two buildings is approximately 267.9 meters. then the angle of elevation and height of the second building is approximately 152.4 meters to the nearest meter.

Step-by-step explanation:

The average rate of change in the elevation of the cyclist from 5 minutes to 10 minutes is: 400 ft/min

The formula for the average rate of change is:

Average rate of change = (y₂ - y₁)/(x₂ - x₁)

Now, we want to find the average rate of change  in the elevation of the cyclist from 5 minutes to 10 minutes.

Elevation at 10 minutes = 1140 ft

Elevation at 5 minutes = 940 ft

Thus:

Average rate of change = (1140 - 940)/(10 - 5)

Average rate of change = 200/5

Average rate of change = 400 ft/min

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The result of z₁/z₂ in rectangular form with fully simplified fractions and radicals is -6√3.

To express the result of z₁/z₂ in rectangular form, divide the complex numbers and simplify the expression.

Given:

z₁ = 18√3(cos(14π)/9 + i sin(14π)/9)

z₂ = 3(cos(11π)/9 + i sin(11π)/9)

To divide complex numbers, multiply the numerator and denominator by the complex conjugate of the denominator.

The complex conjugate of z₂ is:

z₂* = 3(cos(-11π)/9 + i sin(-11π)/9)

Now, perform the division:

z₁/z₂ = (z₁ * z₂*) / (z₂ * z₂*)

Expanding the numerator:

z₁ * z₂* = 18√3(cos(14π)/9 + i sin(14π)/9) × 3(cos(-11π)/9 + i sin(-11π)/9)

= 54√3(cos(14π - 11π)/81 + i sin(14π - 11π)/81)

= 54√3(cos(3π)/81 + i sin(3π)/81)

= 54√3((-1)/81 + i × 0/81)

= -54√3/81

Expanding the denominator:

z₂ * z₂* = 3(cos(11π)/9 + i sin(11π)/9) × 3(cos(-11π)/9 + i sin(-11π)/9)

= 9(cos(11π - 11π)/81 + i sin(11π - 11π)/81)

= 9(cos(0)/81 + i × 0/81)

= 9/81

Now, simplify the expression:

z₁/z₂ = (z₁ * z₂*) / (z₂ * z₂*)

= (-54√3/81) / (9/81)

= (-54√3/81) × (81/9)

= -54√3/9

Simplifying further, divide both the numerator and denominator by 9:

z₁/z₂ = (-6√3)/1

Therefore, the result of z₁/z₂ in rectangular form with fully simplified fractions and radicals is -6√3.

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The dimensions of the rectangle and the scale factor of dilation indicates;

1. (a.) Please find attached the drawing of the rectangle A'B'C'D', created with MS Word

(b) A'B' = 10 m, B'D' = 6 m, A'C' = 6 m, C'D' = 10 m

(c) The image of the dilation is an Enlargement

A dilation transformation is one in which the side lengths of the pre-image are multiplied by a scale factor.

The dimensions of the rectangle indicates that we get;

AB = 5 m, BD = 3 m, AC = 3 m, CD = 5 cm

(1 - a) Please find attached the drawing of the image created with MS Word

(1 - b) The dimensions of the image are found as follows;

The scale factor of the dilation of the rectangle of 2 indicates that the lengths of the side of the image are;

A'B' = 2 × 5 m = 10 m

B'D' = 2 × 3 m = 6 m

A'C' = 2 × 3 m = 6 m

C'D' = 2 × 5 m = 10 m

(1 - c) The lengths of the sides of the image of the rectangle, obtained from the pre-image, (by applying the scale factor of 2) with regards to the lengths of the sides of the pre-image indicates the dilation is an enlargement.

The correct option is therefore; Enlargement

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Answer:

A

Step-by-step explanation:

please say thank you and rate 5 stars and verify

Answer:

Jeffrey has 39 lunch boxes left in his collection.

Step-by-step explanation:

Jeffrey started with 32 superhero lunch boxes, 11 outer space lunch boxes, and 28 rock band lunch boxes, for a total of 32 + 11 + 28 = 71 lunch boxes.After giving his cousin 32 lunch boxes, Jeffrey's collection is reduced by that amount: 71 - 32 = 39 lunch boxes.

Answer:

the rate of the westbound train is 95 miles per hour.

Step-by-step explanation:

Let's denote the rate of the eastbound train as "x" miles per hour. Since the westbound train travels 10 miles per hour slower, its rate can be represented as "x - 10" miles per hour.We know that the total distance covered by both trains after 2 hours is 400 miles.The eastbound train covers a distance of 2x miles in 2 hours.

The westbound train covers a distance of 2(x - 10) miles in 2 hours.Since the total distance covered is 400 miles, we can set up the equation:2x + 2(x - 10) = 400Simplifying the equation:2x + 2x - 20 = 400

4x - 20 = 400

4x = 420

x = 105

Therefore, the rate of the eastbound train is 105 miles per hour.To find the rate of the westbound train, we substitute this value back into the expression "x - 10":Rate of the westbound train = 105 - 10 = 95 miles per hour.Hence, the rate of the westbound train is 95 miles per hour.

Answer:

approx 26%

Step-by-step explanation:

you try find the multiplier

200000 * 1. ???? ^3= 400000

rearrange equation

[tex]\sqrt[3]{\frac{400000}{200000} }[/tex]       =   multiplier

1.25992105

subract one

0.25992105

multiply by 100 to get percentage

25.9%

rounded to whole number = 26%

The statement "C is definable from [tex]p_{1},...,p_{n}[/tex]" means that there is a formula in the language of set theory that can be used to uniquely identify the set C from the sets p1, p2, ..., pn.

In other words, there is a formula that can be used to determine whether a given set is equal to C, or not.

For example, the set of even natural numbers is definable from the set of natural numbers by the formula x ∈ C if and only if x ∈ N and x is even. This formula uniquely identifies the set C of even natural numbers from the set N of natural numbers.

The concept of definability is a fundamental concept in mathematics/

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Answer:

  x²/23 +y²/144 = 1

Step-by-step explanation:

You want an equation of the ellipse with foci at (0, ±11) and a vertex at (0, 12).

The given vertex is in line with the foci, so represents one end of the major axis. The length of the semi-minor axis will be ...

  a = √(b² -f²) . . . . . . where f is the center-to-focus distance

  a = √(12² -11²) = √(144 -121) = √23

The equation is ...

  x²/a² +y²/b² = 1

  x²/23 +y²/144 = 1

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Answer:

d

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)

Slope is rise/run

Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.

Feel free to tell me if I did anything wrong! :)

Also, if you're still confused, I could explain it another way.

The correct solution is:

x = 5π/8, 7π/8, 13π/8, 15π/8.

To solve the equation: -√2sin(2x) = sin²x + cos²x, we can simplify the equation and apply trigonometric identities to find the solutions.

Given that the interval is [0, 2π), we will find solutions within this range.

First, let's simplify the equation:

-√2sin(2x) = 1

sin(2x) = -1/√2

sin(2x) = sin(-45°)

Now, we can use the identity sin(A) = sin(B) to find the possible solutions.

The general solution for sin(2x) = sin(A) is:

2x = nπ + (-1)ⁿ A, where n is an integer.

In this case, A = -45° = -π/4.

Plugging in A = -π/4 into the general solution, we get:

2x = nπ + (-1)ⁿ(-π/4)

Now, let's find the solutions within the interval [0, 2π).

For n = 0:

2x = 0 + (-1)⁰(-π/4)

2x = 0 + π/4

x = π/8

For n = 1:

2x = π + (-1)¹(-π/4)

2x = π - π/4

x = 3π/8

For n = 2:

2x = 2π + (-1)²(-π/4)

2x = 2π + π/4

x = 9π/8

For n = 3:

2x = 3π + (-1)³(-π/4)

2x = 3π - π/4

x = 11π/8

Therefore, the solutions within the interval [0, 2π) are:

x = π/8, 3π/8, 9π/8, 11π/8.

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Answer: the 1st card

Step-by-step explanation:

To determine which credit card is the better choice, we need to compare the annual percentage rate (APR) of the first card and the daily periodic interest rate of the second card.

The first card has an APR of 12.99%. This means that if you carry a balance on this card for a whole year, you would pay an annual interest rate of 12.99%.

The second card has a daily periodic interest rate of 0.038%. To convert this to an annual interest rate, we multiply it by the number of days in a year. Assuming 365 days in a year, the annual interest rate would be approximately 13.87% (0.038% * 365).

Comparing the two, the first card has an APR of 12.99%, while the second card has an approximate annual interest rate of 13.87%. Therefore, the first card with an APR of 12.99% would be the better choice as it offers a lower interest rate compared to the second card.

Answer:

l = √109 in.

Step-by-step explanation:

We see that the 10. in. apothem connecting the top of the cone and the circular base and a radius of the circle creates a right triangle.

Step 1:  First we need to find the radius of the circle.

Since 6 is the diameter of the circle and the diameter is 2 * the radius, the radius is 3 in. since 2 * 3 = 6 and 6/2 = 3.

Step 2:  Because we're working with a right triangle, we can now find l using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

We can plug in 10 for and 3 for b, allowing us to solve for c (aka l since l is the hypotenuse in the right triangle).

10^2 + 3^2 = c^2

100 + 9 = c^2

√109 = c

Thus, the measure of l is √109 in.

The angles which are congruent to angle R in the figure shown above include the following:

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines.

This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to parallel lines M and L, we have the following:

∠P ≅ ∠R

∠R ≅ ∠D

∠P ≅ ∠A

∠D ≅ ∠A

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The number 6 is far from zero on a number line by 6 unit .

We are given that the absolute value of a number is the distance it is from zero on a number line

The absolute value function is given by the following piecewise rule, depending on the input of the function:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

We are given that an absolute value of 6 can be written like

|6| = 6, x ≥ 0.

|6| = -6, x < 0.

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Answer:

[tex]\huge\boxed{\sf A = \frac{9 \pi}{8} \ sq. \ units}[/tex]

Step-by-step explanation:

Radius = r = 3 units

Angle = θ = [tex]\displaystyle \frac{\pi}{4} rad[/tex]

Area of sector = A = ?

[tex]\displaystyle Area \ of \ sector = \frac{1}{2} r^2 \theta[/tex]

Put the given data in the above formula.

[tex]\displaystyle A = \frac{1}{2} (3)^2(\frac{\pi}{4} )\\\\A = \frac{1}{2 \times 4} (9)(\pi)\\\\A = \frac{9}{8} (\pi)\\\\A = \frac{9 \pi}{8} \ sq. \ units\\\\\rule[225]{225}{2}[/tex]

The Volume of the box is 3.75in³

The volume of the box is dependent on the volume of the cube in it.

To obtain the volume of a cube, we use the relation, V = s³

s = side of the cube

Volume = 0.5³ = 0.125 in³

Number of cubes in box = 30

Volume of each cube × Number of cubes

0.125 × 30 = 3.75 in³

Hence, the volume of the box is 3.75in³

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The solution to the inequality expression (6 + x)/2 < (x + 8)/3 is (c) x < -2

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

(6 + x)/2 < (x + 8)/3

Cross multiply the inequality expression

So, we have the following representation

3(6 + x) < 2(x + 8)

Evaluate the products to open the brackets

18 + 3x < 2x + 16

So, we have

3x - 2x < 16 - 18

Evaluate the difference

x < -2

Hence, the solution to the inequality is (c) x < -2

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To find the equation of the line that is parallel to 2y = 3(2 - 3x) and passes through the point of intersection of the lines y = x + 8 and y = -3x + 4, we need to follow these steps:

Step 1: Find the point of intersection of the lines y = x + 8 and y = -3x + 4.

Step 2: Determine the slope of the line 2y = 3(2 - 3x) (which is parallel to the desired line).

Step 3: Use the slope from step 2 and the point of intersection from step 1 to find the equation of the desired line using the point-slope form.

Let's go through each step:

Step 1: Find the point of intersection of the lines y = x + 8 and y = -3x + 4.

To find the point of intersection, we need to solve the two equations simultaneously:

y = x + 8 ...(Equation 1)

y = -3x + 4 ...(Equation 2)

We can set Equation 1 equal to Equation 2:

x + 8 = -3x + 4

Now, solve for x:

4x = -4

x = -1

Substitute the value of x into either Equation 1 or Equation 2 to find the corresponding y-value:

y = -1 + 8

y = 7

So, the point of intersection is (-1, 7).

Step 2: Determine the slope of the line 2y = 3(2 - 3x).

The given equation is 2y = 3(2 - 3x). We can rewrite it in slope-intercept form (y = mx + b) by dividing both sides by 2:

y = (3(2 - 3x))/2

y = (6 - 9x)/2

y = 3 - (9/2)x

The slope of this line is -(9/2).

Step 3: Use the slope from step 2 and the point of intersection from step 1 to find the equation of the desired line using the point-slope form.

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.

Using the point (-1, 7) and slope -(9/2), we can write the equation as:

y - 7 = -(9/2)(x + 1)

Now, simplify and rewrite it in the slope-intercept form:

y - 7 = -(9/2)x - 9/2

y = -(9/2)x - 9/2 + 7

y = -(9/2)x + 5/2

Therefore, the equation of the line parallel to 2y = 3(2 - 3x) and passing through the point of intersection of the lines y = x + 8 and y = -3x + 4 is y = -(9/2)x + 5/2.

Th approximate area of each cross section of the cone and pyramid  is shown below:

Circle 1 = 144πunits²

circle 2 = 36πunits²

circle 3 = 9πunits²

Triangle 1 = 144πunits²

triangle 2= 36π units²

triangle 3= 9π units²

A pyramid is described as  a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense.

for circle 1 + π*12² = 144πunits²

for Circle  2 = 26²* π = 36πunits²

for Circle 3 = 3²* π = 9πunits²

for Triangle 1 = 1/2*(12π)*(24) =  6π(24) = 144πunits²

for Triangle 2 = 1/2* (6π)* (12) = 36π units²

for Triangle 3 = 1/2* (3π)* (6) =- π units²

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Answer:

The answer is D

The measure of angle AOB is 106° and the measure of angle APB is 74° from the given circle.

From the given figure, ∠BCA=53°.

The angle subtended by an arc at the center is twice the angle subtended at the circumference. More simply, the angle at the center is double the angle at the circumference.

Here, ∠AOB=2∠BCA

∠AOB=2×53=106°

So, the measure of angle AOB is 106°.

Now, ∠AOB+∠APB=180°

106°+∠APB=180°

∠APB=180°-106°

∠APB=74°

Therefore, the measure of angle AOB is 106° and the measure of angle APB is 74° from the given circle.

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When a scatter plot is shown on the coordinate plane, the two points that would a line of fit go through to best fit the data is D. (1, 7) and (5, 5)

The line of best fit would go through the points (1, 7) and (5, 5). This is because these two points are the closest to the center of the data, and the line of best fit is supposed to minimize the distance between the line and the data points.

The other two options are not as good because they are further away from the center of the data. The line of best fit should be as close to the data points as possible, so it should go through the points (1, 7) and (5, 5).

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The exact value of a and b is 5 and 5√3 respectively

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

As 30° is the acute angle , the side opposite to it is a and b is the adjascent and 10 is the hypotenuse.

sin30 = a/10

1/2 = a/10

2a = 10

a = 10/2

a = 5

Using Pythagorean theorem

10² = b² + 5²

100 = 25+b²

b² = 100-25

b² = 75

b = √ 75

b = 5√3

Therefore the exact value of a is 5 and b is 5√3

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Answer:

SNSPEUE is the

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