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(Identifying Transformations LC)

Use the image to determine the direction and angle of rotation.

Graph of triangle ABC in quadrant 4 with point A at 1 comma negative 3. A second polygon A prime B prime C prime in quadrant 3 with point

A prime at negative 3 comma negative 1.

180° counterclockwise rotation
90° counterclockwise rotation
90° clockwise rotation
180° clockwise rotation

Answer:

the length of the opposite side of the triangle is approximately 21.8594 miles                    

Step-by-step explanation:

tan(theta) = opposite/hypotenuse

opposite = tan(theta) x hypotenuse

Substituting the given values, we get:

opposite = 0.7536 x 29

opposite = 21.8594 miles (rounded to four decimal places)

Answer:

Step-by-step explanation:

You want the reciprocal function of f(x) = 5x² +13x -6 and the equations of its vertical asymptotes. You also want the graph of f(x) = ((x +4)(x -5))/(x² +2x-8) along with its domain, range, and intervals of positive, negative, increase, and decrease.

The reciprocal function will be ...

 1/f(x) = 1/(5x² +13x -6)

Its vertical asymptotes will be found where f(x) = 0. Those values of x are nicely found by factoring the function.

  f(x) = 5x² +13x -6 = (5x +15)(5x -2)/5 = (x +3)(5x -2)

The product of factors will be zero when one of the factors is zero.

  x +3 = 0   ⇒   x = -3

  5x -2 = 0   ⇒   x = 2/5

The equations of the vertical asymptotes are x = -3 and x = 2/5.

The function can be simplified by factoring the denominator anc cancelling common factors:

  [tex]f(x)=\dfrac{(x+4)(x-5)}{x^2+2x-8}=\dfrac{(x+4)(x-5)}{(x+4)(x-2)}=\dfrac{x-5}{x-2}\quad x\ne -4[/tex]

The function changes sign where the factors are zero, at x = 2 and x = 5. It is approaches the horizontal asymptote y = 1 for large positive or negative values of x, and is increasing everywhere it is defined. There is a vertical asymptote at x = 2, and a "hole" at x = -4 where the numerator and denominator factors canceled, but the function remains undefined. The function can take on any value except those at the horizontal asymptote and the "hole".

Domain, Increasing

The function is increasing everywhere it is defined, so the "increasing" intervals and the domain are the same:

  (-∞, -4) ∪ (-4, 2) ∪ (2, ∞) . . . .  . domain, intervals of increase

The function has no intervals of decrease.

Negative, Positive, Range

The function is positive everywhere it is defined, except for the interval between sign changes.

  negative: (2, 5)

  positive: (-∞, -4) ∪ (-4, 2) ∪ (5, ∞)

  range: (-∞, 1) ∪ (1, 1.5) ∪ (1.5, ∞)

Answer:

Step-by-step explanation:

here is an solution

Answer:

Step-by-step explanation:

25%.There are four possible outcomes of two coin flips:

H H

H T

T H

T T

Thus there is a 1 in 4 chance of getting the combination H T, or 25%.

Answer:

in the image below i believe

Step-by-step explanation:

I will describe the original unrotated shape's coordinates. The top point is L, middle point is M, bottom point is N. The origin is where the axis meet. 180 degrees means to rotate the shape using the origin until it's upside down. The new shape is the one with the arrow pointing towards it. L is (1,-5). M is (2, -4). N is (1,0)

To answer your question, you need to find the rate of bike travel first. The rate is the ratio of distance to time, so you can divide the distance by the time to get the rate. In this case, the rate is 24 miles / 3 hours = 8 miles per hour. This means that the bike travels 8 miles every hour. To find how many miles the bike travels in 10 hours, you can multiply the rate by the time. In this case, the distance is 8 miles per hour x 10 hours = 80 miles. So, the bike travels 80 miles in 10 hours at this rate.

The average rate of bike travel in the United States is about 1% of all trips while in the United Kingdom it is about 2%. The average distance cycled per year in the United States is about 9 billion miles, while in the United Kingdom it is about 3.3 billion miles.

Hope this helps you, bye! :D

Answer:

The bike travels 80 miles in 10 hours.

Step-by-step explanation:

We need to break this up into units.

To do this, we have to find how many miles the bike can travel in per hour.

This can be done by dividing 24 miles by three hours:

24/3 = 8

This is equal to 8 which means the bike travels 8 miles per hour.

Now, we can calculate how many miles the bike travels in 10 hours by multiplying by 10.

8*10 = 80

Therefore, the bike travels 80 miles in 10 hours.

394 subscribers are represented in the venn diagram.

Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.

Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.

according to the venn diagram

196+41+21+52+84 = 394

There are 394 subscribers

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Therefore, the 95% confidence interval for the difference in scores is (9.936, 11.864).

In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence, based on a sample of data.

Here,

To find the confidence interval for the difference in scores, we can use the formula:

CI = (x1 - x2) ± t(α/2, df) * SE

where x1 and x2 are the sample means for groups 1 and 2, t(α/2, df) is the critical t-value based on the level of significance α and the degrees of freedom df, and SE is the standard error of the difference between the means, given by:

SE = √((s₁²/n₁) + (s₂²/n₂))

where s₁ and s₂ are the sample standard deviations for groups 1 and 2, and n₁ and n₂ are the sample sizes.

Given:

x1 = 26.4, s₁ = 4.4, n₁ = 200

x2 = 15.5, s₂ = 2.4, n₂ = 200

α = 0.05

df = n₁ + n₂ - 2 = 398 (assuming equal variances)

First, we need to calculate the standard error:

SE = √((4.4²/200) + (2.4²/200))

= 0.492

Next, we need to find the critical t-value:

t(α/2, df) = t(0.025, 398)

= 1.964

Finally, we can calculate the confidence interval:

CI = (26.4 - 15.5) ± 1.964 * 0.492

= 10.9 ± 0.964

= (9.936, 11.864)

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Answer:

the maximum possible area of a Norman window with a perimeter of 76 meters is approximately 43.24 square meters.

Step-by-step explanation:

Let's first write the equation for the perimeter P of a Norman window in terms of its height h and width w:

P = 2h + w + πh

Simplifying this equation, we get:

P = (2 + π)h + w

We are given that the perimeter is 76 meters, so we can set up the equation:

76 = (2 + π)h + w

Solving this equation for w, we get:

w = 76 - (2 + π)h

The area A of a Norman window is the sum of the area of the rectangle and half the area of the circle:

A = hw + (1/2)πh^2

Substituting the expression for w from above, we get:

A = h(76 - (2 + π)h) + (1/2)πh^2

Expanding and simplifying, we get:

A = (38π - 2)h^2 + 76h

This is a quadratic equation in h, with a negative coefficient for the h^2 term. Therefore, the maximum area will occur at the vertex of the parabola, which is located at:

h = -b / 2a = -76 / 2(38π - 2) = 1 / (19π - 1)

Substituting this value of h back into the equation for A, we get:

A = (38π - 2)(1 / (19π - 1))^2 + 76 / (19π - 1)

Simplifying this expression, we get:

A = (76π - 4) / (19π - 1) ≈ 43.24 square meters (rounded to the nearest hundredth)

Therefore, the maximum possible area of a Norman window with a perimeter of 76 meters is approximately 43.24 square meters.

The equation that would be used to find the angle needed to travel 150 meters is 150 = 197.55 sin (2θ).

option D.

The equation that would be used to find the angle needed to travel 150 meters is calculated as follows;

h = (v₀²/4.9) sinθcosθ

where;

Substitute the value of v₀ in the given equation;

h = (44²/4.9) sinθcosθ

h = 395.1 sinθcosθ

In trig identity, 2sinθcosθ = sin (2θ)

h = ¹/₂ [395.1 (2sinθcosθ)]

h = ¹/₂ [395.1 sin (2θ)]

h = 197.55 sin (2θ)

150 = 197.55 sin (2θ)

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The expression for the length of one side of the square is 4x + 8y.

A square is simply a geometric shape with four equal sides and four right angles.

The perimeter of a sqaure is expressed as:

P = 4s

Where "4s" represents the sum of all four sides of the square, since all sides of a square are equal in length.

Given that:

Perimeter P = 16x + 32y

Then plug into:

P = 4s

16x + 32y = 4s

To find an expression for s, we can divide both sides by 4:

4s = 16x + 32y

4s/4 = 16x/4 + 32y/4

s = 4x + 8y

Therefore, one side of the square is 4x + 8y.

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a). His daily profit cap is $450.

b). To make the most money, 1500 cans must be sold.

Considering the subsequent quadratic function;

P(x) = -0.001x² + 3x - 1800

to calculate his daily profit cap;

P(x), a quadratic equation, would be greatest when x = -b/2a.

A quadratic equation has the conventional form  ax² + bx + c = 0

Using eqns. 1 and 2, we can see that;

a = -0.001, b = 3 and c = -1800

We now calculate the greatest profit;

x = -b/2a

When the values are substituted, we have;

x = -3/2*(-0.001)

erasing the warning signals, we have;

x = 3/2*0.001

x = 3/0.002

maximum x = 1500

the value of "x" is substituted in equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b). In order for the soft drink salesman to make the most money, 1500 cans must be sold.

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The complete Question is,

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

y=8x+4

Step-by-step explanation:

follow the formula y=mx+b where m is the slope and b is the y intercept

first find the slope, which is the rate of change, using the equation (y2-y1)/(x2-x1). i substituted the values from x=0 as (0,4) for the first coordinate and x=1 as (1,12) for the second coordinate from the chart and filled them into the equation:

so (12-4)/(1-0)=8/1= 8

so the slope is 8

and the y intercept is the y value when x=0, which can be seen on the chart as 4. so y=8x+4

Answer:

  (c)  3(cos(135°) +i·sin(135°))

Step-by-step explanation:

You want to identify a solution to x^4 = -81.

The principal fourth root of 81∠180° will be ...

  [tex]\sqrt[4]{-81}=\sqrt[4]{81\angle 180^\circ}=\sqrt[4]{81}\angle \dfrac{180^\circ}{4}=3\angle 45^\circ[/tex]

Additional complex roots will be at angles that are multiples of 360°/4 from this one, so ...

  3∠135°, 3∠225°, 3∠315°

The root that is on the list of choices is ...

  3∠135° = 3(cos(135°) +i·sin(135°))

__

Additional comment

The attachment shows the 4th powers of the numbers with the various angles. The fourth power of 3∠135° gives -81.

The expressions 1/7x + 7/8x are not equivalent to x.

A term is composed of one mathematical expression. A single variable (a letter), a single integer (positive or negative), or a number of variables that have been multiplied but never added or subtracted are all examples of single variables. There is a number in front of certain words that are variables. A word or phrase is preceded by a coefficient.

To simplify the expressions, we can combine the two terms with the same variable (x) by finding a common denominator.

1/7x + 7/8x = (8/56)x + (49/56)x

Now, we can add the two terms:

(8/56)x + (49/56)x = (57/56)x

Therefore, the simplified expression is 57/56x, which is not equivalent to x.

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Answer:

Range: [−4,∞)

Step-by-step explanation:

Hope it helps:)

Answer:

Range: [-4, ∞), {y|y ≥ -4}

Step-by-step explanation:

It helps if you graph the function to better understand what the range is.

In interval and set-builder notation, the range is:

[-4, ∞), {y|y ≥ -4}

This is knowing that the Domain is:

(-∞, ∞), {x|x ∈ R}

The probability of introducing a new product is 0.6.

The probability that the new product will be introduced is calculated as follows:

P(new product) = P(new product | first set wins) * P(first set wins) + P(new product | second set wins) * P(second set wins)

The given probabilities from the statement are as follows:

P(first set wins) = 0.6

P(new product | first set wins) = 0.8

P(second set wins) = 0.4

P(new product | second set wins) = 0.3.

Therefore, the required probability will be:

P(new product) = 0.8 * 0.6 + 0.3 * 0.4

P(new product) = 0.48 + 0.12

P(new product) = 0.6

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The number of cubic inches of sand that this sandbox would hold is 186,624 cubic inches.

The volume of the toy box is equal to 32 1/2 cubic feet.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have;

Volume of sandbox = 96 × 72 × 27

Volume of sandbox = 186,624 cubic inches.

Mathematically, the volume of a triangular prism can be calculated by using this formula:

Volume = base area × height of the prism.

Volume = 6 1/2 × 5.

Volume = 13/2 × 5.

Volume = 32 1/2 cubic feet.

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Answer:

The slower ship is going 240 mph

The faster ship is going 260 mph

Step-by-step explanation:

midnight to 8 am is 8 hours, the distance shortened between the ships each hour was 500 miles so if the slower ship's speed is x and the faster ship's speed is y:

x + y = 500

and the question tells us that

x + 20 = y

Using the substitution method we can substitute the y in the first question for the second's.

x + (x + 20) = 500

solve:

x + x + 20 = 500

2x + 20 = 500

2x + 20 - 20 = 500 - 20

2x = 480

(2x) / 2 = 480 / 2

x = 240

Now that we have x we can now substitute the x into the second equation

(240) + 20 = y

260 = y

y = 260

And after adding the unit of measurement (Miles Per Hour) we get the speed of the slower ship (x) to be 240 MPH, and the speed of the faster ship (y) to be 260 MPH.

Answer:

B. They must be similar

Step-by-step explanation:

If you want to know why shape X and shape Y are similar but not congruent, here's a funny way to remember it. Imagine shape X is a cute little kitten and shape Y is a giant lion. They both have four legs, a tail, and a furry body, so they are similar. But they are not the same size, so they are not congruent. You can't make them congruent by rotating, reflecting or translating them, because that would just change their position or orientation. You would need to use a magic wand to shrink the lion or enlarge the kitten. But then you would have a different problem: how to feed them and keep them happy. A scale factor of 3 means that shape Y is 3 times bigger than shape X in every dimension. That's like having a lion that weighs 900 pounds and eats 90 pounds of meat a day. Good luck with that!

Similar figures have the same angles and proportional sides, but not necessarily the same size. Congruent figures have the same angles and sides, and therefore the same size. Point symmetry means that every point on a figure has a corresponding point that is the same distance from a central point but in the opposite direction. Line symmetry means that a figure can be folded along a line so that the two halves match exactly.

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

no fred is not correct

Step-by-step explanation:

so u say

5/8×6/1

then u say 5×6=30

then u say 8×1=8

then u say 30÷8= 3.75

so yr answer is =3.75

hope u understand

In the figure of a regular polygon that is inscribed in a circle, the parts are identified as follows

In a regular octagon, each interior angle has a measure of 135 degrees. To find the central angle of an inscribed regular octagon, we can divide the full circle (360 degrees) by the number of sides in the regular octagon.

The formula to find the central angle of an inscribed polygon is:

Central angle = 360 degrees / number of sides

In this case, the number of sides is 8, so we have:

Central angle = 360 degrees / 8

Central angle = 45 degrees

Therefore, the central angle of an inscribed regular octagon is 45 degrees.

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Answer:

9

Step-by-step explanation:

For the function g(x) = x^2 - 1, we can calculate the function values at x=3 and x=6, and then find the difference and divide by the length of the interval (6 - 3).

g(3) = 3^2 - 1 = 9 - 1 = 8

g(6) = 6^2 - 1 = 36 - 1 = 35

The difference in function values is g(6) - g(3) = 35 - 8 = 27.

The length of the interval is 6 - 3 = 3.

So, the average rate of change of g(x) from x=3 to x=6 is 27 / 3 = 9.

Answer: 2. 50,688 litres.

Step-by-step explanation:

The volume of a cylinder can be calculated using the formula:

V = πr²h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

V = π(2.4²)(2.8)

V = 50.688 m³

To convert this to litres, we can multiply by 1000:

V = 50.688 × 1000

V = 50,688 litres

Therefore, the answer is option 2: 50,688 litres.

The values from the set {−4,−3,−2, 0, 1, 2} that satisfy this inequality are -4 and -3 only.

To solve the inequality –2x – 6 ≥ 0, we need to isolate x on one side of the inequality sign.

Adding 6 to both sides, we get:

–2x – 6 + 6 ≥ 0 + 6

–2x ≥ 6

Dividing both sides by –2 (and reversing the inequality because we are dividing by a negative number), we get:

x ≤ –3

The values from the set {−4,−3,−2, 0, 1, 2} that satisfy this inequality are -4 and -3 only.

Therefore, the answer is A. –4 and –3 only.

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The solid figure has a 245.04 total area. The area is the measurement of any two-dimensional region confined by a set of lines, and square footage is a measurement of area.

Therefore,

The equation to a cylinder for the area is A=2πrh+2πr^2

Fill in and solve.

A=2(3.14)(3)(10)+2(3.14)(3)^2

So using PEMDAS you get the answer 245.04

The complete question is:

Find the total area of the solid figure.

60 sq. in.

78 sq. in.

90 sq. in.

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Answer: The answer is B and C im 100% correct

Step-by-step explanation:

The equation of the curve is y = x³ - 2x² + 5x - 3

Since the gradient of every point on the curve C with equation y = f(x), satisfies dy/dx = 3x2 – 4x + k, where k is a constant. The points P (0, -3) and Q (2, 7) both lie on C. To find the equation of the curve c, we first integrate the equation for the gradient.

So, we proceed as follows.

Since dy/dx = 3x² - 4x + k

dy = (3x² - 4x + k)dx

Integrating both sides, we have that

∫dy = ∫(3x² - 4x + k)dx

∫dy = ∫3x²dx - ∫4xdx + ∫kdx

y = 3x³/3 - 4x²/2 + kx + C

y = x³ - 2x² + kx + C

Using the points P(0, -3) and Q(2, 7) we have that

y = x³ - 2x² + kx + C

-3 = 0³ - 2(0)² + k(0) + C

-3 = 0 + 0 + 0 + C

- 3 = 0 + C

C = - 3

So, y = x³ - 2x² + kx + C

y = x³ - 2x² + kx - 3

So, using the points Q(2, 7), we have that

y = x³ - 2x² + kx - 3

7 = 2³ - 2(2)² + k(2) - 3

7 = 8 - 8 + 2k - 3

7 = 0 + 2k - 3

7 = 2k - 3

2k = 7 + 3

2k = 10

k = 10/2

k = 5

So, substituting this into the equation for the curve, we have that

y = x³ - 2x² + 5x - 3

So, the equation of the curve is y = x³ - 2x² + 5x - 3

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