A plane rises from take-off and
flies at an angle of 20° with
the horizontal runway. When it
has gained 750 feet, find the
distance that the plane has
flown.
+
A
C =
(Round the answer to the nearest whole number.)
c = ?
20°
B
M
B
750 ft
C
2
L

Answer: G: 9x^2+6x+1; F: 4x^2-12x+9

g: 9x+4; f: 4x-9

Step-by-step explanation: If you’re multiplying the functions by themselves, you’ve got to factor them. Use the FOIL method.

(g•g) = (3x+1)(3x+1) = 9x^2+6x+1

(f•f) = (2x-3)(2x-3) = 4x^2-12x+9

If you’re finding f of x inside of f then it’d be: 2(2x-3)-3 = 4x-9

(f.f)(x) = 4x-9

g of x inside g would be: 3(3x+1)+1

(g.g)(x) = 9x+4

Answer: ∠FCD= 109°

Step-by-step explanation: 71+38= 109

the answer is A.

proj_vu = ((u . v) / |v|^2) * v

Since the magnitude of vector v (|v|) is shorter than the magnitude of vector u, we know that the projection of u onto v will be smaller than u. The answer A (0.195i - 0.244j) has values that are smaller than u, indicating that it is a projection of u onto v.

Therefore, the answer is A.

Answer:

First, we can find the height of the original cone using the Pythagorean theorem:

height = sqrt(slant height^2 - radius^2) = sqrt(12^2 - 2^2) = sqrt(142) inches

The surface area of the original cone is:

SA = πr(r + √(r^2 + h^2)) = π(2)(2 + √(2^2 + (sqrt(142))^2)) ≈ 46.63 in²

The ratio of the radii of the two cones is 6/2 = 3, so the ratio of their surface areas is 3^2 = 9.

Therefore, the surface area of the similar cone is:

SA = 9 × 46.63 = 419.67 in² (rounded to two decimal places)

So the exact surface area of the similar cone with a radius of 6 inches is 419.67 in².

Step-by-step explanation:

Option A is correct, the two triangles are similar because corresponding sides are in proportion and  angles are congruent .

The two triangles are ABC and DEF.

ABC and DEF are similar triangles.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

The corresponding sides are in proportional.

Let us compare the corresponding side and angle.

AB=EF, BC=FD, AC=ED and

angle C is equal to angle D.

Hence, the two triangles are similar because corresponding sides are in proportion and  angles are congruent .

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Answer:

  A.  324 units³

Step-by-step explanation:

You want the volume of a triangular prism with triangle base 9 units, triangle height 4 units, and prism length 18 units.

The volume of the triangular prism is the product of its base area and its length:

  V = Bl

The base area is the area of a triangle.

  B = 1/2bh

Then the volume of the prism is ...

  V = (1/2bh)l = 1/2(bhl) = 1/2(9)(4)(18) = 324 . . . . cubic units

The volume of the triangular prism is 324 units³.

__

Additional comment

You will note that this is half the volume of a rectangular prism with the same overall dimensions.

<95141404393>

The ladder reaches approximately 10.9 feet up the house.

Part I:

To illustrate the scenario, we can sketch a right triangle with the ladder representing the hypotenuse, the distance between the base and the house representing one of the legs, and the height up the house representing the other leg. Label the base as 5 feet, the height as "h," and the hypotenuse (the ladder) as 12 feet.

Part II:

Using the Pythagorean theorem, we can set up an equation to find the height up the house, "h."

According to the Pythagorean theorem:

(hypotenuse)² = (leg₁)² + (leg₂)²

Substituting the given values:

(12 ft)² = (5 ft)² + h²

Simplifying the equation:

144 = 25 + h²

Rearranging the equation:

h² = 144 - 25

h² = 119

Taking the square root of both sides:

h = √119

Rounding the answer to the nearest tenth:

h ≈ 10.9 ft

Therefore, the ladder reaches approximately 10.9 feet up the house.

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The angle measure of the angle in the diagram is 62°.

From the question, we are to determine the angle measure of the angle shown in the diagram.

The angle shown is an acute angle.

An acute angle is an angle whose measure is less than 90°.

To determine the measure of the angle, we will read the angle from the side which the angle is closer to zero (0). We will read from 0 to the line that indicates the angle.

Reading the angle:

Reading the angle as explained above, the measure of the angle is 62°

Hence, the angle measure is 62°.

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Explanation:

Apply the dot product.

u dot v = 2*(-4) + 12*5

u dot v = -8 + 60

u dot v = 52

The dot product result is not zero, so the vectors are not orthogonal. The angle between the vectors is not 90 degrees.

The two equations that represent the two lines of symmetry of the rectangle, respectively, are:

x = 2 and y = 5

There are two symmetry lines in a rectangle.

Specifically, it refers to the line that splits the rectangle into two identical half.

The symmetry line for the horizontal line can be found at y = 5.

We would have two equal parts of the rectangle if a horizontal line were drawn through it at y = 5.

A horizontal line still has a zero slope.

As a result, the following would be the equation for the line of symmetry of the rectangle depicted in the coordinate grid:

y = 5

The vertical second line of symmetry would intersect the rectangle at x = -2.

A vertical line's slope is thus ill-defined.

A vertical line's equation is written as x = h.

Where h is a constant because, regardless of the value of the y-coordinate, any coordinate along the vertical line would unquestionably have an x-coordinate value of 2.

H is therefore -2 in this instance.

As a result, the following equation would describe the rectangle's second line of symmetry:

x = 2

Hence the two equations that represent the two lines of symmetry of the rectangle, respectively, are:

x = 2 and y = 5

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The population of the town in 1955 was 12 thousand people, and the percent increase in population from year to year was 3%.

To find the population of the town in 1955, enter t = 0 into the function f(t) = 12(1 + 0.03)t:

f(0) = 12(1 + 0.03)^0 = 12(1)

      = 12

As a result, the town's population in 1955 was 12,000 people.

We can compare the population at two successive years, t and t+1, to compute the percent increase in population from year to year.

[(Population at year t+1) - (Population at year t)] / (Population in t th year) * 100

Increase in Percentage = [f(t+1) - f(t)] / f(t) * 100

Increase in Percentage = [12(1 + 0.03)(t+1) - 12(1 + 0.03)t] / [12(1 + 0.03)^t] * 100

Because the function f(t) = 12(1 + 0.03)t depicts exponential growth, the annual population increase will be a constant percentage. The percentage increase in this scenario would be 3% since the growth factor is 1 + 0.03 = 1.03.

Therefore, the population of the town in 1955 was 12 thousand people, and the percent increase in population from year to year was 3%.

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The correct question is:-

The function defined by f(t)=12(1+0.03)t can be used to determine the population, in thousands, of a town t years since 1955. According to the function, what was the population of the town in 1955 and what was the percent increase in population from year to year?

Answer:

The first step to graphing an equation that is not in slope-intercept form is to solve for y to get it in the form y = mx + b, where m is the slope and b is the y-intercept.

Step-by-step explanation:

The shape is a Octahedron with 6 vertices, 12 edges and 8 faces. and with Euler value of 2.

Euler's formula states that for any polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation:

      V - E + F = 2.

From the picture, we can tell that that is an octahedron which has the following properties:

- Vertices (V): 6

- Edges (E): 12

- Faces (F): 8

Now, let's substitute these values into Euler's formula:

V - E + F = 6 - 12 + 8

Simplifying the equation:

-6 + 8 = 2

As we can see, the equation holds true, and we obtain the result 2. Therefore, the octahedron verifies Euler's formula.

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Given that the perpendicular bisectors of the sides of AXYZ meet at a single point S, which is the circumcenter of the triangle, I can use the properties of the circumcenter to find the lengths XS, YZ, and VY.

To start, I can use the fact that the circumcenter of a triangle is equidistant from its vertices. Therefore, I can write:

SV = SY (since S is equidistant from V and Y)

SZ = SX (since S is equidistant from Z and X)

SV = VX (since S is equidistant from V and X)

SU = UY (since S is equidistant from U and Y)

From the given information, we know that VS = 66, YU = 86, and ZS = 110. I can use this information to solve for the unknown lengths.

To find XS, I can use the fact that SZ = SX. We know that ZS = 110, so:

XS = ZS = 110

To find YZ, I can first find VY by using the fact that SV = VX. I know that VS = 66, so:

VY = VS - SY = 66 - YU/2

Now I can use the fact that SU = UY to solve for YZ:

YZ = YU - 2UY/2 = YU - UY = 86 - (66 - VY) = 20 + VY

So, YZ = 20 + VY

Therefore, I still need to find the value of VY. We can use the fact that SV = SY and the equation we found for VY above to solve for it:

SV = SY

66 = VY + 86/2

66 = VY + 43

VY = 23

Therefore, we have:

XS = 110

YZ = 20 + VY = 43

VY = 23

So, XS = 110, YZ = 43, and VY = 23.

[a] Answer: 4

Step-by-step explanation:

For shape P to shape Q, we will count the units of the top side. Shape P's top side is 2 units and Shape Q's top side is 8 units. Now, we will divide to find the scale factor.

       8 units / 2 units = 4

There was a scale factor of 4 because Shape Q is 4x larger than Shape P.

[b] Answer: 3

Step-by-step explanation:

       For shape R to shape T, we will count the units of the bottom side. Shape R's bottom side is 2 units and Shape T's bottom side is 6 units. Now, we will divide to find the scale factor.

       6 units / 2 units = 3

There was a scale factor of 3 because Shape T is 3x larger than Shape R.

The length of the altitude is 3√6.

According to Right Triangle Altitude Theorem

The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse has a length that is the geometric mean of the lengths of the two segments of the hypotenuse.

So, AD = √CD.  DB

Here we have CD=6 and DB=9 so

AD = √6 x 9

AD = √54

AD = 3√6

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Answer:

The probability of getting at least two white balls = (15*10 + 20 + 15)/330 = 65/330 or approximately 0.1969.

Step-by-step explanation:

To find the probability of selecting balls, we need to use combinations.

Total number of ways to select 4 balls out of 11 = C(11,4) = 330

1. Probability of getting exactly two white balls and two red balls:

Number of ways to select 2 white balls out of 6 = C(6,2) = 15

Number of ways to select 2 red balls out of 5 = C(5,2) = 10

Number of ways to combine these selections = 15 * 10 = 150

Therefore, the probability of getting exactly two white balls and two red balls = 150/330 = 5/11 or approximately 0.4545.

2. Probability of getting at least two white balls:

Number of ways to select 2 white balls out of 6 = C(6,2) = 15

Number of ways to select 2 balls out of 5 that are not white = C(5,2) = 10

Number of ways to select 3 white balls out of 6 = C(6,3) = 20

Number of ways to select 4 white balls out of 6 = C(6,4) = 15

Therefore, the probability of getting at least two white balls = (15*10 + 20 + 15)/330 = 65/330 or approximately 0.1969.

The solution is: the cosine of an angle cannot be greater than 1 or less than -1, it is not possible for the given triangle to have an angle with a cosine of -1. Therefore, the triangle is not solvable with the given side lengths.

To determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle, we can compare the given information with the formulas for each law.

The Law of Sines states:

a / sin(A) = b / sin(B) = c / sin(C)

The Law of Cosines states:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are given the lengths of all three sides of the triangle (a = 6.0, b = 7.7, c = 13.6). Therefore, we have enough information to use the Law of Cosines to solve the triangle.

Using the Law of Cosines, we can find the measures of the angles:

c^2 = a^2 + b^2 - 2ab * cos(C)

(13.6)^2 = (6.0)^2 + (7.7)^2 - 2 * 6.0 * 7.7 * cos(C)

184.96 = 36 + 59.29 - 92.4 * cos(C)

184.96 = 95.29 - 92.4 * cos(C)

92.67 = -92.4 * cos(C)

cos(C) ≈ -1

Since the cosine of an angle cannot be greater than 1 or less than -1, it is not possible for the given triangle to have an angle with a cosine of -1. Therefore, the triangle is not solvable with the given side lengths.

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complete question:

Consider the following triangle.

a = 6.0, b = 7.7, c = 13.6

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.

O Law of Sines

O Law of Cosines

Solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal pl

A =

B =

C =

Need Help?

0

O

O

Read It

The distance between the points (-6, 4) and (5, 4) is 11 units.

To find the distance between two points in a Cartesian coordinate system, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Given the two points (-6, 4) and (5, 4), we can plug in the coordinates into the distance formula:

Distance = √[(5 - (-6))² + (4 - 4)²]

        = √[(5 + 6)² + 0²]

        = √[11² + 0]

        = √[121]

        = 11

Therefore, the distance between the points (-6, 4) and (5, 4) is 11 units.

In this case, since the y-coordinates of both points are the same (4), the distance between them only considers the difference in their x-coordinates. As the x-coordinate of the second point is 11 units greater than the x-coordinate of the first point, the distance between them is simply the absolute value of the difference, which is 11.

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Answer: A. 138 square centimeters

Step-by-step explanation:

   There are two ways to solve this. The first is to use the formula for the area of a trapezoid. This way is quicker, but if you do not know the formula I have provided a second way below.

A = [tex]\frac{a+b}{2} h[/tex]

A = [tex](\frac{9+14}{2}) (12)[/tex]

A = 138

   The second is to break this shape up into two parts. First, the area of the rectangle.

A = LW

A = (9 cm)(12 cm)

A = 108 cm²

   Next, the area of the triangle on the left side of this shape. To find the base, we will subtract 9 cm from 14 cm.

A = [tex]\frac{bh}{2}[/tex]

A = [tex]\frac{(14\;cm\;\;-\;\;9\;cm)(12\;cm)}{2}[/tex]

A = [tex]\frac{(5\;cm)(12\;cm)}{2}[/tex]

A = [tex]\frac{60\;cm^2}{2}[/tex]

A = 30 cm²

   Lastly, we'll add these two shapes together.

A = 108 cm² + 30 cm² = 138 cm²

Answer:

Step-by-step explanation:

the figure is a trapezoid, the formula for the area is

A = ½ (a + b)×h

A =  ½ (14 + 9) × 12

A =  ½ 23 × 12

A =  ½ × 276

A = 138 cm²

Answer:

  a. x = 15

  b. scalene

Step-by-step explanation:

You want to know the value of x and the classification of the triangle whose circumscribing arcs are (8x-10)°, (6x)°, and (10x +10)°.

The sum of arcs around the circle is 360°.

  (8x -10)° +(6x)° +(10x +10)° = 360°

  24x = 360 . . . . . . . . . . . divide by °, simplify

  x = 15 . . . . . . . . . . . . divide by 24

The arc measures around the circle are ...

  (8x -10)° = 110°

  (6x)° = 90°

  (10x +10)° = 160°

Each arc is double the measure of the inscribed angle that intercepts it. The different arc measures mean the angle measures are different, so the triangle is scalene.

<95141404393>

The statement X = Y + Yxy is True.

The equation given is:

X = Y + Yxy

To find x = (X- Y) / Yy we have to substitute the value of x in X = Y + Yxy as

X = Y + Yxy

X = Y + Yy (X-Y) / Yy

To solve for x, we can rearrange the equation as:
X = Y +  X - Y

X = X

Thus, the statement is True.

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This is the simplified form of the expression[tex](11x^11 - √(64) x 14x^14x14).[/tex]

To simplify the expression [tex](11x^11 - √(64) x 14x^14x14)[/tex], let's break it down step by step:

First, let's simplify the square root of 64, which is equal to 8:

[tex](11x^11 - 8 x 14x^14x14)[/tex]

Next, let's multiply the terms inside the parentheses:

[tex](11x^11 - 8 x 2744x^14)[/tex]

Now, let's simplify further by multiplying the constants:

[tex](11x^11 - 21952x^14)[/tex]

In this simplified form, we have subtracted 21952x^14 from 11x^11. The exponents on x are different for the two terms, so we cannot combine them further.

It's important to note that without specific values assigned to x, we cannot simplify the expression any further or provide a numerical answer. The expression remains in terms of x with different exponents for the terms.

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The degrees of freedom for the f-ratio evaluating the main effect of factor A would be (1, 8).

Here,

A factorial is a mathematical operation denoted by the symbol (!) that multiplies a number (n) by each integer that comes before it. To put it another way, the factorial function instructs you to multiply all the whole numbers starting at the selected number and decreasing by one. The factorial of a number (n!) is equal to n in more mathematical terminology (n-1)

How do you calculate factorial?

The factorial of a number (n!) is equal to n in more precise mathematical terminology (n-1). For instance, if you wanted to compute the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.

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complete question:

for a research study with 2 levels of factor a, 3 levels of factor b, and 5 in each treatment condition, what are the df values for the f-ratio evaluating the main effect for factor a?

Step-by-step explanation:

72 mi / 3hr =  21 mi/hr

72 mi / 12 hr = 6 mi / hr

21 - x = 6 + x

15 = 2x

x = 7.5 mi/hr  current speed

The factorized form of [tex]x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).[/tex]

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is [tex]x^3 - (y - z)^3.[/tex]To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as[tex](a - b)(a^2 + ab + b^2).[/tex]

Applying this identity to our expression, we have:

[tex]x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)[/tex]

Simplifying further, we get:

[tex]= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)[/tex]

So, the factorized form of [tex]x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).[/tex]

the above factorization is derived from the application of a mathematical identity.

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The value of x for the given trigonometric funciton cot(5x) = -√3 is 5x = -π/6 thus it is not exist in the interval  [ 0 , 2 π ).

We have,

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

As per the given equation,

cot5x = -√3

It is known that cotx = 1/tanx

1/tan5x = -√3

tan5x = -1/√3

Since, tan(π/6) = 1/√3 so -tan(π/6) = -1/√3

It is known that -tanx = tan(-x)

So, -tan(π/6) = tan(-π/6) so,

5x = -π/6 or x = -π/30.

Hence "The value of x for the given trigonometric function cot(5x) = -√3 is 5x = -π/6 thus it is not exist in the interval  [ 0 , 2 π )".

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complete question:

Solve for the exact solutions in the interval [ 0 , 2 π ) . Separate solutions with a comma. If the equation has no solutions, respond with DNE. cot (5x) = − √3

Answer:

[tex] \sqrt{34} [/tex]or 5.8309

Step-by-step explanation:

d=√(x2-x1)^2+(y2-y1)^2

[tex] = \sqrt{(( - 4) - 1)^{2} + {(4 - 1)}^{2} }\\ =\sqrt{( - 5)^{2} + {(3)}^{2} } \\= \sqrt{25 + 9} \\ = \sqrt{34} \\ = 5.8309[/tex]

I saw distance, so this is what I thought of. I hope this is the answer you're looking for.