16) In the given picture, line / is parallel to line m. if m<1 = 35°
(A) Find m<3
(B) Find m<7
(C) Find m<8
(D) Find m<5

Answer:

Explanation: Since these two powers have the same base of 5, you can multiply them together by simply adding their exponents to get

5^11

A common mistake in this problem would be to multiply

the bases together and give an answer of

25^11

.

The 5's in this problem can not be multiplied together because they are not coefficients. They are bases.

When applying your exponent rules, your base will never change.

Answer:

no se justamente yo tambien busco respuestas lo siento

Answer:

B. 4/1

Step-by-step explanation:

12/3 can be divided by 3.

Therefore 4/1.

Hello !

You find the GCD of 160 : 224

160

= 2 x 80

= 2 x 2 x 40

= 2 x 2 x 2 x 20

= 2 x 2 x 2 x 2 x 10

= 2 x 2 x 2 x 2 x 2 x 5

224

= 2 x 112

= 2 x 2 x 56

= 2 x 2 x 2 x 28

= 2 x 2 x 2 x 2 x 14

= 2 x 2 x 2 x 2 x 2 x 7

GDC = 2 x 2 x 2 x 2 x 2 = 32

=> 32 childrens

160/32 = 5

224/32 = 7

=> 5 apples and 7 mangoes per child

Answer:A=BxH divided by 2

                  _

Step-by-step explanation:

Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

The missing parts that would make the equation 2x(x-2y) + y(x-2y)-(x-2y) = (2x +_ - _ -2y) true are ² - x  - 3xy - 2y²

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

2x(x-2y) + y(x-2y)-(x-2y) = (2x +_ - _ -2y)

When expanded, we have

2x² - 4xy + xy - 2y² - (x - 2y) = (2x +_ - _ -2y)

Open the brackets

So, we have

2x² - 4xy + xy - 2y² - x - 2y = (2x +_ - _ -2y)

Evaluate the like terms

2x² - 3xy - 2y² - x - 2y = (2x +_ - _ -2y)

Rewrite as

2x² - x  - 3xy - 2y² - 2y = (2x +_ - _ -2y)

This means that the missing parts are ² - x  - 3xy - 2y²

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The height of the building is 242.59 feet.

Let's denote the height of the building as h.

angle of elevation is 35 degrees.

Using the tangent function,

tan(35°) = h / x

h = x tan(35°)

From the second observation point, which is 150 feet closer to the building,

The adjacent side is now (x - 150) since we moved closer to the building.

So, tan(51°) = h / (x - 150)

Now, tan(51°) = (x tan(35°)) / (x - 150)

1.2348 = x (0.7002)/ x-150

1.2348x - 185.22 = 0.7002x

x= 346.4646 feet

and, h = 364.4646 x 0.7002 =  242.59 feet

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Spiderman's elevation above sea level after meeting the Chameleon is 782ft.

An elevation is the view of a 3D shape when it is looked at from the side or from the front.

Angle of elevation: Angle of elevation is the angle between the horizontal line and the line of sight. It is formed at the vertex of intersection of the horizontal line and line of sight. It is the same angle as used in trigonometry.

To calculate Spiderman's elevation above sea level after descending 30ft to meet the Chameleon, we need to subtract 30ft from the initial elevation of 812ft.

812ft - 30ft = 782ft

Therefore, Spiderman's elevation above sea level after meeting the Chameleon is 782ft.

So, the correct answer is C. 782ft above sea level.

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In the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2) forms an isosceles triangle.

To prove that triangle PAT is an isosceles triangle, we need to show that at least two sides of the triangle are congruent.

Let's calculate the distances between the vertices:

Distance between P and A:

PA = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-4 - (-1))² + (5 - (-6))²]

= √[9 + 121]

= √130

Distance between P and T:

PT = √[(5 - (-1))² + (-2 - (-6))²]

= √[(5 + 1)² + (-2 + 6)²]

= √[36 + 16]

= √52

= 2√13

Distance between A and T:

AT = √[(5 - (-4))² + (-2 - 5)²]

= √[(5 + 4)² + (-2 - 5)²]

= √130

We can see that PA = AT = √130, and PT = 2√13.

Since PA = AT, we have shown that two sides of the triangle are congruent.

Therefore, triangle PAT is an isosceles triangle.

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Please find attached the graph of the straight line equation; y = -2·x + 3/2, which is the same as the graph of the equation; 4·x + 2·y = 3, created with MS Excel

An equation of a straight line is an equation of the form; y = m·x + c

b. 1. The equation of the line is; 4·x + 2·y = 3

The above equation of the line can be expressed in slope-intercept form; y = m·x + c, where; m is the slope of the graph of the equation and c is the y-coordinate of the y-intercept, by making y the subject as follows;

2·y = 3 - 4·x

y = (3 - 4·x)/2

y = 3/2 - 2·x

Therefore; y = -2·x + 3/2

The above equation indicates;

The slope, m = -2

The y-intercept, c = 3/2

The coordinate of the y-intercept is therefore; (0, 3/2)

The point (0, 3/2) is to be plotted on the graph

2. In order to draw the graph, the coordinates of a second point can be found as follows;

The slope of the graph = The ratio of the rise to the run of the graph

Slope = Rise/Run = Δy/Δx

The rise = The number of units a point progresses vertically

The run =  The number of units a point progresses horizontally

Therefore, a slope of -2, indicates;

Slope = Rise/run = Δy/Δx = -2 = -2/1

A rise of -2 units is accompanied by a run of 1 unit

In terms of x and y an increase of 1 unit in the x-value is accompanied in the y-value by a -2 units increase.

Therefore, a second point on the graph is; (0 + 1, ((3/2) - 2)) = (1, -1/2)

3. The line of the graph therefore passes through both (0, 3/2) and (1, -1/2)

Drawing a line through the above two points creates the graph of the equation, 4·x + 2·y = 3

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The true statement about a and p is a is positive and p is positive.

We have the equation

y= ax+ p

where a and p are real numbers.

In general, "a" represents the slope of the line (the rate of change of y with respect to x).

and, "p" represents the y-intercept (the value of y when x = 0).

The specific values of a and p can be determined by examining the graph or given data points.

By looking the graph, the slope is positive

b is the y intercept, where x = 0 and that is positive.

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Answer:

  1 = (x/11)² +24y²/605

Step-by-step explanation:

You want the the equation of an ellipse through the point (1, 5) with ends of its major axis at (±11, 0).

The ellipse equation will have the form ...

  (x/11)² + (y/b)² = 1

for some value 'b' that causes (x, y) = (1, 5) to be a solution to this equation.

Using the given point and solving for b (or b²), we have ...

  (1/11)² +(5/b)² = 1

  25/b² = 1 -1/121 = 120/121

Inverting this equation and multiplying by 25, we have ...

  b² = 605/24

Using this value for b², we can write the equation of the ellipse as ...

  [tex]\boxed{1=\dfrac{x^2}{121}+\dfrac{24y^2}{605}}[/tex]

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The z-score of a person who scored 330 on the exam is approximately 2.7.

To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

z is the z-score

x is the raw score (330 in this case)

μ is the mean (195 in this case)

σ is the standard deviation (50 in this case)

Substituting the values into the formula, we get:

z = (330 - 195) / 50

z = 135 / 50

z = 2.7

The z-score of a person who scored 330 on the exam is 2.7.

The z-score measures the number of standard deviations a particular data point is away from the mean.

In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.

The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.

A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.

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The general solution to the differential equation -√3 cscθ = 2 is θ = 2π/3 + nπ.

To find the general solution to the trigonometric equation -√3 cscθ = 2, where n is an integer, we need to solve for θ.

Let's start by rewriting the equation:

-√3 cscθ = 2

Since cscθ is the reciprocal of sinθ, we can rewrite the equation as:

-√3 / sinθ = 2

To solve for θ, we can take the reciprocal of both sides:

sinθ / -√3 = 1/2

Next, we can take the reciprocal of both sides again:

-√3 / sinθ = 2

Now, we can find the values of θ that satisfy this equation. The general solution is given by:

θ = arcsin(-√3/2) + nπ

θ = 2π/3 + nπ

where n is an integer.

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Answer:

x=16.5

Step-by-step explanation:

91+3x=25+7x

-3x            -3x

91=25+4x

-25         -25

66=4x

÷4      ÷4

x=16.5

Answer:

[tex]\frac{9}{48}[/tex]

Step-by-step explanation:

the 3 on the numerator has been multiplied by 3 to get the 9 on the numerator on the right.

the same operation must be applied to the 16 on the denominator of the fraction.

16 × 3 = 48

then

[tex]\frac{3}{16}[/tex] = [tex]\frac{3(3)}{16(3)}[/tex] = [tex]\frac{9}{48}[/tex]

Answer: 80%

Step-by-step explanation:

divide 120 by 150 and you get .8 then you move the decimal over 2

Simone can make two different rectangles with the following side lengths:

Rectangle 1: Length = 16 inches, Width = 1 inch

Rectangle 2: Length = 8 inches, Width = 2 inches

To find the side lengths of the two rectangles that Simone can make using 16 square inch tiles, we need to consider the factors of 16 and check which pairs of factors can form rectangles with the same area.

The factors of 16 are 1, 2, 4, 8, and 16. We can pair these factors to form different rectangles and calculate their areas:

Pairing: 1 and 16

Length: 16

Width: 1

Area: 16 square inches

Pairing: 2 and 8

Length: 8

Width: 2

Area: 16 square inches

Pairing: 4 and 4

Length: 4

Width: 4

Area: 16 square inches

Therefore, Simone can make two different rectangles with the following side lengths:

Rectangle 1: Length = 16 inches, Width = 1 inch

Rectangle 2: Length = 8 inches, Width = 2 inches

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Answer:

175 cm²

Step-by-step explanation:

Calculate each shape separately, then add them together.

Parallelogram:  A = bh = (14)(5) = 70

Trapezium:  A = ((a + b)/2)(h) = ((21 + 14)/2)(11-5) = 105

Total area = 70 + 105 = 175 cm²

We have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.

To show that the path of a moving point parallel to the axes of x and y with velocities u + ey and v + ex is a conic section, we can analyze the motion of the point using the principles of calculus and conic sections.

Let's denote the position of the point at any given time t as (x, y). We are given that the velocities along the x and y axes are u + ey and v + ex, respectively. This means that the derivatives of x and y with respect to time, dx/dt and dy/dt, can be expressed as:

dx/dt = u + ey

dy/dt = v + ex

Now, let's integrate these expressions to obtain x and y as functions of t. Integrating dx/dt with respect to t gives:

x = ut + eyt + C1

Similarly, integrating dy/dt with respect to t gives:

y = vt + ext + C2

Where C1 and C2 are constants of integration.

Now, we can eliminate the parameter t by expressing t in terms of x and y. From the equation y = vt + ext + C2, we can solve for t:

t = (y - ext - C2) / v

Substituting this value of t into the equation for x, we get:

x = u[(y - ext - C2) / v] + ey[(y - ext - C2) / v] + C1

Simplifying this equation, we obtain:

vx - u - evx + ue + vy - [tex]e^2[/tex]x - eyC2 = C1v

Rearranging the terms, we get:

vx - vy + ue + evx - [tex]e^2[/tex]x = C1v + eyC2 - u

Let's define new constants A = ue + ev and B = C1v + eyC2 - u. The equation then becomes:

(v - [tex]e^2[/tex])x + (u + ev)y = A + B

This equation is in the standard form of a conic section, specifically a line. However, we can manipulate this equation further to reveal other possible conic sections.

Let's consider the case when v - [tex]e^2[/tex] ≠ 0. In this case, we can divide both sides of the equation by v - [tex]e^2[/tex], yielding:

x + [(u + ev)/(v - [tex]e^2[/tex])]y = (A + B)/(v - [tex]e^2[/tex])

Now, let's define another constant C = (u + ev)/(v -[tex]e^2[/tex]) and rewrite the equation as:

x + Cy = D

Where D = (A + B)/(v - [tex]e^2[/tex]).

This equation represents a line in the x-y plane.

On the other hand, if v - [tex]e^2[/tex] = 0, the equation becomes:

0x + (u + ev)y = A + B

This simplifies to:

(u + ev)y = A + B

Which is a horizontal line parallel to the x-axis.

Therefore, we have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.

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The time it takes for the investment to grow to $12,000 if the interest is compounded continuously is 23.1 years.

Given that,

Principal amount invested, P = $6000

Rate of interest, r = 3% = 3/100 = 0.03

If the interest compounded continuously,

Final amount, A = P e^(rt)

12000 = 6000 e ^(0.03t)

2 = e ^(0.03t)

Taking logarithms on both sides,

ln (2) = 0.03t

t = 23.1 year.

Hence the time is 23.1 years.

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Note that the resulting image where the above transformation takes place is attached accordingly.

Current coordinates given from the image

A( 2, 7)

B (3, 2)

C (0, 2)

1) To reflect a point across the line x = 1, we need to find the distance between the point and the line and then move it to the same distance on the other side of the line.

In this case, all points will have their x-coordinate mirrored with respect to the line x = 1.

New coordinates after reflection is

A'(0, 7)

B'(−1, 2)

C'(2, 2)

2 - Dilation by a factor of 2 centered at the origin:

To dilate a point by a factor of 2 centered at the origin, we need to multiply both the x and y coordinates of the point by 2.

New coordinates after dilation is

A''(0, 14)

B''(−2, 4)

C''(4, 4)

Plotting the above will given the resultant image int he attached.

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The average of the four odd whole numbers (12) is greater than the average of the four even whole numbers (11).

To determine which average is greater, let's calculate the average of the four even whole numbers from 8 to 15 and the average of the four odd whole numbers from 8 to 15.

The even numbers from 8 to 15 are 8, 10, 12, and 14.

To find their average, we sum them and divide by 4:

Average of even numbers = (8 + 10 + 12 + 14) / 4 = 44 / 4 = 11.

The odd numbers from 8 to 15 are 9, 11, 13, and 15.

Similarly, we find their average:

Average of odd numbers = (9 + 11 + 13 + 15) / 4 = 48 / 4 = 12.

Comparing the two averages, we find that the average of the four odd whole numbers from 8 to 15 is greater than the average of the four even whole numbers from 8 to 15.

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Answer:

x = [tex]\frac{A*t^2}{800}[/tex]

Step-by-step explanation:

First move t² to the left side by multiplying it.

A×t² = 800x - to get rid of 800, we divide both sides by 800. This isolates x.

x = [tex]\frac{A*t^2}{800}[/tex]

The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

The maximum value among 3, π, and √2 is π (approximately 3.14159).

To determine the maximum value among 3, π, and √2, we compare the numbers to find the largest one.

Comparing 3 and π:

Since π (approximately 3.14159) is greater than 3, we can eliminate 3 from consideration.

Comparing π and √2:

To compare these two numbers, we can square both of them. Squaring π yields approximately 9.8696, while squaring √2 gives us exactly 2. Since 9.8696 is greater than 2, we can eliminate √2 from consideration.

Thus, the maximum value among 3, π, and √2 is π (approximately 3.14159).

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Domain: r ≥ 0 (all non-negative real numbers)

Range: V ≥ 0 (all non-negative real numbers)

The formula for the volume of a cylinder with a height of 5 units, given as V(r) = 5πr², is a function that relates the radius (r) to the volume (V) of the cylinder.

Domain:

In this case, the radius (r) cannot be negative since it represents a physical measurement. Additionally, there are no other restrictions mentioned in the problem.

Therefore, the domain for this function is all non-negative real numbers: r ≥ 0.

Range:

In this case, the volume (V) of the cylinder can only be positive or zero since it represents a physical quantity. The range is determined by the values that the function can take. As the radius (r) increases, the volume (V) also increases.

Since the function is V(r) = 5πr², the range of this function includes all non-negative real numbers: V ≥ 0.

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Complete question:

The formula for the volume of a cylinder with a height of 5 units is V(r)=5πr² where r is the radius o the cylinder. What is the domain and range for this function?