please help ! QUESTION 6
What is the acceleration of a runner who completes a 500 m sprint in 50 seconds? Initial velocity of the runner is 0 m/s and the runner is running in a straight line.
Options:
10 m/s²
0.2 m/s²
20 m/s^2
0.4m/s^2

Answer:

the answer is 60

Step-by-step explanation:

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]

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

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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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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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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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 correct option is C. (2, 1).

Given equations:

y = 6x - 11

2x + 3y = 7

We'll start by solving equation 1) for y:

y = 6x - 11

Now, substitute this value of y into equation 2):

2x + 3(6x - 11) = 7

Simplify the equation:

2x + 18x - 33 = 7

20x - 33 = 7

Add 33 to both sides:

20x = 40

Divide both sides by 20:

x = 2

Now, substitute the value of x back into equation 1) to find y:

y = 6(2) - 11

y = 12 - 11

y = 1

Therefore, the solution to the system of equations is (x, y) = (2, 1).

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:A=BxH divided by 2

                  _

Step-by-step explanation:

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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Answer:

12-4r

Step-by-step explanation:

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

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:

The formula for radioactive decay is:

N = N₀ * (1/2)^(t/T)

where:

N₀ = initial amount

N = remaining amount

t = time elapsed

T = half-life

Let's plug in the given values:

N₀ = 20 g

N = 15 g

T = 1620 years

15 = 20 * (1/2)^(t/1620)

Dividing both sides by 20:

0.75 = (1/2)^(t/1620)

Taking the logarithm base 1/2 of both sides:

log(0.75) = t/1620 * log(1/2)

Solving for t:

t = log(0.75) / log(1/2) * 1620

t ≈ 623 years

Therefore, it will take approximately 623 years for a 20 g sample of Radium to decay to 15 g.

Step-by-step explanation:

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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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

The equation of the circle graphed is (x + 6)² + y² = 4

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

The circle

Where, we have

Center = (a, b) = (-6, 0)

Radius, r = 2 units

The equation of the circle graphed is represented as

(x - a)² + (y - b)² = r²

So, we have

(x + 6)² + y² = 2²

Evaluate

(x + 6)² + y² = 4

Hence, the equation is (x + 6)² + y² = 4

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Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

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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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°

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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Answer:

a= 65, b=75

Step-by-step explanation:

Angle a= 180-70-45

=65

Angle b= 180-60-45

=75

Answer:

B. 4/1

Step-by-step explanation:

12/3 can be divided by 3.

Therefore 4/1.

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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Based on the information given in the advertisement, we can conclude that the sale price of the table is $420.

Here's how we can arrive at this answer:

Let the original price of the table be represented by P.

We know that the sale price of the table is obtained by reducing the original price by 30%. Mathematically, this can be represented as:

Sale price = P - 0.3P

Simplifying this expression, we get:

Sale price = 0.7P

We are also given that the sale saves us $180 on this table. Mathematically, this can be represented as:

0.7P - P = -$180

Simplifying this expression, we get:

-0.3P = -$180

Dividing both sides by -0.3, we get:

P = $600

Therefore, the original price of the table was $600.

Using the equation for sale price that we derived earlier, we can now find the sale price of the table:

Sale price = 0.7P = 0.7 x $600 = $420

Hence, the sale price of the table is $420.

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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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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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:

The answer for the width of the building is 5m

Step-by-step Explanation:

3cm=1m

15cm=x

cross multiply

x×3=15×1

3x=15

divide both sides by 3

3x/3=15/3

x=5m