If Sherri and Darren would have stopped playing after Round 1, who would have been the winner? Explain how you know.

Answer:

(C) 10200m

Step-by-step explanation:

Dizem-nos na pergunta que um homem de negócios tem um espaço retangular de 100 m por 750 m para correr.

O primeiro passo é calcular o perímetro do retângulo.

Perímetro de um rectângulo = 2 (Comprimento × Largura)

Da pergunta,

Comprimento = 100m

Largura = 750m

Perímetro do rectângulo = 2 ( 100 + 750)

= 2(850)

= 1700m

Perímetro do rectângulo = 1700m

Somos questionados na pergunta para determinar quantos metros (Distância) um atleta viajou que tem apenas 6 voltas ao redor das extremidades do espaço.

A distância total percorrida pelo atleta ao correr é calculada como:

6 × perímetro do rectângulo.

= 6 × 1700

= 10200m

Quantos metros percorreu um atleta que deu apenas 6 voltas pelas extremidades do espaço = 10200

the equation of the ellipse with foci at (-3,0) and (3,0) and a length of the major axis of 10 is \(25x 2 ​ + 16y 2 ​ =1.\)

To find the equation of an ellipse with foci at (-3,0) and (3,0) and a length of the major axis of 10, we can use the standard form of the equation for an ellipse centered at the origin:

\(\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]\)

where\(\( a \)\) is the semi-major axis and \(\( b \)\)is the semi-minor axis.

The distance between the foci is equal to \( 2c \), where \( c \) is the distance from the center of the ellipse to each focus. In this case, \( c = 3 \), so \( 2c = 6 \).

The length of the major axis is equal to \( 2a \), so \( 2a = 10 \), which means \( a = 5 \).

Now we can find the value of \( b \) using the relationship:

\[ c^2 = a^2 - b^2 \]

Plugging in the values we know:

\[ 3^2 = 5^2 - b^2 \]

\[ 9 = 25 - b^2 \]

\[ b^2 = 25 - 9 \]

\[ b^2 = 16 \]

\[ b = 4 \]

Finally, we can substitute the values of \( a \) and \( b \) into the equation:

\[ \frac{x^2}{5^2} + \frac{y^2}{4^2} = 1 \]

which simplifies to:

\[ \frac{x^2}{25} + \frac{y^2}{16} = 1 \]

Therefore, the equation of the ellipse with foci at (-3,0) and (3,0) and a length of the major axis of 10 is \( \frac{x^2}{25} + \frac{y^2}{16} = 1 \).

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The distance from point A to point C and the bearing from point A to point C is 229.5 miles.

Given that:

AB = 370 miles

angle A = 24 degrees

BC = 240 miles

angle B = 37 degrees 

To determine the distance from point A to C, we can use the cosine law since we are given two angles and two sides of a regular triangle. 

The angle opposite side AC is angle B which is equal to 37 degrees. 

(AC)^2 =(AB)^2 + (BC)^2 - 2(AB)(BC)cos(B)

Now we have to solve for AC:

(AC)^2 =(370)^2 + (240)^2 - 2(370)(240)cos(37) 

AC = 229.48 miles.

Hence the answer is, the distance from point A to point C and the bearing from point A to point C is 229.5 miles. 

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Answer:

49

Step-by-step explanation:

Answer:

They have given us a formula on how to find acceleration. But, they want us to find what 1 velocity is. So, we must revert the formula to find what the 1 velocity is.

a = (vf-vi) / t

a(t) = v1+v0

a(t) - v0 = v1

Now we have the formula. Plug in and Solve!

Step-by-step explanation:

The below would be most important Algebra 1 Formulas for CST.

Linear Equation:

\(Ax + By + C = 0\)

Equation of Straight Line or Slope:

\(y = mx+b\)

Point-slope form:

\(y-y_{1} = m(x-x_1)\)

Slope when 2 points are given:

\(m = \frac{(y_2 - y_1)}{(x_2-x_1)}\)

Quadratic Equation:

\(Ax^2 + Bx +C = 0\)

When lines are parallel:

Slope of both lines are equal. \(m_1 = m_2\)

When lines are perpendicular:

Slope of perpendicular lines are opposite reciprocals, meaning if the slope of a line \(l_1\) is \(\frac{1}{2}\). The line \(l_2\) perpendicular to \(l_1\) is \(-\frac{2}{1}\).

Work Formula:

Total Work Done = Number of Days \(\times\) Efficiency

where Efficiency is inversely proportional to Time Taken.

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The grid-based method first quantizes the object space into a finite number of cells that form a grid structure and then performs clustering on the grid structure.

The grid-based methods are used in data mining and are based on a multi-resolution grid data structure. In the grid-based methods the space of instance is divided into a grid structure. Following the division, clustering techniques are employed using the cells of the grid as the base units instead of individual data points. The great advantage of grid-based clustering technique is its significant reduction of the computational complexity, especially for clustering very large data sets and improving the processing time.

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Answer:

204 in²

Given:

Base: 17 inch

Height: 24 inch

Area of Triangle:

1/2 * Base * Height

1/2 * 17 * 24

1/2 * 408

204 in²

Answer:

4(10x + 3)

Step-by-step explanation:

Since both 40 and 12 are divisible by 4, they can both be found when multipled by 4 and a different number

Answer:

2(20x + 6)

4(10x + 3)

Step-by-step explanation:

Answer:

200N

Step-by-step explanation:

Torque is defined as the turning effect of force about a point. It is expressed as;

Torque = Force × radius

T = Fr

Given parameters

Torque = 100Nm

Radius = 0.5metres

Required

Magnitude of the force F

From the formula T = Fr

F = T/r

F = 100Nm/0.5m

F = 100/(1/2)

F = 100 × 2/1

F = 200Newtons

Hence the magnitude of the force in newtons needed to supply 100 newton-meters of torque to the bolt is 200N

Answer:

\((\frac{1}{k} )^{10}\)

Step-by-step explanation:

When making a negative a positive, all you need to do is flip it, in this case, making it a fraction.

~theLocoCoco

Answer:

Your input: find x in the equation −x2−12=0

x=−24

Step-by-step explanation:

The point-slope form of the line is y - (3/4) = 5(x - (3/4)).

The point-slope form of a line is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line. To find the point-slope form of a line that has a slope of 5 and passes through the point (3/4, 3/4), we can plug in the values for the slope and the point into the point-slope formula. This gives us y - (3/4) = 5(x - (3/4)). This is the point-slope form of the line.

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Answer:

$78.

Step-by-step explanation:

Listing price of watch = $60

Given that the watch price was marked up by 30%,

lets find 30% of listing  price to find increase in price after mark up

30% of listing price = 30/100 * $60 = $18

Thus,

New selling price = Listing price of watch + marked up price

New selling price =  $60 + $18 = $78

Thus, new selling price after mark up is $78.

Answer:

The numbers are 14 and 16.

Step-by-step explanation:

Equation:

x (x - 2) = 224

Solution:

x (x - 2) = 224

x² - 2x = 224

x² - 2x - 224 = 0

Now, we ended up with a trinomial. To find the two numbers, we need to factor it.

Factoring Trinomials

Trinomial is a polynomial with three terms which are connected by plus or minus notations. It is expressed as a² + b + c.

To factor, we need to follow these steps:

1. Find the factors of "ac" that when combined it will result to "b".

2. When "c" is positive, the sign in each binomial is the same as "b".

3. When "c" is negative, the sign in each binomial is different.

4. Write as the product of two binomials ( )( ).

Let us continue.

x² - 2x - 224

(x - 16)(x + 14)

Therefore, x = 16 and x = -14.

Since we are looking for a positive value, we are going to use the positive value of x and that is 16.

Larger number is 16.

x - 2 = 16 - 2 = 14

Smaller number is 14.

Final Answer:

The two numbers are 14 and 16.

Checking:

x (x - 2) = 224

16 (16 - 2) = 224

16 (14) = 224

224 = 224 ✔

Answer:

\(\fbox {x = 2}\)

Step-by-step explanation:

Given :

14x - 12 = 16

Add 12 to each side :

14x - 12 + 12 = 16 + 12

14x = 28

Divide each side by 14 :

14x/14 = 28/14

x = 2

There will be only 6  cubes with only one side painted red.

Cube : A cube is a 3D shape having 6 equal square sides. it has 6 faces , 8 vertices and 12 edges.

According to the question

A 3 cm cube is divided into one centimeter cube.

Every face will have 9 cube each and from that 9 cube there will be only one 1 cube that will have one side painted red.

Since there are 6 faces,

cubes painted one side red = 6x1=6.

Therefore , There will be only 6  cubes with only one side painted red.

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Answer:

X = 2

Step-by-step explanation:

The value of expression is,

⇒ x ÷ 12

We have to given that;

The algebraic expression is,

⇒ x divided by 12

Hence, We can formulate;

The value of correct expression is,

⇒ x ÷ 12

⇒ x / 12

Thus, The value of expression is,

⇒ x ÷ 12

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Answer:

33

Step-by-step explanation:

I believe that the question is asking this

4q+25 and not 4(q+25)

so 4(2)=8+25 is 33

So 4 times a number q means 4*q and when q is 2 you will get 8 and when you add that to 25 you get 33

Answer:

The slope is undefined

Step-by-step explanation:

The area bounded by the region is 2 square units. To find the area of the region bounded by the graph of f(x) = x sin(x^2) and the x-axis between x=0 and x=√x, we need to integrate the absolute value of the function over the given interval.

∫[0, √π] |x sin(x²)| dx

Since the function is symmetric about the origin, we can write the integral as:

2∫[0, √π/2] x sin(x²) dx

Using the substitution u = x^2, du/dx = 2x dx, we get:

∫[0, π/2] sin(u) du

Integrating this gives us:

[-cos(u)] [0, π/2] = [-cos(π/2) + cos(0)] = [1 + 1] = 2

Therefore, the area bounded by the region is 2 square units.

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Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

To find the Taylor polynomials centered at x = 0 for the function f(x) = 16tan(x), we can use the Taylor series expansion for the tangent function and truncate it to the desired degree.

The Taylor series expansion for tangent function is:

tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ...

Using this expansion, we can find the Taylor polynomials of degree 2 and 3 centered at x = 0:

Degree 2 Taylor polynomial:

P2(x) = f(0) + f'(0)(x - 0) + (1/2!)f''(0)(x - 0)^2

= 16tan(0) + 16sec^2(0)(x - 0) + (1/2!)16sec^2(0)(x - 0)^2

= 0 + 16x + 8x^2

Degree 3 Taylor polynomial:

P3(x) = P2(x) + (1/3!)f'''(0)(x - 0)^3

= 0 + 16x + 8x^2 + (1/3!)(48sec^2(0)tan(0))(x - 0)^3

= 16x + 8x^2

Therefore, the Taylor polynomials of degree 2 and 3 centered at x = 0 for the function f(x) = 16tan(x) are:

P2(x) = 16x + 8x^2

P3(x) = 16x + 8x^2

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-14n⁴ + 7n² + 8n + 7

Step-by-step explanation:

(8n - 3n⁴ + 10n²) - (3n² + 11n⁴ - 7)

= 8n - 3n⁴ + 10n² - 3n² - 11n⁴ + 7

= -3n⁴ - 11n⁴ + 10n² - 3n² + 8n + 7

= -14n⁴ + 7n² + 8n + 7

Answer:

C

Step-by-step explanation:

For any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

\(\sqrt{x^2+(y-5)^2}\) = | y + 5 | ← square both sides

x² + (y - 5)² = (y + 5)² ← expand parenthesis on both sides

x² + y² - 10y + 25 = y² + 10y + 25 ( subtract y² - 10y + 25 from both sides )

x² = 20y

The radian measure of the central angle that intercepts an arc of length 9 inches in a circle with a radius of 13 inches is approximately 0.7 radians.

To find the radian measure of the central angle that intercepts an arc of length 9 inches in a circle with a radius of 13 inches, we can use the formula:

θ = s / r

where θ is the radian measure of the central angle, s is the length of the arc, and r is the radius of the circle.

Plugging in the values, we have:

θ = 9 / 13

θ ≈ 0.692

Rounding to the nearest tenth, the radian measure of the central angle is approximately 0.7 radians.

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Answer:

7.5

Step-by-step explanation:

5 x 3 = 15 divided by 2 is 7.5

Answer:

\(\frac{20}{36}\)

Step-by-step explanation:

the total amount of squares within this square is 36

and the number of shaded squares would be 20

so if 20 squares out of 36 squares are shaded, then the fraction is

\(\frac{20}{36}\)

or 55.56%

(to find percentage multiply \(\frac{20}{36}\) by 100)

Answer:

5/9

= 55.56% ( to the nearest hundredth).

Step-by-step explanation:

The total number of little squares in the large square = 6*6 = 36.

Total number of shaded squares = 2*6 + 2*4

= 12 + 8 = 20.

So the fraction of shaded part

= 20/36

= 5/9.

As a percentage this is 5*100/9

= 55 5/9%

= 55.55..... %

Answer:

30.24

Step-by-step explanation:

28% of 42 is 11.76

42 minus 11.76 is 30.24.

Answer:

Part: 42 days

Whole: 150 days

Percent: 28%

Step-by-step explanation: