your brother is 1/3 your age. Your sister is 4 years older than your brother. Your sister is 9 years old. Write and solve an equation to find your age 'a'. An equation is _= 9. You are _ years old.

Answer:

B) 194.7 m

Step-by-step explanation:

You use the radius value in the formula 2(pi)r.

2(pi)31 = 194.7

Answer:

C

Step-by-step explanation:

When we do 30=y/3 we get 90 because of the fraction symbol and its says in the problem 3 times as much so more not less so 3x30 equals 90 so we already take out A and B and when there is nothing but a simple equation like 30=3 we dived so it cant be D Ethier so its C

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Answer:

3(x-4)(x-2)

Step-by-step explanation:

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Answer:

A: -2

B: -10

Step-by-step explanation:

A: the slope of line b is -2

B: Point: (-6,2)

So x= -6 and y = 2

Putting in slope intercept formula for finding b

y=mx+b

2=(-2)(-6)+b

2= 12 + b

b = 2-12

b= -10

The y-intercept of line b is -10

The third term in the expansion of the expression (5x - 7y)³ is 735xy².

Given expression is,

(5x - 7y)³

We have to expand this.

We know that,

(a + b)³ = a³ - 3a²b + 3ab² - b³

Using this,

(5x - 7y)³ = (5x)³ - (3 × (5x)² × 7y) + (3 ×(5x) × (7y)²) - (7y)³

               = 125x³ - (3 × 25x² × 7y) + (3 × 5x × 49y²) - 343y³

               = 125x³ - 525x²y + 735xy² - 343y³

Here the third term is 735xy².

Hence the third term is 735xy².

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The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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Answer:

105

Step-by-step explanation:

Answer:105

Step-by-step explanation:

Answer:

The variables X and Y are dependent.

Step-by-step explanation:

The variable X denotes number of face cards . That is it can take values,

X = {0, 1, 2 }

Compute the probability for all he values of X as follows:

P [X = 0] = P (None of the 12 card is chosen in either draw)

              = (40/52)×(39/51)

              = 1560/2652

              = 0.5882

P [X = 1] = P (One of the card is face card is selected)

              = 2×(40/52)×(12/51)

              = 960/2652

              = 0.3619

P [X = 2] = P (Two of the 12 card is chosen in the draw)

              = (12/52)×(11/51)

              = 132/2652

              = 0.0498

The variable Y denotes number of cards numbered 10 . Thus, it can take values:

Y = {0, 1, 2 }

P [Y = 0] = P (None of the 4 card is chosen in either draw)

              = (48/52)×(47/51)

              = 2256/2652

              = 0.8507

P [Y = 1] = P (One of the 4 card is chosen in either draw)

              = 2×(4/52)×(48/51)

              = 384/2652

              = 0.1448

P [Y = 2] = P (Two of the 4 card is chosen in the draw)

              = (4/52)×(3/51)

              = 12/2652

              = 0.0045

Now compute the probability of (X and Y).

P [X = 0 and Y = 0] = P(None of the 16 card is chosen in either draw)

                              = (36/52)×(35/51)

                              = 1260/2652

                              = 0.4751

The variables X and Y are independent if,

P [X = 0 and Y = 0]  = P [X = 0] × P [Y = 0]

                               =  P [X = 0] × P [Y = 0]

                               = 0.8507 × 0.5882

                               = 0.5204

The two values are not equal.

Hence, the variables X and Y are not independent.

Answer: im late to this answer

Step-by-step explanation:

1.a)1,5

2.b)2,6

3.c)3,8

4.d)4,10

5.e)5,13

All the plotted points are on top.

Considering the given systems of equations, the expressions to obtain the desired results are filled as follows:

A system of equations will have no solution if it can be written in the following format:

0x = constant different of 0.

Hence:

-2x + 5 + 11x = 9x + 6(the final number can be any number different of 5)

As:

9x + 5 = 9x + 6

0x = 1 -> division by 0 does not exist, hence no solution.

A system of equations will have one solution if it can be written in the following format:

cx = d, c different of 0.

Hence:

-2x + 5 + 8x = 9x + 6(the final number on the left side can be any number different of 11)

6x + 5 = 9x + 6

-3x = 1

x = -1/3 (lone solution).

A system of equations will have infinitely many solutions if it can be written in the following format:

0x = 0.

Hence:

-2x + 5 + 11x = 9x + 5

9x + 5 = 9x + 5

0x = 0 (0/0 results in any value).

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The domain can be best described using interval notation. The domain is [1,∞].

A continuous function is graphed here. The function is continuous only on  where it is defined. That is, the graph of the function does not have any discontinuities from 1 to infinity.

The domain of a function is the x-values for which the function is defined. That is for such x-values, the function will attain some y-value, which is called the function value. This function values corresponding to each x-value sketches the graph.

From the figure, the graph is started from x = 1 and is extended to infinity.

So it is better to express the domain in an interval form.

Graph of the function is a curve. So the domain is [1,∞].

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

\(x=11\)

Step-by-step explanation:

It is a linear pair

\(7x + 12 + 8x + 3 = 180\)

\(15x + 15 = 180-15\\15x = 165\)

\(x=11\)

To solve this problem we remember the following statement: a quadrilateral that has opposite sides that are congruent and parallel can be a parallelogram, rhombus, rectangle or square.

From the figure, we see a quadrilateral with congruent opposite sides. Relating this information to the statement above, we see that this quadrilateral can be a parallelogram, rhombus, rectangle or square. So we conclude that there is not enough information to conclude that the quadrilateral is a parallelogram.

Answer

d. Not enough information

Answer:

The angles are 45 and 135

Step-by-step explanation:

The two angles form a straight line, which is 180 degrees

c+ 3c = 180

4c = 180

Divide by 4

4c/4 =180/4

c = 45

3c = 3(45) = 135

The angles are 45 and 135

Answer:

45 and 135 ...

Answer:

16.625 miles

Step-by-step explanation:

The time elapsed between 4:45 pm and 12 noon is 4 hours and 45 minutes

45 minutes is equivalent to 45/60 = 0.75 hour

Total elapsed time = 4.75 hours

At a speed of 3.5 mph the distance that can be covered

= 3.5 x 4.75 = 16.625 miles

The surface areas are 110 in², 87.6 mm² and 49 m².

Given that are solid figure, we need to find the surface area of them,

1) Triangular prism = perimeter × length + 2 × base area

= (5 + 5 + 6) × 5 + 2(3×5) = 110 in²

2) Triangular pyramid = base area + perimeter × slant height / 2

= 1/2 × 5.2 × 6 + 3 × 6 × 8/2

= 87.6 mm²

3) Cube = 4side²

= 4 × (3 1/2)²

= 4 × 3.5²

= 49 m²

Hence the surface areas are 110 in², 87.6 mm² and 49 m².

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The given triangle is a right angled triangle, therefore the rules of basic Trigonometry can be used here to find the solution.

\(\qquad\displaystyle \tt \dashrightarrow \: \sin(45 \degree) = \frac{opposite \:\: side}{hypotenuse} \)

[ sin 45° = 1/√2 ]

\(\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{ \sqrt{2} } = \frac{b}{x} \)

\(\qquad\displaystyle \tt \dashrightarrow \: x = b \sqrt{2} \: \: cm\)

So, the side HG is b√2 cm long

Answer:

Now,

tan15°=

\( \frac{5100}{ae} \)

ae=

\( \frac{5100}{tan15} \)

.: ae = 19033.45

.: the aeroplane is 19033.45 m away from the control tower.

The slope-intercept version of the equation for the tangent line to f(x) at the position (-5, -1) is y =  (-1/5)x -2. Thus,

m = -1/5

y =  (-1/5)x -2

A tangent line is a straight line that οnly has οne cοntact with a functiοn. (See earlier.) The instantaneοus rate οf change οf the functiοn at that exact place is shοwn by the tangent line. At each given pοint οn the functiοn, the slοpe οf the tangent line is equal tο the derivative οf the functiοn at that same lοcatiοn.

We must determine the derivative οf the functiοn and evaluate it at x = -5 in οrder tο determine the slοpe οf f(x) = 5/x at the pοint (-5, -1).

f(x) = 5/x

f'(x) = [-5/x²]

When we enter x = -5, we obtain:

f'(-5) = [-5/(-5)²] = -1/5

As a result, the tangent line to f(x) at the point (-5, -1) has a slope of -1/5.

y - y1 = m(x - x1)

y - (-1) = (-1/5)(x - (-5))

y + 1 = (-1/5)(x + 5)

y = (-1/5)x -10/5

y = (-1/5)x -2

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Answer:

5.72

Step-by-step explanation:

(-16.75 + 16.75) = 0

0 + 5.72= 5.72

Therefore, the answer is 5.72

Answer:

$886.47

Step-by-step explanation:

The charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation.

To determine the number of miles at which the charges for the two car services, A and B, are equal, we can set up an equation based on the given information.

Let's represent the charge for car service A as y_A and the charge for car service B as y_B. We can set up the following equations:

For car service A: y_A = 0.60x + 300 (in cents)

For car service B: y_B = 0.75x (in cents)

To find the number of miles at which the charges are equal, we set y_A equal to y_B and solve for x:

0.60x + 300 = 0.75x

Subtracting 0.60x from both sides:

300 = 0.15x

Dividing both sides by 0.15:

x = 300 / 0.15

x = 2000

Therefore, the charges will be equal when each car travels 2000 miles. To find the charge for that distance, we substitute x = 2000 into either equation. Let's use the equation for car service A:

y_A = 0.60(2000) + 300

y_A = 1200 + 300

y_A = 1500 cents or $15.00

So, when each car travels 2000 miles, the charges will be equal at $15.00.

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

c

Step-by-step explanation:

Plotting the inequalities using geogebra online tool, the solution is the dark region.

An inequality is an expression used to show the non equal comparison between two or more numbers and variables.

Given the system of inequalities:

y > -x + 2

y < (1/2)x - 4

Plotting the inequalities using geogebra online tool, the solution is the dark region.

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Answer:

The square root of numbers like 4, 9, and 16 is a square number.

If the acceleration of the object becomes 9m/s², the force will be 24N

From the information, the moving object, the force acting on the object varies directly with the object's acceleration. When a force of 36N acts on a certain object, the acceleration of the object is 6m/s². The constant will be:

y = k/x

y = force.

x = acceleration

k = constant of proportionality.

k = 36 × 6

k = 216

If the acceleration of the object becomes 9m/s², the force will be:

= 216 / 9

= 24

The force is 24N.

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Answer:

He will earn $180 equation: M= money h = hours m = h15

Step-by-step explanation:

15 dollars times however many hours is equal to the money he earns, in this case 15 x 12 = 180

Charlie will make $180 if he mows lawns for 12 hours next week.

Given that, Charlie mows lawns in his neighborhood. He charges $15 per hour.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of hour be x and the total charge be y.

So, y=15x

Now, if Charlie mows lawns for 12 hours next week

Here, y=15×12

= $180

Therefore, Charlie will make $180 if he mows lawns for 12 hours next week.

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