help please solving systems of equations boat traveled 189 miles downstream and back. The trip downstream took 9 hours. The trip back took 63 hours. Find the speed of the boat in still water and the speed of the current.

If you want to reach Alpha Centauri you will need to go at a speed of 29,666,095,890,410 km/hr.

Alpha Centauri is 4.4 lightyears away from your location, now let's convert this distance into kilometers:

1 lightyear = 9.46 trillion kilometers

4.4 x 9.45 trillion kilometers = 41.58 trillion kilometers

Now, let's calculate the time available:

If there are 24 hours in a day, then in a year there are 24 x 365 = 8760, hours, which means in 160 years there are 1,401,600. Using this, calculate the speed:

41.58 trillion kilometers/ 1,401,600 hours = 29,666,095,890,410 kilometers per hour.

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The number itself equals any integer raised to the power of one.

What is Exponent?

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 23) signifies 2 x 2 x 2 = 8. 23 and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

What is integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

Any number that is multiplied by one has the same value as the original number, according to the exponent rule.

Take this as an example:

You can write x to the power of 1 as x and 100 to the power of 1 as 100.

Therefore, anything raised to the power of one equals that number.

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The value of variable x is,

⇒ x = 42

We have to given that;

In a right triangle,

⇒ sin (x + 10)° = cos (4x - 4)°

Now, We can simplify as;

⇒ sin (x + 10)° = cos (4x - 4)°

⇒ cos (90 - (x + 10))° = cos (x - 4)°

⇒ 90 - (x + 10) = x - 4

⇒ 90 - x - 10 = x - 4

⇒ 80 + 4 = 2x

⇒ 2x = 84

⇒ x = 42

Thus, The value of variable x is,

⇒ x = 42

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Answer:

x represents +50 for every hour. the inequality is y = 4x + 500 or y = x + 500.

they can ride it for 4 hours

Step-by-step explanation:

y(total cost) = x(50 per hour) + 500(y-intercept)

After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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In this problem, we have that

m<6+m<7=180 degrees -------> by forming a linear pair (supplementary angles)

substitute given value

m<6=72 degrees

72+m<7=180

m<7=180-72

The number is 48.

Let's represent the two-digit number as 10x + y, where x is the tens digit and y is the units digit.

According to the given information, the units digit is twice the tens digit. So we have the equation:

y = 2x

If the number is doubled, it will be 12 more than the number reversed. When we double the number, we get 2(10x + y), and the number reversed is 10y + x.

Therefore, we can write the equation as:

2(10x + y) = 10y + x + 12

Simplifying this equation, we get:

20x + 2y = 10y + x + 12

19x = 8y + 12

19x - 8y = 12

We have two equations now:

y = 2x

19x - 8y = 12

Substituting the value of y from the first equation into the second equation, we get:

19x - 8(2x) = 12

19x - 16x = 12

3x = 12

x = 4

Now we can substitute the value of x back into the first equation to find y:

y = 2x

y = 2(4)

y = 8

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Answer:

Step-by-step explanation:

The product of the expression 7 x 63 is 441.

We have,

To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:

7 x 63 = 7 x (60 + 3)

Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:

7 x (60 + 3) = 7 x 60 + 7 x 3

Simplifying further:

7 x 60 + 7 x 3 = 420 + 21

Therefore,

The product of 7 x 63 is 441.

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find D which is the discriminant and with D < 0.

therefore the equation has an imaginary root and not a real root.

Answer:

ratioed by ur name

Step-by-step explanation:

Answer:

7.447 × 10(to the power of 6.)

Step-by-step explanation:

Answer:

7.447 × 106

Step-by-step explanation:

ye

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

He saved $121

Step-by-step explanation:

All you have to do is divide $726/6 which gives you $121.

The value of x from the figure is 9

Pythagoras theorem states that the square of the longest side is equal to sum of the square of other two sides.

From the given diagram, the measure of sides 12 units is tangential to the circle. This shows that the given triangle is right angled where;

Hypotenuse = x + 6

Other sides are  x and 12

Using the theorem

(x+6)² = x² + 12²

Expand

x²+12x+36 = x² +144

12x + 36 = 144

12x = 144 - 36

12x = 108

x = 108/12

x = 9

Hence the value of x from the figure is 9

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The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.

To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.

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Answer:

it's answer is D. 33°

Let the unknown angle be x Then.

x + 100° + 47° = 180° [ being sum of angles of triangle ]

x + 147° = 180°

x = 180° - 147°

x = 33°

Step-by-step explanation:

Answer:

23 is your answer hope this helps

Answer:

The number is 23

Step-by-step explanation:

23*2=46

46-6=40

40/2=20

The answer is 23

Hope that helps!

The length of the hypotenuse is 12.52 yards.

Given that a right triangle, we need to find the value of the hypotenuse x,

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle.

We can evaluate the third side using the Pythagoras theorem, given the measure of the other two sides. We can use the abbreviated form of trigonometric ratios to compare the length of any two sides with the angle in the base.

Let us consider a right-angled triangle with one of its acute angles to be x. Then the cosine formula is, cos x = (adjacent side) / (hypotenuse), where "adjacent side" is the side adjacent to the angle x, and "hypotenuse" is the longest side (the side opposite to the right angle) of the triangle.

We know that, the cosine of the angle is the ratio of the base to the hypotenuse,

So,

Cos 37° = 10 / x

x = 10 / Cos 37°

x = 12.52

Hence the length of the hypotenuse is 12.52 yards.

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

The value of x is 4√11.

Step-by-step explanation:

Here, we have given that the two sides of triangle are 24 and 20.

Finding the third side of triangle by pythagorean theorem formula :

\({\longrightarrow{\pmb{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}}\)

Substituting all the given values in the formula to find the third side of triangle :

\(\begin{gathered}\qquad{\longrightarrow{\sf{{(c)}^{2} = {(a)}^{2} + {(b)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(24)}^{2} = {(20)}^{2} + {(b)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(24\times 24)} = {(20 \times 20)} + {(b)}^{2}}}}\\\\\qquad{\longrightarrow{\sf{{(576)} = {(400)} + {(b)}^{2}}}}\\\\ \qquad{\longrightarrow{\sf{{(b)}^{2} = 576 - 400}}}\\\\ \qquad{\longrightarrow{\sf{{(b)}^{2} = 176}}}\\\\\qquad{\longrightarrow{\sf{b = \sqrt{176}}}}\\\\\qquad{\longrightarrow{\sf{b = 4\sqrt{11}}}}\\\\\qquad\star{\underline{\boxed{\sf{\red{b = 4\sqrt{11}}}}}}\end{gathered}\)

Hence, the value of x is 4√11.

\(\rule{300}{2.5}\)

Answer:

Z=4

Step-by-step explanation:

46/184=1/4, so we just need to do W/4 to get Z, which is just 16 here.

16/4=4

Answer:

Step-by-step explanation:

Z varies directly as W:

We have:

Find k:

The equation is now:

Find Z when W is 16:

Answer: 13

Step-by-step explanation:

Because of the laws of circles BD = DF and EG = AC (They are chords and are at a equal distant from each other).

3x + 4 = 5x - 8

-2x = -12

x = 6

EG = 5x - 4

5(6) - 4

30 - 4

26

Because the chrod is cut in half by line BD we divide 26 by 2

26 / 2

13

The circles are similar because you can translate Circle 1 using the transformation rule (9, 5) and then dilate it using a scale factor of 2.

To prove that Circle 1 and Circle 2 are similar, we need to identify the transformations that can be applied to Circle 1 to obtain Circle 2.

First, let's consider the translation of Circle 1. The translation rule is given by (a, b), where a represents the horizontal shift and b represents the vertical shift.

In this case, to translate Circle 1 to align with Circle 2, we need to shift it 9 units to the right and 5 units up. Therefore, the translation rule for Circle 1 is (9, 5).

Next, let's consider the dilation. A dilation is a transformation that changes the size of the figure but preserves its shape. The scale factor, denoted by k, determines the amount of scaling. In this case, Circle 1 needs to be dilated to match the size of Circle 2.

The scale factor can be determined by comparing the radii of the two circles. The radius of Circle 1 is 3 centimeters, while the radius of Circle 2 is 6 centimeters. The scale factor is obtained by dividing the radius of Circle 2 by the radius of Circle 1: 6/3 = 2.

Therefore, the transformation applied to Circle 1 to prove that the circles are similar is a translation by (9, 5) followed by a dilation with a scale factor of 2.

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Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))

Answer:

x - 4 yards.

Step-by-step explanation:

Given:

Area of rectangle = 3x^2 - 12x square yards

Width = 3x yards

To find:

Length of rectangle

Solution:

The area of a rectangle is equal to the product of its length and width.

Area of rectangle = Length * Width

Substituting the given values, we get:

3x^2 - 12x = Length * 3x

Length =( 3x^2 - 12x )3x

Length = x-4

Therefore, the length of the rectangle is x - 4 yards.

Answer: The length of the rectangle is x - 4 yards.

Step-by-step explanation:

We can create an equation to solve this word problem, where the variable L = length.

3x  ×  L  = \(3x^2 - 12x\)

We need to solve for the variable L, to find the length of the rectangle.

First lets factor the right side of the equation to make it easier to divide with.

3x  ×  L  = \(3x^2 - 12x\)

We can factor out 3x from the right side of the equation.

3x  ×  L  = 3x(x - 4)

Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.

3x ×  L  = 3x(x - 4)

/3x           /3x

L = x - 4

The length of the rectangle is x - 4 yards.

Answer: 30 meters

Step-by-step explanation:Base * width * height = 60 meters then half of that which is 30 meters

Answer:

1/2

Step-by-step explanation:

Answer:

152 miles

Step-by-step explanation:

Let's first find how much they drove individually in two hours.

Maria

d=s*t

d=44 mph*2h

d=88 m

Ming

d=s*t

d=32 mph*2h

d=64 m

Both

d=64+88

d=152 miles

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, in 2 hours, they will be 152 miles apart.