a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in still water and what is the rate of current?

The area of a rectangle is given as:

Area = Length x width

The dimensions of the rectangle are 9 inches and 5 inches.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of a square = 49 in²

Area of a square = side²

This means the side of the square is 7 inches.

Now,

Let the same amount be x.

The area of the rectangle = 45 in²

The length of the rectangle = 7 + x

The width of the rectangle = 7 - x

The area of the rectangle = Length x Width

45 in² = (7 + x)(7 - x)

45 = 49 - 7x + 7x - x²

45 = 49 - x²

x² = 49 - 45

x² = 4

x = 2

Now,

The dimensions of the rectangle are:

Length = 7 + x = 7 + 2 = 9 inches

Width = 7 - x = 7 - 2 = 5 inches

Thus,

The dimensions of the rectangle are 9 inches and 5 inches.

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The area of a circle is found by using the formula A = πr2, where r is the radius.

Area is a measure of the two-dimensional size of a shape or surface. It is commonly measured in square units, such as square meters or square feet. To calculate the area of a shape, you need to know the length and width of the shape. Area can also refer to the amount of space within a three-dimensional shape, such as a cube or sphere. In this case, the area is measured in cubic units, such as cubic meters or cubic feet.

This means that the area of a circle with a radius of 6 yards is A = π(6)2 = 113.04 yd2. Therefore, the area of the circle with a radius of 6 yards is 113.04 yd2.

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Answer:

1/3

Step-by-step explanation:

4 fish, 1 cat,2 dogs,and 2 birds = 9

dogs or 4 legged = cats and dogs = 1+2 = 3

P(dog or 4 legged) = number of dogs or 4 legged / total

                                 =3/9

                                =1/3

Answer:

⅓

Step-by-step explanation:

Total pets:

4+1+2+2 = 9

Dog or four legged pets: 2 + 1 = 3

Probability: 3/9 = 1/3

Answer:

Your answer

313866

Mark it as Brainlist answer. Follow me to get more answer

Step-by-step explanation:

Answer:

3090

Step-by-step explanation:

6 x 515

Answer:

3090

Step-by-step explanation:

Answer:

6 quarters and 20 dimes

Answer:

2 rays that meet at an endpoint

Step-by-step explanation: A ray starts with a dot, or point and continues on forever with an arrow. There are two rays in that drawing that start at the same endpoint.

Answer:

2 rays that meet at an endpoint.

Step-by-step explanation:

A ray is straight but has one endpoint and the other end go on infinitely.

A line is straight and goes on infinitely.

A line segment is straight and has two endpoints.

The picture shows two rays meeting at an endpoint.

Answer:
X-intercepts: -1 and 3

Y-intercepts: 3
Vertex: (1, 4)
Axis of Symmetry: y= -1x + 3x + 4 (I think this is right it might not be and im sorry if it isnt).

Step-by-step explanation: Hope this helps even a little bit <33

The linear function that models the situation is given as follows:

d = 0.85t.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The constant ratio for this problem is given as follows:

k = 0.83, as each division of d by t has a result of 0.83.

Hence the equation is given as follows:

d = 0.83t.

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Answer:30.28 cm^2

Step-by-step explanation: area of the rectangle = 6x4 = 24

area of semicircle -> (πr^2)/2

radius of semcircle = 4/2 = 2

area of this question semicricle = (π2^2)/2

= 6.28 (3 s.f.)

total area = 24+6.28 =30.28 cm^2

remember put units ^^

Answer:

p = 1

Step-by-step explanation:

Given equation,

→ -8(1 + 4p) + 7p = -25 - 8p

Let's solve for the value of p,

→ -8(1 + 4p) + 7p = -25 - 8p

→ -8 - 32p + 7p = -25 - 8p

→ -32p + 7p + 8p = -25 + 8

→ -17p = -17

→ p = (-17)/(-17)

→ [ p = 1 ]

Hence, the value of p is 1.

When 'x' is 5, the Algebraic  expression 3x - 4 evaluates to 11.

To find the algebraic expression for "4 less than the product of 3 and some number," let's break it down step by step.

First, let's define the unknown number as 'x.' Since the problem states "the product of 3 and some number," we can express this as 3 * x or simply 3x.

Next, we want to subtract 4 from this product. The phrase "4 less than" indicates subtraction, so we subtract 4 from 3x. This can be represented as 3x - 4.

In summary, the algebraic expression for "4 less than the product of 3 and some number" is 3x - 4, where 'x' represents the unknown number.

To calculate the value of this expression for a specific value of 'x,' you substitute that value into the expression and simplify. For example, if 'x' is 5, you would substitute 5 into the expression:

3(5) - 4

This simplifies to:

15 - 4 = 11

So, when 'x' is 5, the expression 3x - 4 evaluates to 11.

In general, the algebraic expression allows us to represent a mathematical relationship between quantities using symbols and operations. By substituting specific values into the expression, we can calculate the corresponding results.

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Note the complete question:

Algebraic expression for 4 less than the product of 3 and some number

What is the algebraic expression for "4 less than the product of 3 and some number?

Please help me understand the meaning of how to calculate.

Answer:

7.33

Step-by-step explanation:

l/b=3/2

8.6/b=3/2

3b=8.6*2

b=17.2/3

b=7.33

Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

Answer:

Alternate exterior

Congruent

4

Step-by-step explanation:

The given angles are alternate exterior angles and alternate angles has equal measures so they are also congruent which means to find the value of x:

20x = 80 divide both sides 20

x = 4

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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After doing some quick calculations, we can determine that X = −35.9

I hope this helps! :)

Answer:

x = -35.9

Step-by-step explanation:

Subtract both sides by 11.2                                                                                                 11.2 - 11.2 equals zero leaving x on one side.

x = - 24.7 - 11.2

A negative minus another negative number is a larger negative number.

x= -24.7 - 11.2 = -35.9

x = -35.9

Answer:

she will spend 5 weekings taking out mobey and with 13.50 left over

Step-by-step explanation:

Answer:

(c)Rational

Explanation:

To classify -4.2, we first define the terms in the options.

Integers

Integers are positive and negative whole numbers. Examples of integers are 3, -4,0 etc.

Rational Numbers

These are numbers that can be expressed in fraction form and usually converts to a terminating or repeating decimal. Examples are 1/2, 2/5, 9/11 etc.

Irrational Numbers

These are numbers that cannot be converted to a terminating or repeating decimal. Examples are 22/7, square root of 2 etc.

Natural Numbers

This is the set of whole numbers starting from 1,2,3...

Therefore, since -4.2 is a terminating decimal, we say it is a Rational Number.

The value of x is approximately 2.12 units

What is Pythagoras?

By the Pythagorean theorem, we know that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So, hypotenuse² = Height ²+Base²

Here we have a right angle triangle whose hypotenuse is x unit and base is 3 unit.

Therefore, we have:x² = 3² + b²

Where b is the length of the perpendicular side.

However, we do not know the value of b, so we cannot solve for x yet.

To solve for b, we can use the fact that the angle between the base and the hypotenuse is 90 degrees, so the sine of this angle is equal to the ratio of the length of the perpendicular side (b) to the length of the hypotenuse (x).

Using trigonometry, we have:

sin(90°) = b/x

Simplifying, we have:

1 = b/x

Therefore, b = x.

Substituting this into the equation we derived earlier, we get:

x² = 3² + x²

Simplifying, we get:

2x² = 9

Dividing both sides by 2, we get:

x² = 4.5

Taking the square root of both sides, we get:

x = √(4.5)

Therefore, the value of x is approximately 2.12 units (rounded to two decimal places).

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

-21

Step-by-step explanation:

\(3(-3) - (-4 * -3)\\= -9 - 12 \\= -21\)

The slope of the line which is perpendicular to line AB is 7/10.

What exactly is a Slope?

In mathematics, slope refers to the steepness or incline of a line. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.

The slope formula is given by:

slope = (change in y) / (change in x)

Now,

The slope of line AB can be found using the slope formula:

slope = (change in y) / (change in x)

slope = (7 - (-3)) / (-5 - 2) = 10 / (-7) = -10/7

The slope of a line perpendicular to AB will be the negative reciprocal of this slope, so we can flip the fraction and change the sign:

slope of the perpendicular = 7/10

Therefore, the slope of the line that is perpendicular to line AB is 7/10.

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The inequality that represents the value of x is (b)  x > 80

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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Answer: Its 58382027.038

Step-by-step explanation:

Answer: \(2+i5,\ 29\)

Step-by-step explanation:

Given

Complex number is \(2-i5\)

Its conjugate is obtained by changing the sign of the original number i.e. \(2+i5\)

The product of the two numbers is

\(\Rightarrow (2-i5)(2+i5)=2^2-(5i)^2\quad \quad [(x+y)(x-y)=x^2-y^2]\\\\\Rightarrow (2-i5)(2+i5)=4-25i^2\\\\\Rightarrow (2-i5)(2+i5)=4+25=29\)