a boat traveled 90 miles each way downstream and back. the tip downstream took 5 hours. the trip back took 15 hours. find the speed of the boat in still water and the speed of the current.

Considering the properties of the angles of the given triangle, the required prove is explained below.

When it can be observed that two sides and measure on internal angles of a given triangle are equal, then it can be inferred that it is an isosceles triangle. Thus the measure of the internal angles that are opposite to the equal sides are the congruent angles.

Considering the given isosceles triangle, the properties of angles required for the prove are:

             STATEMENT                                   REASON

1. LO ≅ NO                                 Congruent sides of isosceles triangle.

2. <LOM ≅ <NOM                      Angle bisector property.

3. LM ≅ NM                                Definition of midpoint.

4. <LMO ≅ <NMO                      Definition of a perpendicular bisector.

5. <OLM ≅ <ONM                      Congruent angles of an isosceles triangle.

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The displacement of the particle from time t = 0 and t = 5, with the velocity function, v(t) = arctan(t² + t - 1), using numerical integration which is the difference in the values of the indefinite integral at t = 0 and t = 5, we get option B

B. 5.504

The indefinite integral of a function is the antiderivative of the function, which does not have limits.

The function for the velocity is; v(t) = arctan(t² + t -1)

The position of the particle at time t = 0 is x = 0.085

The duration of the required displacement (between time t = 0 and t = 5)

The displacement = The area under the velocity time graph, therefore;

Displacement = ∫v(t)

Using substitution method, which is the similar to the inverse of chain rule, we get;

[tex]\int\limits {arctan(t^2+t-1)} \, dt = t\cdot arctan(t^2+t-1)-\int\limits {\frac{t\cdot (2\cdot t+1)}{(t^2+t-1)^2+1} } \, dt[/tex]

The value of ∫v(t), using manual steps on an online calculator, is a large expression, however, using numerical integration, we get;

[tex]\int\limits^5_0 {arctan(t^2+t-1)} \, dt \approx 5.504[/tex]

The displacement of the particle from time t = 0 to time t = 5 is about 5.504. The correct option is therefore;

B. 5.504

The displacement is the change in the position of the particle, and is the shortest distance between the particle's current position and the initial position of the particle

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{b + b + b + b + b}\\\mathsf{= 1b + 1b + 1b + 1b + 1b}\\\mathsf{= 2b + 2b + 1b}\\\mathsf{= 4b + 1b}\\\mathsf{= 5b}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{5b}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

Step-by-step explanation:

b+b+b+b+b is 5b

Answer:

\frac{27}{17}+\frac{28}{17}i

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Basically one-half of 32

one-half = 1/2

Hence, 1/2 x 32 = 16

The rest of the information is not needed, it is a trick.

Answer:105

Step-by-step explanation:

let the number is x

Then 15% of x = 0.15x = 45 .

x= 45/0.15

x = 300

now 50 % of x = 0.5x =150

x = 150/0.5

x= 300 (crosscheck correct)

now 35% of 300 = 0.35 ×3000

= 105

The triangles  ΔPQR ≈ ΔXYZ are similar by Angle-Angle Similarity.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are items that feature more than two figures that are the same shape but different sizes.

Given two triangles, ΔPQR and ΔXYZ

both the triangles are right triangles,

∠P = ∠Z = 90°

and given ∠R = ∠Y = 62°

A triangle is said to be comparable to another triangle if any two of its three angles are equal to any two of its three angles.

From the above-described figure

ΔPQR ≈ ΔXYZ

so triangles are similar to Angle-Angle Similarity.

Hence the triangles are similar.

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Answer: 27,800.0 cm[tex]^{3}[/tex] / 1,696.5 cu in.

Step-by-step explanation:

So Basically, If the Diameter is 12 and the height is 15 inches, the radius will be 6 inches making the Volume of the cylinder 1696.46 cu in.

Now if we were to round that to the nearest place it'd be 1,696.5 cu in.

However, If you want the answer in cm[tex]^{3}[/tex] it would be 27,800 cm making the rounded value 27,800.0 cm[tex]^{3}[/tex].

Hope that helped!

Answer:

Step-by-step explanation:

The tractor-trailer rig is a fixed input under the circumstances described because it is necessary for the business to service this profitable market and it cannot be replaced with any other type of capital equipment. The tractor-trailer is a quasi-fixed input because it has a five-year contract that requires monthly lease payments, so it is not completely fixed in the sense that the business can replace it with another piece of capital equipment at any time.

The zeros of f(x) = 4x³ + 4x² -37x + 44, using the Factor Theorem, are given as follows:

x = -4, x = 1.5 + 0.707i and x = 1.5 - 0.707i.

The function for this problem is defined as follows:

f(x) = 4x³ + 4x² -37x + 44.

The first linear factor is given as follows:

x + 4 = 0

x = -4 is the first zero.

The Factor Theorem states that the polynomial can be written as a product of it's linear factors.

x + 4 is of the first degree, while the polynomial is of the third degree, hence the remaining linear factors form a second degree polynomial, thus:

(x + 4)(ax² + bx + c) = 4x³ + 4x² -37x + 44.

Then, multiplying on the left side, we have that:

ax³ + (4a + b)x² + (4b + c)x + 4c = 4x³ + 4x² -37x + 44.

Then the coefficients are given as follows:

Inserting these coefficients into a quadratic function calculator, the remaining zeros are given as follows:

x = 1.5 + 0.707i, x = 1.5 - 0.707i.

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The solution of the equation (x - 5)² + 3(x - 5) + 9 = 0 is x = -7 ± √35/2. Option B

From the information given, we have the equation as;

(x - 5)² + 3(x - 5) + 9 = 0

To solve the equation, take the following steps;

(x -5)(x-5) + 3x - 15 + 9 = 0

x² - 5x - 5x + 25 + 3x - 15 + 9 = 0

Now, collect like terms

x² - 5x - 5x + 3x + 25 - 15 + 9 = 0

add or subtract the like terms

x² - 7x + 21 = 0

The quadratic formula is is given as;

x =[tex]-b[/tex] ± [tex]\frac{\sqrt{b^2 - 4ac} }{2a}[/tex]

substitute the values

x = -(7) ± [tex]\frac{(-7)^2 - 4(1)(21)}{2(1)}[/tex]

expand the bracket

x = -7 ± [tex]\sqrt{\frac{49 - 84}2} }[/tex]

x = -7 ± √35/2

Hence, the value is x = -7 ± √35/2

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Answer:

-------------------------------

As per given drawing PQ is the segment bisector of XY.

The point W is the midpoint of XY. As per property of midpoint, XW and WY have equal length.

XW = 13 units, hence:

Answer:

Step-by-step explanation:

Sure

Answer:

[tex]\huge\boxed{18 + 0i}[/tex]

Step-by-step explanation:

= (3 + 3i)(3 - 3i)

= 3(3 - 3i) + 3i(3 - 3i)

= 9 - 9i + 9i - 9i²

= 9 - 9(-1)

= 9 + 9

In the form a + bi:

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

volume  of cylinder is

[tex]V = \pi r^{2}h[/tex]

In your cylinder, r = 20 and h =20

V = 3.14 x 20^2 x 20

   =25 120.00 ft^3

Please note: The numbers in the question seem wrong if your teacher wants you to round to the nearest hundredth.  Double check if the information.  They might have said " 0.1 times" instead of 1 times or they meant the nearest hundred instead of the nearest hundredth.  Please check.

The value of the specified finite sum is -15.

The correct option is D.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The finite sum,

[tex]\sum^n_{k=1}{a_k = 5[/tex],

and [tex]\sum^n_{k=1}{b_k = 10[/tex].

Now,

[tex]\sum^n_{k=1}{a_k -2b_k = \sum^n_{k=1}{a_k -2\sum^n_{k=1}{b_k[/tex]

Substituting the values,

[tex]\sum^n_{k=1}{a_k -2b_k[/tex] = 5 - 20

                      = -15

Therefore, the value is -15.

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Answer:

me I would guess

Step-by-step explanation:

like break it down step by step or just buy answers

The actual distance between towns on the map is 350km

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given;

The scale on the map is 1:5,000,000

Which implies that 1 cm on the map represent 5,000,000 cm in the actual;

Remember that;

1km = 1000m

1m= 100cm

1km= 100000cm

Convert cm to Km;

Divide by 100,000

5,000,000cm= 5,000,000/100,000= 50km

Now 1:5,000,000= 1cm/50km

That means

1 cm on the map represent 50 Km in the actual

So, 7 cm apart on the map

Multiply by 50

7 x 50= 350km

Hence, the answer to this question in kilometers is 350km

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The factorization of the expressions gives 2(l + w), -2ab(b + 2a), (3x+2)(3x−2) and 3(x²+2x−6)

Factorization, also known as factoring, is the process of breaking a mathematical expression down into its individual factors. In algebra, factorization refers to the process of expressing a polynomial as a product of simpler polynomials, known as its factors.

To factorize an expression, you need to look for factors of that expression. That is:

1. 2l+2w

2l+2w = 2(l + w)

2. -2ab²-4a²b

-2ab²-4a²b = -2ab(b + 2a)

3. 9x²-4

9x²-4 = (3x+2)(3x−2)

4. y²+7x+12

This cannot be factorized

5. 3x²+6x-18​

3x²+6x-18​ = 3(x²+2x−6)

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Answer:

15500 Paise

In 1 rupee there are 100 paise therefore, 155 rupees after multiplying by 100 you will get the answer as 15500 paise

155×155=

24,025 p

This is the correct answer

Answer:

Step-by-step explanation:

B i guess

[tex]\vec A = \left[\begin{array}{cccc}- 3&- 14&7 &18\\-13&-2&-5 & -6\end{array}\right][/tex]

In this problem we find a matrix as result of the addition of two matrices. According to linear algebra, matrix addition is performed between matrices with same number of rows and columns. There, matrix A must have two rows and two columns to make addition operation possible, that is:

[tex]\vec A + \left[\begin{array}{cccc}3&9&-1 &-8\\16&- 2&3 & 13\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]

[tex]\left[\begin{array}{cccc}3 + a_{11}&9+a_{12}&-1+a_{13} &-8+a_{14}\\16+a_{21}&- 2+a_{22}&3+a_{23} & 13+a_{24}\end{array}\right] = \left[\begin{array}{cccc}0&- 5&6 &10\\3&0&-2 & 7\end{array}\right][/tex]

And we shall solve the following equations:

First row

3 + a₁₁ = 0

9 + a₁₂ = - 5

- 1 + a₁₃ = 6

- 8 + a₁₄ = 10

Second row

16 + a₂₁ = 3

2 + a₂₂ = 0

3 + a₂₃ = - 2

13 + a₂₄ = 7

The solutions to the equations are: a₁₁ = - 3, a₁₂ = - 14, a₁₃ = 7, a₁₄ = 18, a₂₁ = - 13, a₂₂ = - 2, a₂₃ = - 5, a₂₄ = - 6.

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The boat and the whale are about 218.5 miles apart.

Using the Pythagorean theorem to calculate the distance between the boat and the whale.

Let's call the distance between the boat and the whale "d" and the time they moved apart "t".

1st movement:

d = 45t

2nd movement:

d = (45t + 25(t+35))²

To calculate the final distance, we need to square d from the second movement and add the result from the first movement.

d² = (45t)² + (25(t+35))²

We know that the boat and the whale were moving apart for 35 minutes and 25 minutes, so we can substitute t = 35 and t = 25 in the equation.

d² = (4535)² + (2560)²

Taking the square root of the result and get the final distance between the boat and the whale.

d =  ([tex]\sqrt{4535 ^{2} +2560^{2} }[/tex])

d ≈ 218.5 miles

Hence, the boat and the whale are about 218.5 miles apart.

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Answer:

2 * 1 ==> 1st option

Step-by-step explanation:

Matrix dimensions are:

number of rows by number of columns

The number of rows is 2   :   ( 2 and 12 are the rows)

The number of columns is 1   :  ( 2      

                                                    12 )    

Hence, the dimensions is 2 * 1.

Answer: The result of the exercise is BRL 15.00

Step by step explanation:

To find the total value, simply multiply the number of sheets and the price per copy.

[tex]\sf{ \bold{30 * 0.50} ={\boxed{\bold{15 \: \: real}}} }[/tex]

Rpt: The result of the exercise is BRL 15.00

Answer: x+y=7, x+3=y

Step-by-step explanation:

The single fraction is 7x/20

A fraction can be defined as the part of a whole variable, number or element.

The different types of fractions are;

Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.

They are made of operations such as multiplication, addition, subtraction, division, etc

Given the expression;

3/4x - 2/5x

Find the LCM

15x - 8x/20

7x/20

Thus, the value is 7x/20

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Answer:

The slope is 3

Step-by-step explanation:

y = mx + b  The slope is the m.  It is the number before the letter x.

Answer:

7v^10

Step-by-step explanation: