b) tan 2A cot A-1 = sec 2A

The velocities of the boat and the person relative to the shore are 1.337 m/s and 2.896 m/s, respectively.

We can use the conservation of momentum equation:

(mboat + mperson) * vboat = mperson * vperson

(160 kg + 70 kg) * vboat = 70 kg * (0.80 m/s + vperson)

230 kg * vboat = 56 kg * (0.80 m/s + vperson)

vboat = (56/230) * (0.80 m/s + vperson)

vperson = 0.80 m/s + vboat

vperson = 0.80 m/s + (56/230) * (0.80 m/s + vperson)

(174/115) * vperson = (504/115) * m/s

Dividing both sides by (174/115), we get:

vperson = 2.896 m/s

vboat = (56/230) * (0.80 m/s + vperson)

Substituting the value of vperson, we get:

vboat = 1.337 m/s

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On a 160-kg boat that is at rest with its bow pointed to the shore, a 70-kg person begins to walk from the bow to the stern at 0.80 m/s relative to the boat. What are the velocities of the boat and the person relative to the shore? Neglect the resistance of water to motion.

The calculated number of plants the flower bed can contain is 120

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

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

Diego is correct as the number of groups result to 6/5 or 1 1/5.

We have to find the number of groups of 5/6 in 1.

So, we need to perform the division as

= 1/ (5/6)

= 1 x 6/5

= 6/5

= 1 1/5

Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.

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The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Okay, let's break this down step-by-step:

* The telephone pole is 54 feet tall

* The guy wire runs 83 feet from point A (top of pole) to point B (ground)

* So the hypotenuse (AB) of the right triangle is 83 feet

* The opposite side (AC) is 54 feet (height of pole)

To find the adjacent side (BC), we use the Pythagorean theorem:

a^2 + b^2 = c^2

54^2 + BC^2 = 83^2

Solving for BC gives:

BC = sqrt(83^2 - 54^2) = sqrt(1296 - 2916) = sqrt(1620) = 40 feet

So the guy wire is secured 40 feet from the base of the telephone pole.

Rounded to the nearest tenth is 40.0 feet.

Therefore, the final answer is:

40.0

Let me know if you have any other questions!

The angle measure of LJK is 27 degrees

Following the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees

Also, we need to know that the sum of angles on a straight line is 180, then, we have;

<JLK = 180 - <LKM = 180 - (8x - 19)

Then, substitute the value, we have that;

<JKL + < JLK + < KJL = 180

Then,

3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180

expand the bracket, we have;

3x - 16 - 8x - 19 + 2x + 15 = 0

add the like terms

-3x + 18 = 0

collect the terms

-3x = -18

x = 6

Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees

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144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.

145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.

For question 144.)

Two triangles are congruent means that the angles are equal to each other. That is;

2.3x +25 = 5.8x + 11

Bring like terms together;

5.8x-2.3x = 25-11

3.5x = 14

X = 14/3.5

= 4.

For question 145.)

When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.

The two given angles are congruent;

That is;

13x -15 = 22x + 9

Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9

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The circle equation x² + 8x + y² -10y - 32 = 0​ can be graphed using (x + 4)² + (y - 5)² = 73

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

x² + 8x + y² -10y - 32 = 0​

Add 32 to both sides of the equation

This gives

x² + 8x + y² -10y = 32

Group the terms in two's

So, we have

(x² + 8x) + (y² -10y) = 32

When we complete the square on each group, we have

(x + 4)² + (y - 5)² = 16 + 25 + 32

Evaluate the like terms

(x + 4)² + (y - 5)² = 73

Hence, the circle equation can be graphed using (x + 4)² + (y - 5)² = 73

See attachment for the graph

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The system of equations has infinitely many solutions, which corresponds to option (OB).

We can use the graphing function on a calculator to find the solution to the system of equations:

[tex]3y - 12x = 18\\\\2y - 8x = 12[/tex]

To do this, we can rearrange each equation to solve for y in terms of x:

[tex]3y = 12x + 18\\\\y =4x + 6[/tex]

For the second equation.

[tex]2y = 8x + 12\\\\y = 4x + 6[/tex]

We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.

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The expression that equals D + 3C in standard form is 2w² + 8w - 25.

To find an expression that equals D + 3C in standard form, we first need to simplify D and C.

Starting with D = 2w² - w - 7, we can rearrange the terms to put it in standard form:

D = 2w² - w - 7

D = 2w² - 2w + w - 7

D = 2w(w - 1) + (w - 7)

Next, simplifying C = 3w - 6:

C = 3w - 6

Now, we can substitute these expressions into D + 3C:

D + 3C = (2w² - w - 7) + 3(3w - 6)

Expanding and simplifying:

D + 3C = 2w² - w - 7 + 9w - 18

D + 3C = 2w² + 8w - 25

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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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Answer:

8y

Step-by-step explanation:

Lets put these two parts into addition to make it easier.

(y)56x + 16y^2

(8y)7x + 2y^2

8y is the GCF(grates common factor)

On rounding the given number to nearest hundred miles will give the result -8.92.

Rounding to nearest hundred miles refers to changing the number present on hundreds place. We see that the number 8 is at unit's place, 9 is at tenth's place and 2 is at hundred's place.

Based on the rules of rounding, we will check the number to the right of number on hundred's place. Since the next number is 5, the number we will round the number 1 present at hundred's place. Hence, the final number will be -8.92.

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The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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The condition that will prove the two triangles similar is

side JL = 8 * side ZX

angle L = angle Z

Similar triangles are  triangles which have the  similar shape however not necessarily the equal size. More officially, two triangles are comparable if their corresponding angles are congruent and their corresponding aspects are in proportion.

This means that if we had been to scale one triangle up or down uniformly, the ensuing triangle could be much like the original triangle.

In the figure, the scale is 8

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Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

The system of inequalities for the graph is

a) y < 3x - 4

b) y = x + 3

Given data ,

Let the inequality equations be represented as A and B

where

Let the first point be P ( 0 , 3 )

Let the second point be Q ( -3 , 0 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 3 - 0 ) / ( 0 + 3 )

m = 1

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 0 = 1 ( x + 3 )

y = x + 3

And , the second equation is

Let the first point be R ( 0 , -4 )

Let the second point be S ( 2 , 2 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( -4 - 2 ) / ( 0 - 2 )

m = -6/-2

m = 3

Now , equation of line is y - y₁ = m ( x - x₁ )

y - 2 = 3 ( x - 2 )

Adding 2 on both sides , we get

y = 3x - 4

Since , it is a dotted line ,

y < 3x - 4

And , the solution to the inequality is point of intersection

where A ( 3.5 , 6.5 ) is the solution

Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution

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Equation which can be used to solve for the value of x is

3x° + 2x° + 80 °= 180° .

Straight angle pair is the sum of two or more angles that are in pair of angles that form a straight line is always equal to 180°.

As shown in the diagram angle on the lines are -

3x ° , 80° , 2x° respectively

Sum of all these angle will be equal to 180°.

3x° + 2x° + 80° = 180

The correct equation to find the value of x is 3x° + 2x° + 80° = 180° .

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The graph will look like a circle centered at (2, 1) with radius 3.

To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex]  by completing the square, we need to rearrange the terms as follows:

[tex](x^2 - 4x + 4) + (y^2 - 2y + 1) = 9[/tex]

This can be simplified to:

[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]

So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.

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According to the information, there are thousands of different lunch options in this restaurant.

To calculate the number of different lunches in the restaurant we must carry out the following mathematical procedure. We must multiply the different options as shown below:

4 green options x 5 protein options x 8 vegetable options x 4 extra options x 6 topping options = 4 x 5 x 8 x 4 x 6 = 4,800 different lunch options.

Based on the above, we can infer that 4,800 different lunch options can be created with the available ingredients.

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Answer:

AA sim post

Step-by-step explanation:

They DO have equal (similar) angles.....but they do not have equal sides

The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to  7x³.

To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.

To find the factors, we can break each term down into its prime factors:

21x⁴ = 3 * 7 * x * x * x * x

49x³ = 7 * 7 * x * x * x

The common factors are 7 and x³. To find the GCF, we multiply these common factors together:

GCF = 7  * x³

GCF = 7x³

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Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.

The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:

cos ∅ = length of hypotenuse/length of adjacent side.

From the image attached below, we have the following:

Reference angle (∅) = 37°

length of hypotenuse = 210

length of adjacent side = y

Plug in the values:

cos 37 = y/210

210 * cos 37 = y

y = 167.7

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Answer:

3



Step-by-step explanation:

Area = 7pi/5

56/360 × pi r² = 7pi/5

Pi is canceled on both sides.

r² = 7/5 ÷ 56/360 = 9

r = root 9 = 3

The experimental probability that more than 10 spins are needed to land on each letter at least once is 75%

Experimental probability is a type of probability that is based on actual observations or experiments.

In experimental probability, the probability of an event occurring is calculated by conducting experiments and observing the outcomes. The probability of the event is then calculated by dividing the number of times the event occurred by the total number of trials or experiments.

In this case, experimental probability = number of times the event occurred / total number of trials

Experimental probability = 0.1 + 0.35 + 0.3 / 1

= 0.75 / 1

= 75%

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Answer:

To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).

So, the area of the top of Katrina's laptop in square centimeters would be:

57,000 mm² ÷ 100 = 570 cm²

Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².

The two men will charge the same amount to complete the job after 3.5 hours.

Let's start with Charles' fee, which is a combination of an upfront fee and an hourly fee. We can represent this as:

C(x) = 115 + 30x

where x is the number of hours Charles works.

For Peter, his fee is a combination of an upfront fee for paint and an hourly fee. We can represent this as:

P(x) = 80 + 40x

where x is the number of hours Peter works.

To find out when the two men will charge the same amount to complete the job, we need to set the two equations equal to each other and solve for x:

115 + 30x = 80 + 40x

Subtracting 30x from both sides: 115 = 80 + 10x

Subtracting 80 from both sides: 35 = 10x

Dividing both sides by 10:

x = 3.5

So, the two men will charge the same amount to complete the job after 3.5 hours.

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1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ

2. His stamp should be worth approximately $7,851.47 after 6 years.

3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵

1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:

y = 81 x (¹/₃)ˣ

2. The increase in value of the stamp can be calculated using the formula:

V = P(1+r)ᵗ

where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

Substituting the given values:

V = 4900(1+0.075)⁶

V ≈ $7,851.47

Therefore, the stamp should be worth approximately $7,851.47 after 6 years.

3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:

y = (1/16) x 2²ˣ ⁺ ⁵

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Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5