A whale-watching tour boat, moving west at a constant speed 45 miles per hour, has finished viewing a whale and is returning to shore. One whale that is right next to the boat swims away in the opposite direction, moving at a constant speed of 25 miles per hour. They swim apart for 35 minutes and then change direction. The boat turns south and again the whale turns in the opposite direction of the boat. They continue moving apart for another 25 minutes. How far apart are the boat and the whale? (Round your answer to the nearest mile).

The exponent x in the equation must be equal to 0.

Here we have the following equation:

16^x^2=8^0

First, notice that any number to the power of zero (except for the number 0) is equal to 1.

a^0 = 1

16^x^2=8^0

16^x^2 = 1

Now, trivially, if we use x = 0 we will get:

c

Particularly, 0^2 = 0

So we can rewrite:

16^0^2 = 1

16^0 = 1

1 = 1

So the solution is x = 1.

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Answer:

116.05

Step-by-step explanation:

15 to 20 = 5 years

compound semiannually = 10 time

annual rate 3% = 1.5% for every 6 mos

so 100*(1+1.5%)^10 =116.05

Answer:

y = 16.25x

Step-by-step explanation:

y is the total number of miles.

x is the number of days.

The probability that a student studied for 4 hours is 0.257 Or 26%.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

A table is given where the first column represents the number of hours a student studied math and the second column represents the number of students.

So, sum of the second column is 35. so it is the total number of students

and, only 9 of them studied mathematics for 5 hours.

Therefore, The probability that a student studied for 4 hours is,

= 9/35

= 0.257 or 26%.

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Answer:

4.98952 kgs in 11 pounds

Step-by-step explanation:

First of all, how many kgs are in a pound?

Well 1 pound = 0.453592 kg.

So, to find how many kg are in 11 pounds you would multiply, 0.453592 by 11, which will be...

4.98952 kgs.

Hope this helps!

Answer:

36290.4$

Step-by-step explanation:

First of all we should find out how much farmer spent on 240 acres

240 × 188.99 = 45357.6

Then, let's find out the price for whole bushels he gets

240 × 60 × 5.67$ = 81648

Therefore his profit is,

81648 - 45357.6 = 36,290.4$//

Answer:

y-int = -1

x-int = -4

HA: y = -2

VA: x = -5

Step-by-step explanation:

For the y-intercept, you need to look where the graph intersects with the y-axis. In this case, the graph intersects at -1.

For the x-intercept, you need to look where the graph intersects with the x-axis. In this case, the graph intersects at -4.

The horizontal asymptote is a y value the graph approaches but does not pass or touch. In this case, the y value is -2.

The vertical asymptote is a x value the graph approaches but does not pass or touch. In this case, the x value is -5.

Answer: Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.

Step-by-step explanation:

Multiplying the first equation by 2 we get:

Now, once we have amplified the original equations, the sum of the first equation and the second equation leads to:

Which is impossible, indicating that the system is inconsistent. Therefore, based on the analysis performed with the elimination method, the system has no solution.

So on solving the provided question we can say that from the given data - (a) and (b) are triangles only/

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

(a) T(-2, 4), R(6, O), 1(-5, -2) - is triangle

(b) p(9, -3), Q(-l, 1), R(-5, -9)- is a triangle

(c) O), E(-6, 10), F(-IO, 4) - can not be determined

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Answer:

D' (9, 10)

E'( 12,-1)

F'(7,8)

Step-by-step explanation:

The coordinates of triangle DEF will be D(9,10), E(12,-1), and F(7,8) after the translation.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The given triangle DEF has vertices D (3,5), E(6,-6), and F(1,3).

Triangle DEF has translated 5 units up and 6 units right.

This means that the x-coordinates of the vertices D, E, and F will each be increased by 6, and the y-coordinates of the vertices will each be increased by 5.

After the translation, the coordinates of vertex D will be (3 + 6, 5 + 5) = (9, 10)

After the translation, the coordinates of vertex E will be (6 + 6, -6 + 5) = (12, -1)

After the translation, the coordinates of vertex F will be (1 + 6, 3 + 5) = (7, 8)

So after the translation, the coordinates of triangle DEF will be D(9,10), E(12,-1), F(7,8)

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Answer:

The cost of 6 m of water pipe = ₹ 192

Step-by-step explanation:

Answer:

given that z=3 and w=2

10z+5w

now by putting the values of z and w

10(3) + 5(2)

30 + 10

40 is your correct answer

The total quantity of the three spices is 7/8

A recipe has three spices

1/8 teaspoon of turmeric

1/4 teaspoon of ginger

1/2 teaspoon of cumin

The total quantity of the three spices can be calculated as follows

1/8 + 1/4 + 1/2

= 7/8

Hence the total quantity of the three spices is 7/8

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Answer:

3 cuuuuuuuuuuuuuupsssssss offfccccdd saaaaaaaallllytttt

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

Inequality becomes 0.21t + 15,040 <= 100,000

Energy consumption remains a principal source of human caused greenhouse gas emissions the predominant cause of climate change.

After 7 a.m., the power usage on a college campus increases at a rate of 21% per hour.

t be the number of hours

the power usage increases at a rate of 21% per hour

21% = 0.21, constant rate = 0.21 . So slope = 0.21

Prior to 7 a.m., 15,040 kWh have been used.

At 7.am , power used = 15,040kWh. so our y intercept is 15,040

We use slope intercept form y= mx+b

slope m = 0.21  and b = 15040

power usage , y = 0.21 t + 15040

The university has a daily goal to keep their power usage less than or equal to 100,000 kWh

Power usage is less than or equal to 100,000

So inequality becomes 0.21t + 15,040 <= 100,000

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The point (-1,5) is not a solution to the equation 2x + 5y = 0 because this point does not satisfy the equation.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question, as follows:

2x + 5y = 0

Substitute x = -1 and y = 5 into the equation and see if it holds true:

2(-1) + 5(5) = 0

-2 + 25 = 0

23 = 0

Since 23 ≠ 0, the point (-1,5) is not a solution to the equation 2x + 5y = 0.

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The missing vertices of the square are B(x, y) = (- 2, 1) and D(x, y) = (6, - 7), respectively.

Squares are quadrilaterals with four sides of equal length and four internal right angles. This kind of quadrilaterals have two diagonals perpendicular to each other. In this case, we know the coordinates of the endpoints of diagonal AC and we need to determine the location of points B and D.

This can be done by means of the following definition: A(x, y) = (a, b), C(x, y) = (c, d), B(x, y) = (a, d), D(x, y) = (c, b). If we know that a = - 2, b = - 7, c = 6 and d = 1, then the location of points B and D are, respectively:

B(x, y) = (- 2, 1), D(x, y) = (6, - 7)

Lastly, we graph the resulting figure.

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The sine function that matches the graph is given as follows:

y = sin(2πx/7) - 1.

The sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The maximum value is of 0, while the minimum value is of -2, hence the amplitude A is obtained as follows:

2A = 2. (as the difference of the maximum value and the minimum value is of 2).

A = 1.

A sine function with amplitude 1 should oscillate between -1 and 1, while this one oscillates between -2 and 0, hence the vertical shift is given as follows:

C = -1.

The period of the function is of 7 units, hence:

2π/B = 7

7B = 2π

B = 2π/7.

Then the function is defined as follows:

y = sin(2πx/7) - 1.

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Using pythagoras theorem formula, c² = a² +b²  We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

What is Pythagoras' theorem ?

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

The two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

Let the sides of the triangles be a, b and c. According to Pythagoras theorem;

c² = a² +b²

where:

a is the hypotenuse (longest side)

For triangle A:

c = 13

b = 12

Get "a"

13² = 12² +b²

b² = 25

=> b = 5 cm

Similarly for triangle B:

c² = 5² +12²  = 169

=> c=13 cm

We can see that the two shorter sides have the same length which is 5cm

Since all the sides of the triangle are the same, hence the two triangles are congruent.

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Answer:

$519

Step-by-step explanation:

We know that the one day sale price of the ski set is $324 and the markdowns are specified.

A markdown means a reduction in price, so to find the original selling price we need to add the amount of markdown to the sale price.

The markdown of the ski set is $75 + $120 = $195

So, to find the original selling price we need to add the markdown amount to the sale price:

$324 + $195 = $519

Therefore, the original selling price of the ski set was $519

Answer: 8 x 96

Explanation: (Commutative Law: A x B = B x A)

Answer: (6,2) (0,-2) (-3,-4)

Step-by-step explanation:

If you find the other coordinate pair groups on the graph, there is at least one that doesn't land on the line on the graph.

In the top left, (-6,-5) is not on the graph. If it had been (-6,-6) then it would've been correct, but it isn't.

In the bottom left, (0,-3) isn't on the graph. Instead, (0,-2) is.

In the bottom right, (3,-4) isn't on the graph, but (-3,-4) is.

Answer:

x=1

Step-by-step explanation:

To solve the equation, we'll need to get the square roots on one side and the non-square root terms on the other side.

First, we'll add √x to both sides to get:

√2x+4 - √x + √x = 2 + √x

√2x+4 = 2 + √x

Next, we'll square both sides to get rid of the square roots:

(√2x+4)^2 = (2 + √x)^2

2x+4 = 4 + 2√x + x

Then, we'll simplify the right side of the equation:

2x+4 = 4 + 2√x + x

2x+4 = 4 + x + 2√x

Now we'll subtract 4 from both sides

2x = x + 2√x

x = 2√x

Finally, we'll divide by x on both sides

1 = 2√x/x

x = √x

x = 1

Therefore, the solution of the equation is x=1

Answer:

To solve the equation √2x+4 - √x = 2, we can first square both sides of the equation to eliminate the square roots.

Squaring both sides gives: (√2x+4)^2 - (√x)^2 = 2^2

Simplifying the left side gives: 2x+4 - x = 4

Next, we can add x to both sides of the equation to get:

2x+4 = 4 + x

then we can subtract 4 from both sides of the equation to get:

2x = x

then we can divide both sides by x

2 = 1

However, it is not possible to divide by zero, so x = 0 is not a valid solution.

This equation is an extraneous solution because the assumption that x is not equal to 0 led to a valid solution, but when x = 0, the equation is not defined.

Therefore, the solution of √2x+4 - √x = 2 is x = any value except 0.

Answer:

1) f(-3)

= 2x + 5

= 2×(-3) +5

= -6+5

= -1

2) g(x)- h(x)

= -3x² + 2x - 6 -(-4 - x)

= -3x² + 2x - 6 + 4 + x

= -3x² + 3x - 2

3) f(x) = h(x)

or, 2x + 5 = -4 - x

or, 2x + x = -4 - 5

or, 3x = -9

or, x = -9/3

or, x = -3

4) i am not sure about the last but the answer is between f(x) and h(x). But i think its f(x).

Therefore , the solution of the given problem of trigonometry comes out to be Sin θ = 5/√34.

Trigonometry is a branch of mathematics that studies how square side length The field's initial development took place during the Baroque era, more likely and around third century BC, as a result of the merger of astronomer and geometry studies. Numerous geometric equations and their potential applications to calculations are covered by precise mathematical approaches. Mathematics has six fundamental operations. They are known by a variety of names and abbreviations, including sine, quadrature, parallel, secant, etc (csc). The study of mathematics is focused mostly on the characteristics of right triangles. The ability to understand geometry, however, necessitates familiarity with each polygon's properties.

Here,

Given : Provided: tan = (-5/3)

With the help of the formula below, you may determine the angle's number, which varies at 90 to 180 degrees.

as tan θ = (-5/3)

The value of the perpendicular is 5, and the value of the base is 3.

The hypotenuse is (25 + 9) according to Pythagoras' Theorem.

= √34

The value of sin is (5/34)

=> sin θ = 5 * √34 / 34

=> sin θ = 5/√34

In the second meiotic division, which contains value, sin is positive.

Therefore , the solution of the given problem of trigonometry comes out to be Sin θ = 5/√34.

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Answer:

Step-by-step explanation:

200 x 115.5/8 = $23,100.00

The solutions for the given equations are x=2 and x=-4

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Fo question 5.

1/2x-2=9-5x

Take the variable terms on one sides\

x/2+5x=11

x+10x=22

11x=22

Divide both sides by 11

x=22/11

x=2

For question 6:

-5+x/4=3x+6

-20+x=12x+24

-20-24=12x-x

-44=11x

x=-4

Hence, the solutions for the given equations are x=2 and x=-4

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