From a top-down 2D perspective, a car moves in a diagonal line and travels a distance equivalent to 80 miles. If the angle between the diagonal line and a horizontal reference line is 25 degrees, how far did the car travel horizontally and vertically? If necessary, round your answers to the nearest tenth of a mile. Horizontal distance? Vertical distance?

Answers

Answer 1

We can use Pythagorean theorem for right angle triangle to solve this problem.

The diagonal line would be hypothenuze. Horizontal and vertical distance would be other two sides of a triangle.

We will use the following formulas:
[tex]sin \alpha = \frac{opposite}{hypothenuze} \\ cos \alpha = \frac{adjacent}{hypothenuze} [/tex]
Where opposite side is vertical distance and adjacent side is horizontal distance.

Solving for these two sides we have:
[tex]opposite = hypothenuze * sin \alpha \\ adjacent = hypothenuze * cos \alpha [/tex]

We insert numbers and we get solution:
[tex]opposite = 80 * sin 25 = 33.8miles \\ adjacent = 80 * cos 25 = 72.5miles [/tex]

Related Questions

(05.02)Find the measure of angle x in the figure below:

Two triangles are shown such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 55 degrees. The lower right angle is marked as 30 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees.

Answers

Answer:

x=95°

Step-by-step explanation:

We are given that: Two triangles are such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 55 degrees. The lower right angle is marked as 30 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees.

The figure of such a triangle is attached to the answer.

As we know that sum of all the angles of a triangle is equal to 180°.

⇒ 55°+30°+x=180°

⇒ 85°+x=180°

⇒ x=180°-85°

⇒ x=95°

Hence, the angle at the vertex is 95°.

The measure of angle x in the inverted triangle formed by two triangles sharing a common vertex is 95 degrees .

Two triangles sharing a common vertex. The angles given are as follows:

Measure of the lower left angle of the lower triangle = 55 degrees.

Measure of the lower right angle of the lower triangle = 30 degrees.

The angle at the vertex of the inverted triangle (at the top) can be found by subtracting the sum of the angles in the lower triangle from 180 degrees .

Since the sum of angles in a triangle is always 180 degrees.

Sum of angles in the lower triangle

= 55 degrees + 30 degrees

= 85 degrees.

Now, subtract the sum of angles in the lower triangle from 180 degrees to find the angle at the vertex of the inverted triangle (x degrees):

x degrees = 180 degrees - 85 degrees

= 95 degrees.

Therefore, the measure of angle x is 95 degrees.

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**Aleta deposited $450 into a savings account earning 3.75% simple interest. How much interest will she earn in 6 years? Explain.

Answers

$101.25;450(0.0375)6=1021.25 is the answer i hope this helps you

Aleta will have 561.23 at the end of the 6 years. You add 3.75% to the previous amount of money from last year for every year.

ie: 'ans' is the total of the previous equation.
450+3.75%
ans+3.75%
ans+3.75%
ans+3.75%
ans+3.75%
ans+3.75%
ans = 561.23.

Find a ⋅ b.

a = 7i - 4j, b = 4i + 3j

A) <28, -12>
B) 16
C) -40
D) <11, -1>

Answers

Answer:

B) 16

Step-by-step explanation:

The dot product of a pair of vectors is the sum of the products of their corresponding parts. It is a scalar.

... a · b = (7i -4j) · (4i +3j) = 7·4 + (-4)·3

... = 28 -12 = 16

A cylindrical tank has a height of 12 feet and a diameter of 16 feet. Jane fills the tank with water at a rate of 6 cubic feet per minute. Calculate how long it would take Jane to fill the tank without overflowing it. Explain your reasoning. Round as needed.

Answers

if the diameter is 16 feet, then the radius for the tank will have to be half that,

[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=8\\ h=12 \end{cases}\implies V=\pi \cdot 8^2\cdot 12\implies V=\stackrel{ft^3}{768\pi} [/tex]

now, that's how many ft³ of water the tank can hold, since she is filling it up at a rate of 6 ft³ per minute, namely in 1 minute 6 ft³ have gone in, then it'll be

768π/6 how many minutes it'll take.

namely, how many times does 6 go into 768π? well, 768π/6.

what is 5/10 + 25/100

Answers

Turn 5/10 to 50/100. Then add 50/100+25/100 which equals 75/100 ---> 3/5 ---> 0.75

3/4 is your answer and if needed as a decimal it would be 0.75

Solve for Y
Y + 1.48 = 6.71

Answers

y+1.48=6.71
-1.48 -1.48
y=5.23

Y + 1.48 = 6.71

Isolate the Y by subtracting 1.48 to both sides

Y + 1.48 (-1.48) = 6.71 (-1.48)

Y = 6.71 - 1.48

Y = 5.23

5.23 is your answer

hope this helps

(64+28+76)÷6 show how you can calculate the number of 3/4 cup servings

Answers

Add first then divide by 6 which gives you 28 then divide by .75 which is 3/4 and it is equal to 37.33

write a real world example that could be solved by using the inequality 4x+8≥32.then solve the inequality

Answers

Sally had 8 dollars right before she was paid for working 4 hours. Sally has at least 32 dollars now.
how much was she paid per hour?
[tex]4x + 8 \geqslant 32[/tex]
[tex]4x \geqslant 24[/tex]
[tex]x \geqslant 6[/tex]
Sally was paid at least 6 dollars /hour.

Final answer:

A real-world situation for the inequality 4x + 8 ≥ 32 could involve calculating the minimum hours required at a part-time job to earn $32. Subtracting 8 and dividing by 4, we find that at least 6 hours of work are needed.

Explanation:

A real-world example that could be solved by using the inequality 4x + 8 ≥ 32 might involve a situation where you need to determine how many hours you must work at a part-time job to earn at least a certain amount of money. Suppose you earn $4 per hour and you have already earned $8. You want to know the minimum number of hours you must work to have at least $32 in total.

To solve the inequality 4x + 8 ≥ 32, you would first subtract 8 from both sides, which gives you 4x ≥ 24. Then, you would divide both sides by 4 to find the number of hours (x) you need to work. Therefore, x ≥ 6. This means you must work at least 6 hours to earn $32 or more.

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HELP ME PLEASEEEEEEEEEEEEEEEEEE

Answers

For this case we have the following solution.
First, let's give the variable a name:
Let
x = gallons of water to be added
For the 10% solution we have:
0.1 * 8 = 0.8
Then, for 5% we have:
(0.8 / x + 8) = 0.05
Rewriting:
(0.8 / x + 8) = (5/100)
Answer:
An equation can be used to find x, the humber of gallons of water he should add is:
(0.8 / x + 8) = (5/100) (option 2).

A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off the ground and rises at 1.5 meters per second. Write and solve an equation to determine when the balloons are at the same height.

Answers

This problem is an example of solving equations with variables on both sides. To solve, we must first set up an equation for both the red balloon and the blue balloon.

Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s:

2.6s + 7.3

Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:

1.5s + 12.4

To determine when both balloons are at the same height, we set the two equations equal to each other:

2.6s + 7.3 = 1.5s + 12.4

Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation:

1.1s + 7.3 = 12.4

Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation:

1.1s = 5.1

Last, we divide both sides by 1.1. So s = 4.63.

This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation:

2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33

1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33

After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.

Final answer:

To find when two balloons are at the same height, set up two equations equal to each other with the starting heights and rates of ascent, and solve for the time. The two balloons will be at the same height approximately 4.636 seconds after they start rising.

Explanation:

To determine when two balloons will be at the same height, we can set up an equation based on their starting heights and their rates of ascent. We have a red balloon that starts at 7.3 meters off the ground and rises at 2.6 meters per second, and a blue balloon that starts at 12.4 meters off the ground and rises at 1.5 meters per second.

Let's let t represent the time in seconds after the balloons begin to ascend. The height of the red balloon at any time t can be expressed as:

Height_red = 7.3 + 2.6t

Similarly, the height of the blue balloon at any time t is:

Height_blue = 12.4 + 1.5t

To find out when the balloons are at the same height, we set the two equations equal to each other:

7.3 + 2.6t = 12.4 + 1.5t

Now, we solve for t by subtracting 1.5t from both sides:

2.6t - 1.5t = 12.4 - 7.3

1.1t = 5.1

Next, we divide both sides by 1.1 to isolate t:

t = 5.1 / 1.1

t ≈ 4.636 seconds

Thus, the balloons will be at the same height approximately 4.636 seconds after they begin to ascend.

Round 3,989.23655 to the nearest tenth

Answers

this would be 3990 if you require a whole number but for a decimal it would be 3989.24

a company is shipping a motorcycle in a box with the dimensions of 4 2/3 feet by 3 3/4 feet by 8 ft the box also has packing material to help protect the motorcycle. what is the volume, in cubic feet, of the box?

Answers

To find the volume we multiply height, length and width. In this case we find
[tex]4 \frac{2}{3} \times 3 \frac{3}{4} \times 8 = 140[/tex]
Hence, the volume of the box is 140 cubic feet.

£850 is invested for 2 years at 6% per annum compound interest. a) Work out the total interest earned over the first 2 years.

Answers

The correct answer to 850 for 2 years at 6% interest is 955

Answer:

6% annum for 850 would be 955

it rained 3/8 of a inch each day for 3 days straight how much rain fell altogether

Answers

Total of 1 and 1/8 inches total.

Hello!

It rained the same amount on each of the 3 days, so the denominator will remain the same. Multiply the fraction by the amount of days:

3/8 × 3 = 1 1/8

ANSWER:

1 1/8 (or 9/8) inches of rain fell altogether on the 3 days.

substitution method for 7x-2y=1 & x-2y=1

Answers

We want to use the Substitution method to solve
7x - 2y = 1 (1)
x - 2y = 1 (2)

From equation (1), obtain
2y = 7x - 1 (3)

Substitute (3) into (2).
x - (7x - 1) = 1
-6x + 1 = 1
-6x = 0
x = 0

From (3), obtain
2y = 7*0 - 1 = -1
y = -1/2

Answer: (0, -1/2) or x=0, y= -1/2.

The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after 200 years.

Answers

To solve this we are going to use the half life equation [tex]N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) } [/tex]
Where:
[tex]N_{0} [/tex] is the initial sample
[tex]t[/tex] is the time in years
[tex]t_{1/2} [/tex] is the half life of the substance
[tex]N(t)[/tex] is the remainder quantity after [tex]t[/tex] years

From the problem we know that:
[tex]N_{0} =100[/tex]
[tex]t=200[/tex]
[tex]t_{1/2} =1600[/tex]

Lets replace those values in our equation to find [tex]N(t)[/tex]:
[tex]N(200) =100e^{( \frac{(-0.693)(200)}{1600}) } [/tex]
[tex]N(200)=100e^{( \frac{-138.6}{1600} )} [/tex]
[tex]N(200)=100e^{-0.086625} [/tex]
[tex]N(200)=91.7[/tex]

We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

state whether the relationship between x and y in y=4x-5 is proportional or not

Answers

The answer is "No they are not proportional" since the line y = 4x-5 doesn't go through the origin. Put another way, the equation is not in the form y = k*x for some fixed value k.

When constructing an inscribed equilateral triangle, how many arcs will be drawn on the circle?

a. 3

b. 4

c. 5

d. 6

Answers

The answer is A(3). 3 arcs will be drawn

It can be done with 2 arcs. In the attached, I started with diameter AD, then drew arcs at B and C of the same radius as the circle from a center at A. Triangle BCD is the inscribed equilateral triangle.

Perhaps a more usual method would be to start at D, draw an arc at E, then from there at B. Resetting the compass to have radius, DB, a third arc can be drawn at C using either B or D as the center. This method would give you
.. selection A: 3 arcs

If you didn't want to reset the compass, you could draw two more arcs, say from B to A, then from A to C. This method would give you
.. selection B: 4 arcs.

The balcony of an apartment is 4 feet by 7 feet. On a scale drawing of the apartment, the balcony is 0.8 inch by 1.4 inches, and the kitchen is 2.4 inches by 2.8 inches. What are the actual dimensions of the kitchen? Enter your answers in the boxes. The actual dimensions of the kitchen are feet by feet.

Answers

4 / 0.8 = 5, 7 / 1.4 = 5. The ratio between actual dimension and the drawing is 5

Thus, 2.4 inches * 5 = 12 feet and 2.8 inches * 5 = 14 feet
12 feet x 14 feet

Answer:

12 by 14

Step-by-step explanation:

took quiz

robert leaves his home to go to his office .he drives 6 km north and then 4km due east.approximatley what is the shortest distance from roberts home to his office,in kilometers

Answers

Visualize the distance traveled as the two side lengths of a right triangle, for this we can use the pythagorean theorem to solve for the hypotenuse (which is the shortest distance from his house to his office).

a²+b²=c²
6²+4²=c²
36+16=c²
52=c²
7.21=c

Answer=7.21km

Sam has bought a camera for $200 when it was on 20% off sale. What was the original price of the camera

Answers

Original price = x
x - .2x = 200 ← original price - discount amount = sale price
.8x = 200 ← 1x - 0.2x = .8x
x = 250 ← divided both sides by .8

The original price was $250

Answer250

Step-by-step explanation:

If the newspaper plans to select an ad at random each week to be published free, what is the probability that the ad for a specific week will be a help dash wanted help-wanted ad

Answers

1/7
1 divided by 7
0.14285714285%
But to round..
0.14%

Answer:Theres a article about that ont he internet

Step-by-step explanation:

Is the quotient of 5 and 1 / 2 greater than or less than 5? Explain your answer.

Answers

the qoutient of 5 and 1/2 is 2.5 so it is less than

The quotient of 5 divided by 1/2 is greater than 5 because dividing by a number less than 1 results in a larger number. In this case, it is equivalent to multiplying 5 by 2, yielding 10.

To determine if the quotient of 5 and 1/2 is greater than or less than 5, we consider the operation of division. Dividing by a number less than 1 will result in a larger number, while dividing by a number greater than 1 will result in a smaller number. The number 1/2 is less than 1, so when 5 is divided by 1/2, the quotient is greater than 5. It is equivalent to multiplying 5 by 2 (since dividing by a fraction is the same as multiplying by its reciprocal), which is 10. Therefore, 5 divided by 1/2 equals 10, which is greater than 5.

The coordinates of the vertices of parallelogram ABCD are A(-3,2) , B (-2,-1) , C ( 4,1) and D ( 3,4). The slopes of which line segments could be calculated to show that ABCD is a rectangle?
1) AB and DC
2) Ab and BC
3) AD and BC
4) AC and BD
When you say what answer you chose can you explain why that’s the answer please in depth?

Answers

The answer is Ab and BC, option 2
I cannot draw the rectangle here. When you draw the line of x and y axis, plot the numbers, when you connect the dot, you will see the rectangle.I don't know how to draw it here, but that is the answer.

NOTE:
To show that a parallelogram is a rectangle, we need to show that ONE of the interior angles is a right angle.
Therefore we need to find the angle between two adjacent sides.

To find two adjacent sides in a parallelogram with vertices in counter-clockwise, we need two sides with a common vertex, for example,
AB+BC, or BC+CD, or CD+DA, or DA+AB.

Any two sides without a common vertex are opposite sides.

7+11v=9v-9 how do you solve by steps

Answers

You're solving this equation for the variable 'v', so the main goal is to isolate it on one side of the equation.

7 + 11v = 9v - 9 Subtract 7 from both sides
7 - 7 + 11v = 9v - 9 - 7 Simplify
11v = 9v - 16 Subtract 9v from both sides
11v - 9v = 9v - 9v - 16 Simplify
2v = -16 Divide both sides by 2
[tex] \frac{2v}{2} [/tex] = -[tex] \frac{16}{2} [/tex] Simplify
v = -8

Check your answer by plugging the value (-8) into the original equation.

7 + 11(-8) = 9(-8) - 9 Simplify the mulitiplication steps
7 + (-88) = -72 - 9 Rewrite 7 + (-88) as 7 - 88
7 - 88 = -72 - 9 Simplify both sides
-81 = -81

The check worked out, so your answer is v = -8 .

which of the following is important in a 2 column proof?
A list of all theorems
Staircase LOgic
Order
Detailed explanations for each step

Answers

Answer:

Order.

Step-by-step explanation:

When we are proving a proposition, it's important to have order in our 2-column proof.

So, we must have a left colum for Statements and a right colum for Reasons, that's the order we need to have.

In the statements colum we write our deductions. In the reasons column, we write the justification or reason about our deduction.

Therefore, the right answer is the third choice: Order.

What angle does this piece of pie form?

Answers

check the picture below.

An employee has an annual salary of $51,300. They receive $2,830 in health insurance and $4,600 in paid time off per year. They drive their personal vehicle for work which costs them $600 per month, but the company reimburses them $0.54 per mile for the total work miles driven. If the employee drives 36,000 miles for work for the year, what will be their total employment compensation?
a.
$70,740
b.
$70,970
c.
$77,570
d.
$78,170

Answers

The answer is B:$70,970

The total employment compensation of the employee is b. $70,970.

What are Arithmetic operations?

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given that,

Annual salary of the employee = $51,300

Health insurance per year = $2,830

Paid time off per year = $4,600

Monthly expense for personal vehicle = $600

Yearly expense = 12 × $600 = $7200

Reimbursement for the vehicle = $0.54 per work mile

Reimbursement for vehicle for 36,000 miles for work for the year = $0.54 × 36,000 miles = $19,440

Total employment compensation = ($51,300 + $2,830 + $4,600 + $19,440) - $7200

= $70,970

Hence the employment compensation is $70,970.

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how do you solve x^2+4x-5=0

Answers

Try this option:
1. root1*root2=-5; root1+root2=-4.
2. root1=-5; root2=1.
answer:1;-5.

Actually the answer is (-1,5)

x^2 – 4x – 5 = 0

x^2 – 4x = 5

x^2 – 4x + 4 = 5 + 4

(x – 2)^2 = 9

x – 2 = ± 3

x = 2 + 3 and x = 2 – 3

x = 5 and x = –1

{–1, 5}

which set of three numbers could be the side lengths of a triangle A.5,5,14 B.3,3,2 C.3,3,8 D. 5,5,10

Answers

Answer:

B. 3, 3, 2

Step-by-step explanation:

The triangle inequality requires the sum of the lengths of the two shortest sides exceed the length of the longest side. That is the case only for the lengths of selection B:

2 + 3 > 3

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