Answer:
The distance between the two jets is approximately 2.947 kilometers.
Step-by-step explanation:
From the statement we know the location of each jet in polar coordinates, which are defined by the following notation:
[tex]\vec r = (r, \theta)[/tex] (1)
Where:
[tex]r[/tex] - Distance of the jet from the origin, measured in kilometers.
[tex]\theta[/tex] - Angle of the jet with respect to the east direction, measured in sexagesimal degrees.
To transform polar coordinates into rectangular coordinates, we use the following expressions:
[tex]x = r\cdot \cos \theta[/tex] (2)
[tex]y = r\cdot \sin \theta[/tex] (3)
And lastly, we determine the distance between the two jets ([tex]d[/tex]), measured in kilometers, by the Pythagorean Theorem:
[tex]d = \sqrt{(r_{2}\cdot \cos \theta_{2}-r_{1}\cdot \cos \theta_{1})^{2}+(r_{2}\cdot \sin \theta_{2}-r_{1}\cdot \sin \theta_{1})^{2}}[/tex] (4)
If we know that [tex]r_{2} = 4\,km[/tex], [tex]\theta_{2} = 150^{\circ}[/tex], [tex]r_{1} = 2\,km[/tex] and [tex]\theta_{1} = 195^{\circ}[/tex], the distance between the two jets is:
[tex]d = \sqrt{[(4\,km)\cdot \cos 150^{\circ} -(2\,km)\cdot \cos 195^{\circ}]^{2}+[(4\,km)\cdot \sin 150^{\circ} -(2\,km)\cdot \sin 195^{\circ}]^{2}}[/tex]
[tex]d \approx 2.947\,km[/tex]
The distance between the two jets is approximately 2.947 kilometers.
several perople form groups with four people in each group. write an expression for the number of groups formed by p people. how many groups are formedif there are 28 people
Answer:
a) an expression for the number of groups formed by p people
number of groups formed = [tex]\frac{p}{4}[/tex]
b) How many groups are formed if there are 28 people
number of groups formed = [tex]\frac{p}{4}[/tex]
=28÷4
= 7
Answer: 7 groups
HOPE THIS WILL HELP :)
A back patio has 127ft^2127 f t 2 of area in Brad's yard. If his patio is perfectly square, what is the side length of the patio? Round your answer to the nearest hundredths place. Group of answer choices 11.27 feet 11.3 feet 11 feet 11.25 feet
Answer:
The length of side of patio is 11.27 feet.
Option A is correct option.
Step-by-step explanation:
Area of patio = 127 ft^2
We need to find side length of the patio.
Since the patio is square, the formula used is:
[tex]Area\: of\: square = l^2[/tex]
where l is the side length of square.
Now, putting value of area we can find area of square.
[tex]Area\: of\: square = l^2\\127=l^2\\Switching\:sides\:\\l^2=127\\Taking\:square\:root\:on\:both\:sides\\\sqrt{l^2}=\sqrt{127} \\l=11.27[/tex]
So, the length of side of patio is 11.27 feet.
Option A is correct option.
A baseball ticket costs $75, but they are having a
promotional game night and all tickets are 35% off. What is
the new price of the ticket?
Is 74.65 correct
Jamal is hanging some lights on his house. His ladder is 12 feet long and makes an 80˚ angle with the ground. How high up the wall of his house will his ladder reach? Round your answer to the nearest hundredths place. Just enter a numeric answer, no units needed.
The ladder will reach 11.82 ft high of the wall of his house.
The situation will form a right angle triangle. Therefore,
The length of the ladder is the hypotenuse of the triangle formed.
The height of the wall is the opposite side of the triangle.
Therefore,
using trigonometric ratio,
sin 80° = opposite / hypotenuse
sin 80° = h / 12
cross multiply
h = 12 sin 80°
h = 12 × 0.98480775301
h = 11.8176930361
height of the wall ≈ 11.82 ft
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Please answer am really failing my math and i need this answer asap
Answer:
[tex]9) \: y = - 1x - 6[/tex]
[tex]10) \: y = \frac{1}{6}x + 4[/tex]
In a winter storm, the amount of snowfall is directly proportional to the time
it has been snowing. After 4 hours, a total of 7 inches of snow has fallen. Determine how many inches of
snowfall have fallen after 6 hours. Show the work that leads to your answer.
Answer:
10.5 Inches of snow after 6 hours
Step-by-step explanation:
First you would divide
7/4=1.75
Then you would multiply by 6
1.75*6=10.5
10.5 inches of snow would be the total
Hope this helped! :D
The amount of snowfall in 6 hours, if the amount of snowfall is directly proportional to the time, is 10.5 inches.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
Given:
In a winter storm, the amount of snowfall is directly proportional to the time,
After 4 hours, a total of 7 inches of snow had fallen,
Calculate the amount of snowfall in one hour as shown below,
amount of snowfall in one hour = 7 / 4
Calculate the amount of snowfall that occurs in 6 hours,
Amount of snowfall in 6 hours = 7 / 4 × 6
Amount of snowfall in 6 hours = 10.5 inches
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Diego has two jobs. He works 3 hours at the library each day, making $8 per hour. In addition, he works at a coffee shop, making $7.50 per hour. At the coffee shop, he works more than 4 hours but less than 7 hours
each day Diego needs to make at least $70 daily to afford his living expenses.
Which of the following systems represents the constraints given in this scenario?
Let I represent the number of hours he works at the library
and c represent the number of hours he works at the coffee shop.
A: l = 3
4 < c < 7
8l + 7.50 ≥ 70
B: l = 3
4 ≤ c ≤ 7
8l + 7.50 ≥ 70
C: 1 = 3
4 ≤ c ≤ 7
7.50l + 8c ≤ 70
D: 1=3
4 < c < 7
7.50l + 8c ≥ 70
Answer:b
Step-by-step explanation:
Answer:B
Step-by-step explanation:
3x²-30x+9=0
PLEASE HELP
COMPLETING THE SQUARE WILL MARK BRAINLIEST
Answer:
i have done the cutting of x's exponent
Step-by-step explanation:
= 3x - 30+9 =0
= 3x - 21 =0
= 3x= 21
= x = 21/3
x= 7 this the answer
hey guys please help me solve this math question
Step-by-step explanation:
When x = -2, x + 2 = (-2) + 2 = 0.
Answer:
0........
Step-by-step explanation:
x= -2
-2+2= 0
| 5t-1 |=6
Show all work
Answer:
t = 1.4
Step-by-step explanation:
If you multiply 5 and 1.4 together, you get 7. Then, you do 7 - 1, and you get 6.
The inverse operation symbol things don't matter if the answer you get inside the two vertical bars is positive.
Answer: t=1
Step-by-step explanation:
|5t-1 |=6
5t+1=6
5t=5
t=1
is 3(5b - 2) and 8b - 5 equivalent
Answer:
No
Step-by-step explanation:
Answer:
I don't think so.
Step-by-step explanation:
3(5b - 2) would be equivalent to 15b - 6
Let v = (-13, 2) and w= (–9,-5). What is w-v?
(-22, -23)
(-4,7)
(4,-7)
(22, 3)
Answer:
C) (4,-7)
Step-by-step explanation:
The value of w-v is (4, -7).
What is Coordinates?Coordinates is an address, which helps to locate a point in two-dimensional space.
Here, given coordinates;
v ≡ (-13, 2) and w ≡ (-9, -5)
Now, we need to find;
w - v ≡ (-9-(-13), -5 - 2)
≡ (-9+13 , -7 )
≡ (4, -7)
Thus, the value of w-v is (4, -7).
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HELP ME PLEASE NOWWW PLEASE AND THANK YOU
Answer:
X= 12
Step-by-step explanation:
3:9 is the ratio
1:3 is equal therefore the multiplicative factor is 3
lastly you do 4 times 3 to get 12 as the value for x
PS fac k you moderators I got my answer correct and u delete them fac k you
Find value of P and Q
Answer:
[tex] P= 6 \frac{1}{7}\\\\
Q = 4 \frac{2}{7}[/tex]
Step-by-step Explanation
[tex] \frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } = P+Q\sqrt 2 \\ \\ \frac{(5 + 3 \sqrt{2}) }{(5 - 3 \sqrt{2}) } \times \frac{(5 + 3 \sqrt{2}) }{(5 + 3 \sqrt{2} )} = P+Q\sqrt 2 \\ \\ \frac{ {(5 + 3 \sqrt{2} )}^{2} }{ {(5)}^{2} - (3 \sqrt{2})^{2} } = P+Q\sqrt 2 \\ \\ \frac{ {5}^{2} + {(3 \sqrt{2} )^{2} + 2.5.3 \sqrt{2} } }{25 - 9 \times 2} = P+Q\sqrt 2 \\ \\\frac{ 25 + 18 + 30 \sqrt{2} }{25 - 18} = P+Q\sqrt 2 \\ \\\frac{ 43 + 30 \sqrt{2} }{7} = P+Q\sqrt 2 \\ \\ \frac{43}{7} + \frac{30 }{7} \sqrt{2} = P+Q\sqrt 2 \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ P = \frac{43}{7} \\ \\ \huge \red { \boxed{ P= 6 \frac{1}{7}}} \\ \\ Q = \frac{30}{7} \\ \\ \huge \orange { \boxed{ Q = 4 \frac{2}{7} }}[/tex]
Lin's job pays $8.25 an hour plus $10 of transportation allowance each week. She has to work at least 5 hours a week to keep the job, and can earn up to $175 per week (including the allowance). Represent this situation mathematically in two inequalities. Let `x` represent the number of hours Lin works in a week.
Answer:
10000
Step-by-step explanation:
A plane is flying at an elevation of 1000 feet, directly above a straight highway. Two cars on the highway are on different sides of the plane. The angle of depression to one car is 10 degrees and to the other car is 8 degrees. How far apart are the cars, to the nearest foot
Answer:
Step-by-step explanation:
Write a story problem in which you would have to multiply 5 × -1/3 to find the answer.
Answer:
It can be for example: if you had to find out the area of a square, and the base was 5 and the height -1/3. To find the answer you would have to multiply these 2 values
Step-by-step explanation:
Item 8 Starting at 1:00 p.M., the temperature changes −4 degrees Fahrenheit per hour. Write and solve an equation to find how many hours x it will take to reach −1°F. An equation is ? =−1. It will take hours to reach −1°F.
Answer:
The answer is "9".
Step-by-step explanation:
Given equation:
[tex]\to 35-4x=-1 \\\\\to 35+1 = 4x\\\\\to 36=4x\\\\\to 4x= 36\\\\\to x=\frac{36}{4}\\\\\to x=9[/tex]
I NEED HELP ASAP, ILL MARK BRAINLIEST!!!
Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:
y < 2x − 7
y is greater than or equal to negative 1 over 2 times x plus 3
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (3, −7) included in the solution area for the system? Justify your answer mathematically. (4 points)
(10 points)
Answer:
A: The line is a dotted line and the shaded part is on the right side of the line
B: Yes it is correct because if u put in the x value and the y value and calculate it the statement is true.
A couch costs $350 to make. Before it is sold, it is marked up in price 80% more. How much will the couch cost?
Answer:$630
Step-by-step explanation:
What is 80% of 350?
Y is 80% of 350
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 80% * 350
Converting percent to decimal:
p = 80%/100 = 0.8
Y = 0.8 * 350
Y = 280
then u add 280 to 350
Which polynomial identity will prove that 49 − 4 = 45?
which is a mathematical property shown here
8(x+7)
1 commutative property
2 distributive property
3 identity of addition
If someone could please answer this for me it’s 9th grade math 12 points:) asap pleaseee
Does anybody know the average individual score for a Mathcounts competition?
Answer:
4.0 hope this helps!!6
Last one lol see picture.. will mark brainliest!!
Answer:
the second one
Step-by-step explanation:
Find the measure of each acute angle.
(3x + 2)∘ = and x∘ =
Answer:
The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.
Step-by-step explanation:
The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.
Then one angle is marked as a right angle meaning it has a measure of 90 degrees.
Using this information and the labels on the diagram we can set up an equation:
x+3x+2+90=180
Now we can solve for x.
4x+92=180
4x=88
x=22 degrees
The measure of one of the acute angles is 22 degrees.
Now to solve for the measure of the other acute angle.
Subsitute the value of x first.
x=22
(3x+2)=?
3*22+2=68 degrees
The measure of the other acute angle is 68 degrees.
In the right-angled triangle given, the measure of each of the acute angles in the given diagram are:
[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]
The triangle given is a right triangle having an angle tat is 90 degrees and two other acute angles given as: x and (3x + 2)
Thus:
[tex]x + (3x + 2) + 90 = 180^{\circ}[/tex] (sum of triangle)
Solve for the value of x[tex]x + 3x + 2 + 90 = 180[/tex]
Add like terms[tex]4x + 92 = 180\\\\[/tex]
Subtract 92 from each side[tex]4x = 180 - 92\\\\4x =88[/tex]
Divide both sides by 4x = 22
Measure of one of the acute angles is 22 degrees.
To find the second acute angle measure, substitute the value of x
3x + 2 = 3(22) + 2 = 68 degrees
Therefore, in the right-angled triangle given, the measure of each of the acute angles in the given diagram are:
[tex]\mathbf{22^{\circ}}\\\\\mathbf{68^{\circ}}[/tex]
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Find the measures of the angles of a triangle in which one angle is 70°& the other two are in the ratio 3:8.
Answer:
30° ; 80°
Step-by-step explanation:
Given that :
One angle of a certain triangle = 70°
The other two angles are in the ratio 3 : 8
Recall :
Sum of angles in a triangle = 180°
Number of angles in a triangle = 3
Hence,
Sum of the other two angles + 70 = 180
Hence, sum of the other two angles = (180 - 70)°
Sum of other two angles = 110°
The angle is in the ratio 3:8
Hence,
(3 / (3 +8)) * 110
= 3/11 * 110
= 330 / 11
= 30°
(8 / (3 +8)) * 110
= 8/11 * 110
= 880 / 11
= 80°
Hence ; 30° ; 80°
Use the table to answer the question. X y -21-1 -1 -1 1 0 3 1 5 2 7 Which equation represents the relationship between x and y shown in the table? 1 O A. y = fx- -1 O B. y = x+3 Oc. C. y=2x-1 D. y = 2x + 3
Answer:
D. y = 2x + 3
Step-by-step explanation:
Use the table to answer the question.
x:-2 -1 0 1 2
y: -1 1 3 5 7
Which equation represents the relationship between x and y shown in the table.
Solution:
The table shows a linear relationship between x and y.
A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.
The table (x, y) has the points (-2, -1) and (0, 3). The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-(-1)= \frac{3-(-1)}{0-(-2)} (x-(-2))\\\\y+1=2(x+2)\\\\y+1=2x+4\\\\y=2x+3[/tex]
Two men are decorating a room. One has painted 20 m² and the
other only 6 m². They continue painting and manage to paint
another x m'each. If the first man has painted exactly three times
the area painted by the second man, find the value of x.
Answer:
1 m²Step-by-step explanation:
The first man painted:
x + 20The second man painted:
x + 6If the first man painted 3 times more, then:
x + 20 = 3(x + 6)x + 20 = 3x + 183x - x = 20 - 182x = 2x = 1Solve each equation.
X – 10 = 4
Math
Answer:
x=14
Step-by-step explanation:
Solving the equation x - 10 = 4, the value of x, which is the solution is calculated as x = 14.
How to Solve an Equation?Solving an equation simply involves determining the value of the variable in the equation, which is the unknown.
For example, we are asked to solve the equation, x - 10 = 4., what it simply means is that we need to determine what the value of x is in the equation that will make it true. Do the following:
x - 10 = 4
x - 10 + 10 = 4+ 10 [addition property of equality]
x = 14
Therefore, the solution of the equation is x = 14.
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