Answer:
7.7 km
Step-by-step explanation:
This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.
Law of SinesThe Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...
t/sin(T) = p/sin(P) = j/sin(J)
We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.
SetupWe know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:
7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j
SolutionThis can be solved in two steps. First, we find angle P, then we use that to find length j.
sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847
P = arcsin(0.642847) ≈ 40.0045°
Now, we can find j:
j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km
The distance from the tower to the plane is about 7.7 km.
__
Additional comment
We have used T, P, and J to refer to the vertices at the tower, plane, and jet.
The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.
а) 5хх
b) 6xxxy
c) 2 xxx3 ху
Answer:
a) 5x
b) 6xy
c) 6xy
hope this answer helps you....
add 7 to 9, then subtract p from the result
16-p
1) 7+9=16
2) It states that "then subtract p from the result" so that means 16-p which is the final answer because we cannot further substitute p without a known result
HURRY PLEASE HELPPPPP
The equivalent of the given Fahrenheit temperature in degree Celsius is 30 °C.
Calculating temperature in degree CelsiusFrom the question, we are to determine the given Fahrenheit temperature in degree Celsius
From the given information,
The given Fahrenheit temperature is 86 °F.
From the given formula
C = 5/9 (F - 32)
To use this formula to determine the equivalent of a Fahrenheit temperature in degree Celsius, we will substitute the Fahrenheit temperature into the formula and simplify.
C = 5/9 (F- 32)
Substitute F = 86
C = 5/9 (86 - 32)
C = 5/9 (54)
C = 5/9 × 54
C = 5 × 6
C = 30 °C
Hence,
The temperature is 30 °C.
Learn more on Calculating temperature here: https://brainly.com/question/26141817
#SPJ1
the information contained in a probability distribution has to be summarized into a single measure to be used to make decisions. what is this measure called?
Poisson distribution is the measure to summarize the information contained in a probability distribution in a single parameter.
Poisson distribution gives the probability of an event occurring a certain number of times (k) within a specified time period.
It is denoted by λ , which is the mean number of events.
To know more about Poisson distribution
https://brainly.com/question/7283210
#SPJ4
the ratio of their ages. Ram is 15 years old and Kalpana is 10 years old. How much do each of them receive
someone help me please
Answer:
3x + 5y = 15
Find gradient:
coordinates taken: (5, 0), (0, 3)
\(\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}\)
\(\rightarrow \sf \dfrac{3-0}{0-5}\)
\(\rightarrow \sf -\dfrac{3}{5}\)
Here the y-intercept: 3gradient: -3/5
equation:
\(\sf \bold{ y = m(x) + b}\)
\(\rightarrow \sf y = -\dfrac{3}{5} x + 3\)
\(\rightarrow \sf y = -\dfrac{3}{5} x + \dfrac{15}{5}\)
\(\rightarrow \sf 5y =-3x+15\)
\(\rightarrow \sf 3x+5y =15\)
Take two points
(0,3)(5,0)x intercept=a=5y intercept=b=3So
equation of line in intercept form
\(\\ \rm\rightarrowtail \dfrac{x}{a}+\dfrac{y}{b}=1\)
\(\\ \rm\rightarrowtail \dfrac{x}{5}+\dfrac{y}{3}=1\)
Multiply each by 15\(\\ \rm\rightarrowtail 3x+5y=15\)
Which set is of whole numbers but not natural numbers?
Step-by-step explanation:
The set of Natural numbers: {1, 2, 3, 4, 5, ...}
The set of Whole numbers: {0, 1, 2, 3, 4, 5, ...} ← it has the number 0
Help me please I need the help right now plss
The fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).
Ryan grew \($\frac{1}{2}$\) feet in a year.
1. To express the fraction \($\frac{9}{12}$\) as a sum of smaller fractions, we can simplify it by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of \(9\) and \(12\) is \(3\).
So, we can rewrite \($\frac{9}{12}$\) as:
\($\frac{9}{12} = \frac{3 \times 3}{3 \times 4} = \frac{3}{4}$\)
Therefore, the fraction \($\frac{9}{12}$\) can be expressed as the sum of the smaller fraction \($\frac{3}{4}$\).
2. To find how much Ryan grew in a year, we need to calculate the difference between his height this year and his height last year.
Let's convert the mixed fractions to improper fractions for easier computation:
Last year's height: \($4 \frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4}feet\)
This year's height: \($5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} feet\)
To determine the growth, we subtract last year's height from this year's height:
\($\frac{21}{4} - \frac{19}{4} = \frac{21 - 19}{4} = \frac{2}{4} = \frac{1}{2}feet\)
Therefore, Ryan grew \($\frac{1}{2}$\) feet in a year.
For more such questions on fraction: https://brainly.com/question/17220365
#SPJ11
PLEASE ANSWER ASAP!!!!!!!!!!!! I WILL GIVE BRAINLIEST!!!!!!!!
Which equation represents a proportional relationship that has a constant of proportionality equal to 5?
y= x - 1/5
y= x+ 1/5
y= 1/5x
y= 5x
Answer:
Y=5x
Step-by-step explanation:
The first the options aren’t even whole numbers
y=5x
that is the correct answer because the constant is 5 and as long as the constant is 5 the upcoming numbers after that will the a multiple of 5. I hope the helps!!
Factor expressions x^2+4x+4
Answer:
Your answer is:
(x+2)^2
Factor x2+4x+4
x2+4x+4
The middle number is 4 and the last number is 4.
Add together to get 4
Multiply together to get 4
2+2 = 4
2*2 = 4
(x+2)(x+2) or (x+2)^2
the sum of the first n even positive integers is (n2 n). that is, 2 4 6 8 .... 2n = n2 n
The sum of the first n even positive integers is n² + n.
We are given that the sum of the first n even positive integers is (n2 n). that is,
2 + 4 + 6 + 8 .... + 2n = n2 n.
This is known as an Arithmetic Progression (AP) of even numbers with common difference of 2, where a = 2 and d = 2.
To find the sum of an AP, the formula isSn = n/2[2a + (n - 1)d]
Where Sn is the sum of n terms, a is the first term and d is the common difference.
Substituting values in the formula, we get the sum of the first n even positive integers is;
Sn = n/2[2a + (n - 1)d]= n/2[2(2) + (n - 1)(2)]= n/2[4 + 2n - 2]= n/2[2n + 2]= n(n + 1)= n2 + n
Therefore, the sum of the first n even positive integers is n² + n.
Know more about integers here:
https://brainly.com/question/929808
#SPJ11
Consider the following system of equations.
Use this graph of the system to approximate its solution.
A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane.
Taking into account the graph, the following is the system of equations' approximative solution:
C. (-13/4, 5/2)
What exactly is an equation system?When two or more variables are related to one another and equations are constructed to determine each variable's value, the result is a system of equations.
The intersection of the curves on a graph provides the solution to a system of equations. As the two curves in this graph overlap near to x = -3.25 and y = 2.5, the answer can be roughly expressed as follows:
(-3.25, 2.5).
Now changing it into fractions we get:
(-13/4, 5/2)
Therefore, the solution of the equations is, (-13/4, 5/2).
To know more about equations, visit:
https://brainly.com/question/24342899
#SPJ1
a lunar month is about 28 days. if the moon were farther from earth than it is now, the lunar month would be
By the definition of lunar month, it can be inferred that-
If the moon were farther from earth than it is now, then lunar month will be more than 28 days.
What is lunar month?
Time taken by the moon to make one complete revolution around the earth is called lunar month.
If the moon were farther from earth than it is now, then the moon will have to travel a greater distance to make one complete revolution around the moon. So time taken by the moon to make one complete revolution around the earth will increase. So lunar month will be more than 28 days.
To learn more about lunar month, refer to the link-
https://brainly.com/question/27851732
#SPJ4
A graph shows the number of texts, numbered 10 to 100, on the x-axis, and the total cost in dollars, numbered 3 to 27, on the y-axis. A straight red line with a positive slope, labeled Emilia, begins at (0, 10), and a straight blue line with a positive slope, labeled Hiroto, begins at (0, 20). Both lines intersect at point (50, 22.5).
Hiroto’s texting plan costs $20 per month, plus $0.05 per text message that is sent or received. Emilia’s plan costs $10 per month and $0.25 per text. Using the graph below, which statement is true?
Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent.
Both plans cost the same when 22 texts are sent.
Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
Both plans cost the same when 50 texts are sent.
Both plans cost the same when 50 texts are sent
Step-by-step explanation:
Let
x ---->the number of texts
y ----> the total cost in dollars
we know that
The linear equation in slope intercept form is equal to
where
m is the slope or unit rate
b is the y-intercept or initial value
we have that
Emilia’s plan (Red line)
The slope is
The y-intercept is
substitute
----> equation A
Hiroto’s plan (Blue line)
The slope is
The y-intercept is
substitute
----> equation B
The solution of the system of equations A and B is the point of intersection both graphs
The intersection point is given
The intersection point is (50,22.5)
That means----> For x=50 texts, the cost is equal in both plans
Verify each statement
case a) Hiroto’s plan costs more than Emilia’s plan when more than 50 texts are sent
The statement is false
Because
Emilia’s plan costs more than Hiroto’s plan when more than 50 texts are sent
Verify
For x=100 texts ----> 100 > 50
Emilia's plans
Hiroto's plans
case b) Both plans cost the same when 22 texts are sent
The statement is false
Because
Both plans cost the same when 50 texts are sent
case c) Emilia’s plan costs more than Hiroto’s plan when more than 22 texts are sent.
The statement is false
Because
Emilia’s plan costs more than Hiroto’s plan when more than 50 texts are sent
case d) Both plans cost the same when 50 texts are sent
The statement is true
Answer:
Both plans cost the same when 50 texts are sent.
Step-by-step explanation: Took test edge 2020: D
22. Write the word sentence as an equation. The product of negative 2 and 5 plus a number d = 14.
also please solve and "product" means multiply.
Chef Grant went to the orchard and picked 8 bags of apples, then stopped at the store
and picked up some lemons, as well. The recipe calls for 9 apples each, which Grant
of computes to be 4 cups of apples, which is a quartus__ or 2 pints_ His recipe (8
also calls for ½ teaspoon_ of cinnamon and ginger each, and 2 tablespoons_
of flour and lemon juice each, as well. After serving the pies to the local business
council, he signs a contract to deliver pies daily. Now he buys the ingredients by the
kilogram _gallon_
and pound_
After answering the provided question, we can conclude that He would expression also need to convert the densities or weights of cinnamon, ginger, flour, and lemon juice.
what is expression ?In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators. Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.
In addition, the recipe calls for 12 teaspoons of cinnamon and ginger, as well as 2 tablespoons of flour and lemon juice.
He served the pies to the local business council and agreed to deliver pies on a daily basis.
1 kilogramme (kg) is equal to 2.20462 pounds (lbs)
1 gallon is equal to 128 fluid ounces (fl oz) or 3.78541 litres.
1 pound equals 16 ounces equals 0.453592 kilogrammes
Chef Grant would need to convert his recipe measurements if he is now purchasing ingredients by the kilogramme and gallon. For example, if he requires 2 pints (or 4 cups) of apples, that is equivalent to 1.89 litres or 1.01 kilogrammes. He would also need to convert the densities or weights of cinnamon, ginger, flour, and lemon juice.
To know more about expression visit :-
https://brainly.com/question/14083225
#SPJ1
Write the expression as a number in scientific notation.
quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
4.2 x 1010
3.4 x 1010
4.2 x 105
3.4 x 105
The expression as a number in scientific notation is 4.2 * 10^5
How to write the expression as a number in scientific notation?The expression is given as:
quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared
Rewrite properly as:
[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]
Evaluate the product of 7 and 5.4
So, we have:
[37.8* 10^3 * 10^4]/[9 * 10^2]
Evaluate the product of 10^3 and 10^4
So, we have:
[37.8* 10^7]/[9 * 10^2]
Evaluate the quotient of 37.8 and 9
So, we have:
[4.2 * 10^7]/[10^2]
Evaluate the quotient of 10^7 and 10^2
So, we have:
4.2 * 10^5
Hence, the expression as a number in scientific notation is 4.2 * 10^5
Read more about scientific notation at
https://brainly.com/question/5756316
#SPJ1
Write the mathematical model and use Solver to answer the following question:
A farm co-op has 6,000 acres available to plant with corn and soybeans. Each acre of corn requires 9 gallons of fertilizer/herbicide and 0.75 hour of labor to harvest. Each acre of soybeans requires 3 gallons of fertilizer/herbicide and 1hour of labor to harvest. The co-op has available at most 40,501 gallons of fertilizer/herbicide and at most 5,250 hours of labor for harvesting. Find the maximum profit if the profits per acre are $75 for corn and $40 for soybeans. Round your answer to the nearest cent if necessary.
a. $210,000.00
b. $393,750.00
c. $371,255.83
d. $180,004.44
e. $318,744.17
The maximum profit if the profits per acre are $75 for corn and $40 for soybeans is $371,255.83. Therefore, the correct option is c.
To find the maximum profit from planting corn and soybeans, we can use linear programming. Let's first define the variables and write the constraints.
Let x be the number of acres of corn and y be the number of acres of soybeans.
1. Total acre constraint: x + y ≤ 6,000
2. Fertilizer/herbicide constraint: 9x + 3y ≤ 40,501
3. Labor constraint: 0.75x + y ≤ 5,250
The objective function to maximize is the profit function: P(x,y) = 75x + 40y
Now, we will use the Solver to find the maximum profit:
Step 1: Set up a spreadsheet with the constraints and the objective function.
Step 2: Go to the Data tab and click on Solver. If Solver is not available, you may need to add it in Excel Options.
Step 3: Set the objective function by selecting the cell with the profit function.
Step 4: Choose "Max" for the objective.
Step 5: Add the constraints by selecting the corresponding cells.
Step 6: Click on "Solve" and the Solver will find the optimal values for x and y.
After using Solver, we find that the optimal values are x = 4,363.89 (corn) and y = 1,636.11 (soybeans), which yields a maximum profit of $371,255.83. Therefore, the correct answer is c: $371,255.83
Learn more about Linear programming:
https://brainly.com/question/14309521
#SPJ11
use green's theorem to find the counterclockwise circulation and outward flux for the field f=(7x−4y)i (9y−4x)j and curve c: the square bounded by x=0, x=4, y=0, y=4.
The counterclockwise circulation around c is 12 and the outward flux through c is zero.
Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.
In this case,
we have a field f=(7x−4y)i+(9y−4x)j and
a square curve c bounded by x=0, x=4, y=0, y=4.
To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.
The curl of f is given by (0,0,3), so the line integral evaluates to 12.
To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.
To learn more about : circulation
https://brainly.com/question/30619471
#SPJ11
1. In rectangle PQRS, PR = 20x - 16 and QS = x + 554. Find the value of x and the length of each diagonal.
Q
R
C. x = 30, PR = 584, QS = 584
А. x = 15, PR = 569, QS = 569
B. x = 30, PR = 292, OS = 292
Answers please help me
Answer:
Rita: r - 5= 2c, or r - 5= 2(36), or r - 5 = 72
Cora: (r - 5)/2 = 36
Step-by-step explanation:
Rita had r apps (let r = Rita original apps)She deleted 5 of them so r-5 She now has twice the number of apps as Cora so r-5 = 2c (let c = Cora's total apps) Cora's total apps are 36 so Rita's equation is r-5= 2(36) which means Rita equation for her number of apps is r-5= 72. As for Cora her equation is c= 36 but in relation to Rita's number of apps it's (r-5)/2 = 36Solve.
1. 5x + 11 ≤ - 4
2. 2x + 7 > 11
3. 5x - 4 ≥ 11
4. -5x + 12 ≤ -3
Answer:
thanks sa pnts pag palain ka sana
Two hikers are 33 miles apart and walking toward each other. They meet in 5 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other.
The rate of the slow hike is 2.2 mph and the rate of the faster hiker is 4.4 mph.
Here in this issue, we are managing linear equations which is a condition of one variable regularly composed within the form ax+b=0 , where a and b are real numbers and x is an unknown variable. Solutions to linear equations allude to a linear equation that can have zero, one, or infinitely various solutions. A linear equation with no solutions simplifies to an untrue statement such as 1=0. A linear equation with one solution rearranges to a solution of the form x=n where n may be a real number. A Linear equation with infinitely various solutions simplifies to a true statement without a variable such as 1=1.
Here we considering the rate of the slow hiker to be x, so the rate for the fast hiker will be x+2.2
Since we know that distance = speed * time
therefore, the Distance covered in 5 hours by a slow hiker is 5x , wheras for fast hiker it will be 5(x+2.2)=5x+11 km
As we are given the condition that it i they are 33 miles apart, So
=>5x + 5x+11 = 33
=>10x = 33-11
=>10x = 22
x =22/10 => 2.2
So the rate of a slow hiker is 2.2 mph and the rate of a fast hiker is x+4.4= 4.4 mph.
To know more about linear equations refer to the link brainly.com/question/11897796?referrer=searchResults.
#SPJ1
Question 1 of 10
Look at this table.
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1250
1400
1550
1700
1850
2000
2150
According to the table, how many hours of training would you
need to have a monthly pay of $2450?
Answer:
90 hours of training would you need to pay
Answer:
90hours
Step-by-step explanation:
Addition of 10 hours= Addition of 150$
an=a+(n-1)d
2450=1250+(n-1)(150)
120/15=n-1
8+1=n
n=9
and 9x10=90 (each n=10hours)
Thus:
B. 90 hours
Brianliest please
Pavi has a credit line of $8,000 on his credit card. Review the summary of his credit card statement. How much credit does Pavi currently have available on this card?
Summary Previous Balance Payments/Credits New Purchases Finance Charge New Balance
$2,500. 00 $1,500. 00 $3,000. 00 $7. 50 $4,007. 50
A.
$3,992. 50
B.
$5,000. 00
C.
$5,500. 00
D.
$6,500. 50
The correct option is option (a) $3,992.50. Pavi currently has a $3,992.50 credit on her current card.
The calculation of the provided data, according to the question, is as follows:
$8000 is the credit limit on the card.
Paid in Full = $2,500
$1,500 has been credited to the account.
The value of recent purchases made by Pavi is $3,000
Applied finance charges equal $7.50
The card's current balance is equal to $4,007.50.
Using the formula below, we can now determine the amount of credit that is now available on the card:
The credit line on the card = Available Credit - New Balance
By entering values into the formula provided, we obtain
Credit available on the current card: $8,000 - $4,007.50= $3,992.50.
Read more about Credit from:
https://brainly.com/question/29024957
#SPJ4
Solve for x
-5(2x+1)-2x-2=17
which equation represents the line closest to the curve of best fit ?
The equation that represents the line closest to the curve of best fit would be the equation of the line with the smallest sum of squared residuals.
In order to determine the equation that represents the line closest to the curve of best fit, we first need to find the equation of the curve of best fit. This can be done using regression analysis, such as linear regression or polynomial regression, depending on the shape of the data.
Once we have the equation of the curve of best fit, we can then find the equation of the line that is closest to this curve. This can be done by finding the line that has the smallest sum of squared residuals, which measures the distance between each data point and the line.
Therefore, the equation that represents the line closest to the curve of best fit would be the equation of the line with the smallest sum of squared residuals.
To determine the equation that represents the line closest to the curve of the best fit, you'll need to analyze the given data points and compare the residual errors for each candidate equation. The equation with the smallest sum of squared residuals is generally considered the best fit.
To know more about equation visit:
https://brainly.com/question/29657983
#SPJ11
STOP AND HELP PLZzzzzzzz
Answer:
k = 2
Step-by-step explanation:
9 = k(6) - 3
12 = 6k
k = 2
Answer:
k = 2
Step-by-step explanation:
We know that in the coordinates (6, 9) 6 is X and 9 is Y. So, we can just plug that into the equation in the problem to get 9 = 6k - 3. Then, after solving, we get the answer as k = 2.
Lana draws a triangle( LMN) on the coordinate plane. What is the perimeter of the triangle( LMN)? Round to the nearest unit.
Answer:
The answer is "25".
Step-by-step explanation:
Please find the graph in the attachment.
\(Longest \ side= 12\)
Calculating the triangle two other sides:
\(=\sqrt{3^2+6^2}\\\\=(9+36)\\\\=45\)
let
\(\to \sqrt{45}= 6.7.\\\\\to 6.7\times 2=13.4\\\\\to 13.4+12=25.4 \approx 25\)
alice drew two triangles on the cordinate plane as shown.
Answer:
nice...but theres nothing shown
Step-by-step explanation: