x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.
What is the solution to the given system of equation?Given the system of equation in the question;
y = 3x - 10 y = -2x - 15Is (-1,-13) the correct ordered pair?To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10 and solve for x.
y = -2x - 15
3x - 10 = -2x - 15
Add 10 to both sides
3x - 10 + 10 = -2x - 15 + 10
3x = -2x - 15 + 10
Add 2x to both sides
3x + 2x = -2x + 2x - 15 + 10
3x + 2x = - 15 + 10
Add like terms
5x = -5
x = -5/5
x = -1
Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.
y = 3x - 10
y = 3( -1 ) - 10
y = -3 - 10
y = -13
Therefore, the solution to the system of equation is (-1,-13).
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a percentage distribution is given below for the size of families in one u.s. city. size percentage 2 42.8 3 21.1 4 19.2 5 11.6 6 3.3 7 2.0 a family is selected at random. find the probability that the size of the family is 4 or more. round your result to three decimal places.
The probability that the size of the family is 4 or more rounded to three decimal places is 0.361.
Given that families are selected at random, to find the probability that the size of family 4 we need to select and add those probabilities whose family size is more than and equal to 4.
P(X ≥ 4) = P(4) + P(5) + P(6) + P(7)
P(X ≥ 4) = 19.2 + 11.6 + 3.3 + 2.0
P(X ≥ 4) = 36.1
Since we need the answer rounded off to three decimal places, we can divide the answer by 100 which will give the final answer which is 0.361.
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Please help me when this question it would mean a lot I’m alll most out of time
The motel revenue based on the number of rooms rented and group rental are as follows;
(a) The price for renting three rooms is $195
(b) The formula through which the unit rate of a room is found is aₙ = 71 - 3·(n -1)
(c) The function for the revenue, R(n) = 74·n - 3·n²
(d) The most amount that can be made is $456
The number of rooms that gives the most amount is 12 rooms
What is a revenue in business?A revenue is the total amount received for the sale of goods and services
The number of rooms in the motel = 44
The price for renting one room = $71
The price for renting two rooms = $68
The per room group rate = $71 - $3 for each additional room
(a) The amount made if a family rents three rooms is given as follows;
The unit price for two rooms = $71 - $3 = $68
The unit price for three rooms = $68 - $3 = $65
The price for the three rooms is therefore;
$65 × 3 = $195
(b) The formula that gives the rate charged for each room to an organization is an arithmetic progression, which can be expressed as follows;
aₙ = a₁ + (n - 1)·d
Where;
n = The number of rooms the organization plans to rent
a₁ = The first term of the arithmetic progression = 71
d = The common difference = -3
Which gives;
aₙ = 71 - 3·(n - 1)
The price for each room when an organization rents n rooms is therefore;
aₙ = 71 - 3·(n - 1)
(c) The revenue for renting n room is given by the formula;
Revenue, R(n) = Unit rate × Number of rooms
∴ R(n) = (71 - 3·(n - 1)) × n = 74·n - 3·n²
(d) The -ve coefficient of n² in the formula with which the revenue can be found indicates that the function has a maximum value. The number of rooms that gives the most revenue is obtained at the from the derivative of the R(n) as follows;
R'(n) = 74 - 6·n = 0
n = 74/6 ≈ 12
Which gives;
[tex]R_{max}[/tex] = R(12) = 74 × 12 - 3 × 12² = 456
The maximum revenue from renting to a single group ≈ $456
The number of rooms to rent that gives the maximum revenue is n ≈ 12
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The Coast Guard cutter Angelica travels at 30 knots from its home port of Corpus Christi on a course of 95 degrees for 2 hrs and then changes to a course of 185 degrees for 2 hrs. Find the distance and the bearing from the Corpus Christi port to the boat.
The distance and bearing of the boat from the port areas follows;
The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.
What is a bearing in mathematics?A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.
The speed at which the Coast Guard cutter travels = 30 knots
Bearing of the Coast Guard cutter Angelica = 95°
The time the coast guard travels in the initial direction = 2 hours
The direction the Coast Guard cutter changes to = 185°
Time of traveling in the new direction = 2 hours
30 knots = 55.56 km/hr
The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km
The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km
From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle
The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15
The distance f the boat from the port is approximately 157.15 kilometers
The base angles of an isosceles right triangle are 45°
Therefore, the bearing is 95° + 45° = 150°
The bearing from the port to the boat is 150°
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A triangle has sided with lengths of 20 miles, 25 miles, and 30 miles. Is it a right triangle ?
Answer:
No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
For a Triangle to be a Right-Angled Triangle, should follow the Pythagoras Theorem which states that
If a is the larger side and b , c are the lengths of the other two sides
Then [tex]a^{2} =b^{2} +c^{2}[/tex]
Here a=30 , Then [tex]a^{2}=30^{2} =900[/tex]
and b=20 , c=25 , Then [tex]b^{2} +c^{2} =20^{2} +25^{2} =1025[/tex]
Since [tex]a^{2} \neq b^{2} +c^{2}[/tex]
Then the Triangle is not Right Triangle
The normal price of a train ticket from Ashford to London is £34.20
Ross gets 1/3
off the price of his train ticket
Work out how much Ross pays for his ticket.
guys please help lol
Answer:
£22.80
Step-by-step explanation:
To work out how much Ross has to pay for his ticket, you first need to calculate how much the 1/3 of the full price is.
To do this, you divide the 34.20 by 3.
34.2 / 3 = 11.4
So Ross gets a discount of £11.40
To work out the price, that Ross has to pay, we substract the discount from the normal price:
34.2 - 11.4 = 22.8
So Ross pays £22.80 for his ticket.
the area of a circle is increasing at a constant rate of 178 square feet per second. at the instant when the radius of the circle is 44 feet, what is the rate of change of the radius? round your answer to three decimal places.
The rate of change of radius of the circle when the radius of the circle is 44 feet is 0.64 ft/s.
The area of the circle with radius R us given by,
A = πR²
It is given that the area is increasing at a constant rate of 178 square feet per second.
dA/dt = 178 ft²/s
Also, A = πR²
Differentiating A with respect to time,
dA/dt = 2πR.dR/dt
The rate of change of the radius is asked when the radius is 44 feet.
So, putting R = 44 ft.
dA/dt = 2π(44)dR/dt
178 = 2π(44)dR/dt
dR/dt = 0.64 ft/s
So, the rate of change of radius is 0.64 ft/s.
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What is the side length of the smaller square in the diagram?
The side length of the smaller square is 3 cm.
Given that:-
Length of the larger square = [tex]3\sqrt{2}[/tex] cm.
We have to find the length of the smaller square.
As the length of the larger square is equal to the diameter of the circle
Hence,
Diameter of the circle = [tex]3\sqrt{2}[/tex] cm
Now,
The diameter of the circle is equal to the diagonal of the square.
Hence, diagonal of the square = [tex]3\sqrt{2}[/tex] cm
Let the length of the square be x cm.
Hence, by pythagoras theorem, we can write,
[tex]x^2+x^2=(3\sqrt{2} )^2\\x^2+x^2=18\\2x^2=18\\x^2=9\\[/tex]
x = 3 cm
Hence, the length of the smaller square is 3 cm.
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5. Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your
reasoning.
Answer:
Andre is taller than Diego
Step-by-step explanation:
There are 100 cm in a meter. If we use this information and convert Diego's height to meters, we find that Diego is 1.65 m. This is a smaller number, and therefore, Diego is shorter than Andre.
Rafael has saved up $650 to buy a new laptop. The laptop he wants is in stores for $749.99 but is on sale for 25% off. After the discount is removed, a tax rate of 5.75% is added on. After Rafael buys the laptop, how much money will he have left over? Remember to round to the nearest hundredth as you go because this is money.
uhmm,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Can anyone write the equation of the graph?
The absolute value function graphed in this problem is given by the rule presented as follows:
y = |x - 3| + 5.
How to obtain the graph of an absolute value function?The first step to obtain the graph of an absolute value function is obtaining the vertex of the function, which is the turning point of the curve in the format of V.
Then, the definition of an absolute value function with vertex (h,k) is defined by the equation presented as follows:
y = |x - h| + k.
For the graphed function, the coordinates of the vertex are given as follows:
(3,5).
The reason for these coordinates are as follows:
h = 3 as the turning point of the graph is at a coordinate of x = 3.k = 5 as the turning point of the graph is at a coordinate of y = 5.Considering the coordinates of the vertex obtained previously on the problem, the absolute value equation graphed is defined by:
y = |x - 3| + 5.
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giving Brainly show work
Answer:
Step-by-step explanation:
5 1/2 +2x = 25
25- 5 1/2 = 2x
19 1/2 = 2x
x = 9.75
It took him about 9.75 weeks to lose at least 25 pounds.
Answer:
10 or more weeks------------------
Weight lossFirst week - lost 5 and 1/2 pounds,Following weeks - lost 2 pounds per week,Total - at least 25 pounds.Set inequality and find the least whole number2w + 5.5 ≥ 252w ≥ 25 - 2.52w ≥ 19.5w ≥ 19.5/2w ≥ 9.75 ≈ 10It took Mr. Henry at least 10 weeks to lose 25 pounds.
Elon is paid by the hour. He earned $50 for a 4 hour workday. How much
does he earn in one hour?
Answer:
$12.50 per hour
Step-by-step explanation:
Elon is paid by the hour. He earned $50 for a 4 hour workday. How much does he earn in one hour?
50 / 4 = $12.50 per hour
the probability of serena serving an ace n tennis is 0.15, and the probability that she double faults is 0.25. what is the probability that serena does not serve an ace or a double fault?
The probability that Serena does not serve an ace or a double fault is 0.63..
Addition rule of probability applies to the calculation of probability for one or another event happen. These events are either mutually exclusive or not .
We have following information,
The probability of Serena serving an ace in tennis (p) = 0.15
Probability that she double faults(q) = 0.25
The probability of Serena not serving an ace in tennis = 1 -p = 1 - 0.15 = 0.85
let A and B be two events Serena not serving an ace and she double faults respectively.
Events A and B are not mutually exclusive events .
i.e, P(A ∩ B ) =/ 0
when Serna not serving an ace implies that either it is double faults or not and both have equally likely chance.
So, the probability of intersection of event A and B = 0.85/2 = 0.47
Adding Rule for probabilities is
P(A or B ) = P(A) + P(B) - P(A ∩ B)
The probability that Serena does not serve an ace or a double fault = 0.85 + 0.25 - 0.47
= 1.10 - 0.47 = 0.63...
Hence, the probability that Serena does not serve an ace or double fault is 0.63..
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Find the values of x and y.
Question content area bottom
Part 1
x
41 (Do not include the degree symbol in your answer.)
Part 2
y
enter your response here (Do not include the degree symbol in your answer.)
Step-by-step explanation:
when a line intersects parallel lines, then the intersecting angles must be the same for each of the parallel lines.
so,
y = 139
and the angles y and x are supplementary (or a linear pair). that means together they have 180°.
that is simply because the sum of all angles around a single point on one side of a line must be 180° (because the line is like the diameter of a circle with the "rotation point" being the center, and one side of the line represents the half-circle).
therefore,
y + x = 180
139 + x = 180
x = 41
What transformation occurs from the graph y = x² to the graph of y = (x − 5)² + 7?
A a vertical shift up 5 units and a horizontal shift right 7.
B a vertical shift down 5 units and a horizontal shift right 7
C a vertical shift up 7 units and a horizontal shift left 5
D a vertical shift up 7 units and a horizontal shift right 5
The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
What do we mean by the graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.So, the transformation from:
y = x² to y = (x - 5)First, plot both graphs.
(Refer to the graph attached below)
Now, notice that the graph of the function y = (x - 5)² + 7 has shifted vertically upwards by 7 units and horizontally right by 5 units.Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.
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Consider the equation 2x^(2)+2y^(2)+2x-2y-7-0 Write the equation in the standard form of a circle? What is the center and the radius
8. 5. 3
Question Help
Gregg manages a small cleaning business. He has 16 employees. The cleaners get paid $13 per hour. The cleaning supervisors get paid $18 per hour. His budget has
set aside a payroll expense of $233 per hour if all of his employees are working. How many cleaners and how many supervisors does he employ?
supervisors.
Gregg employed cleaners and
(Simplify your answers. )
Gregg manages a small cleaning business. He has 16 employees. The cleaners get $13/hour. The cleaning supervisors get paid $18/hour. then Gregg employed 11 cleaners and 5 cleaning supervisors.
Set up a system of equations where c is the number of cleaners and s is the number of cleaning supervisors:
c + s = 16
13c + 18s = 233
Solve by substitution by solving for c in the first equation:
c + s = 16
c = 16 - s
Then, plug in 18 - s as c into the second equation:
13c + 18s = 233
13(16 - s) + 18s = 233
Solve for s:
208 - 13s + 18s = 233
208 + 5s = 233
5s = 25
s = 5
Then, plug in 5 as s into the first equation:
c + s = 16
c + 5 = 16
c = 11
So, Gregg employed 11 cleaners and 5 cleaning supervisors.
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(sec(t)-cos(t))/sin(t)
The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)
How to simplify trigonometric ratios?There are different trigonometric ratios such as;
sin x
tan x
cos x
sec x
cosec x
cot x
Now, we want to simplify the trigonometric expression;
(sec(t) - cos(t))/sin(t)
We know that;
sec (t) can be written as 1/cos t
Thus;
(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t
= (1/(sint cos t) - cos t/ sin t
= (1 - cos²t)/(sin t cos t)
= sin²t/(sin t cos t)
= sin t/cos t
= tan t
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jacob has a jar of nickels and dimes. he has twice as many nickels as dimes. he has 310. how many of each type of coin does he have
No. of coins in jar of nickels is 207 and of dimes is 103.
Let the no. of coins of dimes = x
No. of coins of nickels = 2x
Total = 310
x + 2x = 310
3x = 310
x = 310/3
= 103.33
≈ 103
No. of coins of dimes = 103
No. of coins of nickels = 310 - 103
= 207
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in right angles , side of all angles. how am I supposed to know what is adjacent to angle I'm trying to find and what is opposite from it.
I know the hypotenuse because it is the biggest one
Help me please i really dont understand this question
The measure of θ from the given trigonometric equation is 31°.
Given that, sin47°=cosθ and sinθ=cos(θ+16).
What are complementary angles of trigonometric ratio?We know from geometry if the sum of two angles is 90°, then one angle is called the complement of the other.
The complementary angles are:
sinθ=cos(90-θ)
secθ=cosec(90-θ)
tanθ=cot(90-θ)
A) So, sin47°=cos(90°-47°)
⇒ sin47°=cos43°
Thus, θ=43°
B) sinθ=cos(θ+16)
⇒ sinθ=cos(43+16)
⇒ sinθ=cos 59°
⇒ sin(90-31)=cos 59°
Thus, θ=31°
Therefore, the measure of θ from the given trigonometric equation is 31°.
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3 quarts of blueberries for every 4 quarts of strawberries how many quarts of strawberries do they need for 9 quarts of blueberries?
on a particular stretch of highway, the state police know that the average speed is 62 mph with a standard deviation of 5 mph. on a busy holiday weekend, the police are concerned that people travel too fast. so they randomly monitor speeds of a sample of 50 cars and record an average speed of 66 mph. let's assume, for the moment, that people travel at the same speed on holiday weekends as they typically do on other days. calculate the mean and standard deviation of the sampling distribution of sample means for samples of size n
The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.
What is a standard deviation?
Data dispersion in regard to the mean is quantified by a standard deviation. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Here, we have
µ = 62 , σ = 5
P ( X < 66 )
By applying the standard deviation formula, we get
Z = ( X - µ ) / (σ/√(n)
Z = ( 66 - 62 ) / ( 5 / √50 )
Z = 5.6569
P ( ( X - µ ) / ( σ/√(n)) < ( 66 - 62 ) / ( 5 / √(50) )
P ( X < 66 ) = P ( Z < 5.66 )
P ( X < 66 ) = 1
P ( X > 66 ) = 1 - P ( X < 66 )
By applying the standard deviation formula, we get
Z = ( X - µ ) / ( σ / √(n))
Z = ( 66 - 62 ) / ( 5 / √ ( 50 ) )
Z = 5.6569
P ( ( X - µ ) / ( σ / √ (n)) > ( 66 - 62 ) / ( 5 / √(50) )
P ( Z > 5.66 )
P ( X > 66 ) = 1 - P ( Z < 5.66 )
P ( X> 66 ) = 1 - 1
P ( X> 66 ) = 0
Hence, the probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.
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solve the system by substitution
Answer:
Step-by-step explanation:
since x=y, you can either substitute for x or for y,
lets do x
-3x - x = 4
-4x=4
x=-1
Now we can just plug in
-3(-1) - y = 4
3-y = 4
y=-1
Can someone do this please I need help
Answer:
all are 0
thats why you should do y+4=4-7=×-7=×+4=0
Answer:
for #2 do b
Step-by-step explanation:
Your friend Alex has won a scholarship to
study abroad. (Congratulations!) Alex has
only 8 weeks to earn enough money to buy a
plane ticket, and he wants to work at an
amusement park over the summer to achieve
this goal.
Tech intership
Schedule- Part Time (20hours/week)
Wage-11.50/hour
Amusement park attendant
Schedule- full time (40hours/week)
Wage - 9/hour+ 100 bonus
8 weeks to buy airplane ticket $2200
Please help with the table
In tech internship
Slope of the line m is $11.50, y intercept is 0 and the point slope form is y = 11.50x + 0
In Amusement park attendant
The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100
In tech internship
Schedule = part time (20 hours/week)
The wage = $11.50/hour
The slope intercept form
y = 11.50x
Slope of the line m = $11.50
y intercept = 0
y = 11.50x + 0
In Amusement park attendant
Schedule- full time (40hours/week)
Wage - 9/hour+ 100 bonus
The slope of the line = $9
y intercept = 100
The equation is
y = 9x + 100
Hence,
In tech internship
Slope of the line m is $11.50, y intercept is 0 and the point slope form is y = 11.50x + 0
In Amusement park attendant
The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100
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let k and n be non-negative integers and n be the maximum of the two. what is a k-permutation of n distinct objects? g
If k and n are non-negative integers and n is the greater of the two, then the ordered list of k of the n things without repetition is the k-permutation of the n separate objects.
The total number of ways to select k objects from a set of n elements is n(n1), with (nk+1) alternatives being available for the kth place.when ordering matters and repetition is not permitted. A k-permutation of the elements in set A is any of the chosen lists in the previous configuration (choose k elements, in any order, with no repetition). Pnk=0 if k is greater than n. This makes sense because it is impossible to select k unique elements from an n-element collection if k>n.
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you need to construct a fence around an area of 1600ft2 . what are the dimensions of the rectangular pen to minimize the amount of material needed?
The dimensions of the rectangular pen to minimize the amount of material needed is 4L which gives 160ft.
What is the meaning of minimum dimension?The minimum length or breadth of the open space type, as measured along the longest two (2) straight lines meeting at a right angle to define the lot's maximum length and width.
With regard to the above problem,
let us say L is the lenght of the rectangle and W is the width
Based on the formula for the area of a rectangle,
L x W = 1600ft
To minimize the perimeter, of the rectangle, we must assume that:
L = W
that is L² = 1600
If we applied square root to both sides of the equation, we'd have
L = 40
Thus the minimum perimeter is given as: 4L = 4 x 40 = 160ft.
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What is an equation of the line that passes through the point (2,-2)and is perpendicular to the line 5x-2y=4
Answer:
y=-0.4x - 1.2
A triangle has sides with lengths of 10 yards, 12 yards, and 14 yards. Is it a right triangle?
yes or no?
Answer:
No
Step-by-step explanation:
The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].
The square of the length of the largest side is [tex]14^2=196[/tex].
Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.