Answer:
f(g(-2)) = -3
Step-by-step explanation:
g(-2) = -2 - 3 = -5
f(-5) = 2(-5) + 7 = -10 + 7 = -3
Leslie has 24 coins. They are all nickels and dimes. The total value of the coins is $1.85. How many dimes does Leslie have? Which of the following systems is correct for
this situation?
The number of dimes is 13.
The system of equation for the situation is as follows;
x + y = 24
0.1x + 0.05y = 1.85
How to solve system of equation?The coins are 24.
Therefore, they are all dimes and nickel.
Total value of the coins is $1.85.
Hence, let
x = number of dimes
y = number of nickels
Therefore,
x + y = 24
0.1x + 0.05y = 1.85
0.1x + 0.1y = 2.4
0.1x + 0.05y = 1.85
0.05y = 0.55
y = 0.55 / 0.05
y = 11
x = 24 - 11
x = 13
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Evaluate the function g (x)=6x^(2) at x=2. (need answer within 10 min)
Answer:
24
Step-by-step explanation:
If x were to be 2, then we need to substitute the 2 in for x
So, it would be 6(2)^2
2 times 2 is 4 and 4 times 6 is 24
Hope this helped! :)
Joe used random numbers to select boys from the alphabetized
version of the list shown to make a sample. The random numbers
were 17, 5, 1, and 12, so he selected the 17th, 5th, 1st, and 12th
names. Who was selected?
Alan, Craig, Dale, Eddie, Eugene, Glenn, Herbert, Howard, Jeremy,
Loren, Louis, Martin, Nathan, Randy, Ray, Russell, Sam, Steve, Victor,
Vincent
OA) Glenn, Howard, Nathan, Steve
OB) Craig, Eugene, Loren, Vincent
OC) Jeremy, Martin, Steve, Victor
OD) Alan, Eugene, Martin, Sam
Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.
Who was selected?The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.
The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.
In conclusion, option D is correct.
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Who can help me to solve these questions please?
a) calculate the length of QR
b) calculate the area of trapezium PQRS.
Thanks for helping.
Using the given information, length of QR = 16.6 cm
The area of the trapezium is 304.5 cm²
Calculating area of a trapeziumFrom the question we are to calculate the length of QR and the area of trapezium PQRS
In the given diagram,
Let the midpoint of PS be T
Then, we can write that
|OP|² = |OT|² + |PT|² (Pythagorean theorem)
|OP| = radius = 13 cm
|PT| = 1/2 × PS = 1/2 × 24 cm = 12 cm
∴ 13² = |OT|² + 12²
169 = |OT|² + 144
|OT|² = 169 -144
|OT|² = 25
|OT| = √25
|OT| = 5 cm
Also, let the midpoint of QR be U
Then, we can write that
|OQ|² = |OU|² + |QU|² (Pythagorean theorem)
|OQ| = radius = 13 cm
From the given information,
The distance of QR from O is twice the distance of PS from O
∴ |OU| = 2 × |OT|= 2 × 5 cm = 10cm
Thus,
13² = ||² + 12²
169 = 10² + |QU|²
|QU|² = 169 -100
|QU|² = 69
|QU| = √69
|QU| = 8.3 cm
Now,
Length of QR = 2 × |QU| = 2 × 8.3 cm
Length of QR = 16.6 cm
b)
Area of the trapezium = 1/2(|QR| + |PS|) × |TU|
Area of the trapezium = 1/2(16.6 + 24) × 15
NOTE: |TU| = |OT| + |OU|
Area of the trapezium = 1/2(40.6) × 15
Area of the trapezium = 20.3 × 15
Area of the trapezium = 304.5 cm²
Hence, the area of the trapezium is 304.5 cm²
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What is the effect of multiplying the parent function f(x) = x ^ 2 by a positive constant?
Effect of multiplying the parent function f(x) = x ^ 2 by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
What happens when we multiply a parent function with a positive constant?A parent function in mathematics is the simplest function in a family of functions that preserves the concept of the entire family.When we multiply a function by a positive constant, we get a function with a graph that is stretched or compressed vertically in comparison to the original function's graph. If the constant is larger than one, we get a vertical stretch; otherwise, we get a vertical compression.Therefore, the effect of multiplying the parent function f(x) = x ^ 2 by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
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Sketch the region that is common to the graphs of x ≥ 2,
y ≥ 0, and x + y ≤ 6, and find its area.
a. Find the graph of their common region in the attachment
b. The area of the common region of the graphs is 8 units²
a. How to sketch the region common to the graphs?Since we have x ≥ 2, y ≥ 0, and x + y ≤ 6, we plot each graph separately and find their region of intersection.
The graph of x ≥ 2 is the region right of the line x = 2.The graph of y ≥ 0 is the region above the line y = 0 or x-axis.To plot the graph of x + y ≤ 6, we first plot the graph of x + y = 6 ⇒ y = -x + 6. Then the graph of x + y ≤ 6 is the graph of y ≤ - x + 6.So, the graph of x + y ≤ 6 is the region below the line y = - x + 6
From the graph, the regions intersect at (2, 0), (2, 4) and (6, 0)
Find the graph of their common region in the attachment
b. The area of the common regionFrom the graph, we see that the common region is a right angled triangle with
height = 4 units and base = 4 unitsSo, its area = 1/2 × height × base
= 1/2 × 4 units × 4 units
= 1/2 × 16 units²
= 8 units²
So, the area of the common region of the graphs is 8 units²
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On the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What probability distribution can be used to find the probability that there will be no customers arriving at a checkout counter in the next minute
The probability that there will be no customers arriving at a checkout counter in the next minute is 0.16530.
The number of customers arriving per minute at the checkout counter of a grocery store is following Poisson Distribution.
A Poisson Distribution over a variable X, having a mean λ, has a probability for a random variable x as [tex]P(X = x) = e^{-\lambda} \frac{\lambda^{x}}{x!}[/tex] .
In the question, we are asked to find the probability that no customer arrives at the checkout, hence we put x = 0, and the mean number of customers per minute (λ) = 1.8.
Substituting the values of x and λ in the equation, we get:
[tex]P(X = 0) = e^{-1.8} \frac{1.8^{0}}{0!}[/tex] ,
or, [tex]P(0) = e^{-1.8} = 0.16530[/tex] .
Therefore, the probability that there will be no customers arriving at a checkout counter in the next minute is 0.16530.
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Identify the type of function represented by f(x)=1/2(3)^x
A. increasing linear
B. exponential decay
C. decreasing linear
D. exponential growth
The function represented by f(x) = (1/2)(3)ˣ is an exponential growth
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
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The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
If b > 1, it is an exponential growth but if b < 1, it is an exponential decay.
Given the function:
f(x) = (1/2)(3)ˣ
since 3 > 1, it is an exponential growth.
The function represented by f(x) = (1/2)(3)ˣ is an exponential growth
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I am drinking beer and you are drinking light beer. Your light beer is 1/3 less filling than my regular beer. I drink 3 beers. How many do you have to drink to be equally full
Using proportions, it is found that you have to drink 9 beers to be equally full.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Your drink is 1/3 less filling, hence you have to drink 3 times the amount I drink to be equally full. I drink 3 beers, hence the number you drink is given as follows:
N = 3 x 3 = 9 beers.
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In a movie, a child who was 32 inches tall was ''blown up'' to be 160 feet tall. Find the scale factor (unitless) needed for the props in the movie. (12 inches:1 foot)
Answer:
60 or 60:1 (Depending on the answer choices)
Step-by-step explanation:
160 feet = 1920 inches (160 * 12)
[tex]\frac{1920}{32} = \frac{60}{1}[/tex]
The scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).
What is a scale factor?The scale factor is the simplest ratio between the actual and the model's size of the same object.
How to solve the question?In the question, we are informed that in a movie, a child who was 32 inches tall was ''blown up'' to be 160 feet tall.
We are asked to determine the scale factor needed for the props in the movie.
To find the scale factor, we first find the size of the child in the movie in inches.
Size = 160 feet = 160*12 inches = 1920 inches.
Now, the scale factor is calculated as the ratio of the actual size to the size in the movie, that is,
Scale factor = 32:1920 = 32/1920 = 1:60.
Therefore, the scale factor required will be 1:60 or 60:1 (actual:movie or movie:actual).
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Which statement is correct?
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) less-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than-or-equal-to StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) greater-than StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
(2.06 times 10 Superscript negative 2 Baseline) (1.88 times 10 Superscript negative 1 Baseline) = StartFraction 7.69 times 10 Superscript negative 2 Baseline Over 2.3 times 10 Superscript negative 5 Baseline EndFraction
The correct statement is [tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
How to determine the correct statement?The proper form of the question is added as an attachment
The expressions are given as:
[tex](2.06 * 10^{-2})(1.88 * 10^{-1})[/tex]
[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
Evaluate both expressions
[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) = 2.06 * 1.88 * 10^{-2-1}[/tex]
[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) = 3.87 * 10^{-3[/tex]
[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}} = \frac{7.69}{1.88} * 10^{5-2[/tex]
[tex]\frac{7.69 * 10^{-2}}{2.3* 10^{-5}} = 4.09 * 10^3[/tex]
By comparing both expressions, we have:
[tex]3.87 * 10^{-3} < 4.09 * 10^3[/tex]
This means that:
[tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
Hence, the correct statement is [tex](2.06 * 10^{-2})(1.88 * 10^{-1}) < \frac{7.69 * 10^{-2}}{2.3* 10^{-5}}[/tex]
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f(x)
121x
10
8
co to
6-
**
--6-5-4-3-2-12
6449
-4
-6
-10-
-12-
geg
5 6 x
Which statement is true regarding the functions on the
graph?
Of(2)= g(2)
Of(0) = g(0)
Of(2)= g(0)
Of(0) = g(2)
Answer: f(2)=g(2)
Step-by-step explanation:
The graphs intersect at x=2.
The correct statement which is true regarding the functions on the graph is,
f (2) = g (2)
We have to given that,
Graph of functions f (x) and g (x) are shown in figure.
Now, From the graph,
At x = 2;
f (2) = 0
And, At x = 2;
g (2) = 0
Therefore, At x = 2,
f (2) = g (2) = 0
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If 9/16 represents the ratio of the areas of two similar triangles, the ratio of the
corresponding
sides would be:
Enter the correct answer in the box. Write your answer in the form y - mx + b, using the appropriate inequality symbol in place of
the equal sign.
What inequality is shown in the graph?
Hello and Welcome to Brainly!
Let's take this problem step-by-step:
The problem wants the final answer to be in the form ⇒ y = mx + b
m ⇒ value of the slopeb ⇒ y-interceptLet's find both of these values first
[tex]slope = \frac{y_2-y_1}{x_2-x_1}[/tex](x₁,y₁), (x₂,y₂) are any two points on the line
⇒ let's use (-4,0) and (0,-4)
[tex]Slope = \frac{-4-0}{0--4} =\frac{-4}{4} =-1[/tex]
the y-intercept is any coordinate whose x-coordinate equals '0'⇒, therefore, the y-intercept is -4
Our equation as of now: y __ -x - 4
Now let's use some points to test:
⇒ what way inequality should face:
test with (0,0) (within the shaded region)[tex]0 _._._. -(0) - 4\\0 _._._. -4\\0 \geq -4[/tex]
Therefore our equation is [tex]y\geq -x-4[/tex]
* we use '≤' since the line is solid
⇒ if the line were dotted, we would use '>'
Answer: y ≥ -x - 4
Hope that helps!
#LearnwithBrainly
Answer:
y ≥ -x − 4.
Step-by-step explanation:
How many revolutions will a car wheel of diameter 22 in. make as the car travels a distance of one mile
It would be take upto 999 revolutions.
Let try to solve it,
Let n represent number of revolutions.
We are asked to find the number of revolutions it will take for a car wheel of diameter 30 in. to travel a distance of one mile.
1 mile = 63360 inches.
We will use circumference of circle formula to solve our given problem.
Circumference = pi*d , where, D represents diameter of circle.
Now, we will set the product of n and circumference of circle equal to 63360 inches as:
pi*22*n= 63360
n= 63360*7/ 22*22
n= 443520/444
n= 998.91
Therefore It would be take upto 999 revolutions.
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Jun wei has 12 more 10 cents coins than 20 cents coins. the total value of all the coins is $5.40. find the total number of coins he has.
Jun Wei has a total of 40 coins. An algebraic expression or equation with the given information is formed to calculate the total number of coins.
What is an algebraic expression?An algebraic expression is the combination of one or more variables, coefficients, and constants separated by operators. Each of them is called terms of the expression.
Eg: a + 6x + 5y + 2
Here there are 4 terms with 3 variables, 3 coefficients, and one constant.
Calculation:Given that,
Jun Wei has 12 more 10 cents coins than 20 cents coins.
So,
Consider the number of 20-cent coins = x
Then, the number of 10 cent coins = x + 12
It is given that the total value of all the coins is $5.40.
Where 1 $ = 100 cents. That implies, $5.40 = 540 cents
So,
the total value of the coins = 540 cents
⇒ 20(x) + 10(x + 12) = 540
⇒ 30x = 540 - 120
⇒ 30x = 420
∴ x = 40
Hence, there are 40 coins with Jun Wei.
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Which is a stretch of an exponential decay function?
ofx= [*
O
○ f(x) = -—-—-(5)*
|_ f(x) = 5(---)*|
O
Of(x) = 5(5)*
pls help: a small garden has a perimeter of 24 1/4 ft. If the length is 8 ft, what is the area of the garden.
Answer:
578 sq ft
Step-by-step explanation:
he length of a rectangular garden is twice its width and its area is 578 square feet.
Please answer with everything needed i appreciate everyones help:0)
Answer:
C
Step-by-step explanation:
please mark brainliest
Answer:
the 3rd answer option
Step-by-step explanation:
why ?
similar to the other questions.
we know the total number of coins, which is a sum of quarters and dimes. nothing else is in there.
so,
16 = q + d
and each type of coin has a defined value : a quarter is $0.25, a fine is $0.10.
and so, when you add up the value of all quarters and all dimes you get $3.10.
The large rectangle below represents one whole.
What percent is represented by the shaded area?
Answer:
40%
Step-by-step explanation:
so have 5 rectangles in a whole.we also have 2 shaded potions in that whole which represents 2/5 shaded potions.2/5 in fraction =0.4Now Change 0.4 to percentage by multiplying 0.4 by 1000.4 x 100 = 40Therefore the percentage represented by the shaded area is 40% Hope this helps.Good luck ✅.Question 4 I need help to solve all 3
Answer:
[tex]x^{2} +12x+36[/tex] [tex]\\[/tex]----- factors [tex](x+6)^{2}[/tex][tex]4x^{2} +24x+36[/tex] ----- factors [tex](2x+6)^{2}[/tex][tex]2x^{2} +10x+8[/tex] ------ factors (2x+2)(x+4)[tex]y^{2} -4[/tex] --------- factor (y+2)(y-2)Step-by-step explanation:
First bullet is called Perfect Square Trinomial (PST), the first and last is a perfect square and the middle is twice the product of the squared first and last term. To factor, just copy the middle sign and square the first and last term.
---
2nd bullet is also a PST with a value on a. Likewise you just need to square the first and last term. Then, copy the middle sign.
--
3rd bullet is a trinomial. To get the factor, get the prime factor of the value of a. Then, find the factors of 8 that when add up results to the value of b.
-
4th bullet is a special case. First get the square root of the first and last term, and copy the sign, Then, copy the factors and change it to the opposite sign.
jurgen cuts 5 metre-long timber beam into 3 pieces,first piece 2.34metres second piece 1.85 work out the length of the third piece
The length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have:
Jurgen cuts 5 meter-long timber beam into 3 pieces, first piece 2.34metres second piece 1.85.
Let the length of the third piece is x m.
2.34 + 1.85 + x = 5
4.19 + x = 5
x = 0.81 m
Thus, the length of the third piece is 0.81 m if the Jurgen cuts 5 meter-long timber beam into 3 pieces, the first piece 2.34metres second piece 1.85.
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Which rectangular equation represents the parametric equations x =t superscript one-half and y = 4t?
(PLEASE HELP I WILL MARK BRAINLIEST)
Dilate the figure by the scale factor. Then enter
the new coordinates.
K = 3
C(-4,-2)
A' = ([?],
B' = ([],
B (3-1) C'=(,
A(1,2)
Hint: To calculate the
x-value of A', multiply the
x-value of A by 3.
Answer:
A' = (3, 6)
B' = (9, -3)
C' = (-12, -6)
Step-by-step explanation:
you can mulitply both the x and y coordinates of each point by the scale factor (3)
point (1, 2) becomes point (3, 6)
(3, -1) becomes (9, -3)
(-4, -2) becomes (-12, -6)
hope this helps!! have a lovely day :)
{this is why whoever wrote the problem gave that hint--you can follow through on that logic, but just remember that it has to be a scaled version of the original figure--so the ratios between points (and x/y values) must be consistent}
2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
NEED TO KNOW ASAP
Which of the following is a quadratic inequality?
Oy<2x+7
Oy
Oy
Answer:
(c) y < x^2 -5x
Step-by-step explanation:
A quadratic inequality is one that involves a quadratic polynomial.
IdentificationThe degree of a polynomial is the value of the largest exponent of the variable. When the degree of a polynomial is 2, we call it a quadratic.
For the following inequalities, the degree of the polynomial in x is shown:
y < 2x +7 . . . degree 1y < x^3 +x^2 . . . degree 3y < x^2 -5x . . . degree 2 (quadratic)ApplicationWe see that the degree of the polynomial in x is 2 in ...
y < x^2 -5x
so that is the quadratic inequality you're looking for.
__
Additional comment
When a term involves only one variable, its degree is the exponent of that variable: 5x^3 has degree 3. When a term involves more than one variable, the degree of the term is the sum of the exponents of the variables: 8x^4y3 has degree 4+3=7.
A sports team came to town. the stadium filled all 10,000 seats at two-level pricing. level 1 tickets are $50 each, and level 2 tickets are $150 each. the stadium made $75,000 in ticket sales. the system of equations that models this scenario is: x + y = 10,000 50x + 150y = 75,000 what do the x and y represent in the system?
x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000. This can be obtained by understanding the question and observing the equations.
What do the x and y represent in the system?Given that total number of seats is 10,000 and there are two levels pricing.
Thus by observing the equation, x + y = 10,000,
10,000 is the sum of 2 variable which obviously will be the number of tickets in level 1 and number of tickets in level 2.
Since there are two level pricing,
50x + 150y = 75,000 represent the addition of total cost of tickets of level 1 and 2.
Hence x represents the number of tickets of level 1 and y represents the number of tickets of level 2 in the system given that there are 10,000 seats, level 1 tickets are $50 each, and level 2 tickets are $150 each and equation representing the situation:x + y = 10,000, 50x + 150y = 75,000.
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When a number is divided b 7, the quotient is 247 and the rimainder is 3,what is the number
The number, which on divided by 7 gives a quotient of 247 and a remainder of 3 is 1732. Computed using linear equations.
In the question, we are informed that a number when divided by 7, gives a quotient of 247 and a remainder of 3.
Assuming the number to be x.
We can say that x is our dividend, 7 is the divisor, 247 is the quotient, and 3 is the remainder.
The division algorithm equation is:
Dividend = Divisor*Quotient + Remainder,
Substituting values in this equation, we get a linear equation:
x = 7*247 + 3.
To solve for the unknown number x, we solve the equation as follows:
x = 7*247 + 3,
or, x = 1729 + 3,
or, x = 1732.
Thus, the number, which on divided by 7 gives a quotient of 247 and a remainder of 3 is 1732. Computed using linear equations.
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What is p ÷ r equal to?
tan x°
tan y°
sin y°
cos x°
Answer: tan x
Step-by-step explanation: An angle determines if a side is opposite the angle, or adjacent the angle. Since p/a is something to do with the tangent, as it is not using the hypotenuse (the longest side.) Tangent is Opposite/Adjacent, while Sine is Opposite/Hypotenuse and Cosine is Adjacent/Hypotenuse. The only thing that makes sense is tangent.
So, that leaves us with either tan y or tan x. Well, with x, the angle that x points to (which is the opposite side) is p, and the adjacent is a, so p/a must be Tangent(x) since it is Opposite/Adjacent sides.
Only if it was r/p would it be tan y, since r becomes the opposite and p becomes the adjacent.
If Colorado Springs, Colorado, has 1.2 times as many days of sunshine as Boston, Massachusetts, how many days of sunshine does each city have if there are a total of 482 days of sunshine between the two in a year?
Colorado and Boston have 263 and 219 days of sunshine respectively.
What is the solution to the Equation?Let the number of days of sunshine in Colorado is x and the number of days of sunshine in Boston is y.
Total number of days of sunshine=482
Also, the number of days of sunshine in Colorado is 1.2 times the number of days of sunshine in Boston.
So, the equation is formed as follows:
x+y=482 -(1)
The other equation is formed as:
x=1.2y -(2)
Substitute the value x from equation (2) in (1),
1.2y+y=482
2.2y=482
y=482/2.2
y=219
Substitute the value of y in equation (1),
x+219=482
x=482-219
x=263
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