If the position of 5 m below sea level is expressed as -5, then the number that expresses the position of 7 m above sea level would be + 7.
How to reference point ?In this particular instance, with the position residing 7 m above sea level, we articulate it as +7. This notation elegantly captures the notion of elevation, affirming the distance above the familiar sea level benchmark.
In the realm of vertical measurements, sea level occupies a crucial position as the reference point, embodying the zero mark on the vertical scale. It is from this fundamental reference point that we navigate the vast spectrum of altitudes.
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A curve C and a straight-line L have respective equations.
y = 2x^2 - 6x + 5
and
2y + x = 4
Find the coordinates of the points of intersection between C and L. Given that the line L is parallel to the line P passing through the points of intersection. Find the equation of line P.
The equation of line P passing through the points of intersection is y = -1/2x + 2.
To find the coordinates of the points of intersection between curve C and line L, we need to solve the system of equations formed by their respective equations.
The equations are:
C: y = 2x^2 - 6x + 5 ...(1)
L: 2y + x = 4 ...(2)
We can solve this system by substituting the value of y from equation (1) into equation (2):
2(2x^2 - 6x + 5) + x = 4
4x^2 - 12x + 10 + x = 4
4x^2 - 11x + 6 = 0
To solve this quadratic equation, we can factorize it:
(4x - 3)(x - 2) = 0
Setting each factor to zero, we get:
4x - 3 = 0 --> x = 3/4
x - 2 = 0 --> x = 2
Now, substitute these x-values back into equation (1) to find the corresponding y-values:
For x = 3/4:
y = 2(3/4)^2 - 6(3/4) + 5
y = 9/8 - 18/4 + 5
y = 9/8 - 9/2 + 5
y = 9/8 - 36/8 + 40/8
y = 13/8
For x = 2:
y = 2(2)^2 - 6(2) + 5
y = 8 - 12 + 5
y = 1
Therefore, the coordinates of the points of intersection between C and L are (3/4, 13/8) and (2, 1).
Now, we need to find the equation of line P passing through the points of intersection.
We have two points on line P: (3/4, 13/8) and (2, 1).
First, let's find the slope of line P using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1 - 13/8) / (2 - 3/4)
m = (-5/8) / (5/4)
m = -1/2
Now, we have the slope of line P, -1/2. We can use one of the points, let's say (3/4, 13/8), and the slope to find the equation of line P using the point-slope form:
y - y1 = m(x - x1)
Substituting the values:
y - 13/8 = -1/2(x - 3/4)
Simplifying:
y - 13/8 = -1/2x + 3/8
y = -1/2x + 3/8 + 13/8
y = -1/2x + 16/8
y = -1/2x + 2
Therefore, the equation of line P passing through the points of intersection is y = -1/2x + 2.
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Which of the following is equals .see the pictures
The value of the function f(-1) is 1/3. Option D
What is a function?A function can be defined as a law, an expression or rule that is used to show the relationship between two variables.
These variables are listed as;
Independent variableDependent variableFrom the information given, we have the function written as;
f(x) = 3ˣ
To determine the function f(-1), we need to substitute the value of the variable x as -1 in the function f(x)
Substitute the values, we have;
f(-1) = 3⁻¹
Take the inverse of the value, we get;
f(-1) = 1/3
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Trina has a credit card that uses the adjusted balance method. For the first 10
days of one of her 30-day billing cycles, her balance was $780. She then
made a purchase for $170, so her balance jumped to $950, and it remained
that amount for the next 10 days. Trina then made a payment of $210, so her
balance for the last 10 days of the billing cycle was $740. If her credit card's
APR is 17%, which of these expressions could be used to calculate the
amount Trina was charged in interest for the billing cycle?
OA. (30)($780)
365
B.
O C.
D.
0.17
365
0.17
365
0.17
365
30
30
(10 $780+10 $950 +10 $210)
30
10
$780+10$950+10 $740
30
•30) ($570)
The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is (APR / 365) x 30 days x adjusted balance.
What is the adjusted balance method?The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.
The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.
Credit card interest method = adjusted balance method
Beginning balance = $780
Purchase = $170
Payment = $210
Adjusted balance, AB = $740 ($780 + $170 - $210)
APR = 17% = 0.17 (17/100)
The interest charged = (APR / 365) x 30 days x adjusted balance
= $10.34 [(0.17/365) x 30 x $740]
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Given the vector u equal to 2 (cos 325°, sin 325°) and vector v equal to
6 (cos 155°, sin 155°), find the sum u + v and write your answer in
magnitude and direction form with the magnitude rounded to the nearest
tenth and the direction rounded to the nearest degree, 0° ≤ 0 < 360°.
Answer:
[tex]u+v=4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]
Step-by-step explanation:
When adding two vectors, we add their horizontal components, and then their vertical components:
[tex]u=2\langle\cos325^\circ,\sin325^\circ\rangle=\langle2\cos325^\circ,2\sin325^\circ\rangle\\v=6\langle\cos155^\circ,\sin155^\circ\rangle=\langle6\cos155^\circ,6\sin155^\circ\rangle\\\\u+v=\langle2\cos325^\circ+6\cos155^\circ,2\sin325^\circ+6\sin155^\circ\rangle\\u+v\approx\langle-3.8,1.39\rangle[/tex]
We are not done however as we need to now calculate the magnitude and the direction of the resultant vector:
Magnitude:
[tex]||u+v||=\sqrt{(-3.8)^2+1.39^2}\approx4.1[/tex]
Direction:
[tex]\displaystyle \theta=tan^{-1}\biggr(\frac{1.39}{-3.8}\biggr)\approx-20^\circ=180-20^\circ=160^\circ[/tex]
Therefore, the resultant vector is about [tex]4.1\langle\cos160^\circ,\sin160^\circ\rangle[/tex]
If I have 7.55 how many dimes and quarters is it
Answer:
To convert 7.55 dollars into dimes and quarters, we need to make use of the fact that there are 10 dimes in a dollar and 4 quarters in a dollar. Here's how to do it:
Step-by-step explanation:
1. First, convert the dollar amount into cents: 7.55 dollars x 100 cents/dollar = 755 cents.
2. Next, use long division to find how many quarters are in 755 cents: 755 ÷ 25 = 30 with a remainder of 5.
3. The quotient of 30 tells us that we can use 30 quarters, which equals $7.50.
4. The remainder of 5 cents is less than a quarter, so we cannot use another quarter. Instead, we can use 1 dime, which is worth 10 cents.
Therefore, 7.55 dollars is equivalent to 30 quarters and 1 dime.
Find the indicated angle
A.) 9
B.) 7
C.) 12
D.) 32
The calculated value of the missing side length in the triangle is (c) 12
How to find the indicated angleFrom the question, we have the following parameters that can be used in our computation:
The simiar triangles
Using the theorem of corresponding sides, we hav
?/8 = 9/6
Multiply both sides by 8
So, we have
? = 8 * 9/6
Evaluate
? = 12
Hence, the missing side length in the triangle is (c) 12
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HELP! FOR 100 POINTS
In a sale, all prices are reduced by 22%. A pair of trainers normally cost £80. What is the sale price of the pair of trainers?
Answer: $62.40
Step-by-step explanation:
Original price $80
22% of 80%
.22(80) = 17.60 >This is the discount
Sale price = Original price - discount
Sale price = 80 - 17.60
Sale price = $62.40
Answer:
[tex]\Huge \boxed{\text{\$62.40}}[/tex]
Step-by-step explanation:
In the sale, the prices decrease by 22%. This means that the sale price is 78% of the original price.
[tex]\Large \text{Sale price = (100 - 22)\% of old price}\\\text{Sale price = 78\% of \$80}\\\text{Sale price = 0.78 $\times$ 80}\\\text{Sale price = \$62.40}[/tex]
El angulo en la base de un
triangulo ísósceles esde
34° la altura mide 15m
Calcular la longitud de los lados
iguales
It can be seen that each side of the isosceles triangle measures approximately 29.81 meters.
How to solveThe angles at the base of an isosceles triangle have equivalent magnitudes. It can be deduced intelligently that if one of the base angles measures 34°, the remaining base angle must also be 34°.
Let's denote the length of each side as "x."
In a right triangle formed by half of the base, the height, and one of the sides, we can use the tangent ratio:
tan(34°) = height / (x/2)
tan(34°) = 15 / (x/2)
To isolate x, we can rearrange the equation:
x/2 = 15 / tan(34°)
x = (15 / tan(34°)) * 2
By employing a calculator, we have the capability to determine the numerical worth of x.
x ≈ 29.81 m
Therefore, each side of the isosceles triangle measures approximately 29.81 meters.
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The question in English:
The angle at the base of an isosceles triangle 34° the height measures 15m
Calculate the length of the sides equal
Which graph shows the image of the triangle reflected across the line of reflection shown? On a coordinate plane, a triangle has points (2, 4), (4, 2), (9, 6). A line of reflection is at y = 3. On a coordinate plane, a triangle has points (negative 1, negative 3), (2, 4), (4, 2). On a coordinate plane, a triangle has points (1, 4), (4, 2), (2, 0). On a coordinate plane, a triangle has points (2, 0), (4, 2), (9, negative 2). On a coordinate plane, a triangle has points (2, 2), (4, 4), (9, 0). Mark this and return
The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)
What is a transformation?Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.
The triangle with points at (2, 4), (4, 2), (9, 6) was reflected across the line y = 3 to get the points (2, 2), (4, 4), (9, 0)
Thus, option (D) is correct.
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Using a Net to Find the Surface Area of a Triangular Prism.
Answer:
Step-by-step explanation:
Please quickly help me will give 100 points and brainliest!
A shipping box has dimensions as shown in the diagram. The red, dashed line represents the longest length of item that will fit inside the box. What is the length of the longest item that will fit inside the shipping box?
Enter the correct answer in the box by replacing the values of m and n.
NO LINKS!! URGENT HELP PLEASE!!!
The flowcharts for each proof are shown in the image attachments below.
For problem 1, we use the SSS (side side side) congruence theorem.
Problem 2 uses SAS (side angle side). It might help to rotate one of the triangles in problem 2 so the marked angles align.
Two aircrafts travel from the position P(30°N, 130°W) to Q (50°N, 170°E) all leaving at 0845hrs and at the same speed of 500km/hr. Aircraft A travels due north to the position (50°N, 130°W) and then along a parallel of latitude using the shortest route. Aircraft B travels along a parallel of latitude (30°N, 170°E) and then due north.
(a) If a third aircraft C had left a point R (30°N, 10°W) at the same time as the two above aircrafts left P and flew via the shortest possible distance to point Q, calculate its position when the aircraft A was passing the longitude 180°W. (b) Calculate the arrival local time of the two aircrafts. (5mks) (5mks)
(a) The time taken by aircraft C to travel the distance from R to the longitude 180°W is 25.92 hours
(b) Since aircraft A departed at 08:45 hrs, the arrival time would be:
Arrival time is 13:14 hrs
Aircraft A would arrive at approximately 13:14 hrs, and aircraft B would arrive at approximately 21:01 hrs local time.
To calculate the position of aircraft C when aircraft A was passing the longitude 180°W, we need to determine the distance and direction between R (30°N, 10°W) and Q (50°N, 170°E) via the shortest route.
Distance between R and Q:
The latitude difference between R and Q is 50°N - 30°N = 20°. As each degree of latitude is approximately 111 km, the distance in terms of latitude is 20° × 111 km = 2,220 km.
The longitude difference between R and Q is 170°E - 10°W = 180°.
At the latitude of 40°N (midpoint between 30°N and 50°N), each degree of longitude is approximately cos(40°) × 111 km = 70.7 km.
The distance in terms of longitude is 180° × 70.7 km = 12,726 km.
Using the Pythagorean , the shortest distance between R and Q is:
Distance = √((2,220 km)² + (12,726 km)²)
≈ 12,960 km
Speed of aircraft C is 500 km/hr.
The time taken by aircraft C to travel the distance from R to the longitude 180°W is:
Time = Distance / Speed
= 12,960 km / 500 km/hr
≈ 25.92 hours
Since the aircraft A and aircraft C departed at the same time, when aircraft A was passing the longitude 180°W, aircraft C would also be at the same longitude, assuming they maintained a constant speed.
(b) To calculate the arrival local time of the two aircraft, we need to consider the time taken for each leg of their respective routes.
For aircraft A:
Distance from P to (50°N, 130°W) = (50°N - 30°N) × 111 km/degree
= 2,220 km
Time taken = Distance / Speed
= 2,220 km / 500 km/hr
= 4.44 hours
Since aircraft A departed at 08:45 hrs, the arrival time would be:
Arrival time = Departure time + Time taken
= 08:45 + 4.44 hours
≈ 13:14 hrs
For aircraft B:
Distance from (30°N, 170°E) to Q = (170°E - 130°W) × cos(40°) × 111 km/degree = 6,282 km
Time taken = Distance / Speed
= 6,282 km / 500 km/hr
= 12.564 hours
Since aircraft B departed at 08:45 hrs, the arrival time would be:
Arrival time = Departure time + Time taken
= 08:45 + 12.564 hours
≈ 21:01 hrs
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Dada la circunferencia de ecuación x2+y2-2x+4y-4=0, hallar el centro
y el radio, luego grafique la circunferencia
The equation for the circle is
(x - 1)² + (y + 2)² = 9
Then the radius is 3 units and the center is (1, -2), the graph is on the image at the end.
How to find the center and radius of the circle?Remember that for an equation for a circle of radius R and center (a, b), the equation is:
(x - a)² + (y - b)² = R²
Here we have the equation of the circle:
x² + y² - 2x + 4y - 4 = 0
We need to complete squares, we will get:
(x² - 2x) + (y² + 2*2y) = 4
Now we can add in both sides (-1)² and (2)², then we will get:
(x² - 2x + (-1)²) + (y² + 2*2y + (2)²) = 4 + (2)² + (-1)²
(x - 1)² + (y + 2)² = 4 + 4 + 1
(x - 1)² + (y + 2)² = 9 = 3²
Then we can see that the center is (1, -2), and the radius is 3.
The graph of this circle is on the image at the end.
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What is the volume of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
--
10 yd
9 yd
The volume of the given cylinder is 2543 cubic yards.
For the given cylinder,
Height of the cylinder = 10 yard
Radius of cylinder = 9 yard yard
Then we have to calculate the volume of this cylinder.
Since we know that,
Volume of the cylinder = πr²h
Where,
r represents radius of cylinder = 9 yard
h represents height of cylinder = 10 yard
Noe therefore,
Volume of the cylinder = π(9)²(10)
= 3.14x 81 x 10
= 2543 cubic yards
Thus,
⇒ Volume = 2543 cubic yards.
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2. The area of a figure is 207 m². If the
dimensions are multiplied by what will
3'
be the area of the new figure?
Answer:
Step-by-step explanation:
If the dimensions of a figure are multiplied by 1/3, then the area of the new figure will be 1/9 of the original area.
Therefore, if the area of the original figure is 207 m², then the area of the new figure will be 23 m² (207 m² * 1/9).
I hope this helps!
Answer:
23 m^2
Step-by-step explanation:
As all of the dimensions have been multiplied by a constant, the two figures are similar to one another.
The ratio between the areas of two similar figures is given by the ratio of similarity (= the ratio between two similar sides between the two figures) squared.
In our case, the ratio of similarity is 1/3.
Therefore, the ratio between the two areas is (1/3)^2 = 1/9.
[tex]207 \times \frac19 = 23 \left[\text{m}^2\right][/tex]
If I have $25. How many cheeseburgers can I get if they are 2.50 each?
Answer:
We can get 10 cheeseburgers.
Step-by-step explanation:
To find out how many cheeseburgers we can buy if:
we have $25 andeach cheeseburger costs $2.50,we can divide the money we have by the cost of each cheeseburger.
To make the division simpler, we can multiply both numbers by 10.
$25 / $2.50 = $250 / $25
From this form of the division, we can clearly see that the amount of money we have is 10 times the cost of one burger because it is 25 with a 0 on the end, which is the result of multiplying by 10.
Therefore, we can get 10 cheeseburgers.
Refer to image attached
The rationalized form of the expression √(3/5) is √15/5.
To rationalize the denominator of the expression √(3/5), we need to eliminate the square root in the denominator.
We can achieve this by multiplying both the numerator and denominator by the conjugate of the denominator.
The conjugate of √5 is also √5, so we can multiply the expression by (√5)/(√5):
√(3/5)×(√5)/(√5)
Multiplying the numerator and denominator, we have:
√(3 × 5)/(√(5×5))
Which simplifies to:
√15/√25
√15/5
Therefore, the rationalized form of √(3/5) is √15/5.
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I need help with this Piece-Wise Function Please
With f(1), we're being given an x-value of 1.
Since 1 < 3 (and not ≥3) we need to use the first formula that is used when x<3.
f(1) = 1 - 2 = -1
y^2 + 4 = x. for x the independent variable and the dependent variable. Determine whether the relation is a function.
Answer:
To determine if the given relation is a function, we need to check if there is a unique y-value for every x-value in the relation.
The given relation is:
y^2 + 4 = x
To test for functionality, we need to solve for y in terms of x:
y^2 = x - 4
y = ± √(x - 4)
Notice that for each x-value, there are two possible y-values, one positive and one negative. This means that for a single x-value, there are two potential y-values, violating the condition of a unique y-value for every x-value.
Therefore, the given relation is not a function since it fails the vertical line test, as there are x-values with multiple corresponding y-values.
Find the inverse for: f(x) = 2x^2-3
Unless we restrict its domain, a quadratic function doesn't have the inverse.
To borrow money, you pawn your guitar Based on the value of the guitar, the paunbroker loans you $720. One month later, you get the guitar back by paying the paunbroker $1272. What annual interest rate did you pay?
You will pay a simple interest rate of
(Round to the nearest whole number as needed)
To determine the annual interest rate paid, we need to calculate the simple interest for one month and then convert it to an annual rate.
The formula for simple interest is:
Simple Interest = Principal × Rate × Time
In this case, the principal amount is $720, and after one month, you pay back a total of $1272. Therefore, the interest paid is:
Interest = $1272 - $720 = $552
We can now calculate the monthly interest rate:
Rate = Interest / Principal = $552 / $720 ≈ 0.7667
To convert the monthly interest rate to an annual rate, we multiply it by 12:
Annual Rate = Monthly Rate × 12 = 0.7667 × 12 ≈ 9.20
Therefore, you paid an annual interest rate of approximately 9.20%.
how many square are there in 384 sq ft
The number of squares that are in 384 sq ft is 0
How many square are there in 384 sq ftFrom the question, we have the following parameters that can be used in our computation:
Area expression = 384 sq ft
The above expression is an area expression
This means that it cannot be compared to quantities other then squares
The term "how many squares" is not an area expression
Hence, there are no squares in 384 sq ft
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solve each compound inequality. -28 < -4r < 16
The solution to the compound inequality -28 < -4r < 16 is 7 > r > -4
How to determine the solution to the compound inequalityfrom the question, we have the following parameters that can be used in our computation:
-28 < -4r < 16
Divide through the inequality by -4
so, we have the following representation
-28/-4 < -4r/-4 < 16/-4
When the quotients are evaluated, we have
7 > r > -4
Hence, the solution to the compound inequality is 7 > r > -4
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A population of values has a normal distribution with �=189.7 and �=96.7. You intend to draw a random sample of size �=62.
Find the probability that a single randomly selected value is between 189.7 and 213.
P(189.7 < X < 213) =
Find the probability that a sample of size �=62 is randomly selected with a mean between 189.7 and 213.
P(189.7 < M < 213) =
Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.
Step 1: Calculate the z-scores for the given values using the formula:
z = (x - μ) / σ
For 189.7:
z1 = (189.7 - 189.7) / 96.7 = 0
For 213:
z2 = (213 - 189.7) / 96.7 ≈ 0.2417
Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.
P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939
Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.
To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance
Step 1: Calculate the standard error of the mean (σ_m) using the formula:
σ_m = σ / sqrt(n)
σ_m = 96.7 / sqrt(62) ≈ 12.2878
Step 2: Convert the given qualities to z-scores utilizing the equation:
z = (x - μ) / σ_m
For 189.7:
z1 = (189.7 - 189.7) / 12.2878 = 0
For 213:
z2 = (213 - 189.7) / 12.2878 ≈ 1.8967
Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.
P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702
Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.
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The quilt is made of squares with diagonals.
The length of BD is 4.
a. Find the length of AE. Round answer to the hundredths.
b. Find the area of square ABCD.
The assets and liabilities of a 22-year-old recent college graduate are listed below.
Furniture $4,091
Car Loan $6,060
Credit Card Balances $3,940
Savings Account Balance $2,143
Student Loans $29,400
Car Value $21,500
Equipment $4,805
The college graduate is hired at a law firm with a $10,000 signing bonus, that will be deposited into the savings account. The firm also agrees to immediately pay off $25,000 in student loan debt. What is the college graduate's new net worth?
$11,309
$14,400
$23,643
$28,139
About 99.7 percent of the monthly rental are between 400 and 430
Answer: rental is $415, and the standard deviation is $5.
Step-by-step explanation:
If about 99.7 percent of the monthly rentals fall between 400 and 430, it implies that this range encompasses three standard deviations from the mean.
To calculate the mean, we can find the midpoint of the given range:
Mean = (400 + 430) / 2 = 415
Since the range of three standard deviations covers about 99.7 percent of the data in a normal distribution, we can use this information to estimate the standard deviation (σ).
Standard deviation (σ) = (430 - 415) / 3 = 15 / 3 = 5
Therefore, based on the given information, the mean monthly rental is $415, and the standard deviation is $5.
Tan^-1(√1-sinx÷√1+sinx)
Answer:
tan^(-1)(|cos(x)| / (1 + sin(x)))
Step-by-step explanation:
√(1 - sin(x)) / √(1 + sin(x))
(√(1 - sin(x)) / √(1 + sin(x))) * (√(1 + sin(x)) / √(1 + sin(x)))
√((1 - sin(x))(1 + sin(x))) / (1 + sin(x))
√(1 - sin^2(x)) / (1 + sin(x))
Then, using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can substitute cos^2(x) for 1 - sin^2(x):
√(cos^2(x)) / (1 + sin(x))
|cos(x)| / (1 + sin(x))
tan^(-1)(|cos(x)| / (1 + sin(x)))
*Note : the absolute value |cos(x)| is used to ensure the argument of the inverse tangent is always positive.
(08.01 MC)
Which of the following is the graph of f(x)=x²-5x +4?
Answer: C
Step-by-step explanation:
If I plugged in 0 for x, You get 4 for y. This is the y-intercept
(0,4)
The only graph that goes through (0,4) is C.