Answers
Step-by-step explanation:
I believe there is something missing from the description.
I base my solution and explanation on the following assumptions :
the angle theta is at the origin (0, 0).not only passes the terminal side through (20, -21), but so does also the circle around our trigonometric triangle.in other words, (20, -21) is not just any point on the line, but it is the upper vertex of the triangle.
the baseline of the triangle, which is the radius of the surrounding circle is then the distance from the origin to the point.
Pythagoras (= distance formula) gives us for the distance between 2 points (x1, y1) and (x2, y2) :
distance² = (x1 - x2)² + (y1 - y2)²
in our case
distance² = (20 - 0)² + (-21 - 0)² = 400 + 441 = 841
distance = radius = 29
remember, sine is the up/down leg, cosine is the left/right leg.
so,
sin(theta) = -21/29
FYI : theta ≈ -46.4°
cos(theta) = 20/29
tan(theta) = sin(theta)/cos(theta) = -21/29 / 20/29 =
= -21/20
you were right about tan(theta), not about sin(theta) and cos(theta).
if you mistook theta for a 0, you were still wrong :
sin(0) = 0, cos(0) = 1.
Related Questions
a circular diaphragm 58.06 cm in diameter oscillates at a frequency of 15.69 khz as an underwater source of sound used for submarine detection. far from the source, the sound intensity is distributed as the diffraction pattern of a circular hole whose diameter equals that of the diaphragm. take the speed of sound in water to be 1450. m/s, and find the angle (in degrees) between the normal to the diaphragm and a line from the diaphragm to the first minimum.
Answers
The angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees
To find the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern, we can use the concept of diffraction and the formula for the angle of the first minimum in a single-slit diffraction pattern:
sin(θ) = λ / (diameter)
where θ is the angle, λ is the wavelength of the sound, and the diameter is the diameter of the diaphragm.
First, let's convert the frequency of 15.69 kHz to the corresponding wavelength using the formula:
wavelength = speed of sound / frequency
wavelength = 1450 m/s / (15.69 kHz * 1000 Hz/kHz)
wavelength = 0.09257 meters (rounded to five decimal places)
Next, we can substitute the values into the formula to find the angle:
θ = [tex]sin^{(-1)}[/tex] (0.09257 meters / 0.5806 meters)
θ ≈ 9.43 degrees (rounded to two decimal places)
Therefore, the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees. This angle represents the bending or spreading of the sound waves as they pass through the circular hole of the diaphragm, creating the diffraction pattern.
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Will make brainiest if two people answer ૮ ˶ᵔ ᵕ ᵔ˶ ა
Answers
The length of side LJ as shown in the similar shapes is 12.92.
What is similar shapes?Similar shapes are enlargements of each other using a scale factor.
To calculate the length of side LJ, we use the formula below
Formula:
XZ/XY = KJ/KL....................... Equation 1From the diagram,
Given:
/XZ/ = 8.2/XY/ = 8.7/KJ/ = 12.18Substitute these values into equation 1 and solve for KL
8.2/8.7 = 12.18/KLKL = 8.7×12.18/8.2KL = 12.92Hence, the right option is 12.92.
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Tommy opens a bank account with an initial amount of $650. The account has an annual
interest rate of 3.5%. What will the account balance (principle+interest) be after 8 years if
the account is compounded:
a) annually?
b) quarterly?
c) weekly?
d) daily?
e) continuously?
Answers
Annually: $822.49
Quarterly: $842.67
Weekly: $849.01
Daily: $850.98
Continuously: $853.39
a rectangular lot is 135 yards long and 100 yards wide, give the length and width of another rectangular lot that has the same perimeter but a larger area.
Answers
Directions: Find the volume of each figure. Round to the nearest hundredth.
2.
1.
3.
5.
8 m.
7.
34 m
3 km
** This is a 2-page
EXER
11 cm
P
4.
end 1601 02
6.
11 yd
Tw
10.8 ft
Directions: Find the surface area of each figure. Round to the nearest hundredth.
8.
0-
29 in
8.6 ft
boil Co
II in
3.
13.4 mm
5.
98
7.
1956
Answers
The calculated volumes of the figures are 2145.52 cubic meters, 697.19 cubic yards, 20587.81 cubic meters, 2639.40 cubic feet, 56.57 cubic km and 6387.60 cubic inches
How to find the volume of the figuresThe sphere 1
The volume is calculated as
V = 4/3πr³
Where
r = Radius = 8 meters
So, we have
V = 4/3 * 22/7 * 8³
Evaluate
Volume = 2145.52 cubic meters
The sphere 2
The volume is calculated as
V = 4/3πr³
Where
r = Radius = (11/2) yards
So, we have
V = 4/3 * 22/7 * (11/2)³
Evaluate
Volume = 697.19 cubic yards
The sphere 3
The volume is calculated as
V = 4/3πr³
Where
r = Radius = (34/2) meters
So, we have
V = 4/3 * 22/7 * (34/2)³
Evaluate
Volume = 20587.81 cubic meters
The hemisphere 4
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 10.8 feet
So, we have
V = 2/3 * 22/7 * 10.8³
Evaluate
Volume = 2639.40 cubic feet
The hemisphere 5
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 3 km
So, we have
V = 2/3 * 22/7 * 3³
Evaluate
Volume = 56.57 cubic km
The hemisphere 6
The volume is calculated as
V = 2/3πr³
Where
r = Radius = 29/2 in
So, we have
V = 2/3 * 22/7 * (29/2)³
Evaluate
Volume = 6387.60 cubic inches
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1. If we had a large 16 inch pizza for $14, what is the price per square inch?
$0.07
$0.09
$0.14
$0.25
2. If we had a medium 14 inch pizza for $12, what is the price per square inch?
$0.07
$0.09
$0.14
$0.25
Answers
Answer: $0.07 and $0.08
Step-by-step explanation: 1. To find the price per square inch of a 16 inch pizza for $14, we need to first calculate the area of the pizza.
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the radius is half of the diameter, which is 8 inches.
So, the area of the pizza is A = π(8)^2 = 64π square inches.
The price per square inch is the total price divided by the area of the pizza:
Price per square inch = Total price / Area
Price per square inch = $14 / (64π) square inches
Price per square inch ≈ $0.07
Therefore, the price per square inch of a 16 inch pizza for $14 is approximately $0.07.
Answer: $0.07
2. Following the same method as above, for a 14 inch pizza for $12, the radius is 7 inches and the area is A = π(7)^2 = 49π square inches.
The price per square inch is:
Price per square inch = Total price / Area
Price per square inch = $12 / (49π) square inches
Price per square inch ≈ $0.08
Therefore, the price per square inch of a 14 inch pizza for $12 is approximately $0.08.
Answer: $0.08
The number of times 100 groups took a
selfie is as follows.
Takes
1 2 3
4
Frequency 27 29 18 14
5
12
Find the probability a group will take their
selfie exactly 3 times.
P(3) = [?]
Answers
The probability a group will take their selfie exactly 3 times is 0.18.
We have,
The total groups = 100
The number of groups that took selfies 3 times = 18
Now,
The probability a group will take their selfie exactly 3 times.
= 18/100
= 0.18
Thus,
The probability a group will take their selfie exactly 3 times is 0.18.
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The slope of the line tangent to the graph of y = \ln \left( {1 - x} \right) at x=-1 is
(A) -1
(B) - \frac{1}{2}
(C) \frac{1}{2}
(D) \ln \left( 2 \right)
(E) 1
Answers
To find the slope of the line tangent to the graph of y = ln(1 - x) at x = -1, we can use the derivative of the function.
The derivative of y with respect to x can be found using the chain rule:
dy/dx = d/dx[ln(1 - x)] = 1 / (1 - x) * (-1) = -1 / (1 - x)
Substituting x = -1 into the derivative, we have:
dy/dx = -1 / (1 - (-1)) = -1 / 2
Therefore, the slope of the line tangent to the graph at x = -1 is -1/2.
The correct answer is (B) -1/2.
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PQR is a tangent to circle QABCD. AB || QD. CB=CD. Let 2, -30° and D₂ =70°. P A 1.1 Calculate Q₁. 1.2 Prove that C=110 A 1.3 Calculate B1
Answers
1.1. Calculate Q₁:
Since PQR is tangent to the circle at point Q, we know that angle PQR is 90 degrees. We also know that angle QRD is 70 degrees (given in the problem). Since AB || QD, we know that angle QAB is equal to angle QRD (alternate angles). Therefore, angle QAB is also 70 degrees.
Using the fact that the angles in a triangle add up to 180 degrees, we can calculate angle AQB as follows:
angle AQB = 180 - angle QAB - angle QBA
= 180 - 70 - 90
= 20 degrees
Since angle QAB is 70 degrees, we can use the fact that the angles in a triangle add up to 180 degrees to find angle QBC:
angle QBC = 180 - angle BQC - angle QCB
= 180 - 90 - angle QCB
= 90 - angle QCB
Since CB = CD, we know that angle QBC = angle QCD. Therefore, we can write:
angle QBC = angle QCD = (180 - angle D₂)/2 = (180 - 70)/2 = 55 degrees
Substituting this into the equation we derived earlier for angle QBC, we get:
55 = 90 - angle QCB
Solving for angle QCB, we get:
angle QCB = 35 degrees
Finally, we can use the fact that the angles in a triangle add up to 180 degrees to find angle BQA:
angle BQA = 180 - angle AQB - angle QBA
= 180 - 20 - 90
= 70 degrees
Therefore, Q₁ = angle BQA - angle QCB = 70 - 35 = 35 degrees.
1.2. Prove that C=110:
Since AB || QD, we know that angle AQB is equal to angle QCD (alternate angles). Therefore, we can write:
angle QCD = angle AQB = 20 degrees
We also know that CB = CD. Therefore, triangle BCD is an isosceles triangle, and we can write:
angle BDC = angle CBD = (180 - angle D₂)/2 = (180 - 70)/2 = 55 degrees
Using the fact that the angles in a triangle add up to 180 degrees, we can write:
angle BCD = 180 - angle CBD - angle BDC
= 180 - 55 - 55
= 70 degrees
Therefore, C = 180 - angle QCD - angle BCD = 180 - 20 - 70 = 90 degrees.
Since CB = CD, we know that angle CBD is also equal to (180 - angle D₂)/2 = 55 degrees. Therefore, we can write:
angle BDA = 180 - angle AQB - angle CBD
= 180 - 20 - 55
= 105 degrees
Therefore, C + BDA = 90 + 105 = 195 degrees. Since CB = CD, we know that angle CBD is also equal to angle BDC = 55 degrees. Therefore, we can write:
angle BDC = 180 - angle BDA - angle ADB
= 180 - 105 - angle ADB
Solving for angle ADB, we get:
angle ADB = 20 degrees
Therefore, C = angle ADB + angle CBD = 20 + 55 = 75 degrees
An athlete throws a shot put with an initial vertical velocity of 40 feet per second. He releases the shot put at a height of 5.69 feet.
Use an equation that models the height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown to find the time that the shot put is in the air.
Round your answers to the nearest whole numbers.
Answers
The shot put is in the air for approximately 3 seconds.
The height h (in feet) of the shot put as a function of the time t (in seconds) after it is thrown can be modeled by the equation:
h(t) = h + vt - (1/2)gt²
where v is the initial vertical velocity in feet per second, and s is the initial height in feet.
Here, the initial vertical velocity is 40 feet per second, and the initial height is 5.69 feet. Therefore, we can plug in these values to get:
h = -16t² + 40t + 5.69
To find the time that the shot put is in the air, we need to find the value of t when h = 0, since the shot put will hit the ground when its height is 0.
Therefore, we can set the equation equal to 0 and solve for t:
0 = -16t² + 40t + 5.69
Using the quadratic formula, we get:
t = (-b ± √(b² - 4ac)) / 2a
where a = -16, b = 40, and c = 5.69.
Plugging in these values, we get:
t = (-40 ± √(40² - 4(-16)(5.69))) / 2(-16)
Simplifying, we get:
t ≈ 3 or t ≈ 0.2
Since the shot put cannot be in the air for negative time, the only possible answer is t ≈ 3.
Therefore, the shot put is in the air for approximately 3 seconds.
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[tex]\frac{2x-1}{3} -\frac{3x}{4} =\frac{5}{6}[/tex]
Answers
The value of the variable is -14
What are fractions?Fractions are simple defined as the part of a whole number or variable.
From the information given, we have that;
2x - 1/3 - 3x/4 = 5/6
Find the LCM, we have;
4(2x - 1) - 3(3x) /12 = 5/6
expand the bracket, we get;
8x - 4 - 9x/12 = 5/6
collect the like terms
-x - 4/12 = 5/6
cross multiply the values
-6x - 24 = 60
collect like terms
-6x = 84
make 'x' the subject
x = -14
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what are the properties of a diamond plane shape
Answers
Step-by-step explanation:
A diamond is a two-dimensional flat quadrilateral with four closed straight sides. A diamond is also called a rhombus because it's sides are of equal measure and because the inside opposite angles are equal. Diamonds are also considered to be parallelograms because their opposite sides are parallel to each other
kimberly sent gifts to her friends. for each gift she used either a rectangular gift box or a cylindrical gift box. each box contains exactly one gift: either a fragrant soap or a pack of spicy roasted almonds. if half of the boxes she sent were cylindrical, and a third of the rectangular boxes contained soap, then how many cylindrical boxes contained soap?
Answers
Kimberly sent approximately 34 cylindrical boxes that contained soap
Let's assume Kimberly sent a total of 100 gift boxes. Since half of the boxes were cylindrical, that means she sent 50 cylindrical boxes.
If a third of the rectangular boxes contained soap, then 1/3 * (100 - 50) = 1/3 * 50 = 50/3 ≈ 16.7 rectangular boxes contained soap. Since we cannot have a fraction of a box, let's round it down to 16 rectangular boxes containing soap.
Now, since each box contains exactly one gift, the remaining cylindrical boxes must contain the pack of spicy roasted almonds. Therefore, out of the 50 cylindrical boxes, 50 - 16 = 34 cylindrical boxes contain soap.
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.
Which of the following inequalities has a solution set represented by the following graph?
Answers
There are two ways you could approach this.
The first is to solve each inequality separately and see which one ends up equal to x ≥ -1.
Another and faster option is to test 0 in each inequality, because 0 is in the solution set and 0 is easy to work with. (You could do this for any value in the solution set.)
A: Is 4(0) + 3 > 7 true? No. 3 > 7 is false. This eliminates A.
B. Is 0/3 - 2 ≥ 2 true? No. -2 ≥ 2 is false. This eliminates B.
C. Is -2(0) - 3 ≤ -1 true? Yes. -3 ≤ -1 is false. We cannot eliminate C.
D. Is 0 + 5 < 4 true? No. 5 < 4 is false. This eliminates D.
So based on using x=0, the only possible solution is C.
You can double check this by solving 2x - 3 ≤ -1 for x:
-2x - 3 ≤ -1
-2x ≤ 2 (by adding 3 to both sides)
Now when you divide by -2 to solve for x, remember to flip the inequality.
-2x ≤ 2
x ≥ -1
So this confirms that C is correc.
Which composite figure is made up of a cylinder and a half sphere?
Answers
Find the value of m if polynomial p(x) = 4x2 – 6x – m is exactly divisible by x – 3.
Answers
Answer:
Since p(x) is exactly divisible by x – 3, then p(3) = 0.
Plugging in x = 3 into p(x), we get
4(3)2 – 6(3) – m = 0
36 – 18 – m = 0
m = 18
Therefore, the value of m is 18.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A system of linear equations is given by the tables. One of the tables is represented by the equation y = - + 7.
Answers
The Equation for Table I is y= 1/3x + 5.
The solution of the Equation is (3, 6).
Equation for Table II
y= -1/3 x +7
Table I:
Slope = (6-5)/ (3-0)
slope = 1/3
and, using slope intercept form
y - 5 = 1/3 (x - 0)
y-5 = 1/3x
y = 1/3x + 5
Now, solving the equation for both table we get
x= 3 and y= 6
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If f(3x - 1) = -6x + 3, find f f (2).
Answers
Therefore, function of x f(f(2)) = f(-3) = 9
Function (X) calculationTo find function of f f (2) we need to find the function f(2).
Given f(3x - 1) = -6x + 3
Let 3x -1 = 2 we will get
3x =3
x =1
Therefore, let input x =1
f(3x - 1) = -6x + 3
f(3(1) - 1) = -(1) + 3
Therefore, we need to find function of f(-3) and get f f (2).
f f (2). =f(-3) =9
f(3x - 1) = -6x + 3
f(-3) = -6(-1) + 3 =9
Therefore, if f(3x - 1) = -6x + 3, function of f(f(2)) = f(-3) = 9
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Solve 2x(3x+5)+3(3x+5)=ax 2 +bx+c
Answers
Answer:
6x² + 19x + 15
Step-by-step explanation:
2x(3x+5)+3(3x+5)
= (3x + 5) (2x + 3)
= 6x² + 9x + 10x + 15
= 6x² + 19x + 15
So, the answer is 6x² + 19x + 15
We can start by simplifying the left side of the equation using the distributive property:
2x(3x+5)+3(3x+5) = (2x)(3x) + (2x)(5) + (3)(3x) + (3)(5)
= 6x^2 + 10x + 9x + 15
= 6x^2 + 19x + 15
Now we can compare this expression with the right side of the equation, which is a polynomial in x with unknown coefficients a, b, and c:
ax^2 + bx + c
Since the two sides are equal, their corresponding coefficients must be equal as well. This gives us a system of three equations in three unknowns:
a = 6 (the coefficient of x^2)
b = 19 (the coefficient of x)
c = 15 (the constant term)
Therefore, the solution to the equation 2x(3x+5)+3(3x+5)=ax^2+bx+c is:
2x(3x+5)+3(3x+5) = 6x^2 + 19x + 15
measuring the concentration of a certain pollutant in a lake results in the determination that observations are normally distributed with mean (expectation) 210 units, and that there is a probability of 0.05 that a given measurement will exceed 250 units. 1. what is the standard deviation? 2. assuming that the standard deviati
Answers
The standard deviation is approximately 24.28 units.
1. The standard deviation can be calculated using the formula for the normal distribution:
P(X > 250) = 0.05
Using a standard normal distribution table, we can find the corresponding z-score for a probability of 0.05, which is approximately 1.645.
z = (250 - 210) / σ
Solving for σ, we get:
σ = (250 - 210) / z = (250 - 210) / 1.645 = 24.28 units
Therefore, the standard deviation is approximately 24.28 units.
To determine the standard deviation of a normally distributed pollutant concentration in a lake, we first use the probability of exceeding 250 units (0.05) and a standard normal distribution table to find the corresponding z-score (1.645). Using this z-score and the given mean (210 units), we can solve for the standard deviation using the formula for the normal distribution. The resulting standard deviation is approximately 24.28 units.
The standard deviation is an important measure of variability in a dataset and can be calculated using the formula for the normal distribution. In this case, the standard deviation of a normally distributed pollutant concentration in a lake was calculated using the mean and probability of exceeding a certain value.
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how many units is -1+(-4) from -1
Answers
The expression -1 + (-4) is 4 units away from -1.
How to find the unitsThis can be solved using the concept of number line.
A number line is a visual representation of all real numbers placed on a straight line with an arbitrary point as the origin the origin is usually represented as zero and the numbers increase from left to right or from right to left
Another way is to find how many units -1 + (-4) is from -1, we need to subtract -1 from -1 + (-4) this is done below
= -1 + (-4) - (-1)
= -1 - 4 + 1
= -4
we can say that, -1 + (-4 ) is 4 units away from -1.
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Polar Coordinates
4. Name two different representations of the
point on the interval of [-2π, 2π].
Given P = (2,π /4).
Please help me, I got it wrong.
Please refer to picture.
Answers
The polar coordinates are solved the point is P ( 2 , π/4 )
Given data ,
Given the point P = (2, π/4) on the interval [-2π, 2π], here are two different representations of this point:
Cartesian Coordinates: (2, π/4)
In the Cartesian coordinate system, the point P is represented by its x and y coordinates. The x-coordinate is 2, and the y-coordinate is π/4.
Polar Coordinates: (2, 45°)
In polar coordinates, the point P is represented by its radius (distance from the origin) and angle. The radius is 2, and the angle is π/4, which is equivalent to 45 degrees.
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snow is falling in syracuse ny on wednesday morning there was 3 inches of snow in the morning and it is falling at a constant rate of 2 inches per hour. on friday morning there was 5 inches of snow on the ground and it is falling at a constant rate of 1 inch per hour. after how many hours would the total snow on the ground on each day be equal?
Answers
To solve this problem, we need to use algebra. Let x be the number of hours that have passed since Wednesday morning. Then the total snow on the ground on Wednesday morning is 3 inches, and the total snow on the ground at any time x hours later is:
3 + 2x
Similarly, the total snow on the ground on Friday morning is 5 inches, and the total snow on the ground at any time x hours later is:
5 + 1x
To find out when these two totals are equal, we can set the expressions equal to each other and solve for x:
3 + 2x = 5 + 1x
Subtracting 1x from both sides, we get:
2x = 2
Dividing both sides by 2, we get:
x = 1
Therefore, the total snow on the ground would be equal after 1 hour.
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3.a coin is tossed, and a die is rolled. what is the probability that the outcome is a head or an even number?
Answers
According to the statement the probability of getting either a head or an even number on the die is 3/4.
To calculate the probability of getting a head or an even number, we can use the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
In this case, A represents getting a head, and B represents getting an even number on the die.
P(A) = Probability of getting a head = 1/2 (since there are two sides of the coin: heads and tails)
P(B) = Probability of getting an even number on the die = 3/6 (since there are three even numbers out of six possible outcomes: 2, 4, and 6)
P(A ∩ B) = Probability of getting both a head and an even number. Since these two events are independent, we can find this probability by multiplying the individual probabilities: P(A) * P(B) = (1/2) * (3/6) = 1/4
Now, we can find the probability of the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (1/2) + (3/6) - (1/4) = 1/2 + 1/2 - 1/4 = 3/4
So, the probability of getting either a head or an even number on the die is 3/4.
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How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
A. 0
B. 1
C. 2
D. 3
E. 4
Answers
The number of horizontal asymptotes that graph of y = f(x) can have is (c) 2.
As x approaches negative infinity, the function f(x) approaches the horizontal-asymptote y = 0 because the term 1/x becomes negligible compared to other terms. This occurs in the portion of the function defined as 1/x when x < 0.
As x approaches positive infinity, the function f(x) approaches the horizontal-asymptote y = 2 because the term 2x becomes dominant compared to other terms. This occurs in the portion of the function defined as 2x - 1 when x ≥ 0.
Therefore, the graph of y = f(x) has two horizontal asymptotes: y = 0 as x approaches negative infinity and y = 2 as x approaches positive infinity. The correct answer is (c) 2.
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The given question is incomplete, the complete question is
How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)
f(x) = {1/x , if x<0,
= {2x - 1 , if x≥0.
(a) 0
(b) 1
(c) 2
(d) 3
(e) 4
Factorize a2 - b2
[tex]a {?}^{2} - b {?}^{2} \\ \\ [/tex]
Answers
The factorization of the given expression, a² - b², is (a + b)(a - b)
Factorizing an expressionFrom the question, we are to factorize the given expression.
From the given information, the given expression is
a² - b²
This is a special case in the factorization of polynomials. This is called difference of two squares.
Given the expression
x² - y²
The above expression can be written in the factorized form as
(x + y)(x - y)
Check:
Check by expanding the above factored form
(x + y)(x - y)
Applying the distributive property
x(x - y) + y(x - y)
x² - xy + xy - y²
Simplify further
x² - y²
Thus,
x² - y² = (x + y)(x - y)
In the same manner,
a² - b² = (a + b)(a - b)
Hence, the factorization of a² - b² is (a + b)(a - b)
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Help with my math please
Answers
Answer:
Step-by-step explanation:
x+y=5; x-y=3Adding both equations, we get:
2x = 8
x = 4Substituting the value of x in any of the equations:
x+y=5
4+y=5
y=1So the solution to this system of equations is: x=4, y=1.3x+y=11; y=x+3Substituting y=x+3 in the first equation:
3x+x+3=11
4x=8
x=2Substituting x=2 in the second equation:
y=x+3
y=2+3
y=5So the solution to this system of equations is: x=2, y=5.x+3y=0; 2x-y=-7Multiplying the second equation by 3 to eliminate y:
6x-3y=-21Adding both equations, we get:
7x=-21
x=-3Substituting x=-3 in the first equation:
x+3y=0
-3+3y=0
y=1So the solution to this system of equations is: x=-3, y=1.y=-3x-2; 6x+2y=-4Substituting y=-3x-2 in the second equation:
6x+2(-3x-2)=-4
6x-6x-4=-4
-4=-4This means that the two equations are equivalent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.-4x+5y=27; x-6y=-2Multiplying the second equation by 5 to eliminate y:
5x-30y=-10Adding both equations, we get:
x-4x+5y-30y=-2+27
-x-25y=25
25y=-x-25
y=-(1/25)x-1Substituting y=-(1/25)x-1 in the first equation:
-4x+5(-(1/25)x-1)=27
-4x-5/5x-5=27
-9x=32
x=-32/9Substituting x=-32/9 in the expression for y:
y=-(1/25)(-32/9)-1
y=83/225So the solution to this system of equations is: x=-32/9, y=83/225.
please help me I dont know how to do this please I need it done ASAP!!!!!
Answers
All the solutions are as;
LJ = 18 feet
m GM = 77 deg
m QT = 142 deg
m ∠STR = 23 deg
m ST = 13 deg
m RQ = 38 deg
Now, We can formulate;
Since, KP = PL
Hence, HP = PJ
Then, Δ PKH ≅ Δ PLJ
By HL property.
As point K, L are midpoint of GH and GJ.
Then, KH ≅ LJ = 1/2(JH)
⇒ LJ = 1/2 (36) = 18 feet
As, GH ≅ GJ
Then,
m GM = 1/2 (1/2 (m GM) = 1/4 (360 - 52) = 77 deg.
As, m ∠QST = 71°,
So, m QT = 2 (m ∠QST) = 2 (71) = 142 deg
m ∠STR = 1/2 (m SR) = 1/2 (46) = 23 deg
As RT is a diameter then,
m ∠TSR = 90°
Then, m ∠SRT = 190 - 90 - m ∠STR
m ∠SRT = 67 deg
Hence, m ST = 2 m ∠SRT = 2 (67) = 134 deg
Since, m ∠RSQ = 90 - 71 = 19 deg
And, m RQ = 2 ( m ∠RSQ)
m RQ = 2 × 19 = 38 deg
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Evaluate the following expression.
25
1/25
-25
-1/25
Answers
The expression is evaluated to 1/25. Option B
What are index forms?Index forms are simply described as distinct mathematical forms that are used in the representation of variables or numbers that are too large or too small in more convenient forms.
These index forms are also referred to as scientific notations or standard forms.
Some rules of index forms are;
Add the exponent value of variables or number that have the same bases and are being multipliedSubtract the exponent value of variables or number that have the same bases and are being dividedThe value of a number with negative power is its inverseFrom the information given, we have that;
1/5⁻²
Take the inverse power
1/25
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What is the range of f(x) = 3x + 9?
{y | y < 9}
{y | y > 9}
{y | y > 3}
{y | y < 3}
Answers
The range of the given function is {y|y>9}. Therefore, option B is the correct answer.
The given function is f(x)=3x+9.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
Substitute x=0, 1, 2, 3, 4,....in y=3x+9, We get
When x=0
y=9
When x=1
y=12
When x=2
y=15
When x=3
y=18
So, the range is {9, 12, 15, 18,.....}
Therefore, option B is the correct answer.
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