1: cscX = 1/sinX = 5/2√5.
2: Using the reciprocal identity of tanA and sinA,
tanA/sinA = 1/cosA
√2/2 / -√3/3 = 1/cosA
-2√2/2√3 = 1/cosA
cosA = -2√3/2√2.
What are the responses to other questions?3: Using the Pythagorean theorem, sinX = √(1 - cos^2X)
√(1 - cos^2X) = √((1/cot^2X) - 1) = √((√3/2)^2 - 1) / (-√3/2)
sinX = √2/2.
4: Using the Pythagorean theorem,
cotθ = cosθ / sinθ = 1 / tanθ = 1 / (√(1 - cos^2θ) / cosθ) = cosθ / √(1 - cos^2θ) = 1 / (√(1 - (1/7)^2)) = √(48) / 7.
5: Using the cofunction identity, tan(-x) = -tan(x).
Using the identity that tan(π/2 -x) = cot(x),
-tan(x) = -1/cot(π/2 -x) = -1/(-1.84) = 1.84.
6: Using the even-odd identity, cos(-θ) = cos(θ), and
sin(-θ) = -sin(θ),
cos(θ-π/2) = cosθcos(π/2) + sinθsin(π/2) = 0cos(π/2) + (-0.57)sin(π/2) = -0.57.
7: Using the identity sin^2X + cos^2X = 1,
secX ⋅ sin^2X + cosX = secX ⋅ (1 - cos^2X) + cosX = secX - secXcos^2X + cosX = secX + cosX.
8: Using the identity 1 + tan^2θ = sec^2θ,
(sinθ + 1)(tanθ - secθ) = (sinθ + 1)(tanθ - 1/cosθ) = (sinθ + 1)(tanθcosθ - 1) = (sinθ + 1)sinθ(tanθ/sinθ) - (sinθ + 1) = sinθ + sin^2θ - sinθ - 1 = sin^2θ - 1.
Proof:
Using the identity tan^2X = sin^2X / cos^2X,
1+sec^2X / 1+tan^2X = (1 + 1/cos^2X) / (1 + sin^2X / cos^2X) = cos^2X / (cos^2X + sin^2X) = cos^2X / (1) = 1 + cos^2X.
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It took Mr. Black 2 hours to drive to his friend's house. On the way back the traffic was heavy, and Mr. Black drove 20 mph slower. The trip back took 1 hour longer. What was Mr. Black's speed to his friend's house?
Mr. Black was driving at 60 mph to his friend's house.
What was Mr. Black's speed to his friend's house?Let's call Mr. Black's speed to his friend's house "x".
The trip back took x - 20 mph, since he was driving 20 mph slower.
The trip back took 1 hour longer, so it took 2 + 1 = 3 hours.
Using the formula for distance = rate x time, we can set up the equation:
x * 2 = (x - 20) * 3
Expanding and simplifying, we get:
2x = 3x - 60
Subtracting 2x from both sides:
0 = x - 60
Adding 60 to both sides:
x = 60 mph
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QUESTION 9 1 POINT
Determine the interval(s) for which the function shown below is decreasing.
A function is decreasing if as x-values increase, the y-values decrease. Graphically this means that if you move from left-to-right, the graph goes down.
The downhill portion of this curve is on the interval [tex](1,\infty)[/tex].
Please help can’t find the answer anywhere
Answer:
3 rd choice
Step-by-step explanation:
If you flip ΔABC over and lay it over ΔXYZ, you'll see how the sides correspond:
AB≅XZ
BC≅ZY
CA≅YX
just a quick addition to "MelRUZ" great reply above. Check the picture below.
A dress is on sale for - dollars. The regular price is 3 times as much. Jannie has enough Mooney to buy 2 dresses at the regular price. How many dresses can jannie buy at sale price?
1 dress
3 dresses
6 dresses
9 dresses
The employees at VideoRama get 3 days of vacation as soon as they are hired. They can then earn an extra half day of vacation for every game they agree to test, at home. If Dumi plays 10 games at home, how many vacation days would Dumi have altogether? Label your answer.
Answer:
8 vacation days.
If every game he plays, he gets 1/2 of a vacation day, then to find, we just will multiply the amount of games by 1/2 of a vacation day.
10 * 1/2 = 5
Plus, he already has 3, so just add three to get the total.
5 + 3 = 8
Step-by-step explanation:
Hope it helps! =D
Looking for REAL ANSWER AND SOLUTION please i need it to study. Help me math experts
A function: 9x² - y² = 1.
Differentiating with respect to x is 18x - 2y dy/dx = 0.
The correct option is B.
What is differentiation?Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.
Given:
A function: 9x² - y² = 1.
Differentiating with respect to x,
we get,
d/dx(9x² - y²) = d/dx(1)
18x - 2y dy/dx = 0
Therefore, the derivative is 18x - 2y dy/dx = 0.
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Identify the parent function that can be used to graph the function(x) = -2x + 2
a. f(x)=x²
f(x)=x
b. f(x)=[x]
1
(x) ==
Please select the best answer from the choices provided
OA
B
C.
d.
OD
א
f(x)=x is the parent function of the given function f(x) = -2x + 2
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=-2x+2
We have to find the parent function of the given function.
A parent function is the simplest function of a family of functions that preserves the definition of the entire family.
f(x)=x is the parent function because from this function we can make transformations that allow us to obtain the function f(x) = -2x + 2
Hence, f(x)=x is the parent function of the given function f(x) = -2x + 2
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1 6/11 ft of fabric is needed to make a rug? while 4 1/2 ft of fabric is required to make pillows/ Producing a rug is 2 2/7 times faster than pilliws/ How much more fabric is needed to make pillows versus a rug
2 21/22 feet of more fabric is required to make pillows versus a rug.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, 17/11 ft of fabric is needed to make a rug, while 9/2 ft of fabric is required to make pillows.
Also given that producing a rug is 16/7 times faster than pillows.
Therefore, The amount of extra fabric needed to make a pillow compared to a rug is,
= (9/2 - 17/11).
= (99 - 34)/22.
= 65/22 feet.
= 2 21/22 feet.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options.
2(x2 + 6x + 9) = 3 + 18
2(x2 + 6x) = –3
2(x2 + 6x) = 3
x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot
2(x2 + 6x + 9) = –3 + 9
Inga is solving 2x² + 12x – 3 = 0 therefore the steps which she could use to solve the quadratic equation include the following below:
2(x² + 6x + 9) = 3 + 182(x² + =6x) = 3x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRootWhat is Quadratic equation?This is referred to as an algebraic equation of the second degree in x and its standard form is ax² + bx + c = 0
Solution to the quadratic equation
2x² + 12x - 3 = 0
2x² + 12x = 3
Divide by 2
x² + 6x = ³/₂
(x + 3)² = ³/₂ + 3²
x² + 6x + 9 = 9 + ³/₂
2(x² + 6x + 9) = 18 + 3
Thus, the steps that she could use to solve the quadratic equation is determined as option 1, 3 and 4.
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one ordered pair that is a solution of y is greater then or equal to 4
On solving the provided question, we can say that the inequality formed is 1 ≥ 2(3)-5 => 1 ≥ 1
What is inequality?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
The ordered pair is (3, 1)
Substitute (x, y)=(3, 1) in the given inequality, we get
the inequality formed is
1 ≥ 2(3)-5
1 ≥ 1
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Which numbers are the least to the greatest?
0.9
0.35
11/100
7/10
0.6
0.21
Answer:
0.9, 0.6 7/10, 11/100, 0.21, 0.35
Step-by-step explanation:
At Hometown Hospital, the cancer registrar recorded the age (at the time of initial diagnosis) of patients diagnosed with lung cancer. A total of 68 cases were recorded. The ages are ranked from oldest to youngest.
91 86 83 82 81 80 80 79 78 77 76 75 75 74 74 73 73 72
72 72 71 71 70 70 70 70 69 69 68 68 67 67 67 66 66 66
66 66 65 65 65 64 64 63 63 62 62 61 61 61 60 60 59 59
59 58 58 57 57 57 56 56 55 54 53 53 52 51
Complete the frequency distribution table with the following data:
1. All score limit ranges
2. Frequency
3. Cumulative frequency
4. Relative frequency [round to two decimal places]
5. Frequency percentage [should be a whole percentage without decimals]
6. Graph your frequency distribution in a histogram [grouped data] Make sure to label the histogram and give it a title.
7. One paragraph [4-5 sentences] that would let your readers know what your table means/shows.
score limits f cf rel. f freq. %
91-95
51-55
Then determine the value for:
1) 1st decile
2) 3rd decile
3) 65th percentile
4) 85th percentile
5) Percentile for an age of 71
6) Average age at time of diagnosis
Answer:
First Class Group is given as 25-29 Class size = 29-25=4 Make the reminding classes of same size till 89-93 Count the values and write the frequency against the respective
Describe a situation that you can model with 6m+3 = 27. Explain what the variable represents and solve the equation.
Answer:
Step-by-step explanation:
its 18+27 because you have to do 6x3 wich is 18 and add 27 to 18
Answer:
4
Step-by-step explanation:
Subtract 3 from both sides.Then divide both sides by 6 to give you your answer.Someone help me with this math problem.
Answer:
Good luck man.
Step-by-step explanation:
Ima be honest, I got no idea.
Jada has some cube-shaped boxes. She stacks them inside an empty cube-shaped storage container. The container has side lengths of 60 inches (in.). Each box has side lengths of 20 in. After Jada stacks the boxes inside the container, there are still 32,000 in.3 of empty space remaining in the container. How many boxes does Jada stack inside the container? 22 23 27 31
Jada stacked 23 boxes inside the container.
What are cubes?Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Given that, Jada put some cube-shaped boxes having lengths 20 in, in a cubed container has side lengths of 60 inches in.
After, Jada stacks the boxes inside the container, there are still 32,000 in³ of empty space remaining in the container.
We need to find the number of the boxes in the container.
Volume of cube = (side)³
Volume of container = 60³ = 216000 in³
Volume of the container covered by stacking the boxes =
216000 - 32000
= 184000 in³
Volume of each box = 20³
= 8000 in³
Number of boxes in the container = volume of the container covered by stacking / volume of each box
Number of boxes = 184000 / 8000
= 23
Hence, Jada stacked 23 boxes inside the container.
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Factor out the greatest common factor.
2x³ + 8x² - 4x
Answer:
[tex]2x(x^2+4x-2)[/tex]
Step-by-step explanation:
We can factor out 2x:
[tex]2x^3+8x^2-4x=2x(x^2+4x-2)[/tex]
A church group set off from their
Church at 9:00a.m. The group had to change a tire at 9:38 a.m. the group noted that the trip took them 77 minutes to finish what time did the church group arrive at the canyon
Answer:
Below
Step-by-step explanation:
77 min is 1 hour 17 min...add this to the 9:00 start to find 10 :17 am
Please help me with my math
Answer:
square 3. Multipky the result by -2 and then subtract 4.
Step-by-step explanation:
comment if u need explanation
Find the area of the rectangle
What is the area of the rectangle?
The area of the rectangle = 9x² +18x−16
What is the area of the rectangle?
The area of a rectangle is calculated by multiplying the height by the width. If the height of the rectangle is represented by h and the width is represented by w, then the area is given by:
A = h * w
In this case, the height of the rectangle is given as 3x - 2 yards, and the width is given as 3x + 8 yards. So, substituting these values into the formula:
A = (3x - 2) * (3x + 8)
A = (3x - 2)(3x + 8)
A = 9x² +18x−16
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The answer is:
9x² - 64Work/explanation:
To find the rectangle's area, we use the formula
[tex]\pmb{A=LW}[/tex]
Where A = area;
L = length;
w = width.
Plug in the data
[tex]\sf{A=(3x+8)(3x-8)}[/tex]
To multiply, use FOIL:
F = first
o = outside
i = inside
l = last
Multiply
[tex]\sf{3x\cdot3x=9x^2}[/tex]
[tex]\sf{3x\cdot(-8)=-24x}[/tex]
[tex]\sf{8\cdot3x=24x}[/tex]
[tex]\sf{8\cdot(-8)=-64}[/tex]
-------------------
[tex]\sf{9x^2-24x+24x-64}[/tex]
[tex]\sf{9x^2-64}[/tex]
Hence, the area is 9x² - 64.Identify the graph of the system of linear inequalities.
y>-3 y≥5x
The common region represents the solution set to the both inequalities.
What is an inequality?An inequality is used to compare two or more expressions.
For example -
ax + b > c
ax + b < c
Given are the inequalities -
y > -3
y ≥ 5x
Refer to the graph of the inequalities attached. The common region represents the solution set to the both inequalities.
Therefore, the common region represents the solution set to the both inequalities.
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G
Identifying Exponential Growt
Which is an exponential growth funcion
0f3=61025/
04-0295254
0f=423
0fx)=(-1257
Answer:
The exponential growth function 0f3=61025/ 04-0295254 0f=423 0fx)=(-1257 is not a valid equation.
Step-by-step explanation:
I need this for math homework anyone on tonight to help? 5/8 = x/12 x=
What is the estimated answer of 0.93 x 2.6
Answer:
2.5!
Step-by-step explanation:
round 0.93 up to 1 and 2.6 down to 2.5
1*2.5 = 2.5
Answer:like 3
Step-by-step explanation:
Examine the triangle below, find the m
mZM=The length of NP is 6.28 cm
What do you mean by triangle?A triangle is a two-dimensional geometric shape with three sides and three angles. It is one of the basic shapes in geometry and has many different properties that can be studied. Triangles can be classified into several different types based on the length of their sides and the size of their angles.
The most basic type of triangle is an equilateral triangle, which has three sides of equal length and three equal angles. Another common type of triangle is the right triangle, which has one right angle (90 degrees) and two other angles that add up to 90 degrees. Scalene triangles have no sides or angles of equal length, while isosceles triangles have at least two sides of equal length.
Triangles have many interesting and useful properties that can be used in geometry and other areas of mathematics. For example, the Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side. This theorem can be used to find the length of a missing side in a right triangle.
To find angle P and angle M, we can use the fact that the sum of the angles in a triangle is 180 degrees.
angle P + angle M + 46 = 180
angle P + angle M = 134
Next, we can use the law of cosines to find angle P. Let's call the length of NP "x".
cos(angle P) = (MN² + MP² - x²) / (2 × MN × MP)
We can use the formula for cosine to solve for angle P:
angle P = arccos((MN² + MP² - x²) / (2 × MN × MP))
Substituting in the values for MN and MP:
angle P = arccos((4² + 7² - x²) / (2 × 4 × 7))
Next, we can use the Pythagorean theorem to find x:
x^2 = MN^2 + MP^2 - 2 * MN * MP * cos(angle P)
x^2 = 4^2 + 7^2 - 2 * 4 * 7 * cos(angle P)
x² = 49 - 56 × cos(angle P)
Substituting in the value we found for angle P:
x² = 49 - 56 × cos(arccos((4² + 7² - x²) / (2 × 4 × 7)))
Solving for x, we get:
x = sqrt(49 - 56 × cos(arccos((4² + 7² - x²) / (2 × 4 × 7))))
x = sqrt(49 - 56 × cos(arccos(33 / 28)))
x = √(49 - 56 × (33 / 28) / √(33² + 28²))
x = √(49 - 56 × 33 / 28 / √(33^2 + 28^2))
Finally, we can use the value we found for x to find angle M:
angle M = 134 - angle P
angle M = 134 - arccos((4² + 7² - x²) / (2 × 4 × 7))
So the final answers are:
angle P = arccos((4² + 7² - x²) / (2 × 4 × 7)) = 68.93 degrees
angle M = 134 - angle P = 65.07 degrees
length of NP = x = sqrt(49 - 56 × 33 / 28 / √(33² + 28²)) = 6.28 cm
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There are 27 boys and 35 girls in the assembly hall and there are 15 boys and 17 girls in the laboratory room. Which room has the higher proportion of girls?
Which property is being illustrated x=y+4 and y+4=-22, then x=-22
The property illustrated for the given expression is substitution method.
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Given that the two expressions are:
x=y+4 and y+4=-22
Here, the value of y + 4 is substituted in the value of x for the first expression.
Hence, the property illustrated for the given expression is substitution method.
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Which of the following statements about the image below is true?
Line UR and Line VW are parallel.
The measure of
Line UR and Line VS are perpendicular.
The statement about the image below that is true is option A. Line UR and Line VW are parallel.
What is a parallel line?Parallel lines are two lines that are always the same distance apart and never meet, regardless of how far they are extended.
A perpendicular line, on the other hand, is a line that intersects another line at a right angle (90 degrees)
Therefore, the statement about the image below that is true is option A. Line UR and Line VW are parallel. It could then be concluded that the correct answer is option A.
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The complete question goes thus:
Which of the following statements about the image below is true?
A. Line UR and Line VW are parallel.
B. The measure of angle SWX is 72°
C. Line UR and Line VS are perpendicular..
D. Angle SWR and angle WRS are supplementary.
Solve the following system of equations:
−7x+3y=−48
3x+5y=−36
The solution of the linear equations −7x + 3y = −48 and 3x + 5y = −36 will be (3, −9)
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
−7x + 3y = −48 ...1
3x + 5y = −36 ...2
Multiply equation 1 by 5 and equation 2 by - 3, then we have
−35x + 15y = −240
−9x − 15y = 108
Add both equations, then we have
−44x = −132
x = 132 / 44
x = 3
Then the value of 'y' is given as,
3(3) + 5y = −36
9 + 5y = −36
5y = −45
y = −9
The solution of the linear equations −7x + 3y = −48 and 3x + 5y = −36 will be (3, −9)
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pilar said that the expressions -4x + 3x + 2 and -x + 2 are equivalent. is pilar correct. explain
Yes, this is correct. If you solve the first equation it equals the second equation.
What is the value of y?
The vertical value in a pair of coordinates. How far up or down the point is. The Y Coordinate is always written second in an ordered pair of coordinates (x,y) such as (12,5). In this example, the value "5" is the Y Coordinate.