Part (c)
[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]
Part (d)
[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]
Determine the missing information in the paragraph proof.
Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).
Prove: The slopes of perpendicular lines are negative reciprocals.
On a coordinate plane, 2 perpendicular lines are shown. Line P Q has points (a, b) and (c, d). Line P prime Q prime has points (negative b, a) and (negative d, c).
The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction
The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = negative 1
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = negative 1
(StartFraction d minus b Over c minus a EndFraction) (StartFraction c minus a Over negative d + b EndFraction) = 1
(StartFraction b minus a Over a + b EndFraction) (StartFraction c minus d Over negative d minus c EndFraction) = 1
Mark this and return
The slopes of perpendicular lines are negative reciprocals is proved.
What is Equation of a Straight Line ?An equation of a straight line is given by
y = mx +c
It is given that
Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular.
Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).
The slopes of lines PQ and P’Q’ can be determined using the formula
[tex]\rm m = \dfrac{ v _2 - v _1 }{ x _2 -x _1 }[/tex]
The product of these slopes is -1 .
This product shows that the slopes are negative reciprocals
Therefore , The slopes of perpendicular lines are negative reciprocals is proved,
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A cheesecake has equally sized slices. Each slice is a different flavor. The diameter of the cheesecake is 10 inches, and the area of the slice of blueberry cheesecake is 25π16 square inches.
How many slices does the cheesecake have?
A cheesecake has equally sized slices. Each slice is a different flavor. The cheesecake has 12 slices.
What is the area of the circle?
The area of the circle is defined as the product of the pie and the square of the radius.
The area of the circle = πr²
In order to calculate the total area of the cheesecake, since it's a circle its area is given by:
cheesecake area = πr²
cheesecake area = π(10/2)² = π(5)²
cheesecake area = 25 π square inches
Therefore the number of slices is the ratio of the cheesecake total area by the area of each slice:
The number of slices = 25 π/(25 π/12)
The number of slices = 12
The cheesecake has 12 slices.
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Answer: 12 slices
Step-by-step explanation:
im a year late woo hoo
Please help me solve this
The area bounded by the curves y = 8x – x² and y = 7 will be 36 square units.
The complete question is given below.
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The curves are given below.
y = 8x – x²
y = 7
By solving the equations 1 and 2, then we have
8x – x² = 7
x² – 8x + 7 = 0
(x – 1)(x – 7) = 0
x = 1, 7
Then the area bounded by the curves y = 8x – x² and y = 7 will be
[tex]A = \int _1^7 [(8x - x^2) - 7] \ dx\\\\A = \left [ 4x^2 - \dfrac{x^3}{3} - 7x \right ]_1^7\\\\A = \left [ 4 * 7^2 - \dfrac{7^3}{3} - 7*7 \right ] - \left [ 4*1^2 - \dfrac{1^3}{3} - 7*1 \right ]\\\\[/tex]
On further solving we have
A = 32.667 + 3.333
A = 36 square units
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What are the zeros of this function?
g(x) = 2(x + 2)(x - 9)
The zeros of function g are located at
and
Given parallelogram STUV, what is the length of TV?
The length of TV would be [tex]y^{2}[/tex] + 2y -1.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given parallelogram STUV,
The length of TW = [tex]y^{2}[/tex]
WV = 2y - 1
The length of TV = TW + WV
= [tex]y^{2}[/tex] + 2y -1
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Lily sold 18 items at the street fair. she sold bracelets for $6 each and necklaces for $5 each for a total of $101. which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold? b n = 101 6b 5n = 18 b n = 101 5b 6n = 18 b n = 18 6b 5n = 101 b n = 18 5b 6n = 101
Answer:
[tex]b + n = 18[/tex]
[tex]6b + 5n = 101[/tex]
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
[ ISN} and {TSW} so the answer is D
−3(a−8)+4a=−8(a+3)+3
A road is 450 metres long . It takes a woman 5 minutes to walk along the road . Work out the average speed of the woman . Give your answer in metres per second .
1. Choose the description that matches the inequality. x < 1
A line traveling to the left with an closed dot on x=1.
A line traveling to the right with an open dot on x=1.
A line traveling to the right with an closed dot on x=1.
A line traveling to the left with an open dot on x=1.
Answer:
A line traveling to the left with an open dot on x=1.
Explanation:
The inequality x < 1 basically means "less than 1." On number lines, the further left you go, the smaller the number becomes, and the further right you go, the larger the number becomes. So we know that because it's less or smaller than 1, then the line will be to the left. On the other hand, the inequality does not have a line under it to indicate a "less than or equal to 1," just "less than." Therefore, the dot is open. If there were a line under the inequality, then it would indicate "less than or equal to 1" and the dot would be closed.
evaluate 2x^2-1 when x=3
[tex] \sf{\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's evaluate ~
[tex]\qquad \sf \dashrightarrow \: 2 {x}^{2} - 1[/tex]
plug in the value of x :
[tex]\qquad \sf \dashrightarrow \: 2(3) {}^{2} - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 2(9) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 18 - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 17[/tex]
The required value is 17
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Option B, 17}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{2x}^2\textsf{ - 1}[/tex]
Find: [tex]\textsf{When x = 3}[/tex]
Solution: In order to find the value when x is equal to 3 we just need to equate any x to the value of 3 and simplify.
Plug in the values
[tex]\textsf{2x}^2\textsf{ - 1}[/tex][tex]\textsf{2(3)}^2\textsf{ - 1}[/tex]Simplify the expression
[tex]\textsf{2(3 * 3) - 1}[/tex][tex]\textsf{2(9) - 1}[/tex][tex]\textsf{18 - 1}[/tex][tex]\textsf{17}[/tex]Therefore, the answer that would make most sense would be option B, 17.
As seen in the diagram below, Hawa is building a walkway with a width of a feet to go
around a swimming pool that measures 19 feet by 6 feet. If the total area of the pool
and the walkway will be 770 square feet, how wide should the walkway be?
Answer:
8 feet
Step-by-step explanation:
you have to calculate :(19+2x)(6+2x)=770
you will get X1=8,X2= negetive some value but measurement cant be negative .if you put X=8 you'll find LHS=RHS
Answer:
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
Step-by-step explanation:
So first you need to find the area of the swimming pool:
19*6 = 114
Next you add the area of the swimming pool and the area of the walkway:
114 + 770 = 884
After this you solve for x using this equation:
(19 +2x) * (6 + 2x) = 884
This would normally find the area of the whole swimming pool area and the walkway but because we know that we can use it to solve for x.
The step-by-step is this:
[tex]4x^{2} +50x+114=884[/tex]
[tex]4x^2+50x+114-884=884-884[/tex]
[tex]4x^2+50x+114-884=0[/tex]
Now we'll use the quadratic formula to simplify it farther:
[tex]x= \frac{-(50) + \sqrt{(50)^2-4(4)(-770)} }{2(4)}[/tex]
[tex]x=\frac{-50 + or - \sqrt{14820} }{8}[/tex]
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
The length of a rectangle exceeds its width by 4
inches, and the area is 60 square inches. What
are the length and width of the rectangle?
Answer:
length = 10 in, width = 6 in
Step-by-step explanation:
Let the width be x.
Then, length = (x+4)
Area = 60 in²
Area of a rectangle = width × length
60 = x × (x+4)
60 = x² + 4x
x² + 4x - 60 = 0
Splitting the middle term :-
x² + 10x - 6x - 60 = 0
x (x + 10) - 6 ( x + 10) =0
(x + 10) ( x - 6)
x = -10 (doesn't fulfill our requirement)
x = 6
So, width = 6 in
length = 6+4 = 10 in
Follow the steps to find the
area of the shaded region.
Use trigonometry to find
the height of the triangle.
Hint: Use SOHCAHTOA
h = [?] cm
51%
8 cm
Round to four decimal places.
129°
8 cm
Answer:
6.2172
Step-by-step explanation:
sin129=h/8
h=8(sin129)
8 x 0.77714596... =
6.2172
I just did it.
The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. The height of the triangle is 6.2172 cm.
What is Sine (Sinθ)?The Sine or Sinθ in a right-angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
In the given diagram let the centre of the circle be represented by O, while the point at which line segment h and the circle intersect be represented by B. Also, the point at which the 90° angle is formed is represented by A.
Now, in the ΔABO, for the ∠AOB, the sine ratio of the trigonometric function can be written as,
sin(θ) = perpendicular / Hypotenuse
sin(51°) = AB / OB
sin(51°) = h/ 8 cm
8cm × sin(51°) = h
h = 6.2172 cm
Hence, the height of the triangle is 6.2172 cm.
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How is the graph of the parent function y = x squared transformed to produce the graph of y = 3 (x + 1) squared?
It is translated 1 unit right and compressed vertically by a factor of 3.
It is translated 1 unit left and compressed vertically by a factor of 3.
It is translated 1 unit right and stretched vertically by a factor of 3.
It is translated 1 unit left and stretched vertically by a factor of 3.
Answer:
D.
Step-by-step explanation:
Consider the equation. Which graph shows a line that is perpendicular to the line defined by the given equation? A. In a linear graph line diagram, A line passes through (minus 4, minus 2) and (2, minus 0.5) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. B. In a linear graph line diagram, A line passes through (2, 0.5) and (minus 4, 2) which intersects the x-axis at 4 units and the y-axis at minus 1 unit. C. In a linear graph line diagram, A line passes through (2, 4) and (0.5, minus 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units. D. In a linear graph line diagram, A line passes through (2, minus 4) and (0.5, 2) which intersects the x-axis at 1 unit and the y-axis at minus 4 units.
The graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The question is incomplete:
The complete question is:
Consider the equation y = 4x - 2 Which graph shows a line that is perpendicular to the line defined by the given equation?
Please refer to the attached picture.
The given line:
y = 4x - 2
The slope of the line m = 4
The slope of the line which is perpendicular to the above line:
M = -1/4 = -0.25
The graph second has a slope of -0.25
[tex]\rm y\ -2\ =\ \dfrac{\left(2-0.5\right)}{-4-2}\left(x+4\right)[/tex]
y - 2 = -0.25x - 1
y = -0.25x + 1
Thus, the graph second represents the line that is perpendicular to the line y = 4x - 2 option (B) is correct.
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A drawer is filled with 2 black shirts, 7 white shirts, and 11 gray shirts. One shirt is chosen at random from the drawer. Find the probability that it is not a black shirt.
Answer: Probability = 90%
Step-by-step explanation:
In a drawer we have:
2 black shirts
7 white shirts
11 gray shirts
If we would randomly pick a shirt, what are the chances of it not being black?
To do that, we first need to calculate the probability of getting a black shirt.
To calculate that, we need to divide the number of black shirts by the total number of shirts.
Black shirts = 2
Total shirts = 2 + 7 + 11 = 20
That will be 2 black shirts divided by 20.
We get 0.1
If we multiply 0.1 by 100%, we get a 10% chance to get a black shirt.
Now, to know to chances of not getting a black shirt, we just need to subtract 10% from 100%.
And that will be 90% chances of not getting a black shirt.
Probability = 90%
Hope I Helped!
A group of 35 people are running a race. The top 9 finishers advance to the finals. The number of possibilities for this situation involves a combination. A group of 35 people are running a race. The top 9 finishers advance to the finals. The number of possibilities for this situation involves a combination. True False
Answer:
false
Step-by-step explanation:
falswe
Part 1 - Application Pick one of the two graphs below. Describe a situation which could be modeled by this polynomial graph. Be sure to label the x and y axis with what each will represent in your real life graph. Sample labels could include time, temperature, speed, distance and more. Be sure to add numbers to your axes as well and explain how you came up with your situation.
One good example of a situation that can be modeled by this Polynomial Graph is the price-time relationship between currency pairs being traded on the Foreign Exchange Market.
What is a Polynomial Graph?A polynomial parameter graph is essentially a smooth continuous curve.
Although the forex graph attached has sharp undulations, when regressed and viewed via Polynomial Regression Indicators, they exhibit strong polynomial qualities that meet the requirements of the definition above.
It is to be noted that the Y-Axis is indicative of the price of the currency pairs (which could be any currency against another) and the X-Axis expresses time. See the attached graphs for a better picture.
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Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary?
Quadrilateral CDEF is inscribed in circle A. Quadrilateral CDEF is inscribed in circle A, so m arc CDE+ m arc CFE= 360°. ∠CFE and ∠CDE are _________________, which means that their measures are _________________. So, m arc CDE= 2 ⋅ m∠CFE and arc CFE = 2 ⋅ m∠CDE. Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.
central angles; equal to the measure of their intercepted arcs
inscribed angles; equal to the measure of their intercepted arcs
central angles; one half the measure of their intercepted arcs
inscribed angles; one half the measure of their intercepted arcs
The missing statements with regard to the mathematical proof are:
It is to be noted that an intercepted arc is the arc that sits inside the inscribed angle. See the attached image.
Thus, it is correct to state that
The missing statements with regard to the mathematical proof are:
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Can someone please help me
Answer:
minimum value is 3, maximum value is 4.459
Step-by-step explanation:
[tex] log_{2}(8) = \frac{ log(8) }{ log(2) } = 3[/tex]
[tex] log_{2}(22) = \frac{ log(22) }{ log(2) } = 4.459[/tex]
Which type of geometry best describes the following statement?
The boundaries of an arc are considered to be at infinity.
A. spherical geometry
B. Euclidean geometry
C. hyperbolic geometry
D. non-euclidean geometry
Answer:
B=hyperbolic geometry
which expression represents the volume of the prism
Answer:
Volume = (1/2)[tex]x^{3}[/tex] [(1/2)x^3]
Step-by-step explanation:
The volume of a right rectangular prism is given by:
Volume = (length)*(width)*(height)
Volume = (x)*(x)*((1/2)x)
Volume = (1/2)[tex]x^{3}[/tex]
Find the indicated length and explain your reasoning
Answer:
LM=25
MN=12
Now,
(M एउटै विन्दु हो)
LM+MN= LN
25+12=37
solve 15/4 -7 X=9 answer the question
[tex] \frac{15}{4} - 7x = 9 \\ \\ \frac{15}{4} - 9 = 7x \\ \\ 7x = \frac{15 - 36}{4} \\ \\ 7x = \frac{ - 21}{4} \\ \\ x = \frac{ - 21}{4 \times 7} \\ \\ x = \frac{ - 3}{4} .[/tex]
What is the value of x in the equation 8x – 2y = 48, when y = 4?
Answer: x = 7
Step-by-step explanation:
First, we will plug 4 in for y. Then, to solve we will isolate the variable "x" in the equation.
Given:
8x – 2y = 48
Plug in the y value of 4:
8x – 2(4) = 48
Multiply -2 times 4:
8x – 8 = 48
Add 8 to both sides of the equation:
8x = 56
Divide both sides of the equation by 8:
x = 7
Answer:
x=7
Step-by-step explanation:
8x – 2y = 48
Let y=4
8x -2(4) = 48
8x - 8 = 48
Add 8 to each side
8x-8+8= 48+8
8x = 56
Divide by 8
8x/8 = 56/8
x = 7
If the means of 5,11,6,4,7,p and 10 is 8,find the value of p.
Answer:
p = 13
Step-by-step explanation:
The mean of 5, 11, 6, 4, 7, 10, p is 8
So 8 = 5+11+6+4+7+10+p divided by 7.
So 56 = 43+p
Therefore p = 56-43
= 13
Hope I helped
⇒ 5 + 11 + 6 + 4 + 7 + p + 10 / 7 = 8
⇒ 43 + p = 56
⇒ p = 13
The value of p is 13.
Principal: $4,000 at 6% for a) 4 years, b) 4 months, and c) 4 days.
Answer:
If you're asking for the interest:
a) 960
b) 80
c)2.63 approx.
Step-by-step explanation:
interest = principal x rate x time OR [tex]I = prt[/tex]
TIME IS IN YEARS.
Thus, the first would be [tex]I = 4000 *4 *6%[/tex]% = 960
Second: 4 months = [tex]\frac{1}{3}[/tex] year
I = 4000x[tex]\frac{1}{3}[/tex]x6% = 80
Third: t = 4 days =[tex]\frac{4}{365}[/tex]year
I = 4000x6%x[tex]\frac{4}{365}[/tex] ≈ 2.63
Select all equations that are equivalent to x² + 6x = 16.
A.
x² + 6x + 9 =0
B.
x² + 6x + 9 = 16
C.
x² + 6x + 9 = 25
D.
(x+3)² = 0
E.
(x + 3)² = 16
F.
(x+3)² = 25
Answer:
C and F
Step-by-step explanation:
2×2+6×2=16
×=2
C ) 2×2+6×2+9=25 ×=2
F) (2+3)2=25 ×=2
Which of the following is not an example of unit rate?
3 dollars per toy
4 dollars per toy
1 toy per 5 dollars
6 dollars per toy
The unit rate is the rate for one of something (Taken from HMHCO).
For instance, you could say that Bob can make 6 gift cards in 3 hours. The unit rate would be 2 gift cards per hour. We solved for this by dividing both values by 3.
Solving the Question3 dollars per toy
This is a unit rate. Why? Because it gives us the rate, 3 dollars, and it is for one of something, which this case would be toys.
1 toy per 5 dollars
This is not a unit rate. Why? We still get the rate, 1 toy, but this time it isn't for one of something, which in this case is dollars. It is a rate for 5 dollars, not 1 dollar.
Answer1 toy per 5 dollars
