There are two ways to confirm the identity.
Method 1
[tex]\tan(x)\cot(x) = 1\\\\\tan(x)\frac{1}{\tan(x)} = 1\\\\\frac{\tan(x)}{\tan(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\[/tex]
--------------------------------------------
Method 2
[tex]\tan(x)\cot(x) = 1\\\\\left(\frac{\sin(x)}{\cos(x)}\right)\left(\frac{\cos(x)}{\sin(x)}\right) = 1\\\\\frac{\sin(x)\cos(x)}{\cos(x)\sin(x)} = 1\\\\\frac{\sin(x)}{\sin(x)} = 1\\\\1 = 1 \ \ \checkmark\\\\[/tex]
if 50 grams of sweets cost 250 rupees find the cost of 380 grams of sweets.
Graph the function f(x) = x+4 -1.
This can be simplified to [tex]f(x)=x+3[/tex], and is thus a line with a slope of 1 and a y-intercept of 3.
need to know asap
Which of the following best describes the correlation between two variables if the correlation coefficient is -0.544?
weak positive
weak negative
strong negative
strong positive
Mrs. jones has a body fat to body mass of 1:3.She has a body mass of 60kg.
Answer:
20 kg of body fat
Step-by-step explanation:
Multiple both sides of the ratio so that the side with body mass is 60 kg:
body fat : body mass
1 : 3
× 20 × 20
20 kg : 60 kg
Mrs. Jones has 20 kg of body fat.
1. What is the length of XU?
X
U
Y
36 in
V
Z
W
23 in
Answer: 49 in
Step-by-step explanation:
[23 + XU]/2 = 36 [trapezoid midsegment theorem]23 + XU = 72 [multiply both sides by 2]XU = 49 [subtract 23 from both sides]What is the volume of the complex figure
The volume of the given figure is 104 m³.
We need to find the volume of the given figure.
What is volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Divide the given figure into two convenient cuboids. That is one with dimensions length=4 m, breadth=4 m and height=3 m. Another with length=4 m, breadth=7 m and height=2 m.
We know that, the volume of cuboid =l×b×h cubic units.
Now, the volume of cuboid=4×4×3=48 m³ and the volume of another
cuboid=4×7×2=56 m³.
The volume of the given figure=48+56=104 m³.
Therefore, the volume of the given figure is 104 m³.
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Solve, finding all solutions in [0, 2(pi)]
Answer:
x = π/12, 5π/12
Step-by-step explanation:
We can work this problem a couple of ways. We can convert it to single trig function, shifted horizontally. Or we can convert it to a double-angle equation.
__
horizontal shiftWe recall the sum of angles formula is ...
sin(x+y) = sin(x)cos(y) +cos(x)sin(y)
Using this, we can rewrite the left side of the equation using some angle offset y, and some scale factor k.
k·sin(x +y) = k·sin(y)·cos(x) +k·cos(y)·sin(x) = 2cos(x) +2sin(x)
finding the shift
Equating coefficients of cos(x) and sin(x), we can solve for k and y:
k·sin(y) = 2
k·cos(y) = 2
The ratio of these equations is ...
(k·sin(y))/(k·cos(y)) = 2/2
tan(y) = 1 ⇒ y = π/4
k = 2/sin(π/4) = 2√2
shifted equation
So, our original equation becomes ...
2√2·sin(x +π/4) = √6
Dividing by √2 and using the inverse sine function, we have ...
x +π/4 = arcsin((√3)/2) = π/2 ±π/6
x = π/4 ±π/6
x = π/12, 5π/12
__
double-angle equationIf we square both sides of the original equation, we get ...
(2sin(x) +2cos(x))² = (√6)²
4sin²(x) +8sin(x)cos(x) +4cos²(x) = 6
2sin(x)cos(x) = (6 -4)/4 = 1/2 . . . . use sin² +cos² = 1, subtract 4, divide by 4
Using the trig identity 2sin(x)cos(x) = sin(2x), we can find ...
2x = arcsin(1/2) = π/2 ±π/3 +2kπ . . . . k = an integer;
x = π/4 ±π/6 +kπ . . . . for integer k
x = {π/12, 5π/12, 13π/12, 17π/12}
We know that squaring the equation can introduce extraneous solutions, so we need to try these out. For x in the third quadrant, the sine and cosine values are both negative, so the only useful solutions here are ...
x = π/12, 5π/12
_____
Additional comment
Based on the above, we now know that any trig expression of the form ...
a·sin(x) +b·cos(x)
can be rewritten to the form ...
(√(a² +b²))·sin(x +arctan(b/a)) . . . . . a scaled and shifted sine function
The arctangent will have to take the signs of 'a' and 'b' into account in order to get the angle quadrant right.
Please help! I don't know how to do slopes.
The slope of the given line in the image is -4 , Option A is the answer.
What is the equation of a straight line ?The equation of the straight line is given by
y =mx +c ,
Where m is the slope , C is the intercept
The line is passing through the point
(-1,8) ,(2,-4)
The slope is given by
m = (y₂-y₁) /(x₂-x₁)
m = (-4 - 8 )/(2 +1)
m = -12/3
m = -4
Therefore the slope of the given line in the image is -4 , Option A is the answer.
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38. How much does Mike Carson earn every
day?
A. $89.33
B $76.80
C. $27.00
D. $9.60
39. Mike Carson takes home approximately
what percent of his gross pay?
A. 33%
B. 50%
C. 75%
D, 90%
40. Approximately what percent of total
carnings is deducted for city and state
withholding tax?
A. 3%
B. 10%
C. 15%
D. 25%
40600 in standard form
Answer:
40600 = 4.06 × 104.
Step-by-step explanation:
What is the circumference of a circle with a diameter of 5 feet? Use 3.14 for
TT.
Answer: 15.7
Step-by-step explanation:
[tex]C=\pi d\\\\C=5\pi[/tex]
Using [tex]\pi=3.14[/tex], we get [tex]C \approx 5(3.14)=\boxed{15.7 \text{ ft}}[/tex]
[tex]\triangleright[/tex]Hii! [tex]\triangleleft[/tex]
___________________________________________________________
Answer: Circumference = 15.7 ft ✅
Step-by-step explanation:
Do you need to know the circumference of a circle with a diameter of 5 ft? No problem! Luckily, there's a formula to find it! (:
CircumferenceLet's work out the circumference. This is the formula that is going to help us. [tex]\rightsquigarrow\boldsymbol{C=\pi d}[/tex] C=circumference π=pi d=diameter
Now, stick in the values (note that we can use 3.14 for pi; pi is irrational, so we use 3.14 instead of pi to avoid irrational numbers)
[tex]\boldsymbol{C=3.14\cdot5}[/tex]. Upon simplifying we obtain
[tex]\boldsymbol{C=15.7\;ft}[/tex]. Which is our final answer.
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Hope that this helped! Best wishes.
[tex]\boldsymbol{Reach \quad far. \quad Aim \quad high. \quad Dream \quad big.}[/tex]
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Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base 6.4 inches. Find the surface area. Round to the nearest tenth.
The surface area of the square pyramid will be 78.08 square inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
Given that:-
Sara purchased a porcelain sculpture that is in the shape of a square pyramid. The slant height is 6.1 inches and the base is 6.4 inches. The surface area will be.
The surface area of the square pyramid will be calculated by the formula:-
[tex]SA = P\times\dfrac{l}{2}[/tex]
[tex]SA = 25.6\times \dfrac{6.1}{2}[/tex]
SA = 78.08 square inches
Therefore the surface area of the square pyramid will be 78.08 square inches.
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Select the graph for the solution of the open sentence. Click until the correct graph appears.
3|x| > 6
I would really appreciate the help!:)
The solution of the inequality will be x > 2 and x < -2. And the graph is drawn below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The inequality is given below.
3|x| > 6
By solving the equation, we have
|x| > 2
x > 2
x < -2
Then the graph will be drawn.
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The frequency table shows the results of a survey asking people how many
hours they spend online per week. On a piece of paper, draw a histogram to
represent the data. Then determine which answer choice matches the
histogram you drew.
Hours online Frequency
5
8
10
9
7
0-3
4-7
8-11
12-15
16-19
Based on the frequency table given, The option that closely matches the histogram I drew is option C but the last one suppose to be 7 and not 6.
What is the histogram about?Hours online Frequency
5 0-3
8 4-7
10 8-11
9 12-15
7 16-19
Note that in the image attached, you can see how the Hours online were said to be matched with the Frequency.
So since option A and B was not shown to see which matches the option, i can say option c is closest but if look at my own image, you can use it to find the right one.
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Which graph represents a reflection of f(x) = One-third(9)x across the x-axis?
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 3) and increases to (1.25, 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It goes through (negative 1, 3) and (negative 1.25, 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, negative 3) and (1.25, negative 7).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 4 and decreases into quadrant 3. It goes through (negative 1, negative 3) and (negative 1.25, negative 7).
Using translation concepts, the graph that represents a reflection of [tex]f(x) = \frac{1}{3}(9)^x[/tex] across the x-axis is:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, - 3) and (1.25, -7).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function is:
[tex]f(x) = \frac{1}{3}(9)^x[/tex]
Which approaches y = 0 in quadrant 2 and increases into quadrant 1. For the reflection over the x-axis, the function assumes inverse(negative) values, that is, quadrant 2 -> quadrant 3 and then quadrant 1 -> quadrant 4, hence the correct statement is:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, - 3) and (1.25, -7).
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The graph which represents a reflection of f(x) = One-tenth(10)x across the y-axis is:
B. On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1).
Coordinate Plane
This refers to the two-dimensional surface which is made up of two number lines, x and y.
With this in mind, we can see that from the complete text, we can see that the given graph on the function of x on the y-axis is on a coordinate plane.
Therefore, the correct answer is option B
Which of the following could represent the
interval (5, 100]? Select two that apply.
Answer:
5 < x ≤ 100
(this is inequality form)
{x| 5 < x ≤ 100}
(this is set notation form)
(options B and C)
Step-by-step explanation:
In interval notation,
( or ) : does not include value
[ or ] : does include value
{and remember:
< or > : does not include value
≤ or ≥ : does include value}
when we write something in interval notation, the range of values is from (lowest value, highest value)
for this equation, we know that we are looking for : (5, 100]
which means that the range of numbers goes from
5 (does not include 5) to 100 [does include 100]
so, x > 5 (not equal to); x ≤ 100
we can combine these two concepts: 5 < x ≤ 100
(inequality form)
{when {x | ...} is present, it means the same thing as without it, so
{x| 5 < x ≤ 100} is also correct
(set notation)
hope this helps!!
Answer:
B and C
Step-by-step explanation:
from interval notation we are including 100 but not 5,
x > 5 and x ≤ 100
so B and C are correct
What are the possible zeros for f(x) equals X to the third power minus 2X to the second power minus 4X +15
The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.
What are the roots of the polynomial?The polynomial is given below.
[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]
The roots of the polynomial are equal to n or less than n.
And if one imaginary root is a + bi, then the other imaginary root will be a – bi.
The roots of the polynomial are done by using a calculator.
x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i
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Fill in the missing (yellow) exterior angle with (5x) to solve for x. Diagram may not be to scale.
Step-by-step explanation:
the sum of all exterior angles in a polygon is always 360° (one time around the full circle).
so,
360 = 71 + 85 + 44 + 3x + 5x = 8x + 200
160 = 8x
x = 20
A parallelogram ABCD is shown with DC equal to 8 feet and the perpendicular distance between AB and DC equal to 3 over 4 foot. Part A: What is the area of the parallelogram? Show your work. (5 points) Part B: How can you decompose this parallelogram into two triangles? If this parallelogram was decomposed into two triangles, what would be the area of each triangle? (5 points)
Answer:
6,3
Step-by-step explanation:
hope this helps
the math section in part B shows the equation for the area of a triangle, but this math could be skipped with a similar problem if you just divide the parraellogram by 2. (logic section)
Use interval notation to indicate all real numbers between and including −3 and 5.
Answer:
[-3,5]
Step-by-step explanation:
Interval notation is a shorthand way of writing and interval of values. To describe an interval, imagine the two endpoints on the number-line. Then, list the two endpoint values, leftmost point from the number-line first, separated by a comma. Lastly, include the appropriate brackets for each endpoint:
Only two brackets total will be used for each interval, a bracket to start it, and one bracket to end it.If a number is included, a square bracket should be used -- either "[" or "]"If the endpoint number is not meant to be included, a 'curved bracket' (which we usually just call a parenthesis) should be used -- either "(" or ")"For our situation, the two endpoints are -3 and 5. -3 is to the left of 5 on the number-line, so -3 should be listed first
[tex]-3,5[/tex]
Lastly, the directions say "including -3 and 5", so both endpoints should be included.
To include the -3 on the left, we'll use "["To include the 5 on the right, we'll use "]"The final result for the interval is [tex][-3,5][/tex]
what is the volume of this complex figure
The volume of the given figure is 210 cubic in..
We need to find the volume of the given figure.
What is volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Divide the given figure into two convenient cuboids. That is one with dimensions length=4 in., breadth=2 in. and height=3 in. Another with length=4 in., breadth=4 in. and height=12 in.
We know that, the volume of cuboid =l×b×h cubic units.
Now, the volume of the cuboid=4×2×3=18 cubic in. and the volume of another
cuboid=4×4×12=192 cubic in.
The volume of the given figure=18+192=210 cubic in.
Therefore, the volume of the given figure is 210 cubic in.
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Given the equation below, which of the following shows the quadratic formula
correctly applied?
2x² -9x+4 =0
Answer:
Step-by-step explanation:
[tex]x=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(4)} }{2 \times 2} \\x=\frac{9\pm\sqrt{81-32} }{4} \\x=\frac{9\pm\sqrt{49} }{4} \\x=\frac{9 \pm 7}{4} \\either~x=\frac{9+7}{4} =\frac{16}{4} =4\\or\\x=\frac{9-7}{4} =\frac{2}{4} =\frac{1}{2}[/tex]
A company gives each worker a cash bonus every Friday, randomly giving a worker an amount with these probabilities: $10 - 0.75, $50 - 0.25. Over many weeks, what is a worker's expected weekly bonus?
The worker's expected weekly bonus is $30.0
How to determine the worker's expected weekly bonus?The amounts and the probabilities are given as:
x $10 $50
P(x) 0.75 0.25
The worker's expected weekly bonus is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
E(x) = $10 * 0.75 + $50 * 0.25
Evaluate the product
E(x) = $17.5 + $12.5
Evaluate the sum
E(x) = $30.0
Hence, the worker's expected weekly bonus is $30.0
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If the center of a circle is at (5,-7)
and its radius is 6, complete its
equation:
Answer:
(x-5)²+(y+7)²=36
or
x²+y²-10x+14y+38=0
Given f(x) = 8x+1 2x-9 O As x-00, f(x) → 9; as x → ∞o, f(x) → 9. -> - O As x-00, f(x) O As x-00, f(x) O As x-00, f(x) - - what is the end behavior of the function? ->> -9; as x -4; as x ∞o, f(x) → -9. - ∞o, f(x) → -4. - 4; as x → ∞o, f(x) → 4. -> - Given f ( x ) = 8x + 1 2x - 9 O As x - 00 , f ( x ) → 9 ; as x → ∞o , f ( x ) → 9 . - > - O As x - 00 , f ( x ) O As x - 00 , f ( x ) O As x - 00 , f ( x ) - - what is the end behavior of the function ? - >> -9 ; as x -4 ; as x ∞o , f ( x ) → -9 . - ∞o , f ( x ) → -4 . - 4 ; as x → ∞o , f ( x ) → 4 . - > -
Answer:
D
After graphing, you can analyze it accordingly.
The vertices of a trapezoid are points (0,x), (0,0), (y,0), and (z,x). Find the area in terms of x, y, and z.
I put 1/2x (y+z), I just want to make sure! thank you.
Your answer is correct. The two "bases" of the trapezoid are the line segments (0, 0)-to-(y, 0) and (0, x)-to(z, x), with lengths y and z, respectively. Then the average of the bases is [tex]\frac{y+z}2[/tex]. (We know they're the bases because the line segments are parallel.)
We multiply this by the height, which is given by the length of the line segment (0, 0)-to-(0,x), or x.
Hence the area is
[tex]\dfrac{x(y+z)}2[/tex]
(which is identical to what you have).
Use the graph or table to find the equation that represents the relationship.
please HELP!!!!!!
100 points and a Brainliest if your answer is clear and correct
#1
(5,-10)(10,-25)Find slope
m=-25+10/10-5m=-15/5m=-3y=-3x+5 is the equation as there is no other having slope -3
#2
(7,3)(1,-3)slope
m=-3-3/1-7m=-6/-6m=1y=x-4 as no other have slope m
#3
(0,-1)y intercept is -1
y=2x-1 is the equation as it has y intercept -1
#4
(0,-4)y intercept is -4
y=4/5x-4Determine the x and y intercepts of the equation y = -3x + 4.
Select one:
O a. y-int y = 4 and x-int x = 4/3
O b. y-int y = 4/3 and x-int x = 4
O c. y-int y = 4 and No x-int
O d. No y-int and x-int x =4/3
Answer:
O c. y-int y = 4 and No x-int
Step-by-step explanation:
In the slope-intercept equation y = -3x + 4, only slope and y-intercept are displayed as it is in slope-intercept format which is y = mx + b; m being the slope and b being the y-intercept.
There is no x-intercept present in a slope-intercept equation.
But due to the 4 being in the place of the y-intercept is the y-intercept of the graph and line depicted off this linear equation (slope-intercept equation).
Hence, the answer is C. Y-intercept = 4 and No x-intercept.
The May bank statement for Rental shows a balance of $6,000, but the balance per books shows a cash balance of $8,000. Other information includes: 1. A check for $190 to pay the electric bill was recorded on the books as $10. 2. Included on the bank statement was a note collected by the bank for $450 plus interest of $30. 3. Checks outstanding totaled $270. 4. Bank service charges were $60. 5. Deposits in transit were $2,510.
The adjusted cash Balance is $8060 .
What is Bank Balance ?The amount of money in a person's account at any given time is the Bank Balance of that person's account.
Unadjusted bank balance 6000
Difference in the electricity bill -180
Add: Deposit in transit 2510
Less: Outstanding Checks -270
Adjusted cash balance 8060
So answer is a) $8060
Therefore the adjusted cash Balance is $8060 .
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Question 10 of 33
Which of the following is a characteristic of a regular tessellation?
O A. It uses only one type of regular polygon.
OB. It uses more than one type of regular polygon.
O C. It allows for overlaps and spaces between shapes.
OD. It does not cover a surface completely.
SUBMIT
A tessellation that uses only one type of regular polygon.
What is Polygon?
The definition of a polygon is given as a closed two-dimensional figure with three or more straight lines.
When we cover a surface with a pattern of a flat geometric shapes such that there should have no overlaps or gaps, then the surface is called a tessellation.
A regular tessellation is tessellation made up by using only one type of regular polygon. These are made up of entirely congruent regular polygons all that joining vertex to vertex.
Hence, A is the correct option.
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