What are domain and range of these two and how step by step please?
Answer:
Step-by-step explanation:
[tex]\sf f(x) = \dfrac{1}{Sin \ x}[/tex]
f(x) does not contain values where sin x = 0. Sin x is 0 at integral multiples of π.
Domain = R - nπ , n is integers.
The range of Sin x is [-1 , 1] and in this range we cannot find 1/sin x .
Range = (-∞, -1] U [1,∞)
[tex]\sf f(x) =\dfrac{1}{Cos x}[/tex]
f(x) does not contain values where Cos x = 0 . Cos x is 0 at integral of multiples of (π/2)
[tex]\sf Domiain =R -\dfrac{(2n+1)\pi }{2}[/tex]
The range of Cos x is [-1,1] and in this range we cannot find 1/Cos x.
Range = (-∞, -1] U [1,∞)
Find F(5) for f(x)= 1/4(2)^x
If we have a function f(x), f(5) is f(x) but replacing x with 5. The result give us a value of y and a point of the function, (x, y).
[tex]f(5) = \frac{1}{4} ({2})^{5} = \frac{32}{4} = 8[/tex]
ANSWER A
Hello!
Substitute x = 5 to find f(5).
⇒ f(5) = 1/4(2)⁵
⇒ f(5) = 32/4
⇒ f(5) = 8
∴ The correct option is A.
. A new employee at an auto detailing shop is offered one of three options for earning pay: Option 1: Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Option 2: Receive $38.75 per automobile detailed in a day. Option 3: Receive $100 per day plus 2% of sales in a day. A typical day consists of 12 bottles of wax sold per detailer, 4 automobiles detailed per employee, and average daily sales are $1,500. Which option should the new employee choose in order to make the most money on an typical day, and how much will he earn in a 20-day month at this rate?
The new employee should choose the second option to make the most money on a typical day. The amount that the new employee will earn 20-day at this rate is $3,100.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
For Option 1,
Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Also, A typical day consists of 12 bottles of wax sold per detailer.
Earning = ($15.25 × 8) + ($0.50×12)
= $122 + $6
= $128
For Option 2,
Receive $38.75 per automobile detailed in a day. Also, 4 automobiles are detailed per employee. Therefore, the earnings are,
Earning = $38.75 × 4
= $155
For Option 3,
Receive $100 per day plus 2% of sales in a day. Also, the average daily sales are $1,500. Therefore, the earnings are,
Earning = $100 + 0.02($1500)
= $130
Hence, The new employee should choose the second option to make the most money on a typical day.
2.)
The amount that the new employee will earn 20-day at this rate is,
Amount earned = $155 × 20 days
= $3,100
Hence, The amount that the new employee will earn 20-day at this rate is $3,100.
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If measure of AC= 50 degrees, then…
1) How many degrees measures the central angle O?
2) How many degrees measures the inscribed angle B?
1) Because [tex]\angle AOC[/tex] is a central angle, the answer is 50 degrees.
2) By the inscribed angle theorem, the answer is 25 degrees.
How can the basic fact help find 3,000 divided by 5?? I need help
Answer:
3000/5 = 600
Step-by-step explanation:
Every multiplication fact is equivalent to two (2) division facts:
a·b = c ⇒ c/a = b and c/b = a
Multiplication or division by 10 involves moving the decimal point one place to the right or left (respectively).
Recasting the problemThe division ...
[tex]\dfrac{3000}{5}[/tex]
is fully equivalent to ...
[tex]\dfrac{30}{5}\times 100[/tex]
Using the basic factWe assume your "basic fact" is 5×6 = 30. In accordance with the above equivalence to division problems, this tells you ...
[tex]\dfrac{30}{5}=6\\\\\dfrac{30}{5}\times100 = 6\times100\\\\\dfrac{3000}{5}=600[/tex]
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer to all of them, Tysm!
#1
No
#2
We can see f(1) has 3 values so it's not a function as it's failed in vertical line test
#3
f(10) has two values -2 and 11
So not a function
#4
As per definition of function
every domain has an unique rangeSo it's not a function
Find the value of X.
Answer:
151°
Step-by-step explanation:
The above shape is a quadrilateral.
sum of exterior angle of a quadrilateral is 360°.The exterior angles are :
82°, 70°, 62°, and (x -5)°
Therefore,
82 + 70 + 62 + x - 5 = 360
214 -5 + x = 360
209 + x = 360
x = 360 - 209
x = 151°
What is the vertex of the graph of the function below?
y=x²-4x+3
O A. (1,-1)
OB. (2,-1)
O C. (2,0)
O D. (1.0)
Answer:
B
Step-by-step explanation:
given a quadratic function in standard form
y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² - 4x + 3 ← is in standard form
with a = 1, b = - 4 , then
x = - [tex]\frac{-4}{2}[/tex] = 2
substitute into the equation for corresponding y- coordinate
y = 2² - 4(2) + 3 = 4 - 8 + 3 = - 1
vertex = (2, - 1 )
A(N) _______________ questions require respondents to select one or more response options from a set of predetermined choices. Group of answer choices
Closed-end
You can answer "yes" or "no" to the completed question. Or, the number of answers is limited (eg A, B, C, or all of the above). Closed-end questions are often suitable for voting, as response rates are high when users don't have to type too much.
Closed-end questions are defined as question types that require respondents to choose from a specific set of predefined answers. B. Between "yes/no" or fixed multiple-choice questions. In a typical scenario, closed-end questions are used to collect quantitative data from respondents.
An indefinite definition represents a situation or question with a predetermined number of results. An example of a closed ending is the question "Do you need help?" This usually has only four answers-yes, no, maybe, or not.
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Write a piecewise-defined step function f(x) that has the following characteristics:
f(x) has more than one x intercept.
The domain of f(x) is the real numbers.
The range of f(x) consists of four unique integers.
Here use general math mind
F(x) has more than one x inetercept .
We shall take one quadratic function in which will give 2 intercepts(Real)Domain is for real numbers
Four unique numbers?
Add 4 constants for 4 unique definations and that shouldn't fall under quadratic regionLets see
[tex]\sf f(x)=\begin{cases}\sf (x+2)²,x\neq \left\{0,-1,1,2,3\right\}\\ \sf 0,x=0\\ \sf 1,x=-1\\ \sf 9,x=1\\ \sf 16,x=4\\ \sf 25,x=5\end{cases}[/tex]
Has 2 x interceptsFor -2
y=(0)²=0(-2,0)For 0 it's (0,0)
And for extra ,it's discontinuous on x=0
. The Pancake Restaurant served 348 pancakes. If 87 customers ate an equal number of pancakes, how many did each person eat?
Answer:
4
Step-by-step explanation:
348 / 87 = 4
There are 87 Customers. The restauraunt served 348 pancakes. You divide 348 by 87 and conclude that each customer ate 4 pancakes.
Answer:
4
Step-by-step explanation:
348 ÷ 87 = 4
each person ate 4 pancakes
66. Extensions
Find the equation of the line that passes through the following points: (2a, b) and (a, b + 1)
Answer:
The equation of the line that passes through the points (2a, b) and (a, b+1) is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
Step-by-step explanation:
The given points are (2a, b) and (a, b+1).
It is required to find the equation of the line that passes through the points. the slope-intercept form.
Step 1 of 4
Using the given two points, to find the slope.
Given points are (2a, b) and (a, b+1).
Substitute [tex]$x_{1}[/tex]=2a,
[tex]$$\begin{aligned}&y_{1}=b \\&x_{2}=a \text { and } \\&y_{2}=b+1\end{aligned}$$[/tex]
into the formula, [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
Step 2 of 4
Simplify [tex]$m=\frac{b+1-b}{a-2 a}$[/tex], further
[tex]$$\begin{aligned}m &=\frac{b+1-b}{a-2 a} \\m &=-\frac{1}{a}\end{aligned}$$[/tex]
As a result, the slope is [tex]$m=-\frac{1}{a}$[/tex].
Step 3 of 4
Use the slope [tex]$m=-\frac{1}{a}$[/tex] and the coordinates of one of the points (2a, b) into the point-slope form, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex].
Substitute [tex]$m=-\frac{1}{a}$[/tex],
[tex]x_{1}=2 a$ and$y_{1}=b$[/tex]
into the formula, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]
[tex]$y-b=-\frac{1}{a}(x-2 a)$[/tex]
[tex]$y-b=-\frac{1}{a} x+2$$[/tex]
Step 4 of 4
Rewrite the above equation as a slope-intercept equation. So, from the above term [tex]$y-b=-\frac{1}{a} x+2$[/tex], Add b on each side.
[tex]$$\begin{aligned}&y-b=-\frac{1}{a} x+2 \\&y=-\frac{1}{a} x+2+b\end{aligned}$$[/tex]
Therefore, the equation of the line that passes through the points is [tex]$y=-\frac{1}{a} x+2+b$[/tex].
In circle N with the measure of arc \stackrel{\Large \frown}{MP}= 114^{\circ} MP ⌢ =114 ∘ , find \text{m} \angle MNPm∠MNP
According to the central angle theorem, the measure of angle MNP = 114°.
What is the Central Angle Theorem?According to the central angle theorem of a circle, the measure of central angle MNP equals the measure of intercepted arc MP.
Measure of arc MP = 114°
Measure of angle MNP = arc MP
Measure of angle MNP = 114° [central angle theorem]
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What is the measure of the central angle of a circle with radius 18 centimeters that intercepts a12π centimeters arc?
Answer: [tex]120^{\circ}[/tex]
Step-by-step explanation:
[tex]12\pi=2(\pi)(18)\left(\frac{\theta}{360} \right)\\\\12\pi =36\pi \left(\frac{\theta}{360} \right)\\\\\frac{1}{3}=\frac{\theta}{360}\\\\\theta=120^{\circ}[/tex]
The inverse of F(x) is a function.
-5
OA. True
OB. False
The inverse of any function F(x) is also a function.
A function is an abecedarian notion in mathematics and computer programming. In both contexts, a function is a regulation or relationship that maps input values to corresponding output values. It takes one or more input values, performs a set of operations or calculations, and produces a single output value.
There are many types of functions such as trigonometric function, logarithmic function, exponential function, and so on.
If a function f(x) gives output y then its inverse will be [tex]f^{-1}(y)[/tex] and will return x as output.
So, the statement is true.
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construct a right angle triangle abc where m b is equal to 90 degree BC is equal to 4.5 cm and ac is equal to 7 cm
The triangle will be computed based on the information illustrated below.
How to compute the triangle?The steps needed for the construction will be:
Draw a segment XY.
Locate B, C on XY such that BC = 4.5cm.
Construct a line segment such that B = 90°.
With C as center and radius 7cm, draw a arc cutting BD at A.
Then, the required triangle ABC will be gotten.
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Please help me out. im struggling
Answer: 48
Step-by-step explanation:
By the geometric mean theorem,
[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]
Kelly offers to pay for 9 of her friends to play laser tag, but 2 of them don't want to play.
if laser tag costs $4 per person, how much will Kelly spend on her friends /
Answer:
$28Step-by-step explanation:
If she offers to 9, but 2 reject, that means she paid for 7 friends.
If each friend costs $4, multiply 4 by 7.
The answer is $28
Hope this helps! (:
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time, t in seconds, and the number of bacteria, Bsecond(t) in the petri dish is modeled by the following function:
Using the given exponential function, we have that:
Every minute, the number of bacteria decays by a factor of 0.98.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the function is, for the amounts each second:
[tex]Bs(t) = 6000\left(\frac{15}{16}\right)^{t}[/tex]
The initial amount is of 6000 bacteria. After 60 seconds = 1 minute, the amount will be of:
[tex]Bs(60) = 6000\left(\frac{15}{16}\right)^{60} = 125[/tex]
The decay factor after 1 minute is:
(6000 - 125)/6000 = 98% = 0.98.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.
Step-by-step explanation:
Definition
A relation is called to be a function if every domain has an unique range
f(x)=yHere
f(3)=-9,4As
f(3) has 2 corresponding values it's not a function
Someone please help !! :(
Question 22 of 25
What is the average rate of change for this quadratic function for the interval
from x = 0 to x = 2?
The sum of two numbers is 8 and sum of their reciprocal is 8/15. Find the numbers.
Answer:
The 2 numbers are 3 and 5.
Step-by-step explanation:
x + y = 8
1/x + 1/y = 8/15
From first equation y = 8 - x so
1/x + 1 / (8-x) = 8/15
Multiply through by the LCM 15x(8-x):-
15(8 - x) + 15x = 8x(8-x)
120 - 15x + 15x = 64x - 8x^2
8x^2 - 64x + 120 = 0
x^2 - 8x + 15 = 0
(x - 3)(x - 5) = 0
x = 3 or 5
so y = 8-3 = 5 or 3.
Points U, M, And D are collinear with U between U and D.
Given:
UM=5x+30
MD=3x+80
UD=10x+20
What is x
The value of x from the given equation is 5/3
How to determine the valueSince the three points are collinear to U, they are on a straight line which equals 0
Then we have,
UM + UD = MD
5x+30 + 10x+20 = 3x+80
Collect like terms
5x + 10x + 50 = 3x + 80
15x - 3x = 80 - 50
12x = 30
x = 30/12 = 15/6 = 5/3
Thus, the value of x from the given equation is 5/3
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3. This is a graph of the function f(x) = -3x + 1.
-2
8
4f(x) = -3x + 1
0
y
4
2
X
a) Determine the range value when the
domain value is 1.
b) Determine the domain value when the
range value is 4.
a) [tex]-3(1)+1=\boxed{-2}[/tex]
b) [tex]4=-3x+1 \longrightarrow -3x=3 \kongrightarrow x=\boxed{-1}[/tex]
Given: S is the midpoint of QR, QR¯⊥PS¯ and ∠RSP and ∠QSP are right angles.
Prove: PR≅PQ
ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.
What is the CPCTC Theorem?If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.
Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)
∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)
SP ≅ SP based on the reflexive property (one pair of congruent sides)
Therefore, ΔRSP ≅ ΔQSP by SAS.
Conclusively, PR ≅ PQ by CPCTC theorem.
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Please assist me with this question
Answer:
? = 45
Step-by-step explanation:
the inner and outer triangles are similar ( AA postulate )
Then the ratios of corresponding sides are in proportion, that is
[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex] , that is
[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )
[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )
7(105 + ? ) = 1050 ← distribute parenthesis on left side
735 + 7? = 1050 ( subtract 735 from both sides )
7? = 315 ( divide both sides by 7 )
? = 45
In a sample of 400 voters, 360 indicated they favor the incumbent governor. The 95% confidence interval of voters not favoring the incumbent is
The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).
Sample size, n=400
Sample proportion, p = 40 / 400
= 0.1
We use normal approximation, for this, we check that both np and n(1-p) >5.
Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation = root( p * (1-p) /n )
= 0.015
For constructing Confidence interval,
Margin of Error (ME) = z x SD = 0.0294
95% confidence interval is given by Sample Mean +/- (Margin of Error)
0.1 +/- 0.0294 = (0.0706 , 0.1294)
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and the other answer that you didnt see is ( 2+3×2+5+6+7+9 units ) .
pls give me the answer .. and ty <3 .
There is a rule for finding perimetre of all polygons that perimetre is the sum of all the side's lengths ; according to this rule add the length of the sides of this polygon and you'll get the answer , the answer is the choice that you've written ( 2+3×2+5+6+7+9 ) or ( 2+3+3+5+6+7+9 ) both are correct because 3+3 is same as 3×2
perimetre is 2+3×2+5+6+7+9 = 35 units
HOPE IT HELPS
what does 160=7x+6 equal to?
Answer:
x=22
Step-by-step explanation:
7x+6=160.
Lets start by moving 6 over to the other side. We can do this by subtracting 6 from both sides of the equation.
7x+6-6=160-6
7x=154
Now, let's isolate x by getting rid of the 7. The 7 is being multiplied with x, so to get rid of it we have to divide both sides by 7.
7x/7 = 154/7
x=22
Look Below :
Step-by-step explanation:
160 - 6 = 7x
154 = 7x
Or
7x = 154
x = 22
Please help soon! I have a trig question...
The value of x will be 33 units approximately. Thus, option A is correct.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We need to find the value of x
so first
Tan 60 = Perpendicular / 11√6
Perpendicular = 1.732 (11√6)
Perpendicular = 46.66
Then,
Sin 45 = Perpendicular / x
Sin 45 = 46.66/ x
x = 33.00
So, the value of x will be 33 units approximately.
Thus, option A is correct.
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