Answer:
1
Step-by-step explanation:
[tex]\sin 2x=2\sin x \cos x \\ \\ \sin 90^{\circ}=2\sin 45^{\circ} \cos 45^{\circ} \\ \\ =2(1/\sqrt{2})(1/\sqrt{2}) \\ \\ =2(1/2) \\ \\ =1[/tex]
Let g(x)=5 x-2 and h(x)=x²+1 . Find the value of each expression. (g⁰ h)(2)
For the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (2) will be 23.
We are given the functions:
g (x) = 5 x - 2
h (x) = x² + 1
We first need to find the composite function g o h (x).
So, we get that:
g o h (x) = g ( h (x) )
g o h (x) = 5 ( x² + 1 ) - 2
g o h (x) = 5 x ² + 5 - 2
g o h (x) = 5 x² + 3
Now, we need to find the value of the composite function for x = 2. So, we get that:
g o h (x = 2) = 5 (2)² + 3
g o h (2) = 5 (4) + 3
g o h (2) = 20 + 3
g o h (2) = 23
Therefore, for the functions g (x) = 5 x - 2 and h (x) = x² + 1, the value of the composite function g o h (2) will be 23.
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Terry was measuring the volume of water on a graduated cylinder but did not notice that the measurements incremented by 2 instead of by 1. As a result, he misread the volume of the liquid as 33.0 instead of 36.0. What is his percent error?
The percent error on Terry's reading is 8.3%
What is the percent error?If there is something with a real measure of M, and you perform a measure that gives the value M', then the percent error on your measure is:
P = 100%*|M - M'|/M
In this case, the real measure is 36.0 and Terry's measure is 33.0 (I don't know the units, these are volumes).
So we have:
M = 36.0
M' = 33.0
Then we can use the formula for the percent error to get:
P = 100%*|36.0 - 33.0|/36.0 = 8.3%
We can see that the percent error in Terry's measure is 8.3%
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Suppose we have a special number N with the following properties:
a) If we divide N by 3, we get a remainder of 1
b) If we divide N by 4, we get a remainder of 1
c) If we divide N by 5, we get a remainder of 1
What is the smallest possible value of N?
The smallest possible value of N if we we divide N by 3, we get a remainder of 1 is 61.
How to calculate the value?It should be noted that based on the information, we simply have to find the lowest common multiple for 3, 4, and 5. It should be noted that this will be 60 then we add 1.
The number will be:
= 60 + 1
= 61
Therefore, the smallest possible value of N if we we divide N by 3, we get a remainder of 1 is 61.
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write an equation in slope intercept form that describes a line that has a y-intercept of 4 and a slope of 3
Answer:
The equation will be y= 3x + 4
Step-by-step explanation:
Hope this helps :)
The equation in slope-intercept form describes a line that has a y-intercept of 4 and a slope of 3 will be y= 3x + 4.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, a line that has a y-intercept of 4 and a slope of 3.
The standard equation in the slope-intercept form is,
y = mx +c
Where m is the slope and c is the intercept. The ratio that y increase as x increases is the slope of a line.
Substitute the given value,
y = 3x + 4
Thus, the equation in slope-intercept form describes a line that has a y-intercept of 4 and a slope of 3 will be y= 3x + 4.
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The quotient 250+5/8 tells abou ow far a sloth may move in one hour. How an a sloth go in 90 minutes? Justify your asoning.
Ans :
90 minutes, the sloth may move 600 units .
Given :
250*5/8 = 250 × (8/5) = 400
Hour :
a period of time equal to the twenty-fourth part of a day and night and divided into 60 minutes.
1 hour = 60 minute
Slot :
a long, narrow aperture or slit in a machine for something to be inserted.
sloth may move 400 units per hour.
a sloth may move in 400 units = 60 minutes.
A slot of 200 units = 30 minutes.
Therefore,
it will move (400 + 200) units = (60 + 30) minutes.
Hence,
in 90 minutes, the sloth may move 600 units.
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determine the range of (-10,7)
can someone please help me out?
Answer:
The rate of change is 1/2. And it is consistent.
Step-by-step explanation:
Start from the first point. As you see, the second point is 2 units right and 1 unit up from the first point. According to the formula for slope, (y1-y2)/(x1-x2)=slope, (24-16)/(2-0)=4, I know that the y-value increased by 4 as x-value increased by 1. Hope you find the answer helpful.
Find any points of discontinuity for each rational function. y= x-1 / (x+1)²
Point of discontinuity for each rational function. y= x-1 / (x+1)² is x = -1
What is the discontinuity of a function?
In algebra, a discontinuous function is one that has a point at which the function is not defined, at which the left-hand limit and right-hand limit are equal but not equal to the value of the function at that point, or at which the limit of the function does not exist. Discontinuous functions may have three different sorts of discontinuities: jump, removable, and essential. The graph of a discontinuous function contains gaps.
Given the function is -
y= x-1 / (x+1)²
It can be expressed in the form of -
y = x-1 / (x+1)(x+1)
The function will be undefined if the denominator will be 0
⇒ x+1 = 0
⇒ x = -1
So we can conclude that the function will be undefined at point x = -1
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identify 6x+3+4x+8 identify
Answer:
10x + 11
Step-by-step explanation:
6x + 3 + 4x + 8x
6x + 11x +4x
if f(x)=-2x-5find the value of f(-3)
How many years would it take to make $1,000,000? Justify your answer.
If your solution is x>1. The circle that
goes on the graph at 1 is
open
closed
Answer:
open
Step-by-step explanation:
It would be open, since the inequality: [tex]x > 1[/tex] only contains solutions greater than 1, and if you were to plug in 1 as x, you would get: [tex]1 > 1[/tex] which is of course not true, so 1 is excluded and thus has an open circle.
The only case where it would be closed is if it's: [tex]x\ge1[/tex] where plugging in 1 as x would result in a true statement, thus 1 is included in the interval
What is the slope of the line in the graph below?
Please view picture for the graph! Thank you so much!
What is 20/65 i had some trouble with it
Answer:
srry if this is wrong but 13!
I NEED HELPP
Mai said, "I'm not sure the graph is right. For example, the point is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."
Write an inequality to represent Mai's last statement.
The inequality to represent the last statement that was made by Mai will be t <= 2.
How to illustrate the information?It should be noted that an equation simply means the relationship that can be used to show the relationship among the variables.
It should be noted that the last statement made by Mai is that I think triathlon athletes generally train for no more than 2 hours a day.
Therefore, the inequality to represent this will be t <= 2.
where t = number of hours trained.
This implies that t is less than or equal to 2 hours
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what is equivalent to –24 = x − 98
- - - - - - - - - - - - - - - - - - - - - - - -
Hello! The explanation is below.
- - - - - - - - - - - - - - - - - - - - - - - -
Here, we're trying to figure out what x means. So, let's!
Basically, this equation says, "What number must you have to reach -24?"
Well, if you subtract 98, you have zero already. So, find a lesser number to remove 98 from.
(after playing with numbers)
74 - 98 = -24
Have a wonderful day/night!
~pinetreee
Give the coordinates of the point obtained from each reflection.
The coordinates of the spot received from each reflection.
a. When a point is reflected across the x-axis:
(-4 , -5) → (-4 , 5)
b. When a point is reflected across the y-axis:
(-4 , -5) → (4 , -5)
What exactly is the meaning of reflection?A reflection in mathematics is a mapping from such a Euclidean space to itself that is an isometry with just a hyperplane as a fixed point set; this set is known as the axis or plane of reflection. A figure's mirror image with in axis or plane or reflection is its image by reflection.
Briefing:When a point is reflected across the x-axis, every x-coordinate remains unchanged, but the y-coordinate is assumed to represent the additive inverse. Point (x, reflection )'s from across x-axis is (x, -y).
When you reflect from across y-axis, the coordinates change as follows:
(x, y) → (-x, y)
To obtain your new set, multiply your x-coordinate by -1 as well as leave the y-coordinate alone.
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Let f(x)=x-4 and g(x)=x²-16 . Perform each function operation and then find the domain. g(x)/f(x)
The domain for g (x) / f( x) = x + 4 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
We are given the two functions as:
f (x) = x - 4
g (x) = x² - 16
Now, first, we need to divide g (x) by f (x).
So, we get that:
g (x) / f (x) =( x² - 16) / (x - 4)
g (x) / f(x) =( x - 4) (x + 4) / (x - 4)
g (x) / f( x) = x + 4
Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.
Therefore, we get that the domain for g (x) / f( x) = x + 4 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
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what is x and y and x and y?
Answer:
x= 1/7Step-by-step explanation:
Solve for x by cross multiplying. Hope this helps! <3
Select all ratios equivalent to 5:1
Answer: 5.1 = 20.4 and = 30.6
Step-by-step explanation: Add a fraction to 5.1 + 5.1 if you keep adding by 5.1 gets an answer
B & C
A= 3.6:1
B= 5:1
C= 5.1
A lottery has 46 numbers. How many ways can six numbers be drawn if the numbers are not repeated?
There are ____ ways the number can be drawn.
If you buy a ticket, what is the probability that your ticket will have the winning numbers?
P(win) = _____
The number of ways six numbers can be drawn are 9366819.
Combinations also are referred to as choices or selections. Combinations correspond to the choice of factors from a given set of factors. Here we do now no longer intend to set up things. We intend to choose them.
The combination formula to find out number of ways is,
where n is the number of objects to select from and r is the variety of objects that want to be picked. This system is used while no repetition is allowed and order does not matter.
From the given question let us consider,
n= 46
r=6
By applying the combination formula
46C6= 46!/6!(46-6)!
= 46.45.454.43.42.41/6!
= 6744109680!/6!
= 6744109680/720
=9366819
Therefore the required answer is 9366819 ways.
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Answer:
Step-by-step explanation: nPr
= n!
(n-r)!
= 46!
(46-6)!
= 46!
40!
= 6744109680
Determine whether each logarithm is a common logarithm.
d. (log₅5)
the logarithm function ( log ₅ 5 ) is not a common logarithm function as it does not have a base 10.
In mathematics, the common logarithm is the logarithm with base 10.
It is also known as the decadic logarithm and as the decimal logarithm function.
Here, we have the logarithm function as:
( log ₅ 5 )
Now, we can see that:
It has a base of 5.
So, it will not be a common logarithm function as having base 10 is an important characteristic of a common logarithm function.
Therefore, we get that, the logarithm function ( log ₅ 5 ) is not a common logarithm function as it does not have a base 10.
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Multiply -13y(8y - 4) please!!
Answer: − 104 y^2 + 52y
Answer:
Option C (the third option) or option A (the first option) may be correct.
Step-by-step explanation:
-13y(8y-4)
Use the distributive property to multiply -13y by 8y - 4.
-104y2+52y
0.9-8.8+11+2.6 es tarea de matemáticas
Resolviendo las sumas y restas de la expresión podemos ver que:
0.9-8.8+11+2.6 = 5.7
¿Como resolver la expresión en la imagen?
Tenemos un problema que involucra sumas y restas, tenemos que resolver la siguiente expresión:
0.9-8.8+11+2.6
Vamos a hacerlo de izquierda a derecha, lo primero que debemos resolver es:
0.9 - 8.8 = -7.9
reemplazar esto nos da:
-7.9+11+2.6
Lo siguiente que debemos resolver es:
-7.9 +11 = 3.1
Reemplazando eso obtenemos:
3.1 + 2.6 = 5.7
ese es el resultado de la expresion.
Entonces podemos concluir que:
0.9-8.8+11+2.6 = 5.7
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Simplify each expression. 25¹/₂
The simplified form is 5.
Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.
The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.
[tex]( 5^{2} )^{1/2}[/tex]
[tex]5^{2} . \frac{1}{2}[/tex]
[tex]2.\frac{1}{2} =1[/tex]
[tex]5^{1}[/tex][tex]= 5[/tex]
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PLEASE VERY IMPORTANT! What is the domain of the function shown in the graph below?
Step-by-step explanation:
the domain is the interval or set of all valid input (x) values.
so, x goes through what values ?
we see, from left to right, it is coming from a limitless left (-infinity) and goes seemingly against x = 2 without ever reaching that value.
so, the domain is
-infinity < x < 2
|3j-1|+6>0? Pls help I’m confused
Answer:
j has infinite solutions
Step-by-step explanation:
|3j-1|+6>0
|3j-1|+6-6>0-6
|3j-1|>-6 ==> all absolute value functions are greater than negative values
Hence, j has infinite solutions.
Expand each logarithm.
logb b/x
If the expression is [tex]log_{b}[/tex](b/x), then the expanded form of the expression looks like [tex]log_{b}b-log_{b}x[/tex].
Given that the expression is [tex]log_{b}[/tex](b/x).
We are required to find the expanded form of the expression.
The change of base formula is basically used to re-write a logarithm operation as a fraction of logarithms with a new base.
We know that log (m/n)= log m- log n.
The expression is [tex]log_{b}[/tex](b/x).
We have to first multiply b with the inside fraction.
[tex]log_{b}[/tex](b/x)=[tex]log_{b}b -log_{b}x[/tex]
Hence if the expression is [tex]log_{b}[/tex](b/x), then the expanded form of the expression looks like [tex]log_{b}b -log_{b}x[/tex]
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Which expression is equivalent to (4x-³y4)-²?
PLEASE HELP ME ASAP!!
Answer:
[tex] \sf \: \frac{ x {}^{6} }{16y {}^{8} }[/tex]
Step-by-step explanation:
(4x-³y^4)-²
=x^6/16y^8
CAN ANYONE HELP ME PLSS