Therefore , the solution of the given problem of function comes out to be f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].
Explain function.The mathematics programme covers a wide range of topics, including mathematics, numbers, but also their subsets, along with building, construction, and the both real and fictional geographic locations. A work covers the connections between different variable elements that all work together to produce the same result. A utility is made up of several distinctive components that, when combined, produce specific results for each input.
Here,
We must first assess g(x) in order to determine f[g(x)], and then we can use the outcome to determine f[g(x)].
=> g(x) = x² + 1
When we substitute g(x) for f(x), we obtain:
=> f[g(x)] = f(x² + 1)
=> 3(x² + 1) - 5 = 3x² + 3 - 5
=> 3x² - 2
Therefore, f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].
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Can someone explain me how to do this task please? Thank you
Step-by-step explanation:
common multiples are numbers that can be divided without remainder by both numbers.
12. 3 and 5
3 and 5 are both prime numbers, so their common multiple are multiples of their product (3×5 = 15).
so,
1×15 = 15
2×15 = 30
3×15 = 45
13. 4 and 6
the prime factors of 4 are
2×2
the prime factors of 6 are
2×3
the last common multiple is the product of the longest chains of prime factors of the numbers :
2×2 × 3 = 12
6 has only one 2 factor, 4 has two 2 factors, so that is the longest chain. and 6 has one 3 factor, which makes it the longest chain for that.
the multiples for 4 and 6 and now the multiples of 12 :
1×12 = 12
2×12 = 24
3×12 = 36
4×12 = 48
14. 3 and 7
they are both again prime numbers, so we are looking for multiples of their product (3×7 = 21).
1×21 = 21
2×21 = 42
15.
what do we need to do to change the denominator by keep the overall value of the fraction ?
we need to multiply numerator and denominator by the same value (e.g. by 2/2, 3/3, 4/4, ...)
3/4 = 6/8 = 9/12 = 12/16
16.
as before.
2/3 = 4/6 = 6/9 = 8/12
17.
as before
4/5 = 8/10 = 12/15 = 16/20
18.
now we need to find the largest n/n factor hidden in the fraction. by eliminating that we get the core (simplified) value of the fraction.
4/12 = 1/3 × 4/4
so,
1/3 is the simplified fraction.
19.
as before
6/10 = 3/5 × 2/2
3/5 is the simplified fraction.
20.
as before
4/8 = 1/2 × 4/4
1/2 is the simplified fraction.
[tex]2^{2} . 2^{3}[/tex]
Answer:
32
Step-by-step explanation:
add the exponents
2 + 3 = 5
2⁵ = 32
A soundscape can only be written by using a table and diagrams.
A. False, a soundscape can also be written out in words.
B. True
C. False, a soundscape can only be written out in words.
Answer:
C . False, a soundscape can only be written out in words.
Step-by-step explanation:
Because :
False, a soundscape cannot be written by using a table and diagrams.
Explanation:
A soundscape is the acoustic environment as perceived by humans, in context. The term was originally coined by Michael Southworth, and popularised by R. Murray Schafer. There is a varied history of the use of soundscape depending on discipline, ranging from urban design to wildlife ecology to computer science.
write as a product: b^2*c^2-4bc-b^2-c^2+1
Answer:
(b*c+c-1+b)*(-c+b*c-b-1)
or
(b*c + c - 1 + b)*(-c + b*c - b -1)
put both in the same order:
(bc + b + c - 1)( bc - b - c - 1)
Turn the crank:
(bc)2 + b2c + bc2 - bc -b2c -b2 - bc + b -bc2 - bc - c2 + c -bc - b - c + 1
Cancel things....
(bc)2 - bc -b2 - bc - bc - c2 -bc + 1
(bc)2 - 4bc - b2 - c2 + 1
Explain why the nature of roots depends on the value of the dicriminant.
Answer:
The discriminant of a quadratic equation is the expression found under the square root sign in the quadratic formula, which is b^2 - 4ac. The discriminant reveals information about the nature of the roots of the equation.
If the discriminant is positive, the quadratic equation has two distinct real roots. This means that the equation can be factored into two linear factors, each of which can be set equal to zero to solve for the roots.
If the discriminant is zero, the quadratic equation has one real root, which is a repeated root. This means that the equation can be factored into a linear factor that occurs twice.
If the discriminant is negative, the quadratic equation has two complex (non-real) roots, which are conjugates of each other. This means that the equation cannot be factored into two linear factors with real coefficients.
In summary, the nature of roots of a quadratic equation is determined by the value of the discriminant, which depends on the coefficients of the quadratic equation.
Step-by-step explanation:
What is the value of x? Enter your answer in the box. x = The figure shows 2 right triangles, triangle R S T with right angle S and triangle Q R T with right angle R. The measure of angle R T S is 60 degrees. The measure of angle Q T R is 45 degrees. The length of side R S is 2 square root 3. The length of side Q R is x.
The value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
using the trigonometric ratio of tan 45°
{recall that tan 45° = 1}
tan 45° = QR/RT {opposite/adjacent}
tan 45° = x/2√3
x = tan 45 × 2√3 {cross multiplication}
x = 1 × 2√3
x = 2√3
Therefore, the value of the side QR labelled x is equal to 2√3 using the trigonometric ratio of tan 45° for the right triangle QRT.
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If 9% of a number equals 10, find 27% of that number.
Answer: 27% of the number is 30.
Step-by-step explanation:
Let's start by setting up an equation to solve for the number:
0.09x = 10
Here, x represents the number we are trying to find. To solve for x, we can divide both sides of the equation by 0.09:
x = 10 ÷ 0.09
x = 111.11...
So the number we are looking for is approximately 111.11.
To find 27% of this number, we can multiply it by 0.27:
27% of 111.11... = 0.27 × 111.11...
27% of 111.11... = 30
Therefore, 27% of the number is 30.
Draw the graph of y= 2x + 3 on the grid
In response to the query, we can state that The line passes through the graphs y-axis at point (0,3) and has a slope of 2, which means it rises 2 units for every 1 unit it moves to the right.
What is graphs?Mathematicians use graphs to visually represent or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
Here is the graph of the equation y= 2x + 3 on the grid:
|
6 + .
| \
5 + \
| \
4 + \
| \
3 + .
| \
2 + \
| \
1 + .
| \
0 +-------+-------+-------+-------+-------+
| -2 -1 0 1 2
|
The line passes through the y-axis at point (0,3) and has a slope of 2, which means it rises 2 units for every 1 unit it moves to the right.
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Find the equation of the line that passes through the given points. (Use x as your variable.) (0,5),(6,0)
Answer:
y = - [tex]\frac{5}{6}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5 ) and (x₂, y₂ ) = (6, 0 )
m = [tex]\frac{0-5}{6-0}[/tex] = [tex]\frac{-5}{6}[/tex] = - [tex]\frac{5}{6}[/tex]
the line crosses the y- axis at (0, 5 ) ⇒ c = 5
y = - [tex]\frac{5}{6}[/tex] x + 5 ← equation of line
kiran bent some wire around a rectangle to make a picture frame.The rectangle is 8 in by 10 in
Answer:
Step-by-step explanation:
The perimeter of the wire picture frame will be 62.8 inches.
What is the circumference of a circle?
Let d be the radius of the circle.
The circumference of the circle will be
C = 2πr units
Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.
From the figure, the radius of each semi-circle is 1 inch.
The number of the semi-circle is 14 and the number of the three-fourth circle is 4. Then the perimeter of the wire will be
I HOPE THIS IS FINE!!!!
Help! Does the rule represent an exponential function?
y = -5x^7
Consider the following function.
p(x)=1−12x
Plot two points on the line to graph the function.
We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
What is functiοn?A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.
A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.
Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).
Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).
Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.
If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.
Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.
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what do i do this is confusing for me
Answer:
Translate 3 right and 1 up.
Step-by-step explanation:
Looking at the picture and count the movement.
Answer:
Step-by-step explanation:
3 units right.
1 unit up.
Each of the letters is moved by these amounts to create the new image.
2064 0 No. 10 Old if the compound interest on Rs 500 for years is Rs 398 find the compound interest on Rs. 625 15) Ans: Rs. 450 la 15 years at the same rate 5
Proportionately, if the compound interest on Rs 500 for years is Rs 398, the compound interest on Rs. 625 is Rs. 497.50.
What is proportion?Proportion is a part or portion of the whole.
Proportion indicates the ratio that one quantity or value possess in relation to or when compared or equated to another.
We determine proportion as the quotient of one value divided by another. Proportion can also be expressed as a percentage by multiplying the resultant quotient by 100.
The compound interest on Rs. 500 = Rs. 398
Thus, proportionately, the compound interest on Rs. 625 will be Rs. 497.50 (Rs 398/Rs. 500 x 625).
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Written as a simplified polynomial in standard form, what is the result when
(x − 7)² is subtracted from 6x?
Thus, the simplification of the polynomial in standard form for (x − 7)² is subtracted from 6x is found as: : (- x² + 20x - 49)
Explain about quadratic polynomial?A degree two polynomial is a quadratic polynomial. The formula for a quadratic polynomial is f(x)=ax2 + bx + c.
A quadratic equation is one that contains a quadratic polynomial. For the answers of any arbitrary quadratic problem, there is a closed-form solution described as the quadratic formula.
standard form of quadratic polynomial:
ax² + bx + c
The given quadratic polynomial:
= (x − 7)²
On expansion:
= x² + 7² - 2*7*x
= x² + 49 - 14x
Now, (x − 7)² is subtracted from 6x.
= 6x - (x − 7)²
= 6x - (x² + 49 - 14x)
= 6x - x² - 49 + 14x
= - x² + 20x - 49
Thus, the simplification of the polynomial in standard form for (x − 7)² is subtracted from 6x is found as: (- x² + 20x - 49).
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Oliver’s batting average, b, is at or above the league’s average of 0.300. Which inequality best represents his average?
Group of answer choices
b > 0.300
b ≥ 0.300
b ≤ 0.300
b < 0.300
According to this disparity, his batting average is larger than or equal to inequality 0.300, which meets the requirement that it be equal to or higher than the league average.
What is inequality?A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
Oliver's batting average is at or above the league average of 0.300, hence the following inequality would be the most accurate way to describe it:
b ≥ 0.300
According to this disparity, his batting average is larger than or equal to 0.300, which meets the requirement that it be equal to or higher than the league average.
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I need help with this immediately
The digits in the hundreds place is 2.
The digits in the hundredths place is 9.
The digits in the ten thousandths place is 1.
What is a place value?A place value can be defined as a numerical value which denotes a digit based on its position in a given number and it includes the following:
TenthsHundredthsThousandthsTen thousandthsHundred thousandthsMillionths.UnitTensHundredsThousands.Tens of thousands.Based on the numerical data (number) provided above 248.7961, we can reasonably infer and logically deduce that the place value of one (1) is ten thousandths, nine (9) is hundredths, and two (2) represent hundreds.
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If (-2,8) and (1,-10) are two anchor points on a trend line, then find the equation of the line
Answer:
The equation would be y = 3x - 7
Step-by-step explanation:
The equation of the trend line given the two coordinates is: y = -6x - 4
How to find the equation of a line?
The formula to find the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula to find the equation of a line between two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
From the given two coordinates, we can say that:
(y - 8)/(x + 2) = (-10 - 8)/(1 + 2)
(y - 8)/(x + 2) = -6
y - 8 = -6x - 12
y = -6x - 4
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for the simple harmonic motion equation d=4sin(8pi), what is the maximum displacement from the equilibrium position?
The maximum value οf the functiοn is 4.
What is simple harmοnic mοtiοn?Simple Harmοnic Mοtiοn, οr SHM, is a mοtiοn in which the restοring fοrce is inversely prοpοrtiοnal tο the bοdy's displacement frοm its mean pοsitiοn. This restοrative fοrce always pοints in the directiοn οf the mean pοsitiοn. A particle mοving in simple harmοnic mοtiοn accelerates as a(t) = -2 x. (t). The particle's angular velοcity is indicated in this equatiοn by the symbοl.
Given functiοn οf simple harmοnic mοtiοn is d= 4 sin(πt/8)
Nοw we need tο find abοut what is the maximum value οf .
We knοw that value οf sine functiοn varies frοm -1 tο 1.
that means fοr any value οf t, maximum value οf sine functiοn is 1.
sin(πt/8)<1
d≤4
Hence the maximum value οf the functiοn is 4.
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NO LINKS!!! URGENT HELP NEEDED!!!
Which additional point can be plotted so that the graph continues to represent y as a function of x?
a. (1 ,0)
b. (2, 2)
c. (3, 4)
d. (-4, 2)
Answer:
a. (1 , 0)
Step-by-step explanation:
A function is a special type of relationship where each input (x-value) is related to exactly one output (y-value).
From inspection of the given graph, the points on the graph of the function are:
(-4, 4)(-2, 3)(-1, -2)(0, 2)(2, -1)(3, 0)For the graph to continue to represent a function, any additional points cannot have the same x-value as any of the defined points.
Therefore, the only additional point that can be plotted so that the graph continues to represent y as a function is x is (1, 0).
In a high-quality coaxial cable, the power drops by a factor of 10 approximately every 2.75 km. If the original signal power is 0.375 W (= 3.75 × 10-1 W), how far will a signal be transmitted before the power is attenuated to 37.5 μW?
Every [tex]2.75[/tex] kilometres in an elevated coaxial cable, the energy decreases by a factor of 10. This indicates that the transmit strength drops with one (0.1) of its original value after every [tex]2.75[/tex] kilometres.
Let's write "d" to represent the signal's maximum range before it loses strength and dips to [tex]37.5 W[/tex]. The following formula can be used to determine the distance [tex]d: P(d) = P(0) / 10^(d / L)[/tex]
[tex]P(d)[/tex] is the signal's power after travelling a distance of d,[tex]P(0)[/tex] is the signal's initial strength,[tex]L[/tex] is indeed the attenuation length in this instance ([tex]2.75 km[/tex]), and "([tex]37.5 W[/tex])" stands for "to the power of d/L".
Inputting the values provided yields: [tex]37.5 μW = 0.375 W / 10^(d / 2.75 km)[/tex]0 The result of dividing both sides with [tex]0.375 W is: .0 /001 = 1 10^(d / 2.75 km)[/tex]The result is: when we take the logarithmic (based 10) of both sides. [tex]-4 = -(d / 2.75 km)[/tex]By dividing all sides by [tex]2.75[/tex] kilometres, we arrive at:[tex]11 km = d[/tex]
As a result, the signal may travel 11 kilometres before losing power and becoming weaker [tex](37.5W) .[/tex]
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The median of the data 10 16 12 15 7 is
The Ministry of Transport and Mining hired a firm to conduct a traffic study before expanding the city streets. Two companies submitted bids for the job. The ministry hired the second company (company B) because they had more experience and offered a better rate. They studied the movement of the traffic on a specific roadway. The first day of the study was the second Monday in September. They found that 12,665 cars, 23,709 small commercial vehicles, 1,024 medium trucks, 7,096 lange macks, and 660 other vehicles used the roadway during the evaluation period.
0f the vehicles classified as "other vehicles," 213 of them are morcycles How many of the other vehicles were not motorcycles?
Answer: i got 213
Step-by-step explanation:
what's the value of z ?
[tex] \sqrt{z + y} = - 369[/tex]
when y = 65
Answer:
There is no solution
Step-by-step explanation:
There is a mound of g
pounds of gravel in a quarry. Throughout the day, 200
pounds of gravel is added to the mound. Two orders of 700
pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,000
pounds of gravel.
Answer:
2400
Step-by-step explanation:
before anything got taken away they added 200 wich means before they added that they had 2200 and if 700 pounds were removed twice that would mean the mound lost 1400 pounds and so if you add 1000 to the 1400 that they took you can find the amount that was there before.l
What is the surface area of the rectangular prism formed by the pattern below?
Answers -
56 cm
108
136
162
Answer:
C. 136
Step-by-step explanation:
Add up the surface areas of each individual section. Area is length times width.
Lets start by figuring out the area of the 2 by 6 rectangle on the bottom. 2cm*6cm=12 sq cm. The rectangle on the top right also has an area of 2cm*6cm. So it also has an area of 12 sq cm. lets figure out the area of the smaller rectangle on the right side. 7cm times 2 cm equals 14 cm squared. There is also a 7cm by 2cm box in the middle of the pattern. so 14 + 14 = 28, + 12 + 12= 52. so all of the tiny rectangles added up equal 52. Finally, lets figure out the area of the two 6*7 rectangles. 6*7= 42. 42*2= 84. 84 is the area of the two big rectangles added together. So add the two totals to get 52 sq cm+ 84 sq. cm = 136 sq. cm.
Robin earns a 5% Commission on her sales. If robin sold an item for $530, how much did she earn in commission?
Answer:
26.5$
Step-by-step explanation:
Calculate the 5% of 530, which is 530 * 0.05, whic is equal to 26.5$
What are the key features of the equation y = (x + 12)(x + 6)? Question 5 options: The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute maximum, (–9, –9). The x-intercepts are (12, 0) and (6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 6). The vertex is an absolute minimum, (–9, –9). The x-intercepts are (–12, 0) and (–6, 0). The y-intercept is (0, 72). The vertex is an absolute minimum, (–9, –9).
Answer:
y= -x+3
Step-by-step explanation:
We can see that our given equation is in slope-intercept form
, where m represents slope of line and b represents the y-intercept.
Upon looking at our given equation, we can see that the slope of our given line is 1
and the y-intercept is at point
.0,3
Upon graphing our given equation, we will get our required graph as shown below:
Question 8 Find BC Show work
The value of BC in triangle ABC is 23.
What is triangle?
A closed plane figure with three straight sides and three angles is known as a triangle. It is made by joining three non-collinear points. Triangles are important in geometry and have various types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.
Given:- triangle ABC and DEF are similar.
So , AC = DF
Therefore,
4x-23 = 2x+2
4x – 2x = 2 + 23
2x = 25
x = 25/2 = 12.5
therefore, AC = 4x – 23
= 4 * 12.5 – 23
= 50 – 23
AC =27
So ,From triangle DEF
EF = 2x-2
= 2*12.5 – 2
= 25 – 2
EF = 23
As triangle ABC and DEF are similar.so,
BC = EF = 23
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the figure below is dilated by a factor of 4 centered at the orgin. plot the resulting image
(where are the points pls im so confused)
The image that results from the dilation transformation is as shown in the attached file with coordinates as:
G'(0, -8)
H'(8, 0)
I'(-8, 4)
What is the coordinate of the triangle after dilation?A dilation is defined as a transformation that produces an image that is the same shape as the original, but is a different size.
The coordinates of the given triangle are:
G(0, -2)
H(2, 0)
I(-2, 1)
Now, when an object with coordinates is dilated by a factor about the origin, what we will do is to multiply each coordinate by that factor . The factor of dilation is 4 and as such we have:
G(0, -2) * 4 = G'(0, -8)
H(2, 0) * 4 = H'(8, 0)
I(-2, 1) * 4 = I'(-8, 4)
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