Answer:
Step-by-step explanation:
hello :
a)
let f(x) = y so : x = g(y)
in expression = f(x) =3x+12
means : y = 3x +12 calculate : x
3x = y -12
x = (1/3)y - 4
the inverse is : g(x) = (1/3)x - 4
b)f(g(-2) = f(-14/3)
because: g(-2) = (1/3)(-2)-4 = -2/3-4 = -14/3
so : f(g(-2) = f(-14/3)=3(-14/3)+12 = - 2
1. The inverse of the function is g(x) = (1/3)x - 4.
3. The value of f(g(–2)) is -2.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)= 3x+ 12
1. let f(x) = y then x = g(y)
y = 3x+ 12
y- 12 = 3x
x= y/3 + 4
So, the inverse of the function is g(x) = (1/3)x - 4.
2. For showing the function are inverse we have to that
(fog)(x) = f(g(x)) =x and (gof)(x) =g(f(x)) = x
Take (fog)(x) = f(g(x))
= f( (1/3)x - 4.)
= 3 ((1/3)x - 4) 12
= x - 12 + 12
= x
Now, (gof)(x)
=g(f(x))
= g(3x+ 12)
= (1/3) ( 3x+ 12) -4
= x + 4 - 4
= x
3. f(g(-2))
So, g(-2)
= (1/3)(-2)-4
= -2/3-4
= -14/3
Then, f(g(-2)) = f(-14/3)
=3(-14/3)+12
= - 2
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Area of a rectangle is 100 sq ft. The length is 10 ft longer than twice it’s width. What is the length and the width.
The length of the rectange is 20ft and width of the 5ft.
Step-by-step explanation:
Let us consider a rectangle and its area is known to be 100 sq ft.
We are given the information that the length of the rectangle is 10ft longer than twice its width.
⇒Length l = 2w+10.
Where w is the width of the rectangle.
The formula for area of the rectangle A = length × width.
A= (2w+10)×w.
100 = [tex]2w^2+10w[/tex].
0=[tex]2w^2+10w-100[/tex].
Thus it forms an quadratic equation we have to solve for the solution.
0=(2w-10)(w+10).
2w-10=0. w+10=0.
2w=10. w=-10. (negative value cannot be choosed.)
w=[tex](\frac{10}{2} )[/tex].
w=5ft.
Thus width is is 5 ft.
Length = 2(5)+10.
=10+10.
=20ft.
Thus the length is 20ft.
HELP NOW BRANLIEST AND 15 points
Answer: C A L C U L A T O R probably on calculator soup
Step-by-step explanation:
Answer:
look at the picture shown
Loc weighs 14 pounds. The HCP prescribes an IV infusion of 5% dextrose in 1/4 normal saline to be infused at 8mL/kg/hr. How many mL of the prescribed solution should the nurse infuse each hour?
To infuse the prescribed solution each hour, the nurse should administer 51 mL.
Explanation:To calculate the amount of solution that should be infused each hour, we first need to calculate the weight of the patient in kilograms. We can do this by converting the weight from pounds to kilograms using the conversion factor of 0.4536 kg/pound. So, the weight of the patient in kilograms is 14 pounds x 0.4536 kg/pound = 6.3504 kg. Next, we multiply the weight in kilograms by the infusion rate of 8 mL/kg/hr to find the total volume of solution to be infused each hour. Thus, the nurse should infuse 6.3504 kg x 8 mL/kg/hr = 50.8032 mL, which can be rounded to 51 mL each hour.
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Which expression is a factor of 12x2 + 29x - 8?
Answer:
Factors are: 3x+8 & 4x-1
Step-by-step explanation:
12x² + 29x - 8
12x² + 32x - 3x - 8
4x(3x + 8) -1(3x + 8)
(3x + 8)(4x-1)
Answer:
3x+8
Step-by-step explanation:
Yall know i be doing edg2020 to right?
Suppose that circles A and B have a central angle measuring 100°. Additionally, the measure of the sector for circle A is 1071 m²
and for circle B is 407 m²
If the radius of circle A is 6 m, what is the radius of circle B?
10 m
12 m
16 m
Answer:12 m
10π40π = 62x2
x = 12
When circles have the same central angle measure, the ratio of measure of the sectors is the same as the ratio of the radii squared.
Step-by-step explanation:
On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
Final answer:
there were 127 children and 264 adults.
Explanation:
To solve this problem, we use a system of equations. Let's denote the number of children as C and the number of adults as A. We know two facts: the total number of people is 391, and the total amount of money collected is $752.75. Therefore, we have the equations:
C + A = 3911.25C + 2.25A = 752.75To solve this system, we first multiply the first equation by 1.25 to align the coefficient of C with the second equation:
1.25(C + A) = 1.25(391)1.25C + 1.25A = 488.75Next, we subtract this result from the second equation to eliminate C, leaving an equation in terms of A only:
2.25A - 1.25A = 752.75 - 488.75
A = (264) / 1 = 264
Substituting the value of A into the first equation, we find the value of C:
C + 264 = 391
C = 127
Therefore, there were 127 children and 264 adults who swam at the public pool that day.
Find the measure for ∠XQL.
Answer: [tex]C)62\°[/tex]
Step-by-step explanation:
The missing picture is attached. And the missing options are: [tex]A) 58\°\\ B)60\°\\ C)62\°\\ D)64\°[/tex]For this exercise it is necessary to remember the definition of "Vertical angles".
Vertical angles are defined as those angles that are opposite to each other and share the same vertex. These angles are congruent, which means that they have equal measure.
You can identify in the picture that [tex]\angle XQL[/tex] and [tex]\angle MQR[/tex] are Vertical angles, then they are congruent.
Based on the above, you can set up the following equation:
[tex]-5b+82=-3b+74[/tex]
Now you must solve for "b" in order to find its value:
[tex]82-74=-3b+5b\\\\8=2b\\\\\frac{8}{2}=b\\\\b=4[/tex]
Finally, substituting the value of "b" into [tex]\angle XQL=-5b+82[/tex] and evaluating, you get:
[tex]\angle XQL=-5(4)+82\\\\\angle XQL=62\°[/tex]
The value of y varies directly as the square of x and y=36 when x=3. What is y when x=4?
Answer: y = 64
Step-by-step explanation:
y <> x² ----------------------- 1
y = kx² ----------------------- 2
36 = 3²k
36 = 9k
K = 36/9
= 4.
To find y when x = 4, we substitute for x in equation 2
y = kx²
y = 4²k
y = 16 x 4
y = 64
The value of y, which varies directly as the square of x, is determined by first identifying the constant of variation from the given values, in this case, y = 36 when x = 3. The constant is found to be 4. Using this constant (k), when x is 4, y will be 64.
Explanation:The value of y varies directly as the square of x, which is represented mathematically as y = kx², where k is the constant of variation. Using the given that y = 36 when x = 3, we can determine k by substituting these values into the equation. Thus, k = y/x² = 36/9 = 4. Now, having the value for k, we can find y when x = 4 by substituting these values into the equation: y = kx² = 4×16 = 64. Therefore, y equals 64 when x equals 4 in the given relation.
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if sin theta = cos theta then find the value of theta
Step-by-step explanation:
[tex] \because \sin \theta = \cos \theta \\ \\ \therefore \: \sin \theta = \sin(90 \degree - \theta) \\ \\ \therefore \: \theta = 90 \degree - \theta \\ \\ \therefore \: \theta + \theta= 90 \degree \\ \\ \therefore \: 2\theta = 90 \degree \\ \\\therefore \: \theta = \frac{90 \degree }{2} \\ \\ \huge \orange{\boxed{\therefore \: \theta = 45 \degree}}\\ \\[/tex]
The table shows how a leading automobile dealer plans to spend its advertising dollars for this year. If this company plans to increase its budget by 5% next year, approximately how much will it spend on social media ads? Advertising Budget: $81,000 48.5% Television 23% Magazines 20% Newspapers 7% Radio 1% Billboards 0.5% Social Media $405 $20 $425 $4,250
Answer:
$425
Step-by-step explanation:
Answer:
the answer is c, $425
Step-by-step explanation:
just did the quiz
Ella and her children went into a bakery and where they sell cookies for $0.50 each and brownies for $2.25 each. Ella has $15 to spend and must buy a minimum of 9 cookies and brownies altogether. If Ella decided to buy 5 cookies, determine the maximum number of brownies that she could buy. If there are no possible solutions, submit an empty answer.
Answer: 5 brownies
Step-by-step explanation:
cookies = 5 x $0.50 = $2.5
$15 - $2.5 = $12.5
$12.5 divided by $2.25 = $5.555
so at the most ella can buy 5 brownies if she buys 5 cookies
Answer:
If each cookie is .50 and she wants to buy 5 cookies @ .50= $2.50
Than subtract $2,50 from $15.00 (which she has to spend you have $12.50
Then divide 2.25 into $12.5 and you get an answer of 5 brownies with a $1.30 extra to spend
Step-by-step explanation:
Leah wrote 2 different fractions with the same denominator.Both fractions were less than 1. Can their sum equal 1? Can their sum be greater than 1? Explain.
Answer:
1. Yes
2. Yes
Step-by-step explanation:
Leah wrote 2 different fractions with the same denominator. Both fractions were less than 1.
1. Can their sum equal 1?
Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{1}{7}.[/tex] Both these fractions have the same denominators and are less than 1. Find their sum:
[tex]\dfrac{6}{7}+\dfrac{1}{7}=\dfrac{7}{7}=1[/tex]
2. Can their sum be greater than 1?
Let Leah fractions be [tex]\dfrac{6}{7}[/tex] and [tex]\dfrac{5}{7}[/tex]. Both these fractions have the same denominators and are less than 1. Find their sum:
[tex]\dfrac{6}{7}+\dfrac{5}{7}=\dfrac{11}{7}=1\dfrac{4}{7}>1[/tex]
Two fractions with the same denominator can sum to 1 if their numerators add up to the denominator, or they can sum to more than 1 if their numerators together exceed the denominator. This is based on the concept of adding fractions where only the numerators are summed.
Leah wrote two different fractions with the same denominator, and both were less than 1. Can their sum equal 1? Can their sum be greater than 1? The answer to both questions depends on the value of the numerators. Fractions represent parts of a whole. For two fractions with the same denominator to have a sum of 1, the numerators must add up to the denominator. If their sum is greater than the denominator, then the total sum would be greater than 1.
For example, if we have fractions ½ and ¾, their sum is ½ + ¾ = ¾ which is less than 1. However, if we have ¾ and ¾, the sum equals 6/4, which reduces to 1½, a sum greater than 1.
In conclusion, two fractions with the same denominator and each less than 1 can sum to 1 if the numerators total the denominator, or can sum to greater than 1 if the numerators together exceed the denominator. An important aspect of adding fractions is that we only add the numerators and never the denominators.
Question text
If x − 2 = 1/3, then what is the value of x to the power of 2 − 4x + 4?
Answer: 1/9
Step-by-step explanation:
Consider the formula
d
=
m
V
d=
V
m
d, equals, start fraction, m, divided by, V, end fraction, where
d
dd represents density,
m
mm represents mass and has units of kilograms
(kg)
(kg)left parenthesis, start text, k, g, end text, right parenthesis, and V
Represents volume and has units of cubic meters
(m3)
(m
3
)start text, left parenthesis, m, end text, cubed, right parenthesis.
Select an appropriate measurement unit for density.
Option C:
[tex]$\frac{\text{kg}}{\text{m}^3}}[/tex]
Solution:
Given data:
[tex]$\text{d}=\frac{\text{m}}{\text{V}}[/tex]
where "d" represents density
"m" represents mass
"V" represents volume
The unit of mass is kilogram (kg).
The unit of volume is cubic metres [tex](\text{m}^3)[/tex].
To find an appropriate measurement unit for density:
[tex]$\text{d}=\frac{\text{m}}{\text{V}}[/tex]
Substitute kg and [tex](\text{m}^3)[/tex] in mass and volume respectively.
[tex]$\text{d}=\frac{\text{kg}}{\text{m}^3}}[/tex]
Option C is the correct answer.
An appropriate measurement unit for density is [tex]$\frac{\text{kg}}{\text{m}^3}}.[/tex]
Answer:
option b Kg/m3
Step-by-step explanation:
same as other answer
Simplify (2 3/5) divided by (-3 3/4)
Rewrite the numbers as improper fractions:
2 3/5 = 13/5
-3 3/4 = -15/4
Now you have 13/5 divided by -15/4
When dividing fractions flip the second one over and then multiply:
13/5 x -4/15 = (13 x -4) / (5 x15) = -52/75
the sum of two consecutive integers is one less than three times the smallest integer. find the two integers
Answer:
n + (n+1) = 3n -1
n = 2
the integers are 2 and 3
Step-by-step explanation:
A line has a slope of 9 and passes through the point (4,7). What is its equation in point-slope form?
Answer:
Y = 9X-29
Step-by-step explanation:
y = mx + b
P1 : ( 4 , 7 )
m = 9
using equation of line ,
y = mx + b
7 = ( 9 ) (4 ) + b
7 - 36 = b
b = -29 ,
hence equation of line is ,
y = 9x - 29 answer
Answer:
y - 7 = 9(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 9 and (a, b) = (4, 7), thus
y - 7 = 9(x - 4) ← equation in point- slope form
A patient’s weight is recorded as 75 kilograms. How many pounds does the patient weigh? Round your answer to the nearest pound.
answer: about 165 lbs
to go from kilograms to pounds, you multiply by 2.205 to get the approximate answer.
75x2.205≈165
How many times does 7 go into 52
Answer:
7.43
Step-by-step explanation:
52/7 = 7.4285714...
that can be shortened to 7.43
7.43
Step-by-step explanation:
52/7 = 7.428
3x+2y=-10
2x-5y=3
Solve using elimination
Answer:
look at the picture shown
The solution to the system of equations 3x+2y=-10 and 2x-5y=3 using the elimination method is x = -44/19 and y = -29/19.
Explanation:To solve the system of equations 3x+2y=-10 and 2x-5y=3 using the elimination method, we need to multiply the equations by respective constants so that a variable gets eliminated when we add or subtract them. Let's try to eliminate y.
Multiply the first equation by 5 (the coefficient of y in the second equation) and the second equation by 2 (the coefficient of y in the first equation):
5*(3x+2y) = 5*(-10)
2*(2x-5y) = 2*3
15x + 10y = -50
4x - 10y = 6
Add the two equations:
(15x + 10y) + (4x - 10y) = -50 + 6
19x = -44
Divide both sides by 19 to solve for x:
x = -44/19
x = -44/19
Now substitute x back into one of the original equations to solve for y:
3x + 2y = -10
3*(-44/19) + 2y = -10
Multiply 3 by -44/19:
-132/19 + 2y = -10
Now solve for y:
2y = -10 + 132/19
2y = (-190/19) + (132/19)
2y = -58/19
Divide by 2:
y = -58/38
y = -29/19
Therefore, the solution to the system of equations is x = -44/19 and y = -29/19.
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Four trucks were used to make deliveries. The drivers recorded the number of miles driven and the amount of gasoline
Which truck drove the fewest number of miles per gallon of gas?
Answer:
b
Step-by-step explanation:
Answer:
Truck D
Step-by-step explanation:
36:4 = 9 best mpg
Fill in the table using this function rule. y=-3x+5
The missing values are 11, 8, 5 and 2 respectively.
The picture of the question in the attached figure
we have
y=-3x+5
Substitute the different values of x in the linear equation, to obtain the
different values of y in the table
For x-2-> y=-3(-2)+5=11
For x=-1-> y=-3(-1)+5=8
For x-0->9=-3(0)+5=5
For x-1->y=-3(1)+5=2
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Solve the equation for the variable
X/2+1=6
The soda can is a cylinder with a diameter of 2 inches and a height of 5 inches. What is the area
Answer:
?
Step-by-step explanation:
Describe a data set that has a mean absolute deviation of 0.
Answer:
the difference between a data value in a set and the mean of the set. the mean of all deviations in a set equals zero. absolute value. the distance of any value on a number line from zero. the sum of the absolute values of deviations on each side of the mean are equal.
Step-by-step explanation:
A data set that has a mean absolute deviation of 0 means the average difference between the elements in a data set and mean of the same data set is very less.
What is Mean absolute Deviation?The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
As we know the mean absolute deviation is the average distance between each data point and the mean.
If more than 50% of your data have identical values, your MAD will equal zero.
Also, the mean absolute deviation of a dataset is the average distance between each data point and the mean.
If the mean absolute deviation (MAD) is close to 0,it means the average difference between the elements in a data set and mean of the same data set is very less.
Thus, the average difference between the elements in a data set and mean of the same data set is very less.
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What is x in the following equation -3(-4x-3) = 20
Answer:
Step-by-step explanation:
-3(-4x-3) = 20
Opening bracket
12x + 9 = 20
12x = 20 - 9
12x = 11
x = 11/12
Prime factor of 2080
Answer:
2 x 2 x 2 x 2 x 2 x 5 x 13
Step-by-step explanation:
The Prime Factorization is:
2 x 2 x 2 x 2 x 2 x 5 x 13
In Exponential Form:
25 x 51 x 131
CSV Format:
2, 2, 2, 2, 2, 5, 13
The prime factors of 2080 are 2, 2, 2, 2, 5, and 13.
Divide 2080 by the smallest prime number, which is 2:
2080 ÷ 2 = 1040
Continue dividing by 2:
1040 ÷ 2 = 520
Continue dividing by 2:
520 ÷ 2 = 260
Continue dividing by 2:
260 ÷ 2 = 130
Continue dividing by 2:
130 ÷ 2 = 65
Now, 65 is not divisible by 2.
Move to the next prime number, which is 5:
65 ÷ 5 = 13
13 is a prime number.
So, the prime factors of 2080 are 2, 2, 2, 2, 5, and 13. In exponential form, this can be written as 24 * 5 *13.
Which system of equations can you use to find the roots of the equation 2x3 + 4x2 – x + 5 = –3x2 + 4x + 9? y = 2x3 + x2 + 3x +5 y =9 y = 2x3 + x2 y = 3x + 14 y = 2x3 + 4x2 – x + 5 y = –3x2 + 4x + 9 From least to greatest, what are the roots of the polynomial equation?
Answer:
The answer is actually (-4, -0.5, 1) in order from least to greatest.
Step-by-step explanation:
A system of equation is a collection of more than one equation
The system of equations to determine the roots of [tex]2x^3 + 4x^2 - x + 5 = -3x^2 + 4x + 9[/tex] are [tex]y = 2x^3 + 4x^2 - x + 5[/tex] and [tex]y= -3x^2 + 4x + 9[/tex]The roots of the polynomial equation are -0.5 and 1The equation is given as:
[tex]2x^3 + 4x^2 - x + 5 = -3x^2 + 4x + 9[/tex]
Split the equation to a system of equations:
[tex]y = 2x^3 + 4x^2 - x + 5[/tex]
[tex]y= -3x^2 + 4x + 9[/tex]
So, the system of equations to determine the roots of [tex]2x^3 + 4x^2 - x + 5 = -3x^2 + 4x + 9[/tex] are [tex]y = 2x^3 + 4x^2 - x + 5[/tex] and [tex]y= -3x^2 + 4x + 9[/tex]
See attachment for the graphs of [tex]y = 2x^3 + 4x^2 - x + 5[/tex]
[tex]y= -3x^2 + 4x + 9[/tex]
The graphs of both functions intersect at x = -0.5, and x = 1
Hence, the roots of the polynomial equation are -0.5 and 1
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it cost $45.75 for 5 apple pies. give the point of the unit rate
What is 1/4 * 4x + 8