Answer:
Step-by-step explanation:
abcdefgh
Find the equation of the inverse of the following function: f (x) = 7x + 3. State the answer in slope-intercept form
The equation of the inverse function is f⁻¹(x) = x/7 - 3/7
How to determine the inverse functions?The function f(x) is given as
f(x) = 7x + 3
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = 7x + 3
The next step is to switch/swap the positions of x and y in the above equation y = x + 5
The equation becomes
x = 7y + 3
The next step is to make y the subject of the formula in the above equation
The equation becomes
y = x/7 - 3/7
Express as an inverse function
f⁻¹(x) = x/7 - 3/7
Hence, the inverse is f⁻¹(x) = x/7 - 3/7
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Line g passes through points (2, 4) and (10, 1). Line h is parallel to line g. What is the slope of line h?
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line G
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{10}-\underset{x_1}{2}}} \implies \cfrac{ -3 }{ 8 } \implies {\Large \begin{array}{llll} - \cfrac{3 }{ 8 } \end{array}}[/tex]
work
Find the savings plan balance after 4 years with an APR of 4% and monthly payments of $250.
The balance is
(Do not round until the final answer. Then round to the nearest cent as needed.)
The balance is $12989.90.
From the question, we have
[tex]A= P\times \frac{\left ( 1+\frac{APR}{n} \right )^{nt}-1}{\frac{APR}{n}}[/tex]
where,
A is the balance after t years,
P is the periodic payment,
APR is the annual percentage rate,
n is the number of periodic payments per year, and t is the number of years.
[tex]A=250\times \frac{\left ( 1+\frac{0.04}{12} \right )^{12\times 4}-1}{\frac{0.04}{12}}[/tex]
=$12989.90
The balance is $12989.90.
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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6. Which shows the decimals in the
correct order?
A. 5.271> 5.217 > 5.38
B. 5.38 5.217 > 5.271
C.
5.271
5.38 > 5.217
D. 5.38
5.271 > 5.217
Answer: D. 5.38 > 5.271 > 5.217
1. Jasmine buys 4 bottles of water for $1.30 each. She buys a large bag of popcorn for $3.75. How much more money did Jasmine spend on water than pop
Answer:
Jasmine spent 1.45$ more on water than popcorn.
Step-by-step explanation:
Jasmine buys 4 bottles of water and spends 1.30$ for each one individually. To find out how much all of these 4 costs, we multiply 4 by 1.30$ which is 5.20$
To find out how much more money Jasmine spent on the water than popcorn, we subtract 5.20$ - 3.75$ = 1.45$
4 Select the correct answer. A circle with center O (0,0) has point B (4,5) on its circumference, which is joined by a line to O. What is the general form of the equation for the given circle centered at O(0, 0)? A. x2 + y2 + 41 = 0 B. x2 + y2 − 41 = 0 C. x2 + y2 + x + y − 41 = 0 D. x2 + y2 + x − y − 41 = 0 Reset Next
The equation of the circle is x² + y² - 41 =0.
What is a circle?A circle is a round-shaped 2-dimensional geometrical figure in which the points on the boundary are equidistant from a fixed point called a center.
Given, a circle centered at O(0,0)and has a point B (4,5) on its circumference.
The radius of the circle is the distance between the points O(0,0) and B (4,5), therefore,
r = √((4-0)² + (5-0)²)
r = √(16+25)
r = √41
The equation of a circle, centered at the origin with a radius of r =√41 units, is given by,
x² + y² = √41²
x² + y² = 41
x² + y² - 41 =0
Hence, the equation of the circle is x² + y² - 41 =0.
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Which is the following rational functions is graphed below
Answer:
B.) 1/(x+3)(x+5)
Step-by-step explanation:
Look for the x-intercepts and asymptotes on the graph to get the numerator and denominator
There are no x-intercepts, so the numerator is an integer
The asymptotes are -3 and -5, so the denominator would be (x+3)(x+5) since if you were to set that = to 0 you would get -3 and -5.
A rectangle has side links of 3X +6 inches and 2X -4 inches right in expression to represent perimeter of the rectangle then find the perimeter if X equals 9
Answer:
ez hi
Step-by-step explanation:
ez
31-62=152+2-6(3+21) i need the answer to this please help
A bacteria culture initially contains 3000 bacteria and doubles every half hour.
1) Find the size of the baterial population after 80 minutes.
2) Find the size of the baterial population after 7 hours.
The size of the bacterial population after 80 minutes is 19048.81
The size of the bacterial population after 7 hours is 49152000.
Given,
A bacterial culture initially contains 3000 bacteria and doubles every half hour.
we are asked to determine the size of the bacterial population after 80 minutes.
The exponential growth law for this problem is
p(t) = 3000 (2)^t/30
where t is the time in minutes. To find the population after 80 minutes, plug in t=80 and evaluate P(80).
p(80) = 3000 (2)^80/30
p(80) = 3000(2)^8/3
p(80) = 19048.81
now, we are asked to determine the size of the bacterial population after 7 hours.
To find it after hours, plug in t=420 minutes (since 7 hrs equals 420 minutes) and evaluate p(420).
p(420) = 3000(2)^420/30
p(420) = 3000(2)^14
p(420) = 49152000
hence we get the required size of the population.
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a pitcher of water is three-fourths full. six cups of water are served from the pitcher. then the pitcher is two-thirds full. how many cups of water can the pitcher hold?
The total cups of water the pitcher can hold is 72
What is a fraction?A fraction is the ratio of two integers.
It is divided into two parts by a division line and the part above the line is called the numerator and the part below the line is called the denominator.
Fraction are of three types: proper, improper and mixed fractions.
Let the total number of cups to fill the pitcher be x.
The pitcher is 3-fourths full of water, that is 3/4 of x = [tex]\frac{3x}{4}[/tex]
when 6 cups were taken away from the Pitcher it became 2/3 of x = [tex]\frac{2x}{3}[/tex]
So that,
[tex]\frac{3x}{4}[/tex] - [tex]\frac{2x}{3}[/tex] = 6
multiply [tex]\frac{2x}{3}[/tex] by 4/4 and [tex]\frac{3x}{4}[/tex] by 3/3
it becomes
[tex]\frac{9x}{12}[/tex] - [tex]\frac{8x}{12}[/tex] = 6
simplifying the numerator
x/12 = 6
cross multiplying
x = 12 x 6
x = 72
In conclusion, the total number of cups to fill the pitcher is 72
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Nick bikes 39 miles in 2 hours while Jane bikes 34 miles in 5 hours. Who bikes faster Nick or Jane?
Answer:
Nick
Step-by-step explanation:
Nick: 39 miles / 2 hours = 19.5 miles per hour
Jane: 34 miles / 5 hours = 6.8 miles per hour
Nick is biking faster!
What expression represents the verbal phrase?
one-half times a number m plus twenty-five
Answer: m/2 + 25 or (0.5)m + 25
Step-by-step explanation:
Can you solve please
Answer:
Green x = 10
Purple x = 19
Step-by-step explanation:
Are we solve for x?
Green:
It is not staighted, but this looks like a straight angle. That would total 180
3x + 5 + 6x -5 +90 = 180 A right angle is 90 Combine like terms
9x + 90 = 180 Subtract each side by 90
9x = 90 Divide both sides by 9
x = 10
Purple:
5x - 19 + 2x + 5 = 119 Combine like terms
7x -14 = 119 Add 14 to both sides
7x = 133 Divide both sides by 7
x = 19
the net of a prism is shown
a)how many faces
b)what is the mathmatical name
Answer:
????? you did not show the net of the prism
Step-by-step explanation:
Answer:
b) it's a polyhedron
I don't know what else to say
Rhea has 36 homework problems to complete. She completes 12 on Monday. On Tuesday, she completes 2/3 of the remaining problems. How many problems does Rhea still have to complete after Tuesday?
The number of problems Rhea still have to solve is 8
What is a fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator and the number at the bottom is called denominator. It tells how many equal parts of the whole or collection are taken.
On Monday Rhea solved 12 out of 36 problems. This means she has 36-12 = 24 problems remaining. On Tuesday she solved 2/3 of the remainder, which means she did 2/3×24= 16problems on Tuesday.
Therefore she will have 24- 16= 8problems to complete after Tuesday.
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12. Two functions are given below, one in equation form and the other in table form. Using these functions, give
the value of g (f (4)). Show how you arrived at your answer.
-2
f(x) -1
0
3
4
12
7
9
19
6
g(x)=3.25x+6
The composition of the fuctions g(x) and f(x) evaluated in x = 4 is equal to:
g( f(4)) = 45
How to find the value of the composition?Here we have two functions f(x) and g(x), such that:
g(x) = 3.25*x + 6
And f(x) is defined by the table:
x f(x)
-2 -1
0 3
4 12
7 9
19 6
And we want to find the composition of g(x) and f(x) evaluated in x = 4.
g( f(4))
By using the table of f(x), we can see that f(4) = 12
Then:
g( f(4)) = g(12)
Evaluating g(x) in x = 12 we get:
g(12) = 3.25*12 + 6 = 45
Then we conclude that g( f(4)) = 45
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Help please
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions
The values of [tex]D, D_x, D_y[/tex] are, [tex]D = 13, D_x = 8, D_y = 19[/tex].
What is Cramer's rule?
One of the key techniques used to solve an equation system is Cramer's rule. The determinants of matrices are used in this method to derive the values of the system's variables. Thus, the determinant technique is another name for Cramer's rule.
Consider, the given system of equations
-3x + 4y = 4 ...(1)
2x = 7y - 9 ...(2)
equation (2) can be written as,
2x - 7y = -9 ..(3)
Using Cramer's rule, we have to find the determinant of the coefficient matrix
matrix,
D= [tex]\left[\begin{array}{ccc}-3&4\\2&-7\end{array}\right][/tex] = (-3)(-7) - 8 = 21 - 8 = 13
Secondly, find the determinant of x coefficient matrix,
[tex]D_x[/tex] = [tex]\left[\begin{array}{ccc}4&4\\-9&-7\end{array}\right][/tex] = (4)(-7) - (4)(-9) = -28 + 36 = 8
Similarly, find the determinant of y coefficient matrix,
[tex]D_y[/tex] = [tex]\left[\begin{array}{ccc}-3&4\\2&-9\\\end{array}\right][/tex] = (-3)(-9) - (4)(2) = 27 - 8 = 19
Hence, values of the determinants are, [tex]D = 13, D_x = 8, D_y = 19[/tex].
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There are 240 boxes with 25 bags of coffee each. I’d each bag weighs 0.62kg, what is the total weight of all the coffee? Round your answer to the nearest whole number
Answer:
3720 kg
Step-by-step explanation:
one bag of coffee weighs=0.62 kg
total no. of coffee bags= 240×25=600
total weight of coffee=6000×0.62= 3720
Please help nobody wants to help me with this problem :,(
Answer:
x = 17
y = 2
Length of DF = 20
Step-by-step explanation:
Step 1: Solve x - 3
Since GH is the mid-segment it is equal to half of EFHalf of EF is 28/2 = 14x - 3 = 14x = 14 + 3x = 17Step 2: Plug x = 17 into x - 7 and solve
x - 7(17) - 7 = 10Since DH and HF are equal then x - 7 = y + 8So, 10 = y + 8y = 2Step 3: Find the length of DF
DF = y + 8 + x - 7DF = y + x + 1DF = 2 + 17 + 1 = 20Simplify the expression (x)(6+x)−2x. Write products as powers when possible.
(x)(6+x)−2x=
Simplifying the expression (x)(6 + x)−2x gives x^2 + 4x
How to simplify the expressionInformation given in the question
the expression (x)(6 + x)−2x
The expression is simplified by first expanding
(x) (6 + x) − 2x
6x + x^2 - 2x
x^2 + 4x (products as powers when possible)
The result here is a quadratic equation without the constant variable. it can be simplified further to give
x(x + 4)
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The two-way frequency table contains data about how students access courses.
Traditional Online Row totals
Computer 28 62 90
Mobile device 46 64 110
Column totals 74 126 200
PLEASE What is the joint relative frequency of students who use a mobile device in an online class?
64%
55%
32%
23%
The joint relative frequency of students who use a mobile device in an online class is approximately 32%.
The joint relative frequency of students who use a mobile device in an online class, we need to divide the frequency of the intersection of the "Mobile device" and "Online" categories by the total number of students (200 in this case) and express it as a percentage.
From the given two-way frequency table, we can see that the frequency for the intersection of "Mobile device" and "Online" is 64.
The joint relative frequency can be calculated as:
Joint Relative Frequency = (Frequency of intersection / Total number of students) × 100
Joint Relative Frequency = (64 / 200) × 100
Joint Relative Frequency ≈ 32%
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Write the equation of the line that passes through the points (2,-8)(2,−8) and (-1,4)(−1,4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The simplified point-slope form is y = 2x -12
A simple definition of point-slope form is a line equation written with only one point on the line and the slope of the line. (x, y) is the point form, and the slope is the rise over run or the ratio of the change in y values to the change in x values.
Given points (2,-8) and (-1,4)
We have to determine the answer in point-slope form
The slope formula provides the slope of the line:
m = (y2 -y1)/(x2 -x1)
m = (4 -(-8))/(-1-2) = 12/-3 = -4
the point-slope formula is given by
y-y1 = m(x-x1)
In terms of this formula:
m = 2
y1 = -8
x1 = 2
Let's simplify by plugging these values into the point-slope formula:
y - y1 = m (x - x1)
y - (-8) = (2)(x - 2)
y + 8 = 2(x - 2)
y + 8 = 2x -4
y = 2x -12
Therefore the simplified point-slope form is y = 2x -12
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Using Pythagoras' theorem, work out the
length of the hypotenuse of this right-angled
triangle.
Give your answer to the nearest centimetre.
7 cm
19 cm
Not drawn accurately
Answer: About 20.25 or [tex]\sqrt{410}[/tex]
Step-by-step explanation:
a²+b²=c²
c is the hypotenuse in this equation, so we can substitute the given side lengths for a and b.
7²+19²=c²
49+361=c²
410=c²
Then we take the square root to get
about 20.25 or [tex]\sqrt{410}[/tex] to be exact
Answer:
Step-by-step explanation:
a² + b². =. c²
7² + 19². =. c²
49 + 361 (400). =. c²
. c = √400= 20cm
IXL Please Help Fast!
Equation of line c parallel to line d and passing through points (2, -6) is
How to equation of line dThe equation of line d will be written in the slope intercept form of the form just like line c,
the slope intercept form is as below
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
y = -5x + 3
slope
m = -5
slope of parallel lines are equal hence slope of line d = -5
using the formula for the slope intercept the equation is written
(y - y₁) = m (x - x₁)
point (2, -6) and m = -5
(y - -6) = -5 (x - 2)
y + 6 = -5x + 10
y = -5x + 4
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Make w the subject of the formula y - aw = 2w - 1
Answer:
[tex]w=\frac{y+1}{a+2}[/tex]
Step-by-step explanation:
[tex]y-aw=2w-1 \\ \\ y+1=2w+aw \\ \\ y+1=w(a+2) \\ \\ w=\frac{y+1}{a+2}[/tex]
Answer the questions on the function below:
What is the slope of the line?
What is the y-intercept?
What is the x-intercept?
Answer:
The slope of the line is 1/2.
The y-intercept of the line is 5.
The x-intercept of the line is 10.
Step-by-step explanation:
The y-intercept is where the line intercepts the y axis. (vertical line)
The x-intercept is where the line intercepts the x axis. (horizontal line)
The slope (rise over one) is a bit more complicated to find. First, pick two points on the line and determine their coordinates. Then, determine the difference in y-coordinates of these two points (rise). After that, determine the difference in x-coordinates for these two points (run). Then you have your slope!
i will give brainly if someone helps with thisIf △ABC is translated 3 units left and 2 units up, what would be the translated coordinates of Point C?
Answer: (-2, -2)
Step-by-step explanation:
Right now, the coordinates of point C are (1, -3).
It is first moved 3 units to the left, so the point C would change to (1 - 3, -3) = (-2, -3)
It is then moved 2 units up, so point C would change to (-2, -3 + 2) = (-2, -1)
James is having a birthday party. It costs $350 to rent the hall plus $35 per person for food. Write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.
y=35x+350 is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
James is having a birthday party.
It costs $350 to rent the hall plus $35 per person for food
We need to write an equation to show the total cost of the party (y) based on the number of guests (x) he invites.
y=35x+350
Where x represents the number of guests.
350 is a constant value because it is the cost of the hall.
As 35 is the cost per person, 35x
Hence y=35x+350 is the equation to show the total cost of the party (y) based on the number of guests (x) he invites.
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a triangle has a base of 1.5
Answer: bro You need To add more about the question
Step-by-step explanation: