Answer:
The inverse function is f(x) = (x + 7)/2
Step-by-step explanation:
To find the inverse of any function, start by switching the x and f(x) values.
f(x) = 2x -7
x = 2f(x) - 7
Now solve for the new f(x). The result will be your inverse function.
x = 2f(x) - 7
x + 7 = 2f(x)
(x + 7)/2 = f(x)
The inverse of Y = 2x - 7 can be found by swapping the x and y variables and then solving for y, which gives the inverse function y = (x + 7) / 2.
Explanation:To find the inverse of the function Y = 2x - 7, you can follow these steps:
First, interchange the variables. Replace Y with x and x with y, which gives you x = 2y - 7. Next, solve for y. Add 7 to both sides to get x + 7 = 2y, and then divide both sides by 2 to solve for y. This will give you y = (x + 7) / 2.
So, the inverse of Y = 2x - 7 is y = (x + 7) / 2.
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To multiply a decimal number by 100, move the decimal point two places to the right. true or false?
Answer:
Answer:
True
Step-by-step explanation:
Ex. 0.0100 * 100 = 001.00
The sum of two numbers is 34. The smaller number is 14 less than the larger number. What are the numbers?
larger number:
Smaller number:
Answer:
larger number : 24
smaller number : 10
Step-by-step explanation:
Final answer:
To find the two numbers whose sum is 34 with one being 14 less than the other, equations were set up and solved. The larger number is 24, and the smaller number is 10.
Explanation:
The sum of two numbers is given as 34, and it is known that the smaller number is 14 less than the larger number. To find these numbers, we can set up a system of equations. Let's denote the larger number as L and the smaller number as S. According to the problem, we have two equations:
L + S = 34 (The sum of the larger and smaller number is 34)S = L - 14 (The smaller number is 14 less than the larger number)Substituting the second equation into the first one gives us:
L + (L - 14) = 34
Combining like terms, we get:
2L - 14 = 34
Adding 14 to both sides, we obtain:
2L = 48
Dividing both sides by 2 gives us the value of L:
L = 24
Now that we have the larger number, we can find the smaller number by subtracting 14 from L:
S = 24 - 14
S = 10
The numbers are 24 and 10, with 10 being the smaller number.
Can someone help me out pls
its A. look at the other percents when considering about the question.
hope this helps!!
What is the answers
Answer:
Step-by-step explanation:
1 case = $7
81*7=$567
81 case = $567
76*7=$532
76 case = $532
Draw a bar model to represent the expression z-4
Answer:
Just like x, but -4. x on a graph means that the graph will always be (x, x) instead of (x, y)
Used desmos.com to create this.
Step-by-step explanation:
Look at picture below.
At the zoo, there are 3 fewer ferrets than twice the number of tigers. If there are 21 ferrets, what's an equation for the number of tigers at the zoo?
What is the number of ferrets?
12x2-3=21
this would be your equation because there are 12 tigers
Jorge mows his 1/3 acre lawn in 5/6 hour. How many acres will he mow in an hour
Answer:
2/5 an acre
Step-by-step explanation:
We multiply the 5/6 hour by 6/5 to get 1 hour.
We then have to do this to the 1/3 and we get 6/15 or 2/5
Jorge mows 2/5 acres per hour. This is calculated by dividing the fraction of the acre mowed by the fraction of the hour taken. The result from the calculation shows that Jorge’s mowing rate is 2/5 acres per hour.
To find out how many acres Jorge will mow in an hour, we need to determine his mowing rate in acres per hour. We know that Jorge mows 1/3 acre in 5/6 hour. We can use the formula for rate:
Rate = Distance / Time
Here, the distance is 1/3 acre and the time is 5/6 hour. So, we can calculate his rate:
Rate = (1/3) / (5/6)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Rate = (1/3) * (6/5) = 6/15 = 2/5
Therefore, Jorge mows 2/5 acres per hour.
If c=16 and B=67 degrees, find a
Answer:
C
Step-by-step explanation:
No explanation required
From your rules from SOHCAHTOA, you can solve for a using the cosine of B. See picture attached.
You are making payments for a $1,475 loan that has a simple interest rate of 7.54% for 5 years.
What is the total amount you will owe? How much is each monthly payment?
Answer:
$2,031.08
Step-by-step explanation:
You want to calculate the interest on $1475 at 7.54% interest per year after 5 year(s).
The formula we'll use for this is the simple interest formula, or:
I=P x r x t
P is the principal amount, $1475.00.
r is the interest rate, 7.54% per year, or in decimal form, 7.54/100=0.0754.
t is the time involved, 5....year(s) time periods.
So, t is 5....year time periods.
To find the simple interest, we multiply 1475 × 0.0754 × 5 to get that:
The interest is: $556.08
Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),
or 1475.00 + 556.08 = 2031.08. For example:
If you borrowed the $1475.00, you would now owe $2031.08
If you loaned someone $1475.00, you would now be due $2031.08
If owned something, like a $1475.00 bond, it would be worth $2031.08 now.
Jayden has already jarred 1 liter of jam and will jar an additional 6 liters of jam every day. Write an equation that shows the relationship between the days d and the jam made j.
Write your answer as an equation with j first, followed by an equals sign
please help
Answer:
[tex]j=1+6d[/tex]
Step-by-step explanation:
Jayden jars jams at a rate of 6 liters per day which can be represented by the variable [tex]6d[/tex]. In other words, the amount of jam Jayden will have made in the end (j) is 6 liters multiplied by the number of days (d) he spent jarring jam.
However, Jayden has already jarred 1 liter of jam which has to be factored into the end total (j). To factor this liter in, you can add 1 (liter) to 6d.
Write −(1/4⋅1/4⋅1/4⋅1/4) using exponents.
The product −(1/4⋅1/4⋅1/4⋅1/4) can be written as exponents as - (1/4)⁴.
What are Exponents?Exponents are the method of writing numbers, especially large numbers, in terms of a base and an exponent, which is written as the power of base.
Given expression is,
−(1/4⋅1/4⋅1/4⋅1/4)
We have to write the expression using exponents.
Taking the minus sign as such, it is given that three are 4 times 1/4 is repeating.
So, −(1/4⋅1/4⋅1/4⋅1/4) = - (1/4)⁴.
Hence the exponent form of the given expression is - (1/4)⁴.
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Final answer:
The expression −(1/4· 1/4· 1/4· 1/4) is written using exponents as −(1/4)⁴.
Explanation:
The expression −(1/4· 1/4· 1/4· 1/4) can be rewritten using exponents by recognizing that we are multiplying 1/4 by itself four times. Converting a repeated multiplication into exponential form means we use a base (which is 1/4 in this case) and an exponent (the number of times we multiply the base by itself). Thus, we write the expression as −(1/4)⁴. The negative sign just indicates that the result should be taken as the opposite (negative) value of (1/4)⁴.
which expression is a factor x^2-5x-6
Answer:
x^2 - 5x - 6 = (x - 2)(x - 3).
Step-by-step explanation:
f(x) = x^2 - 5x - 6
We need 2 numbers whose product is - 6 and whose sum is -5. They are -3 and -2:
The factors are x- 2 and x - 3.
Final answer:
The factors of the expression x²-5x-6 are (x-6)(x+1).
Explanation:
This question demands basic understanding of methods of factorization and finding solutions of an equation.
The method to find factors of an equation, ax² + bx + c = 0, find two numbers that multiply to get c and add to give b.
To find the factors of the expression x²-5x-6, we need to factorize it. We look for two numbers that multiply to give -6 and add to give -5. The numbers -6 and 1 fit these conditions.
So, x²-5x-6
=> x² - 6x + x- 6
=> x(x - 6) +1(x - 6)
=> (x - 6)(x + 1)
Therefore, the factors of the expression are (x-6)(x+1).
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The correct answer is 104 fl oz = 13 c
if u convert grams to kilograms what operation would you use
Answer:
You have to divided by 1000
Best regards
sam completed 12 math questions in 24 minutes what are the unit rates in math questions per minute and minutes per math question
Final answer:
Sam completed math questions at a rate of 0.5 questions per minute and took 2 minutes per question.
Explanation:
To find the unit rates of math questions per minute and minutes per math question, we use the information given: Sam completed 12 math questions in 24 minutes.
To find math questions per minute, divide the number of questions by the number of minutes: 12 questions ÷ 24 minutes = 0.5 questions per minute.To find minutes per math question, divide the number of minutes by the number of questions: 24 minutes ÷ 12 questions = 2 minutes per question.These unit rates provide us with an understanding of Sam's pace when completing the questions.
According to this diagram, what is cos 28?
ASAP PLEASE !!
Answer: Option A; cos(28°) = 15/17
Step-by-step explanation:
You must remember that for a triangle rectangle we have that:
Sin( angle) = (opposite cathetus)/hypotenuse
cos(angle) = (adjacent cathetus)/hypotenuse
tan(angle) = (opposite cathetus)/(adjacent cathetus)
We want to find the cos(28°), then we can use the second relation, where the adjacent cathetus is 15 units long, and the hypotenuse is 17 units.
cos(28°) = 15/17
Then the correct option is A.
The value of cos(28) = 15/17.
Based on the diagram, the cosine of angle 28 degrees can be determined using the given information. In a right triangle, cosine is defined as the ratio of the length of the adjacent side to the hypotenuse.
Given that the base of the triangle is 15 units and the hypotenuse is 17 units, we can conclude that the adjacent side is the base. Therefore, the adjacent side has a length of 15 units.
Now, we can apply the cosine formula: cos(angle) = adjacent/hypotenuse. Plugging in the values, we have cos(28) = 15/17.
Hence, the cosine of angle 28 degrees, with a base of 15 units and a hypotenuse of 17 units, is approximately 0.882.
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I require assistance, please
When x = -1, f(x) = 0 because
(-1)^4 - 2(-1)^2 + 1 = 1 - 2 + 1 = 0.
Answer:
see explanation
Step-by-step explanation:
In order to determine the end behaviour, we only need to look at the term of highest degree, that is the leading term in standard form.
Given
f(x) = [tex]x^{4}[/tex] - 2x² + 1
So the term of highest degree is [tex]x^{4}[/tex]
Which is of even degree with positive coefficient
As a result the end behaviour is
As x approaches positive infinity, f(x) approaches positive infinity
As x approaches negative infinity, f(x) approaches positive infinity
----------------------------------------------------------------------------------------------
Substitute x = - 2 into f(x)
f(- 2) = [tex](-2)^{4}[/tex] - 2(- 2)² + 1 = 16 - 8 + 1 = 9 ≠ 0
Substitute x = - 1 into f(x)
f(- 1) = [tex](-1)^{4}[/tex] - 2(- 1)² + 1 = 1 - 2 + 1 = 0
Thus x = - 1 is a root of f(x) and (x + 1) is a factor of f(x)
Joanna receives 8$ an hour when she works at the coffee shop plus she earns tips as well. Last week she made 40$ in tips and earned a total of $256. Write an equation and use to find the number of hours Joanna worked last week.
Answer:
she worked 17 hours
Step-by-step explanation:
first you subtract 256-40
then you get 216 and divide by 8
then you get 27 as an answer
7x2 - 9x - 10 factor completely
( x - 2) ( x + 5/7 )
Answer:
Since I did this on Odyssey, the answer is (7x+5)(x-2)
What is the equation of the line parallel to the given line with an x-intercept of 4? y = x +
Answer:
What is the equation of the line parallel to the given line with an x-intercept of 4?
y = 4 x + -16
Step-by-step explanation:
The resulting equation is y = x - 4.
Firstly, a line that is parallel to another line has the same slope. Since the given line is in the form y = mx + b, we need the slope (m) from this equation. Let's assume it is y = x + c, then the slope (m) is 1 since no explicit value is provided for c.
Next, we need the equation of a new line that has the same slope (which is 1) and an x-intercept of 4. An x-intercept of 4 means the line passes through the point (4, 0).
Start with the general form of the line's equation: y = mx + b.Substitute the slope (m = 1): y = 1x + b or y = x + b.Use the point (4, 0) to find b: 0 = 4 + b. Solving for b, we get b = -4.Therefore, the equation of the line parallel to the given one with an x-intercept of 4 is y = x - 4.
On January 22nd , 2006, Kobe Bryant scored 81 points against the Toronto Raptors. Including three‐pointers, two‐pointers, and free‐throws he made 46 shots. He made three times as many two‐point shots as three‐point shots. How many free-throws did Kobe Bryant make?
Answer:
18
Step-by-step explanation:
x = the number of free throws
y = the number of 2 pointers
z = the number of 3 pointers
x + 2y + 3z = 81
x + y + z = 46
y = 3z
x = 18 free throws
y = 21 two pointers
z = 7 three pointers
Kobe Bryant made 18 free throws.
Answer:
Step-by-step explanation:
good question
Triangle abc is reflected over x axis triangle abc has points a (-6,-1) b (-2,-1) and c (-5,-6) what is b coordinate
You switch the sign of the y coordinate for point b, so the new b coordinate is (-2,1)
Answer:
(-2,1)
Step-by-step explanation:
The point b (-2,-1) lies in the third quadrant. A reflection over the x-axis will map the point in the second quadrant. In this quadrant, y is positive while x will still be negative. so we end up with;
(-2,1)
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Let f (×)=2/5x^2-2. The function g (x) is a vertical stretch of f (x) by a factor of 2. What is the equation of g (x)?
g(x)=________
Answer:
g(x) = (4/5)x^2 - 2
Step-by-step explanation:
f(x) = (2/5)x^2 - 2 is the equation of a parabola with vertex at (0, -2).
Applying a vertical stretch of factor 2 to f(x) requires multiplying both the slope (2/5) and the y-intercept (-2) by 2:
g(x) = (2)(2/5)x^2 - 4, or
g(x) = (4/5)x^2 - 4.
Find the amount of sap the maple syrup producer would have collected from each tree if the total amount if the total amount is (5gallons) was redistributed equally among trees
There are 10 crosses, which means that there are 10 trees in total. If we distribute 5 gallons among 10 trees, we give each tree
5/10=1/2=0.5 gallons
Answer:
Each tree will get 0.5 gallons of Syrup redistributed to it.
Step-by-step explanation:
According to the line graph shown in the picture there are 10 trees in total. We have 5 gallons of syrup that needs to be distributed equally among all ten trees. We can solve this by simply dividing the amount of syrup by the amount of trees that will be sharing the syrup.
5/10 = 0.5 gallons each
So each tree will get 0.5 gallons of Syrup redistributed to it.
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For which values of x is the inequality 2(1 + x) > x + 8 true?
Answer:
[tex]\large\boxed{\text{For}\ x>6\to x\in(6,\ \infty)}[/tex]
Step-by-step explanation:
[tex]2(1+x)>x+8[/tex] use distributive property
[tex]2+2x>x+8[/tex] subtract 2 from both sides
[tex]2x>x+6[/tex] subtract x from both sides
[tex]x>6[/tex]
Which expression is equivalent to.
Answer:
(6*6*6*6)*(6*6*6)
Step-by-step explanation:
6^4 = 6.6.6.6.
6^3= 6.6.6
Then
(6^4)(6^3) =(6*6*6*6)*(6*6*6)
Best regards
Answer:
6*6*6*6*6*6*6 = 6^7
Step-by-step explanation:
The third expression is equivalent to 6^4*6^3, or 6^7.
6 is used as a factor 4 + 3, or 7, times.
What is the nearest integer to90
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ 90 is an integer, and the closest others are 89 and 91
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
Hence, the nearest integer to [tex]90[/tex] is the closest others are [tex]89[/tex] and [tex]91[/tex].
What are the integers?
Integers are the collection of whole numbers and negative numbers. Similar to whole numbers, integers also does not include the fractional part.
Here given that,
The nearest integer to [tex]90[/tex] is the closest others are [tex]89[/tex] and [tex]91[/tex].
Hence, the nearest integer to [tex]90[/tex] is the closest others are [tex]89[/tex] and [tex]91[/tex].
To know more about the integer
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What is the value of a?
Answer:
Step-by-step explanation:
7
what is the part of a line that contains two points and all other points between them ?
Answer:
A segment
Step-by-step explanation:
A line is a straight path that is infinitely long.
A line segment is a section of a line. It consists of two points, which mark the beginning and the end of the segment, and all points in between.
In the diagram, the segment consists of the points A and B and all the points between them.
The line itself extends infinitely both left and right.
A line segment is the part of a line that encompasses two points and every point between them. It is defined by its extremities, and its characteristic property is that for any three distinct points on it, one must lie between the other two.
The part of a line that contains two points and all other points between them is known as a line segment. Essentially, if you have two points, A and B, the line segment AB includes every point that lies between point A and point B on the straight line that passes through them both. This is captured in geometry by saying that A and B are the extremities of the segment AB and any point C that lies between A and B is part of that segment.
Important properties of a line segment:
If A and C are points on a straight line, there will always be at least one point B such that B lies between A and C.
For any three points situated on a straight line, one of them will always be between the other two.
If four points are considered, they can be arranged in such a way that one of them invariably lies between any two others.
what does a proportion look like?
A proportion looks like this:
[tex]a\div b = c\div d[/tex]
It means that the quantity a,b,c and d are in the same proportion: the ratio between a and b is the same ratio between c and d.
They are particularly useful in situation when you have an example given, and you want to extrapolate the relationship for another couple.
For example, you can think of the following problem: "Five apples cost 2 dollars. How much will 8 apples cost?"
You can build the proportion
[tex]5\div 2 = 8\div x[/tex]
And then solve it for x:
[tex]\dfrac{5}{2}=\dfrac{8}{x} \iff 5x=16 \iff x = \dfrac{16}{5} = 3.2[/tex]