Answer:
6x²+11x
Step-by-step explanation:
1. Group like terms
[tex]8x^2-2x^2+3x+8x-10+10[/tex]
2. Add like terms
[tex]6x^2+3x+8x-10+10[/tex]
3. Add the numbers
[tex]6x^2+11x[/tex]
Find the inverse of each function.
y=log 10 x
The inverse of the function is f ⁻¹(x) = 10ˣ
Given the function is y = log₁₀ x
In relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain. By replacing (x, y) with (y, x) with reference to the line y = x, one can obtain the graph of the inverse function.
steps to find the inverse of the function:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.Here, find y and solve for x = ay + b. Then we get y = (x - b/a).Finally, we can substitute y = f-1(x) with f-1(x) = (x - b)/a.now replace y with x.
x = log₁₀ y
change the dependent variables.
f ⁻¹(x) = 10ˣ
Learn more about Inverse functions here:
brainly.com/question/14391067
#SPJ4
i will give yall 100 points if this get answered fast:
HELP ME PLEASE FAST
write a linear function to model the following situation:
An airplane is 30,000 ft. in the air and descending 1,000 ft. for each mile it travels.
descending means its going ____.
write the equation.
Y= _____________
or as a function
f(x) = 30,000 - 1,000x
the question is: How far away from the airport does the airplane have to start to descend to land safely? To answer that, we need to find the x- intercept
Answer:
x = 30
Step-by-step explanation:
To find the x intercept, you need to substitute [tex]y = 0[/tex], as all points on the x axis's y-coordinate is 0.
[tex]0 = 30000 - 1000x\\ \\ \to 0 + 1000x = 30000 \cancel{- 1000x + 1000x} \\\\ \to 1000x = 30000 \\ \\\to \frac{1000x}{1000} = \frac{30000}{1000} \\ \\\to x = 30[/tex]
Answer: Its x= 30
Step-by-step explanation:
Find the product of (134−2.4)⋅[0.5⋅(25+2.6)]
Answer: the product is 1816.08
Step-by-step explanation:
The required product of the expression is 1816.08.
Given that,
To determine the product and simplified value of the expression (134−2.4)⋅[0.5⋅(25+2.6)]
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= (134−2.4)⋅[0.5⋅(25+2.6)]
= (131.6) * [0.5 * 27.6]
= 131.6 * 13.8
= 1816.08
Thus, the required product of the expression is 1816.08.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
1. f(x)= (x+4)(x-6) 2. f(x)= (2x-4)(x-3)
Find the x-intercept
FOIL to convert functions to standard
Find the y-intercept
Answer both.
The intercepts and the standard form of each polynomial are listed below:
x-Intercept: x = - 4 or x = 6, Standard form: f(x) = x² - 2 · x - 24, y-Intercept: f(0) = - 24x-Intercept: x = 1 / 4 or x = 3, Standard form: f(x) = 2 · x² - 10 · x + 12, y-Intercept: f(0) = 12How to find the intercepts and the standard form of quadratic equationsIn this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.
Now we proceed to find each element:
Case 1
x-Intercept
x = - 4 or x = 6
Standard form
f(x) = (x + 4) · (x - 6)
f(x) = x² - 2 · x - 24
y-Intercept
f(0) = - 24
Case 2
x-Intercept
x = 1 / 4 or x = 3
Standard form
f(x) = (2 · x - 4) · (x - 3)
f(x) = 2 · (x - 2) · (x - 3)
f(x) = 2 · (x² - 5 · x + 6)
f(x) = 2 · x² - 10 · x + 12
y-Intercept
f(0) = 12
To learn more on quadratic equations: https://brainly.com/question/1863222
#SPJ1
Stock Market At the beginning of the day the stock market goes down 70 1/4
points and stays at this level for most of the day. At the end of the day the stock market goes up 110 1/2
points from the low at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
Question content area bottom
Part 1
The total change in the stock market is
enter your response here points.
The total change in the stock market from the beginning of the day to the end of the day is [tex]40\frac{1}{4}[/tex]
What is the total change?When the value of the stock market goes down, its value has decreased. The decrease in the value of the stock market would be represented with a negative number. A negative number is a number that is less than 0. The sign that is used to represent a negative number is -.
When the value of the stock market goes up, its value has increased. The increase in the value of the stock market would be represented with a positive number. A positive number is number that is greater than 0.
The total change in the stock market is the sum of the decrease and the increase in the stock market.
Total change = increase in the stock market - decrease in the stock market
[tex]110\frac{1}{2} - 70\frac{1}{4}[/tex]
[tex]40\frac{2-1}{4}[/tex] = [tex]40\frac{1}{4}[/tex]
To learn more about fractions, please check: https://brainly.com/question/915789
#SPJ1
How do the domains and ranges of the functions f(x)=√x-1 and g(x)=√x-1 compare?
The domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).
Domain of function f(x) :
√ (x - 1) ≥ 0
So, we get that:
x ≥ 1
= [1, ∞)
Range = (0, ∞) as square of a number is always positive.
Domain of function g(x):
√ x ≥ 0
on adding 1 both sides we get
x ≥ 0
= (0,∞)
Range = [-1, ∞).
Therefore, the domain and range of the function f(x) is [1, ∞) and (0, ∞) and g(x) is (0,∞) and [-1, ∞).
Learn more about domain and range here:
https://brainly.com/question/2264373
#SPJ4
The grid above shows the graph of the parent function f(x)= |x| and a translated functions graph.
Use f(x)=|x| f(x) is shifted left 5 and shifted up 2 to create g (x). write the equation g(x).
The equation of the translated graph from the parent function is g(x) = |x + 2| + 1
How to write the equation of the translated graph?The parent function is given as
f(x)= |x|
From the graph, we can see that the parent function f(x) is translated as follows:
2 units left translation1 unit up translationThe above sequence of translation is represented as
(x, y) = (x + 2, y + 1)
So, we have
g(x) = |x + 2| + 1
Hence, the equation of the translated graph is g(x) = |x + 2| + 1
Read more about transformation at
brainly.com/question/4289712
#SPJ1
work out what the values of three consecutive even
integers must be if their sum is 6000.
The values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.
What is an integer?it is defined as a whole number it can be a negative whole number or a positive whole number for example 2, 4, 1, -8, 0, etc. When it comes to integers, even numbers can be divided by two exactly while odd numbers cannot. 2, 6, 10, 20, 50, and other even numbers serve as examples.
Suppose the value of the three consecutive even integers is n, n + 2, and n + 4
The sum of the integers is 6000.
Sum = n + n + 2 + n + 4
Sum = 3n + 6
Sum=6000
3n + 6 = 6000
3n = 5994
n = 5994/3
n = 1998
The three consecutive even integers are,
n=1998
n+2=1998+2=2000
n+4=1998+4=2002
Thus, the values of three consecutive even integers must be if their sum is 6000 will be 1998, 2000, and 2002.
Learn more about the integer here:
https://brainly.com/question/15276410
#SPJ2
The perimeter of a rectangular pool is 160 meters. The length of the pool is 20 meters more than its width. What is the length?
Answer:
50 meters
Step-by-step explanation:
Width is x
So length will be x + 20
Perimeter = 2 (W + L) = 2 (x + x + 20) = 2 (2x + 20) = 4x + 40
so 4x + 40 = 160
4x = 120
x = 30
so length = x + 20 = 30 + 20 = 50
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator 45 to 9
Answer:
[tex]\frac{5}{1}[/tex]
Step-by-step explanation:
45 : 9
= [tex]\frac{45}{9}[/tex] ← divide numerator and denominator by 9 )
= [tex]\frac{5}{1}[/tex] ← in simplest form
Which expression is equivalent to -1/2 ( 1/4x - 3/8)?
The expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.
Which expression is equivalent to the expression given as in the task content?It follows from the task content that the expression which is equivalent to that given in the task content be determined.
On this note, by distributing the coefficient of.tne parents; we have;
-1/2 ( 1/4x - 3/8)
= {(-1/2) × (1/4)x} + {-1/2 × -3/8}
= (-1/8)x + 3/16
Ultimately, the expression which is equivalent to the expression given; -1/2 ( 1/4x - 3/8) according to the task content is; (-1/8)x + 3/16.
Read more on equivalent expressions;
https://brainly.com/question/22365614
#SPJ1
An activity director in a long-term care facility is purchasing recreational supplies. Find the sum of the purchases: 3 bingo games at $13 each, 10 puzzles at $9.00 each, 24 jars of paint at $3.00 each and 2 rolls of paper for $31.00 each.
Samantha claims that 4x + 2 is equivalent to the expression x + 17 + 3x - 15.
Check whether Samantha's equivalent expression is correct using x = 2.
A.)Samantha S incorrect because when
using x = 2, the resulting values in
both expressions are different
B.)Samantha is
incorrect because the expressions cannot be checked using x = 2.
C.)Samantha is correct
because when using x 2, the resulting values in
both expressions are equal.
Option C: Samantha is correct because when using x=2, the resulting values in both expressions are equal.
Consider, 4x + 2
When x = 2,
=> 4x + 2 = 4*2 + 2
=> 10
Now consider, x + 17 + 3x - 15
When x = 2,
=> 2 + 17 + 3*2 - 15
=> 10
Therefore, Samantha is correct as both expressions equal 10 when x=2.
In other words, if we consider, x + 17 + 3x - 15
=> x + 17 + 3x - 15
=> x(1+3) + 17 - 15
=> 4x + 2
This shows that for any value of x, the expression x + 17 + 3x - 15, simplifies to 4x + 2.
Therefore, both the expressions, 4x + 2 and x + 17 + 3x - 15, are equal.
To learn more about simplifying algebraic expressions, check out,
https://brainly.com/question/8690932
#SPJ9
Solve each equation.
log x-log 3=8
log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
log (x) - log (3) = 8
=> log (x) = 8 + log (3) = 8 + 0.477
=> log (x) = 8.477
Since, generally the base of log is 10, raising them to 10.
=> [tex]10^{log_{10}x} = 10^{8.477}[/tex]
=> x = 299916251.899 (as [tex]a^{log_a(x)} = x[/tex])
Hence, log(x) - log (3) = 8 => x = 299916251.899, by properties of logarithm.
To learn more about logarithms, refer to the link: brainly.com/question/25710806
#SPJ4
-4x-1+x4/10-2x2 in standard form
The standard form will be
1/10 x⁴-2x²-4x-1
Polynomials in standard form can also be referred to as the standard form of a polynomial which means writing a polynomial in the descending order of the power of the variable. To write a polynomial in a standard form, the degree of the polynomial is important as in the standard form of a polynomial, the terms are written in decreasing order of the power of x. The standard form of polynomial is given by, f(x) = anxn + an-1xn-1 + an-2xn-2 + ... + a1x + a0, where x is the variable and ai are coefficients.
A mathematical expression of one or more algebraic terms in which the variables involved have only non-negative integer powers is called a polynomial. The terms have variables, constants, and exponents. The standard form polynomial of degree 'n' is
aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+.......
To write a polynomial in standard form ,simplyfy and then arrange the terms in descending order.
ax²+bx+c
move -1
-4x+x⁴/10-2x²-1
Reorder terms
1/10x⁴-2x²-4x-1
To know more about polynomials
visit-:https://brainly.com/question/11536910
SPJ9
What is the formula for the equation of a proportional line?
Answer: y=kx
Step-by-step explanation:
Which of the binomials below is a factor of this expression?
100A²-498²
OA. A+ 7B
OB. 10A+7B
OC. A + B
OD. 10A+B
Answer: B. 10A + 7B
Step-by-step explanation:
To find the correct binomial, we will factor the given expression. I assume that by "-498²" you mean "-49B²".
This is a difference of squares:
(10A + 7B)(10A - 7B)
The binomial 10A + 7B is an answer option, so our answer is:
B. 10A + 7B
If someone could help soon that would be great
Answer:
a,b,c and no d
Step-by-step explanation:
welcome
Answer:
a, b, and c.
Step-by-step explanation:
Use the line test. :)
Jonathan is buying string to make friendship bracelets. He buys 7 bundles of string in different colors. Each bundle costs $0.56. Tax for the 7 bundles is $0.35. How much money does Jonathan pay in all for the string?
Answer:
4.27
Step-by-step explanation:
1 bundle= $0.56
7bundles=o.56x7=$3.92
Tax=0.35
3.92+0.35=4.27
Henry is working two summer jobs, washing cars and walking dogs. He can work at most 15 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, ww, and the number of hours walking dogs, dd, that Henry can work in a given week.
y=5x 7.5w+7.5d Answer:
Step-by-step explanation:
The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week is , w + d ≤ 15 .
What is an inequality?The relationship between two expressions or values that are not equal to each other is called 'inequality.
here, we have,
Given that w is the number of hours for washing a car and d is the number of hours to walking dogs.
The work hours at most 15 hours altogether between both jobs in a given in a week.
Hence, w + d ≤ 15 is the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours walking dogs, d, that Morgan can work in a given week.
To learn more about inequality, use the link given below:
brainly.com/question/20383699
#SPJ2
I need help with this, can someone help me?
Answer: 5y^2
Step-by-step explanation: hope this helps
Answer: it is the third option
Explanation: as any number with a negative power will be the reciprocal
----> y^-2 = 1/y^2
----> 5 x 1/y^2
----> 5/y^2
i hope this helps
Solve the compound inequality
|x-3|<4 and |x+2|>8
The solution of the compound inequality are:
| x - 3 | < 4 -1 < x < 7
| x + 2 | > 8 -10 < x or x >6
How to solve the inequality
Given data
| x - 3 | < 4 and | x + 2 | > 8
Solution the first inequality | x - 3 | < 4
| x - 3 | < 4
x < 4 + 3 OR x > - 4 + 3
x < 7 OR x > - 1
-1 < x < 7
Solution for the second inequality | x + 2 | > 8
| x + 2 | > 8
x < -8 - 2 OR x > 8 - 2
x < - 10 OR x > 6
-10 < x or x >6
Read more on compound inequality here: https://brainly.com/question/1485879
#SPJ1
How many ounces of honey would you need to mix with 11 ounces of strawberries?
55 ounces of honey will need to mix with 11 ounces of strawberries.
Question is not complete so lets suppose that,
For each ounce of mix, we use honey five times of a ounces of strawberry.
And then we will find that how many ounces of honey we would to mix with 11 ounces of strawberries.
According to above statement
one ounce of strawberries = 5 ounce of honey
So, for the mix we will need to add honey which will we equal to five times of strawberries.
If we have 11 ounces of strawberries then,
the amount of honey will be = 5 × 11 = 55 ounces
To learn more about this Patterned Question visit :
https://brainly.com/question/23820061
#SPJ9
Find the sum or difference.
Answer:
The sum is the third answer
Step-by-step explanation:
you add together the numbers that are in the same spot in both matrixes.
-3 + -4 0 + 2
5 + -1 -7 + 8
That would give you
-7 2
4 1
Angles A and B are complementary to each other. If m∠A = 41° and m∠B = (2x + 19)°, find the value of x.
x = 15
x = 11
x = 58
x = 30
Given that Angles A and B are complementary to each other, the numerical value of x is 15.
What is the numerical value of x?Complementary angles are angles that sum up to 90 degrees.
Given the data in the question;
Angles A and B are complementary to each other.Measure of angle A = 41°Measure of angle B = (2x + 19)°Since Angles A and B are complementary to each other, the sum of angle A and B is 90 degrees.
Measure of angle A + Measure of angle B = 90°
Plug in the given values and solve for x.
41 + (2x + 19) = 90
41 + 2x + 19 = 90
2x + 60 = 90
2x = 90 - 60
2x = 30
x = 30/2
x = 15
Given that Angles A and B are complementary to each other, the numerical value of x is 15.
Learn more about complementary angles here: https://brainly.com/question/28584107
#SPJ1
Answer: A is the answer
Step-by-step explanation: i took the test and got it right
Eva went miniature golfing with Taylor. She shot
4 under par and Taylor shot 2 under par. By how
many strokes did Eva beat Taylor?
Question 1 (1 point)
Willorie Ford moves to Lake Havasu City Arizona to try out a food truck. She sets up shop
under London Bridge and notices that her business is "seasonal".
On December 1, she makes $450 per day.
On March 1, she makes $800 per day.
On June 1, she makes $450 per day.
On September 1, she makes $100 per day.
On December 1, she makes $450 per day.
Estimate how much she would make on certain days and draw a model.
By this model, she would make $
By this model, she would make $
By this model, she would make $
By this model, she would make $
on February 1. (Round to the nearest dollar)
on May 1. (Round to the nearest dollar)
on July 1. (Round to the nearest dollar)
on August 1. (Round to the nearest dollar)
Step-by-step explanation:
2,250 was made in a month
Oh no! Mike solved the equation below for y:
10x - 3y = 6
Let's help him fix it!
1. Circle the mistake within the problem (on the
whiteboard at the left).
2. Describe his mistake in the box below (be sure to
be specific).
The mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y
How to determine the mistake in the equation solution?The solution of the equation is given as
10x - 3y = 6
+3y +3y
----------------------------
10x = 3y + 6
-6 -6
----------------------------
(10x - 6)/3 = 3y/3
10x - 2 = y
In the above steps, we have the following equation
(10x - 6)/3 = 3y/3
When the above equation is expanded, we have
10x/3 - 6/3 = 3y/3
Evaluate the quotient in the above equation
So, we have
10x/3 - 2 = y
The abvoe equation is different from Mike's result
Hence, the mistake in Mike's steps is in step 3 and the correct solution is 10x/3 - 2 = y
Read more about equations at
https://brainly.com/question/2476251
#SPJ1
translation: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
Answer: 7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(5, -1)
Step-by-step explanation:
If you want to translate a point 7 units right, you'll need to add 7 to its x-coordinate. If you want to translate a point 1 unit down, you'll need to subtract 1 from its y-coordinate. Do both of these things to perform a translation 7 units right and 1 unit down.
So, we can write,
7 units right means add the +7
1 unit down means subtract the -1
Then,
J(-3, 1) = J'(-3 + 7, 1 - 1)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(-2 + 7, 3 - 1)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(-2 + 7, 0 - 1)
N(-2, 0) = N'(5, -1)
Therefore,
These points to make sure they have shifted 7 units right and 1 unit down.
7 units right and 1 unit down/ J(-3, 1), F(-2, 3), N(-2, 0)
J(-3, 1) = J'(4, 0)
F(-2, 3) = F'(5, 2)
N(-2, 0) = N'(5, -1)
Learn more about event correlation here: brainly.com/question/1869196
#SPJ9
If $15,000 is invested at 6. 5% annual interest compounded annually, how long would it take for the account balance to reach $50,000? Round your answer to the nearest tenth
The account balance invested at 6. 5% annual interest compounded annually will take 19.1 years to reach $50,000.
Compound interest refers to the amount of interest added on the principal amount plus interest. The formula for compound interest is:
B = P(1 + r/n)^t
where B is the ending balance, P is the principal amount or original balance, r is the interest rate in decimal form, n = number of times interest is compounded annually, and t is the time in number of year
Using this formula, find t, the time it will take the account to reach $50,000 when
B = $15,000
r = 6.5% = 0.065
n = 1
B = P(1 + r/n)^t
$50,000 = $15,000(1 + 0.065/1)^t
(1 + 0.065)^t = $50,000/$15,000
1.065^t = 10/3
t = 19.1 years
Learn more about compound interest here: brainly.com/question/24924853
#SPJ4