The inequality is:
[tex]70+6x\geq 150[/tex]
You must do more than 14 sales to get at least $ 150
Solution:
Given that,
As a salesperson you are paid $70 per week plus $6 per sale
Let "x" be the number of sales
This week you want your pay to be at least $150
We have to frame a inequality to represent the number of sales you need to make to achieve your goal
This week he must earn at least $ 150
Thus, he can spend $ 150 or more then 150 also
So we have to use "greater than or equal to" symbol
From given,
[tex]70 + 6(\text{number of sales})\geq 150[/tex]
[tex]70+6x\geq 150[/tex]
Thus the inequality is found
Solve the inequality
[tex]70+6x\geq 150\\\\Subtract\ 70\ from\ both\ sides\\\\6x\geq 150-70\\\\6x\geq 80\\\\Divide\ both\ sides\ by\ 6\\\\x\geq 13.3\\\\Thus\ approximately\ we\ get\\\\x\geq 14[/tex]
So he must do more than 14 sales to get at least $ 150
Find the slope of the following and then write the equation
Answer:
See explanation
Step-by-step explanation:
Assuming we want to find the slope and equation of the line going through:
(0,1) and (1,2).
Then the slope is given by:
[tex]m = \frac{2 - 1}{1 - 0} [/tex]
This implies that:
[tex]m = 1[/tex]
The equation is given by:
[tex]y = mx + b[/tex]
Where b=1 is the y-intercept since the line passes through (0,1).
Hence the equation is:
[tex]y = x + 1[/tex]
solve 4√2 as the square root of a single number
Step-by-step explanation:
[tex]4 \sqrt{2} = \sqrt{ {4}^{2} \times 2} = \sqrt{16 \times 2} = \sqrt{32} [/tex]
The drink dispenser in a fast food restaurant holds 250 liters
Question:
A drink dispenser in a fast-food restaurant holds 250 litres of lemonade. How many 0.6-litre drinks can be dispensed before a refill is needed?
Answer:
The number 0.6-litre drinks can be dispensed before a refill is needed is 416
Step-by-step explanation:
Given:
The capacity of the drink dispenser = 250 litres
To Find:
Number of 0.6-litre drinks can be dispensed before a refill is needed = ?
Solution
Let the number of 0.6-litre drinks can be dispensed before a refill is needed be x
Then
[tex]x = \frac{ \text{total capacity of the dispenser}}{\text{0.6-litre drinks}}[/tex]
On substituting the values we get
[tex]x = \frac{250}{0.6}[/tex]
x = 416. 667
Thus only 416 can be filled
Solve the system of linear equations below.
2х + Зу = 2
х+ 6у = 4
А. x = 0, y=2/3
Bх = 2, y = -2/3
C. х = 4/3, у=2/9
D. x = 4, y = -2
Find the sum of 8 + 11 + 14 + ... + 602 + 605.
Answer:
61300
Step-by-step explanation:
A function is given:
f(x) = 3x + 12
a. Determine the inverse of this function and name it g(x).
b. Use composite functions to show that these functions are inverses.
c. Evaluate f(g(–2)). Explain: What is the domain?
WILL GIVE BRAINLIEST PLEASE EXPLAIN WELL
100 POINTS
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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a line with a slope of -3 and an x-intercept of 15 passes through wich of the following points
A. (0,30)
B. (5,15)
C. (10,10)
D. (−5,60)
The Answer is D) because it is
Let f(x) = (x^2+3x-5)/(x^2-8x+15) What is the domain of f(x) ?
Answer:
So, Domain = {set of all the real numbers except 3, 5}
Interval notation = {x ∈ set of all real numbers/ x ≠3 and x ≠ 5}
Step-by-step explanation:
The given function is f(x) = [tex]\frac{x^2 + 3x - 5}{x^2 - 8x + 15}[/tex]
Here we need to find the domain.
To find the domain, let's find the restricted domain.
If we set the denominator equal to zero and solve for x, we can find the restricted domain.
Here the denominator is [tex]x^2 -8x + 15 = 0[/tex]
Now we can factorize and solve for x.
(x - 3)(x - 5) = 0
(x - 3) or (x - 5) = 0
x -3 = 0 and x - 5 = 0
Solving the above equations, we get
x = 3 and x = 5
The restricted domains are x = 3 and x = 5.
Now we can find the domain.
Except 3 and 5, all the real numbers can be domain of this function.
So, Domain = {set of all the real numbers except 3, 5}
= {x ∈ set of all real numbers/ x ≠3 and x ≠ 5}.
Answer: all real numbers except 3, 5
Step-by-step explanation:
When is a zero not significant?
O
A. When it comes after the decimal point, as in 4.000
O
B. When it is included in scientific notation, as in 3.04 x 10-2
O
C. When it precedes a non-zero digit but falls after a decimal point,
as in 0.0004
O
D. When it falls between two non-zero digits, as in 4.09
Answer: A. When it comes after the decimal point, as in 4.000
Step-by-step explanation: If there are no other numbers after the zeros, there is no reason for them to be place holders. Zeros in decimals act as place holders such as in 4.09 or 4.0009. This actually does change the value of the decimal but 4.000 is just the same as a regular old 4. Hope this helps!
Given the point (-5,6), what is the value of the y-coordinate?
The y-coordinate of the point is
(Type an integer or a decimal.)
Answer:
6
Step-by-step explanation:
The numbers in an ordered pair are usually (x, y). That is, the y-value comes second in the pair.
The second number in your ordered pair is 6. The y-coordinate is 6.
A segment is dilated, and the resulting segment is shorter than the original.
Which of the following options could be the scale factor of the dilation?
Select all that apply.
3/8
1
5
1/5
Answer:
3/8 and 1/5
Step-by-step explanation:
If the scale factor is 1 then it stays the same. If it's larger than 1 then is gets larger, so the fractions, which are smaller than 1, would make it shorter.
hope this helped :)
Answer:1/5 and 3/8
Step-by-step explanation:
A jar contains 12 caramels, 7 mints and 16
dark chocolates. What is the probability of
selecting a mint expressed as a fraction?
Answer:
Step-by-step explanation:
Add the three digits together:
12+7+16=35
7/35, or 1/5.
Kevin and Marcus were comparing their ages. The same of their ages was at least 9 years but was at most 24 years. If Kevin is 6 years old, which of the following inequalities represents all possible values for Marcus age, m?
The inequality that represent age of marcus is:
[tex]24\geq 6+m\geq 9[/tex]
The possible values for age of Marcus is:
m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Solution:
Given that,
The sum of ages of Kevin and Marcus was at least 9 years but was at most 24 years
Kevin is 6 years old
Let "m" be the age of Marcus
Thus we frame a inequality as:
[tex]24\geq \text{ sum of ages } \geq 9[/tex]
at least 9 years means that "greater than or equal to 9"
at most 24 years means "less than or equal to" 24
From given,
Sum of ages = kevin age + marcus age
Sum of ages = 6 + m
Thus the inequality is:
[tex]24\geq 6+m\geq 9[/tex]
Solve the inequality
[tex]\mathrm{If}\:a\ge \:u\ge \:b\:\mathrm{then}\:a\ge \:u\quad \mathrm{and}\quad \:u\ge \:b\\\\24\ge \:6+m\quad \mathrm{and}\quad \:6+m\ge \:9\\\\Solve\ them\ separately[/tex]
[tex]24\ge \:6+m\\\\\mathrm{Switch\:sides}\\\\6+m\le \:24\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\le \:24-6\\\\\mathrm{Simplify}\\\\m\le \:18[/tex]
Now solve another inequality
[tex]6+m\ge \:9\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\ge \:9-6\\\\\mathrm{Simplify}\\\\m\ge \:3\\\\\mathrm{Combine\:the\:intervals}\\\\m\le \:18\quad \mathrm{and}\quad \:m\ge \:3\\\\\mathrm{Merge\:Overlapping\:Intervals}\\\\3\le \:m\le \:18[/tex]
[tex]24\ge \:6+m\ge \:9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:3\le \:m\le \:18\:\\ \:\mathrm{Interval\:Notation:}&\:\left[3,\:18\right]\end{bmatrix}[/tex]
Thus possible values for age of Marcus is:
m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
Will give Brainliest if answer is correct!
Answer:
a|| b then
<6=<4=<2=146
How do you write 40.545 in word form
The requried word form of the given number is forty and five hundred forty-five thousandth.
What is a number system?A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
Since the given number is of decimal form.
A word form of the given number 40.545 is given as,
40.545 = forty and five hundred forty-five thousandth.
Thus, the requried word form of the given number is forty and five hundred forty-five thousandth.
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Kelsey solved the following equation:
7x − one over two (8x + 2) = 6
Step Work Justification
1 7x − 4x − 1 = 6
2 3x − 1 = 6
3 3x = 7
4 x = 7 over 3
Which of the following has all of the correct justifications Kelsey used to solve this equation?
1. distributive property
2. combine like terms
3. addition property of equality
4. division property of equality
Solution:Given that,
Kelsey solved the following equation:
[tex]7x - \frac{1}{2}(8x+2) = 6[/tex]
Step 1:By distributive property,
a(b + c) = ab + bc
Therefore,
[tex]7x - (\frac{1}{2} \times 8x)+( \frac{-1}{2} \times 2)= 6\\\\7x - 4x - 1 = 6[/tex]
Step 2:Combine the like terms
7x - 4x - 1 = 6
3x - 1 = 6
Step 3:Addition property of equality
The property means that when we add the same number to both sides of an equation, the sides remain equal
3x - 1 = 6
Add 1 on both sides
3x - 1 + 1 = 6 + 1
3x = 7
Step 4:Division property of equality
The Division Property of Equality means that when we divide both sides of an equation by the same non zero number, the sides remain equal
3x = 7
Divide both sides by 3
[tex]\frac{3x}{3} = \frac{7}{3}\\\\x = \frac{7}{3}[/tex]
Thus the correct justifications Kelsey used to solve this equation is:
1. distributive property. 2. combine like terms. 3. addition property of equality. 4. division property of equality
Answer:
I took the test it is 1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
A landscaping company is putting small stones around a circular fish pond with a diameter of 5.5 yards. If each bag of stones fills a distance of 4 yards, how many bags do they need
Answer:
2
Step-by-step explanation:
If one bag of stones is sufficient to fill the distance of 4 yards , then to complete 5.5 yards of pond boundary, 2 bags are enough.
What is distance?Distance is a physical quantity measuring the length over an area covered by an object or place. The change in distance is called displacement. For a moving object the distance is the product of its speed and time take to cover the distance.
Distance can be measured in meter, kilometer, feet, yard etc. These units can be interchanged in between based on the relationship between them.
It is given that the diameter of the circular fish pond is 5.5 yards. One bag of stones can fills a distance of 4 yards. of the pond. Then two bag of stones is enough to fill up the total distance of 5.5 yards.
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It’s a statistics mathematical question
Answer: About 0.8034 of the items will be classified as good.
Step-by-step explanation:
Let's first understand that because 13% of the items are defective, that means 87% of the items are not defective. And because the inspector incorrectly classifies the items 9% of the time, it's important to understand that that means both the defective and the not defective items may be incorrectly classified. In order to figure out what proportion will be classified as 'good,' let's set up a tree diagram:
--0.13--defective
|__0.09__ classified as 'good'
|__0.91__ classified as 'defective'
--0.87--not defective
|__0.09__ classified as 'defective'
|__0.91__classified as 'good'
This chart essentially reiterates the information in the prompt, showing that 9% of each type of item will be incorrectly classified. Now we need to find the proportion of items that will be classified as 'good.' To do this, we must multiply the proportion of items classified as 'good' by the proportion of items that are either defective or not defective for both types, like this:
(0.13 * 0.09) + (0.87 * 0.91)
this expression in words means: "13% of the items will be classified as good 9% of the time, and the other 87% of the items will be classified as good 91% of the time"
When we multiply and add these numbers together, we get 0.8034, but you should round to 2 or 3 decimal places like the prompt instructs. Hope this helped! :)
How do you write nine and two hundred thirty five thousandths?
Answer:
9.235
Step-by-step explanation: There you g. Hope it helps!
Check your answer for 3(p+2)=18
3(p + 2) = 18
3p + 6 = 18
3p = 12
p = 4
Check:
3(p + 2) = 18
3(4 + 2) = 18
3(6) = 18
18 = 18
This proves that p = 4.
⭐ Answered by Hyperrspace (Ace) ⭐
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⭐ If you have questions, leave a comment, I'm happy to help! ⭐
Answer: p = +4
Step-by-step explanation: To solve this equation for p, our first step is to distribute the 3 through the parentheses on the left side.
3 times p is 3p and 3 times 2 is 6.
So we have 3p + 6 = 18.
Next, we need to isolate the p term by subtracting 6 from both sides of the equation to get 3p = 12.
Finally, we divide both sides of the equation by 3 to get p = +4.
this is how dora subtracts 73-26. 73-3=70. 70-?=50. ?-?=? fill in the blanks to solve
Answer:
73-3=70
70-20=50
50-24=26
To solve 73-26, subtract 3 from 73 to get 70. Then, subtract a number from 70 to get 50. The missing number is 20.
Explanation:To solve the equation 73-26, we can subtract it step by step. The first step is to subtract 3 from 73, which equals 70. The next step is to subtract a number from 70 to get 50. To find that number, we subtract 50 from 70, which is 20. So, the missing number is 20.
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What is x equal to in this equation: 6(x - 2) = -18
PLEASE HELP I NEED TO PASS THIS TEST!!! (first actual answer gets brainliest)
Iliana rotated trapezoid WXYZ 180° about the origin.
*graph below*
What is the correct set of image points for trapezoid W’X’Y’Z’?
Answer:
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)
I hope this helps you. If you can give brainliest that would be greatly appreciated.
Answer:
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
Step-by-step explanation:
look at picture
I am a fraction that is greater than 1 but less than 2 the sum of my numerator and denominator is 11 my denominator subtracted from my numerator is 1 what fraction am I
Answer:
that fraction is an improper fraction I think.
What situation can be represented by the expression-3 + 3?
A. Nancy owes $3 on an account and then withdraws another $3.
B. Jason pays $3 on the $3 he owes in fines.
C. There is a change in temperature from -3 degrees F to 0 degrees F.
D. A toy car travels at a rate of 3 meters per minute for 3 minutes.
E. Teri’s score in a word game is 0 after scoring 3 points.
My son has chosen C and E as the answers. Correct?
Answer:
Step-by-step explanation: It B
-3 + 3 = 0
WILL GIVE BRAINLIEST You can draw a quadrilateral with no parallel lines and at least one right angle. True/ False
Answer:
True because a right angle can't exist with any parallel lines.
Answer:
true hope this helped.
Step-by-step explanation:
Evaluate the expression 1/3(4+18) -2 squared
Answer:
Evaluate the expression 1/3(4+18) -2 squared
Step-by-step explanation:
First of all we will add brackets to understand the question as:
= ((1/3) * (4+18) - (2 squared))
= ((1/3) * ( 22) - 2² )
According to Math's rule that Multiplication and division must be completed before addition and subtraction.
= (( 1/3 * 22) - 4 )
= (( 7.33) - 4 )
= ( 7.33 - 4 )
= 3.33
3.33 is the correct answer.
Find the equation of the line with slope m = 3/2 that contains the points (2,1).
Answer:
y=3/2x-2
Step-by-step explanation:
m=3/2 A(2,1)=A(x1, y1) ... x1=2,y1 =1
y-y1=m(x-x1)
y-1=3/2(x-2)
y-1=3/2x-3/2*2
y-1=3/2x-3
y=3/2x-3+1
y=3/2x-2
PLEASE HELP ME FAST. WILL MARK AS BRAINLIEST IF GIVEN GOOD ANSWER
The following data set is graphed on a coordinate plane: (10,45), (25,70), (46,105). If the y-intecept of the line of best fit is at 28.5 ,what would be the most reasonable slope of line: 1/3, 5/3, or -4/3? Show/explain how you know.
Slope is the change in Y over the change in. X
Using two of the given points:
Slope = 70-45 / 25-10
Slope= 25/ 15
Slope = 5/3
Ashley is deciding between two jobs. Job A pays $2000 per month with a monthly raise of $85. Job B pays $2000 per month with a monthly raise of 4%. Write a function to represent the monthly salary for Job B after x months.
The monthly salary for Job B after x months, which includes a 4% monthly raise, can be represented by the exponential function S(x) = 2000 * (1 + 0.04)^x, where S(x) is the salary and x is the number of months.
Explanation:To represent the monthly salary for Job B after x months, we need to account for the 4% raise each month. Since the starting salary is $2000, and the raise is 4% (or 0.04 in decimal form) of the previous month's salary, the function to represent the monthly salary can be written using a geometric sequence formula.
Let S(x) be the salary at month x. The function will be an exponential function in the form:
S(x) = 2000 * (1 + 0.04)^x
Here, 2000 is the initial salary, 0.04 represents the 4% raise, and x is the number of months that have passed.