The domain of the given function f(x)= 1/2x-1 is ( -∞ , 1/2) ∪ (1 /2 , ∞) .
The set of all potential values that qualify as inputs to a operate is understood because the domain of the operate, or it also can be outlined because the entire set of values potential for freelance variables. The domain is found in – the divisor of the fraction isn't up to zero and also the digit underneath the root bracket is positiveWe have given an function f(x)= 1/2x-1 .
To find the domain, we'd like to appear at the values of the freelance variables that area unit allowed to use as explained on top of, i.e. no zero at all-time low of the fraction and no negative sign within the root.
2x - 1 ≠ 0
2x ≠ 1
x ≠ 1/2
Domain is given by ( -∞ , 1/2) ∪ (1 /2 , ∞) .
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The complete question is given below :
Find domain of the function f(x)= 1/2x-1
(69 1/3)-(45 14/15)=
Answer:
-19
Step-by-step explanation:
1/3 of 69=23
14/15 of 45=42
23-42=-19
Answer:
23 2/5
Step-by-step explanation:
69 1/3 - 45 14/15
= (69 - 45) + (1/3 - 14/15)
= 24 + 1 x 5/3 x 5 - 14/15
= 24 + 5/15 - 14/15
= 24 + 5 - 14/15
= 24 + -9/15
= 24 + -9 ÷ 3/15 ÷ 3
= 24 + -3/5
= 23 2/5
An auto company's sales volume can be modeled by 7.8x? + 3.2x + 3.5, and its cost
can be modeled by 3.4x2 - 0.8x + 3.5, where o represents the number of cars
produced, and y stands for money in thousand dollars. We can calculate the company's
net profit by subtracting cost from sales. Find the polynomial which models the
company's sales in thousands of dollars.
The polynomial which models the company's sales in thousands of dollars will be 4.4x² + 4x.
What is a profit?A monetary profit, particularly the distinction between the amount gained and the actual cost of purchasing, running, or creating anything.
The profit is given as,
Profit = Selling price - Cost price
Sales volume for an auto manufacturer may be calculated as 7.8x² + 3.2x + 3.5 and costs as 3.4x² - 0.8x + 3.5.
The net profit by subtracting cost from sales will be
Net profit = (7.8x² + 3.2x + 3.5) - (3.4x² - 0.8x + 3.5)
Net profit = 7.8x² + 3.2x + 3.5 - 3.4x² + 0.8x - 3.5
Net profit = 4.4x² + 4x
The polynomial which models the company's sales in thousands of dollars will be 4.4x² + 4x.
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54. The cone in the diagram has radius x cm and height 2x cm. The volume of the cone is 500 cm³. Find the value of x.
Value of x is 6.2 cm when x is the radius of cone.
What is Volume of cone?
The amount of space occupied by a cone is referred to as the volume of a cone. The volume of the cone depends on the base radius of the cone and the height of the cone. It can also be expressed in terms of its slant height wherever necessary.
Volume of cone formula, V= 1/3*[tex]\pi[/tex]*r∧2*h
given,
Height h= 2x
radius = x
Volume V= 500cm3
V= 1/3*[tex]\pi[/tex]*r∧2*h
500 = 1/3 *22/7*x2*2x
x∧3 = 5*3*5*5*2*2*7/11*4
x∧3 = 5*3*5*5*7/11
x = ∛(5*3*5*5*7/11)
x = 5(∛21/11)
x = 6.2 cm
Therefore, the radius of the cone x is 6.2 cm
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help asap math question
The two equations that represent the remaining angle relationships are
x = 2(y + z) - 20 and x = 3z - 20
Writing equationsFrom the question, we are to determine the two equations that represent the remaining angle relationships
From the given information, we have that
x is the largest angle, y is the next largest angle and z is the smallest angle
Also, from the information,
"The measure of the largest angle is 20 degrees less than twice the sum of the measure of the other two angles"
That is,
x = 2(y + z) - 20
and
"The largest angle is 3 times the smaller angle minus 20 degrees"
x = 3z - 20
Hence, the two equations that represent the remaining angle relationships are x = 2(y + z) - 20 and x = 3z - 20
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Fractions and mixed numbers
Use the given minimum and maximum data entries, and the number of classes, to find the class width, the lower class limits, and the upper class limits. minimum equals 13, maximum equals 94, 6 classes
The minimum and maximum data entries is the to arrive at the values as follows:
The class width is solved to be 13lower class limits = 13, 26, 39, 52, 65, 78, 91upper class limits = 25, 38, 51, 64, 77, 90, 94How to find the class width, the lower class limits, and the upper class limitsGiven data
minimum equals 13, maximum equals 94, 6 classes
The class width
= ( maximum - minimum ) / 6
= ( 94 - 13 ) / 6
= 13.5
The class width is solved to be 13
Lower class limit
From the lowest 13,repeated addition of the class width gives the lower class limits as follows:
lower class limits = 13, 26, 39, 52, 65, 78, 91
Upper class limits
The upper class limit is gotten from the lower class limit by reducing one from the class width to get 13 - 1 = 12. This value is added to the lower class limits to get the upper class limits.
upper class limits = 25, 38, 51, 64, 77, 90, 94
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Triangle ABC is translated 6 units to the left and 1 unit up to create
Answer:
can you add a picture of the triangle
Step-by-step explanation:
Cronus and Zeus are two competing cell phone companies. Cronus charges a flat rate of $8 per GB
of data. Zeus charges $3 per GB of data in addition to a monthly $10 fee that everyone pays
regardless of how much data they use. You expect to use between 0 GB and 8 GB of data each
month.
Part A: Graph the cost function associated with each company for data usage between 0 GB and 8
GB. Choose an appropriate scale for your graph.
The graph of the cost function is
Cost function refers to the functional relationship between cost and output. It studies the behavior of cost at different levels of output when technology is assumed to be constant.
Given: There are two companies Cronus and Zeus. Cronus charges a flat rate of $8 per GB of data. Zeus charges $3 per GB of data in addition to a monthly $10 fee that everyone pays. You expect to use between 0 GB and 8 GB of data each month.
Let y be the cost for data consumed.
Let x be Gb of data consumed.
Cost function of Cronus is y = 8x
Cost function of Zeus is y = 10+3x
Graph of both the companies is
where green line denotes the graph for Cronus and red line denotes the graph for Zeus.
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Madelyn Logan is an office furniture dealer who earns a $19,000 base salary. She also earns a 4% commission on
sales. How much must she sell to earn a total of $58,000
The total sales done by Madelyn Logan is $975,000.
What is defined as the commission on sales?Sales commission is an important component of sales compensation. It is the value of the money earned by a salesperson in relation to the number of sales made. This is extra money that often supplements a regular salary.Madelyn Logan earns $58,000 in total.
Madelyn Logan's total commissions are;
$58,000 - $19,000 (base salary) = $39,000.
That is, $39,000 equals 4% of her sales.
So,
0.04x = $39,000, in which x would be the total sales amount.
Then, x = $39,000 /0.04
x = $975,000.
Therefore, Madelyn Logan must sell the goods of worth $975,000. for making the amount of $58,000.
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Pleas help me with this im trying to figure it out open the picture please
Answer:
21 because if you can add like terms
Factor 2x^4-20x² - 78.
Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
In the graph the Inefficient point of production is represented by the point A , option(a)Point A is correct .
The graph given in the question is for Skateboards vs Bikers.
we need to find the point which represents the Inefficient point of Production.
The points in the Production Possibility Curve are said to be inefficient when the resources are not utilized to the fullest.
The given Production possibility curve between the Skateboards and the Bikers have Point A as the Inefficient Point .
Therefore , the point A represents the Inefficient point of production in the given Production possibility curve , the correct option is (a)Point A.
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How would you go about putting this into a calculator? It keeps saying 0 or error
I have a TI-30XS and a CATIGA CS-121
What is 2,443,802,280 rounded to the nearest ten million
Answer:2,440,000,000
Step-by-step explanation:
Find a translation that has the same effect as the composition of translation.
(x,y)-> (x+8,y+4) followed by
(x,y)-> (x-7,y+8)
Answer:
you need to show the options at the bottoma
Step-by-step explanation en:
7. Match each polynomial with its end behavior. Some end behavior options may not have a
matching polynomial.
A. f(x)=2x² + 3x + x²-1
B. f(x)=1-3x + x²
C. f(x)=9+x¹
D. f(x) = 2x+5
1. As x gets larger and larger in either the positive or negative direction, f(x) gets larger and
larger in the positive direction.
2. As x gets larger and larger in the positive direction, f(x) gets larger and larger in the
positive direction. As x gets larger and larger in the negative direction, f(x) gets larger and
larger in the negative direction.
3. As x gets larger and larger in the positive direction, f(x) gets larger and larger in the
negative direction. As x gets larger and larger in the negative direction, f(x) gets larger and
larger in the positive direction.
4. As x gets larger and larger in either the positive or negative direction, f(x) gets larger and
larger in the negative direction.
End behavior of the polynomials f(x) = 2x² + 3x + x² - 1 and f(x) = 1 - 3x + x² is; As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more positive.
How to describe the end behavior of a Polynomial?
A) We are given the polynomial; f(x) = 2x² + 3x + x² - 1
This is a second degree polynomial with a positive leading coefficient. Thus, the end behavior is; As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more positive.
B) We are given the polynomial; f(x) = 1 - 3x + x²
This is a second degree polynomial with a positive leading coefficient. Thus, the end behavior is; As x gets larger and larger in the positive direction, f(x) gets more positive. As x gets larger and larger in the negative direction, f(x) gets more positive.
C) We are given the polynomial; f(x) = 9 + x¹
This is a first degree polynomial with a positive leading coefficient. Thus, the end behavior is; As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.
D) f(x) = 2x + 5
This is a first degree polynomial with a positive leading coefficient. Thus, the end behavior is; As x gets larger and larger in either the positive or negative direction, f(x) gets larger and larger in the negative direction.
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At 6 AM, the temperature in New Crampton, California was 64℉. By 4 PM, the temperature had risen to 76℉. What was the change in temperature over the 10-hour period?
The change in temperature over the 10 hours using a mathematical operation, is 12℉.
What is a mathematical operation?A mathematical operation uses input values (variables, numbers, mathematical operators, and operands) to determine an output value.
Some of the mathematical operators include addition, subtraction, division, and multiplication.
For instance, we can subtract the temperature in New Crampton at 6 A.M. from the temperature at 4 P.M. to determine the temperature change.
Data and Calculations:The temperature at 6 A.M. in New Crampton = 64℉
The temperature at 4 P.M in the same city = 76℉
Change in temperature over 10 hours = 12℉ (76℉ - 64℉)
Thus, the change in temperature over the 10 hours using a mathematical operation, is 12℉.
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Given that 4x4-12x³-b²x²-7bx-2 is exactly divisible by 2x + b,
(i) show that 3b³ +7b²-4 = 0,
(ii) find the possible values of b.
Assume running consumes 111 Calories per mile. If you run 7-minute miles, what is your average power output, in watts?
By changing units from calories per minute to watts, we conclude that your power output is 1.11 Watts.
How to get the average power output?
Power is the ratio between energy consumed and the time in which it was consumed.
Here we know that you consume 111 calories per mile, and you run a mile in 7 minutes, then your power is:
P = (111 cal)/(7 min) = 15.86 cal/min
Now, we know that:
1 watt = 14.33 cal/min
Then we can rewrite our power as:
P = 15.86 cal/min = (15.86/14.33) W = 1.11 W
Your power output is 1.11 watts.
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p=A/(1+rt) for r pls help me
The solution of the equation P = A/(1 + rt) for r is r = (A/P - 1)/t
How to solve the equation for r?The equation is given as
P = A/(1 + rt)
Multiply both sides of the equation by (1 + rt)
So, we have
P(1 + rt) - A
Divide both sides by P
So, we have
1 + rt = A/P
Subtract 1 from both sides
rt = A/P - 1
Divide by t
r = (A/P - 1)/t
Hence, the solution of the equation P = A/(1 + rt) for r is r = (A/P - 1)/t
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HELP ME PLEASE! ILL GIVE EVERYTHING JUST ANSWER CORRECRTLY PLEASE!
Which expression is equivalent to (5x−5y3)−2?
−25x10y6
negative quantity 25 times x raised to the tenth power end quantity over y raised to the sixth power
x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity
1 over quantity 25 times x raised to the tenth power times y raised to the sixth power end quantity
Answer:
It should be negative quantity 25 times x raised to the tenth power end quantity over y raised to the sixth power
Step-by-step explanation:
The other options have operations that don't match with the answer so it can't be them
Maria uses 2/3 cup of powdered mix for every 2 gallons of water. Franco uses 1 1/4 cups of powdered mix for every 5 gallons of water. What is the strength of each sports drink?
The strength ratio of each sports drink is 4:3.
What is ratio ?Ratio can be defined as comparison of two or more similar quantities.
According to the given question Maria uses 2/3 cup of powdered mix for every 2 gallons of water.
Therefore the no. of cups of powdered mix per gallon in Maria's sports drink is
= (2/3)÷2
= (2/3)×(1/2)
= 2/6.
= 1/3 cups per gallon of sport drink.
In case of Franco the no. of cups of mix in his sport drink per gallon is
=(5/4)÷5
= 5/4×1/5
= 5/20
= 1/4 cups per gallon of sport drink.
∴ The strength of each sport drink is
= 1/3:1/4
= 12/3:12/4 ( LCM of 3,4 is 12 to remove the fractions)
= 4:3.
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Evaluate. Write your answer in fraction simple form.
(1/9)^2
To calculate a fraction, it is almost the same as calculating a number normal to the power. The numerator and denominator of the fraction are multiplied as many times as possible indicated by its exponent, then:
[tex]\boldsymbol{\sf{\left(\dfrac{1}{9}\right)^{2}=\dfrac{1\times1}{9\times9}=\cfrac{1}{81} }}[/tex]
Therefore the fraction 1/81 is already in reduced form, so it is no longer possible to simplify it.
f(X) is the solid line graph below. G(X) is the dashed line below.
On what interval of x is f(X) increasing?
On what interval of x is f(X) decreasing?
In the graph, [tex]f(x)[/tex] is increasing in the interval (-7, -5).
What is a graph in mathematics?
A graph is a graphic that uses a line or a sequence of bars, dots, or other symbols to depict a connection between two variables, most typically sets of numbers. Whatever else is in your graph, you can't construct it without scales. A vertical scale and a horizontal scale are used in bar graphs.
From the given graph, it can be concluded that
[tex]f(x)[/tex] is increasing in the interval (-7, -5)
[tex]f(x)[/tex] is decreasing in the interval (2, 10)
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What was the overall percent increase in the stadium capacity between 1920 and 2000
The overall percent increase in the stadium capacity between 1920 and 2000 considering the capacity was "x" in 1920 and "y" in 2000 is [tex][\frac{(y-x)}{x}*100][/tex].
As per the question statement, we are required to calculate the overall percent increase in the stadium capacity between the time period of 1920 and 2000. But no data about the stadium capacity is mentioned in the question statement. Hence, we will assume the capacity was "x" in 1920 and "y" in 2000. Assigning two variables to solve the question produces a generalized form of our required answer, in which, we can substitute any data to get the desired output.
Since Percentage change is calculated as
[{(Change from original)/(Original Value)}*100],
Our change in seating capacity of the stadium in 2000 from the year 1920 is [tex](y-x)[/tex] and original value being "x",
Overall percent increase in the stadium capacity between 1920 and 2000 is [tex][\frac{(y-x)}{x}*100][/tex].
Percent Increase: It is a measure of the difference (Increment) between the final value and the initial value, expressed in the form of a percentage.To learn more about Percent Increase, click on the link below.
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Ezra and his wife’s monthly payment includes $2,165.61 for principal and interest, as well one twelfth of the annual property taxes of $6,478.50 and one twelfth of the annual insurance premium on the property of $2,186. What is their total monthly payment?
Using proportions, it is found that their total monthly payment is of $2,887.37.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, the payments are given as follows:
$2,165.61 for principal and interest.1/12 = 0.0833 of $6,478.50 for taxes.1/12 = 0.0833 of $2,186 for insurance.Hence:
2165.62 + 0.0833 x 6478.5 + 0.0833 x 2186 = $2,887.37
Their total monthly payment is of $2,887.37.
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HELP PLEASE ASAP
i suck at math please help me
Answer:
2
Step-by-step explanation:
look at where x = 1 on the graph and see that there is a point at (1,2)
solve for x, showing all your steps using inverse operations
5-4x=-19
Answer:
x = 6
Step-by-step explanation:
5 - 4x = -19
-5 -5
-4x = -24
divide both sides by -4
x = 6
to check your work- plug in 6 for x.
Hope this helps!
Also- I am not entirely sure what inverse operations is in terms of algebra but I hope what I did is right!
Jana baked some muffins. After she served 13 of them to her friends for brunch, she had 17 left. How many muffins did she bake?
Answer:
30
Step-by-step explanation:
Add 13 served to 17 left over to get how many muffins she originally baked.
Answer:
30
Step-by-step explanation:
served muffins=13
left muffins=17
13+17=30
Six more than the product of a number and 4 is equal to 7. Use the variable b for the unknown number
The value of the unknown number b is 1/4.
What is substitution ?Substitution is putting a specific value in a given variable.
According to the given question Six more than the product of a number and 4 is equal to 7 and we have to use b for the unknown number.
7 is 6 more than the product of 4 and b which can be numerically expressed as
7 = 6 + 4b...(i)
7 - 6 = 4b.
1 = 4b.
b = 1/4.
To check if it is correct or not we will substitute the numerical value of b.
in eqn (i).
7 = 6 + 4b
7 = 6 + 4×1/4
7 = 6 + 1
7 = 7.
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