The functions f(x)=x²-1 and g(x) = -x² + 4 are shown on the graph.
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
Answers
The solution to the given graph is (-√5/2, √5/2)
Quadratic graphGiven the following quadratic graph f(x)=x²-1 and g(x) = -x² + 4
The solution will be the point of intersection of the two curves.
Equate the functions
x²-1 = -x² + 4
Equate to zero
x²+x² - 1- 4 = 0
2x² -5 = 0
2x² = 5
x² = 5/2
x = ±√5/2
Hence the solution to the given graph is (-√5/2, √5/2)
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Related Questions
2011?
7. Maria, a sales representative for a large consumer goods company, is paid 3% of the total profits earned by her company.
Her company averages 10% profit on sales. If Maria's total income for the year was $60,000, what total sales did her
company realize?
Answers
Step-by-step explanation:
60000÷ 10 = 600 and 600 ÷ 3 =20
The total sales realized by the company was $20,000,000.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Let x be the total sales realized by the company.
Maria's pay is 3% of the total profits, which is 3% of 10% of total sales
0.03(0.1x) = 0.003x.
Her total income is given as $60,000, so we have:
0.003x = 60000
Solving for x:
x = 60000/0.003 = 20,000,000
Therefore, the total sales realized by the company was $20,000,000.
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Let R(x)=3x^3+2x^2+x and S(x)=4+1. Find R(x) * S(x)
Pls help!!!!
Answers
3x^3 x 4x^2 = 12x^5
3x^3 x 1 = 3x^3
2x^2 x 4x^2 = 8x^4
2x^2 x 1 = 2x^2
1x x 4x^2 = 4x^3
1x x 1 = 1x
12x^5 + 3x^3 + 8x^4 + 2x^2 + 4x^3 + 1x
Simplify
12x^5 + 7x^3 + 8x^4 + 2x^2 + 1x
Thus, answer is B
Hope this helps!
For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $50 .
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).
Answers
The equation for the profit from selling the items is P = 40x-0.5x²-300. The values of x are 10 and 70.
How to solve for the expressionWe have the cost function in this question to be
Cx = 60x+300
Revenue = 100x−0.5x²
A. The revenue function is stated as the revenue - cost
= (100x−0.5x²)-60x+300
We have to open the equation
40x-0.5x²-300
B. when profit is 50 dollars
50 = 40x-0.5x²-300
We have to multiply both sides by 10
500 = 400x - 5x² - 3000
We have to collect like terms and form a quadratic equation
5x² - 400x - 3500 = 0
We have to solve the quadratic equation above using a quadratic calculator.
Hence
x = 10, 70
So the two values that would create a profit of 50 dollars is 10 and 70.
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please please out of certain people of all locality 50% speak Nepali language 55% speak English language and 5% speak not if 40 people speak both the language find total number of people,people who speak nepali language only english language only.Show the result in a venn diagram.
Answers
The given pics are your answers... Thank you
Evaluate the following.
Answers
Step-by-step explanation:
1) 3 + 4 = 7
2) 6 - 6 = 0
3) 1 + 3 = 4
4) 6 + 9 = 15
5) 10 - 14 + 2 = -2
6) 2 + 3 - 5 = 0
Which ordered pairs make both inequalities true? Check all that apply.
Answers
We can actually deduce here that the ordered pairs that make both inequalities true are:
(1,1)(2, 2)What is inequality?An inequality is known to be an expression that shows that certain variables or values are not equal to each other. It is usually seen in an inequality expression as:
> (greater than)< (less than)≥ (greater than or equal to) ≤ (less than or equal to).We see the attached image that shows the graph of inequality and which completes the question.
The options that complete the question are:
A. –2, 2
B. (0, 0)
C. (1,1)
D. (1, 3)
E. (2, 2)
When we insert the values of each axes into the inequality expressions given, we will discover that the ordered pairs that the inequalities true is (1,1) and (2, 2).
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Solve the inequality −38<5x+7≤17
Answers
66877383
Step-by-step explanation:
I made a single dad be single of ⅝
let A and B sets. when do we say set A is equal to set B
Answers
Step-by-step explanation:
It is said A=B I have drawn the Venn diagram of A=B
Help please quueens i need help
Answers
Answer:
x = 3
Step-by-step explanation:
We can use the following equation to solve for x:
[tex]315=9x-27+8x+24+5x-17+2x+23\\315=(9x+8x+5x+2x)+(-27+24-17+23)\\315=24x+3\\312=24x\\13=x[/tex]
In what situation would you use an ANOVA statistical test over T-test?
Answers
Step-by-step explanation:
when means of more than two groups are to be compared, ANOVA is perferred
x is increased by 50% and decreased by 30%. What is the result?
Answers
Answer:
its the same as increasing x by 5 percent
Answer:
1.05x is the answer
Step-by-step explanation:
Select all of the equations that represent linear relationships. 5 + 2y = 13 y = 7 y – 5 = 2(x – 1) = x + 7 x = –4
Answers
The equations that represent linear relationship is y – 5 = 2(x – 1)
What are linear functionsLinear functions are functions that has a leading degree of 1. According to the question, we need to determine the function that represents linear equation.
The required equation must have a degree of 1 and must contain both dependent and independent variables.
The equations that represent linear relationship is y – 5 = 2(x – 1)
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Answer:
The anser is:
A
C
D
E
Step-by-step explanation:
I hope this helps, have a blessed day :)
Solve for x. Enter the solutions from least to greatest.
Round to two decimal places.
(x + 8)^2 - 7 = 0
asap will give brainliest
Answers
The value of x according to the equation in the task content is; -5.35 or -10.65.
What is the value of x in the equation?The equation given in the task content is; (x + 8)² -7 = 0.
Hence, the equation can be solved as follows;
(x + 8)² - 7 = 0
x² + 16x +64 -7 = 0
x²+ 16x +57 = 0
By solving by means of the quadratic formula, we have;
x = -5.35
x = -10.65
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People were asked if they prefer Pepsi or Coke. The results are in the table below.
Pepsi Coke
Female 23 44
Male 28 39
a) If two people are chosen, what is the probability that they both prefer Pepsi?
b) If one person is chose, find the probability that they are Female or prefer Coke.
Answers
Using it's concept, it is found that the probabilities are given as follows:
a) 0.1431 = 14.31%.
b) 0.7910 = 79.10%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
The number of people is:
23 + 44 + 28 + 39 = 134.
The number of people that prefer Pepsi is:
23 + 28 = 51.
Hence, for the two people, the probability is:
p = 51/134 x 50/133 = 0.1431 = 14.31%.
Item b:
There are 23 + 44 = 67 females, and 39 males who prefer Coke, hence the probability is:
p = (39 + 67)/134 = 0.7910 = 79.10%.
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8 sin x cos3 x + 8 sin3 x cos x = ?
Answers
Answer:
Step-by-step explanation:
We use the known identity:
sin (A + B) sin A cos B + cos A sin B.
8 sin x cos 3x + 8 sin 3x cos x
= 8 (sin x cos 3x + sin 3x cos x)
= 8sin (x + 3x)
= 8 sin 4x
Identity :
sin (A + B) sin A cos B + cos A sin B
= 8 sin x cos 3x + 8 sin 3x cos x
= 8 (sin x cos 3x + sin 3x cos x)
= 8sin (x + 3x)
= 8 sin 4x
A rectangle with base b and height h has an area of 235 square-inches. Express the perimeter of the rectangle as a function of its base
Answers
The perimeter of the rectangle as a function of its base is P = 2(b + 235/b)
What are perimeters?The perimeter of a shape is the sum of the side lengths of the shape For all regular quadrilaterals, you add up the side lengths to determine the area
How to express the perimeter of the rectangle as a function of its base?The given parameters are
Area = 235 sqare inches
The area of a rectangle is calculated using
Area = Base * Height
Note that the area of a shape is the amount of space on the shape
Recall that the area of a rectangle is calculated using
Area = Base * Height
Rewrite the above equation as
A = bh
So, we have
bh = 235
Make h the subject of the formula
h = 235/b
The perimeter of the rectangle is
P = 2(b + h)
So, we have
P = 2(b + 235/b)
Hence, the perimeter of the rectangle as a function of its base is P = 2(b + 235/b)
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5 pts Which side would create a right triangle if the first two sides have lengths 7 and 123 5 pts Which side would create a right triangle if the first two sides have lengths 7 and sq rt 123
Answers
Answer:
sqrt(172) = hypotenuse
Step-by-step explanation:
IF those are the leg lengths (sides) and not the hypotenuse, then use Pythagorean theorem
c^2 = 7^2 + sqrt (123) ^2
c = sqrt (172)
If sqrt 172 is the hypotenuse :
(sqrt123)^2 = 7^2 + x^2
then x = sqrt (74 )
Please Answer! It is a emergancy! SUPER EASY
Answers
Answer:
x^-3
Step-by-step explanation:
1 / (x^3) = x^(-3)
A garden table and a bench cost $700 combined. The garden table costs $50 less than the bench. What is the cost of the bench?
Answers
Cost of bench = x
Cost of garden table = x - 50
x - 50 + x = 700
2x - 50 = 700
2x = 750
x = 325
A bacteria culture starts with 1000 bacteria and the number doubles every 40 minutes. (a) find a formula for the number of bacteria at time (b) find the number of bacteria after one hour (c) after how many minutes will there be 50000 bacteria?
Answers
The formula for the number of bacteria at time t is 1000 x (2^t).
The number of bacteria after one hour is 2828
The number of minutes for there to be 50,000 bacteria is 324 minutes.
What is the number of bacteria after 1 hour?The exponential function that can be used to determine the number of bacteria with the passage of time is:
initial population x (rate of increase)^t
1000 x (2^t).
Population after 1 hour : 1000 x 2^(60/40) = 2828
Time when there would be 50,000 bacteria : In(FV / PV) / r
Where:
FV = future bacteria population = 50,000PV = present bacteria population = 1000r = rate of increase = 100%In (50,000 / 1000)
In 50 / 1 = 3.91 hours x 60 = 324 minutes
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Suppose that an individual has a body fat percentage of 15.9% and weighs 159. How many pounds of her weight is made up of fat? Round to the nearest tenth
Answers
Answer:
25.3 lb
Step-by-step explanation:
We can multiply the whole by the percentage to find the part. Since 15.9% is equal to 0.159, the weight of fat is 159*0.159 = 25.281. Round this to the nearest tenth, and we get 25.3 pounds.
Which of the expressions below cannot be rewritten using the associative
property?
.
OA. 15 (410)
OB. (5+14) + 10
OC. 12 (17 ÷ 2)
OD. (12.9) •10
SUBMIT
Answers
Answer:
OA
Step-by-step explanation:
Median weekly earnings for women with some college for an associate degree.
1980.......$231
2013.............$657
Using today's dollars, the data in the bar graph can be described by the mathematical model
W = 13n + 231,
Where W represents median weekly earnings n years after 1980.
Does the formula underestimate or overestimate the median weekly earnings in 2013? By how much?
Answers
Using the given linear function, the formula underestimates the median weekly earnings in 2013 by $3.
What is the linear function for the estimate?The function that estimates the median weekly earnings n years after 1980 is given by:
W = 13n + 231.
2013 is 2013-1980 = 33 years after 2000, hence the estimate is given by:
W = 13 x 33 + 231 = 660.
Since 657 < 660, the formula underestimates the median weekly earnings in 2013 by $3.
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DEF and RST are complementary angles. If DEF is (3(-5 + 2x)) and RST is (x - 7), what is the measure of DEF?
Answers
From the given information, the measure of DEF is 81°
Calculating the measure of anglesFrom the question, we are to determine the measure of DEF
From the given information,
DEF and RST are complementary angles. This means they sum up to 90°
Thus,
(3(-5 + 2x)) + (x - 7) = 90
(3(-5 + 2x)) + (x - 7) = 90
(-15 + 6x) + (x - 7 ) = 90
-15 + 6x + x - 7 = 90
6x + x = 90 + 15 + 7
7x = 112
x = 112/7
x = 16
Then, substitute the value of x to determine the measure of DEF
(3(-5 + 2x))
= (3(-5 + 2(16)))
= (3(-5 + 32))
= (3(27))
= 81°
Hence, the measure of DEF is 81°
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11.
An IV of D5W 1000 mL was ordered to infuse over 8 hr at a rate of 42 gtt/min (42 macrogtt/min). Drop
factor: 20 gtt/mL. After 4 hr, you notice that only 400 mL has infused.
Recalculate the rate in gtt/min for the remaining solution
Answers
The rate is 50gtt per minutes.
How to calculate the growth rate?From the information, out of the total hours of 8 hours, four hours were used.
The volume will be:
= 1000 - 400
= 600ml
Time = 4 × 60 = 240 minutes
Drop factor = 20
Therefore, the growth rate will be:
= 600/240 × 20
= 50gtt/min
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Find the surface of the cube with length of a side
Answers
Answer: 319.74 square mm
Step-by-step explanation:
[tex]6(7.3)^2=319.74[/tex]
1) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino. What would you expect to be true for all expected values for these seven games? In your discussion, also state whether the expected value is positive or negative. 1 ) Suppose a mathematician computed the expected value of winnings for a person playing each of seven different games in a casino . What would you expect to be true for all expected values for these seven games ? In your discussion , also state whether the expected value is positive or negative.
Answers
As per the question seems, the expected value can be positive, negative or zero.
The given question is of probability, which cannot be negative so don't get confused between expected values and probability, expected value and be negative, positive or zero.
What is probability?
Probability can be defined as the ration of favorable outcomes to the total number of events.
If person playing different games in casino , the probability of that person winning could be varying from 0/7 to 7/7 which implies that person can win from zero games to all games. If that person wins all the 7 games that mean he the gain in values, but if the loses 1 games or more games there than he supposed have gain or have loosen expected values so it can be positive, negative or zero. however the person loosen every game their is certain negative expected values.
Thus, The expected value can be positive, negative or zero.
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solve which 2 digit number is one more than a square and one less than cube?
Answers
The 2-digit number is 26:
26 - 1 = 25 is a square number.
26 + 1 = 27 is a cube number.
How to find the number?
Here we want to find a 2-digit number N, such that:
N + 1 is a cube number.N - 1 is a square number.To do that, we can just create a list of cubic and square numbers of 2 digits, these are:
Square numbers:
4*4 = 16
5*5 = 25
6*6 = 36
etc...
Cube numbers:
3*3*3 = 27
4*4*4 = 64
etc...
Now, we can see that 25 is a square number and 27 is a cube number, then our 2-digit number can be 26.
Because:
26 - 1 = 25 is a square number.
26 + 1 = 27 is a cube number.
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Suppose that $4000 is placed in a savings account at an annual rate of 6.4%, compounded quarterly. Assuming that no withdrawals are made, how long will it
take for the account to grow to $4916?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answers
Answer:
3.25 years (nearest hundredth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $4916P = $4000r = 6.4% = 0.064n = 4 (quarterly)Substitute the given values into the formula and solve for t:
[tex]\implies \sf 4916=4000\left(1+\frac{0.064}{4}\right)^{4t}[/tex]
[tex]\implies \sf 4916=4000\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \dfrac{4916}{4000}=\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \dfrac{1229}{1000}=\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=\ln \left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=4t \ln \left(1.016\right)[/tex]
[tex]\implies \sf t=\dfrac{\ln \left(\frac{1229}{1000}\right)}{4\ln \left(1.016\right)}[/tex]
[tex]\implies \sf t=3.247594892...[/tex]
Therefore, it will take 3.25 years (nearest hundredth) for the account to grow to $4916.
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Martin has written the first 50 terms of the sequence with nth term 150 -4n. Work out which term is the first negative term.
what is the answer to this help
Answers
The first negative term of the sequence is -2
How to find the terms of a sequence?The terms of the sequence which is the first negative term can be calculated as follows:
The sequence with nth term is 150 - 4n.
The first negative term will be the first term you will multiply by 4 that will be greater than 150.
Therefore,
nth term with first negative number = 150 - 4(38)
nth term with first negative number = 150 - 152
nth term with first negative number = -2
Therefore, the first negative term of the sequence is -2
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