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?
y ≤ x2 – 3
y > –x2 + 2
Answers
The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Inequality is an expression that shows the non equal comparison of two or more numbers and variables
The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.
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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)
How to modify the graphsThe complete question is in the attached image (the first graph)
From the graph, we have:
f(x) = x^2 - 3 and g(x) = -x^2 + 2
To derive y ≤ x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.
To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than
How to identify the solution setThe inequalities of the graphs become
y ≤ x^2 - 3 and y > -x^2 + 2
From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)
Hence, the solution of the set of inequalities is (±1.581, -0.5)
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Related Questions
Mr. Bellman orders a cube of clay for each of his art classes. The height of the
cube is 20 inches. How much clay, in cubic inches, would Mr. Bellman order
for three classes?
Write and evaluate an expression to find your answer.
20 cubed is 20 times 20 and then that answer times 20.
length X width x height = cube
20 to the 3rd power or 203
A
B
C
60 cubic inches
400 cubic inches
8,000 cubic inches
Answers
Answer:
20 x 20 x 20 = 8000
Determine a limit for a piecewise function
Answers
The limit for the given piecewise function does not exist(DNE).
4th option is correct.
What is the limit of a function?In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.
Unique real numbers are limits in mathematics.
According to the question,
Left hand limit of the function= -5(3)+4 = -15+4 = -11
Right hand limit of the function= (3)(3)+2 = 11
As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.
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for csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
Answers
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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If np>5 and nq>5, estimate P (at least 10) with n=13 and p=0.5 by using the normal distribution as approximation for the binomial distribution, if np, or nq,5, then state that the normal approximation is not suitable.
Answers
Using the normal distribution, the probability is given as follows:
[tex]P(X \geq 10) = 0.0485[/tex].
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are:
p = 0.5, n = 13.
Hence the mean and the standard deviation are:
[tex]\mu = np = 13 \times 0.5 = 6.5[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{13 \times 0.5 \times 0.5} = 1.8028[/tex]Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, then:
[tex]P(X \geq 10) = 0.0485[/tex].
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The earth travels around the sun at about 1,110 miles per minute.
About how many miles does the earth travel around the sun per second?
Drag and drop the answer into the box.
The earth travels around the sun about ___ Response area miles per second.
Answers
Answer:
18.5 miles
Step-by-step explanation:
the Sun at an average speed of 67,000 mph, or 18.5 miles a second.
if sinA=4/5 solve sin2A, cos2A and tan2A
Answers
Step-by-step explanation:
1) if m(∠A)∈[0;90°), then
[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]
[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]
[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]
[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]
2) if m∠A∈[90°;180°), then
cos(A)=-0.6;
sin2A=-0.96;
cos2A=-0.28;
tan2A=-24/7.
FRACTIONS
Equivalent fractions
Fill in the blank to make the two fractions equivalent.
blank over 30=4/5
Answers
The complete fraction is 24/30=4/5
How to create an equivalent fraction?The expression is given as:
blank over 30=4/5
Represent the blank with x.
So, we have:
x/30=4/5
Multiply both sides by 30
x = 30 * 4/5
Evaluate
x = 24
Substitute x = 24 in x/30=4/5
24/30=4/5
Hence, the complete fraction is 24/30=4/5
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PLSSSSSSSSSSSSSSS HELP pls
Answers
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: 10x + 30 = 90[/tex]
[ according to given figure ]
[tex]\qquad \sf \dashrightarrow \: 10x = 90 - 30[/tex]
[tex]\qquad \sf \dashrightarrow \: 10x = 60[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 60 \div 10[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 6 \degree[/tex]
Correct choice is D
(-2) * n * (8) * n * (-n)
Answers
Answer:
16[tex]n^{3}[/tex]
Step-by-step explanation:
we evaluate from left side to right side
so -2*n =-2n
-2n *8 = -16n
-16n * n =-16n^2
-16 n * -n =16 n^3
hope this helps
True or false? The graph represents a function.
5
O A. True
O B. False
Answers
A college graduate expects to earn a salary of $55,000 during the first year after graduation and receive a 3% raise every year after that. What is the total income he will have received after ten years?
Answers
Answer:
$73915.40
Step-by-step explanation:
→ Find the multiplier
( 3 + 100 ) ÷ 100 = 1.03
→ Multiply by principal amount and raise it to the power of years
55000 × 1.03¹⁰ = 73915.40
Answer: $630,513.36
Step-by-step explanation:
Making a Formula for His Salary on a Given YearLet's make a table of values to see how much he earns every year after graduation.
1 year -> $55,000
2 years -> 55,000 * 103% = $56,650
3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50
4 years -> 58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³
Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.
We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.
Using this, let's generalize this for n.
n years -> [tex]55000(1.03)^{n-1}[/tex]
Finding the Sum after Ten YearsWe are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this
[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]
This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.
Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:
[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]
where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.
[tex]a_1[/tex] -> 55000
r -> 1.03
n -> 10
Now that we have the values for each variable, let's plug them in and solve
[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]
The total income he will have received after ten years is $630,513.36.
_+_+_= 30
Use only
1,3,5,7,9,11,13,15
You can repeat it
Answers
Answer
1 possible solution:
(5x7) in the first blank
(-3!) in the second blank
(-1) in the third blank
Step-by-step explanation:
(5x7) + -(3!) + -(1) 3! equals 3x2x1 or 6
35 + (-6) + (-1)
How does the graph of g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3?
A. g(x) is shifted 2 units to the right and 6 units down.
B. g(x) is shifted 2 units to the right and 6 units up.
C. g(x) is shifted 2 units to the left and 6 units down.
D. g(x) is shifted 6 units to the left and 2 units down.
Answers
Answer: B. g(x) is shifted 2 units to the right and 6 units up.
Step-by-step explanation:
See attached image.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
Inequality expressionInequality expressions are expression not separated by an equal sign
Given the following inequality expression
–3(2x – 5) < 5(2 – x)
Expand
-6x + 15 < 10 - 5x
Collect the like terms
-6x + 5x < 10 -15
-x < -5
x > 5
Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
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F(x) =5^2x find the derivative of X
Answers
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
Finding the derivative of a functionThe derivative of a function f(x) is the ratio of the change in f(x) to the change in x
The given function is:
[tex]f(x)=5^{2x}[/tex]
Let u = 2x
Find the derivative of u. That is, du/dx
du/dx = 2
f(x) = 5^u
[tex]\frac{df}{du} =5^ulnu[/tex]
Using the chain rule of derivative
[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]
[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]
The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]
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Write an equation for a line perpendicular to y=5x+1 and passing through the points (5,-2)
Answers
__________________________________________________________
[tex]\text{\textbf{Hello!} In this question, we are trying to find the equation of a line}\\\text{that is \underline{perpendicular} to our given equation}[/tex]
__________________________________________________________
[tex]\textbf{Explanation:}\\\\\text{To help us answer our question, we need to note some of our given info:}\\\\\text{Equation: y = 5x + 1}\\\\\text{Point passed through: (5, -2)}\\\\\text{We can use the above information to help us find our perpendicular equation.}\\\\\text{We will be using the slope-intercept form equation to help get us our answer:}\\\\\text{y = mx + b}[/tex]
[tex]\text{When a line is perpendicular to an equation, it means that its slope is }\\\text{\textbf{opposite} which results in the lines to meet at a \underline{90-degree} angle.}[/tex]
__________________________________________________________
[tex]\textbf{Solve:}\\\\\text{To get our perpendicular slope, we will use the formula:}\\\\\text{m1 = }-\frac{1}{m2}\\\\\text{m1 will be our given slope (5) and m2 will be our already provided slope. }\\\\\text{This is also known as a \underline{negative reciprocal}. }\\\\\text{Therefore: m1 = }-\frac{1}{5}\\\\\text{Since we now know our slope, we can plug it into our "m" variable in the}\\\text{slope intercept equation:}\\\\\text{y = }-\frac{1}{5}x+b\\[/tex]
[tex]\text{To find where the point is on the y-intercept, we will plug in our point}\\\text{(5, -2) to it's corresponding spots in our new equation above.}\\\\\text{Plug "5" to x and "-2" to y and solve:}\\\\\text{-2 = }-\frac{1}{5}(5)+b\\\\\text{-2 = }-1+b\\\\\text{Add 1 to both sides.}\\\\\text{-1 = }b\\\\\text{Therefore, our y-intercept is -1.}[/tex]
[tex]\text{When we plug -1 into our new equation, we get:}\\\\\text{y = }-\frac{1}{5}x-1\\\\\text{Therefore, our perpendicular equation is: }\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Answer:}\\\\\boxed{y = -\frac{1}{5}x-1}[/tex]
__________________________________________________________
[tex]\textbf{Additional Info:}\\\\\text{You can learn more about \textbf{slope-intercept form} below:}[/tex]
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here is a polygon. draw a scaled copy of the polycon with scale factor 3
Answers
The scaled copy of the polygon is added as an attachment
How to draw the scaled copy?The complete question is added as an attachment
The coordinates of the polygon are
A = (-7, 6)
B = (-10, 8)
C = (-10, 10)
D = (-6, 10)
The scale factor is 3.
So, the rule of dilation is
(x, y) = (3x, 3y)
Using the above rule, we have:
A' = (-21, 18)
B' = (-30, 24)
C' = (-30, 30)
D' = (-18, 30)
See attachment for the scaled copy of the polygon
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A coin has two sides head and tails a die has six sides if you roll the die what is the probability that you flip heads and roll a number greater than 5
Answers
Using it's concept, the probability that you flip heads and roll a number greater than 5 is: [tex]\frac{1}{12}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
The probability of a head is 1/2.The probability of a number greater than 5 is 1/6.Hence the probability of both events is:
[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex].
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a) Out of all items sent for refurbishing, %40 had mechanical defects, %50 had electrical
defects, and %25 had both. Denoting defectmechanicalahasitemanA and
defectmechanicalahasitemanB . Fill the probabilities into the Venn diagram and
determine the quantities listed below.
(i) AP [2 Marks]
(ii) BAP [1 Mark]
(iii) BAP c
Answers
i. P(A) = 0. 4
ii. P(AB) = 0. 9
iii. P(A∩B) =0. 25
How to determine the probability
From the information given,
Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25
A = Mechanical defects = 40%
B = Electrical defects = 50%
A∩B =25%
i. Probability of A , P(A)
= [tex]\frac{40}{100}[/tex]
= [tex]0. 4[/tex]
ii. Probability of B, P(AB)
= [tex]\frac{40}{100} + \frac{50}{100}[/tex]
= [tex]0. 4 + 0. 5[/tex]
= [tex]0. 9[/tex]
iii. Probability of A∩B entails the common factor between A and B
P(A∩B) = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]
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A lawn can be mowed by 8 people in 6 hours. If 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn? Please show me how you figured this out.
A. 6 2/5
B. 9 3/5
C. 2 1/4
D. 5 1/2
Answers
If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.
How many hours will it take to mow the lawn?Let's say that each person works at a rate R.
8 people can mow the lawn in 6 hours, then we can write:
(8*R)*6 hours = 1 lawn.
Solving for R:
R = (1/48 lawns per hour).
If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:
(5*R)*T = 1 lawn.
Replacing the value of R:
(5/48 lawns per hour)*T = 1 lawn.
Then we have:
T = (48/5) hours.
We can rewrite that as:
T = (45/5 + 3/5) hours
T = 9 + 3/5 hours.
Then we conclude that the correct option is B.
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w^14+w^16
what will be the answer pls help
Answers
Answer:
there shouldnt be an answer, they are not like terms, for a proper answer it would have to be like terms, for example:
x^2+x^2=2x^2
or
w^12+w^12=2w^12
they need to have the same exponent for addition to happen
Find the coordinates of the vertices of the triangle if it’s rotated 270° counterclockwise.
Answers
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
X' = (3, -1)
Y' = (2, -2)
Z' = (-1, -3)
Rotation of coordinatesIf the coordinates (x, y) is rotated 270° counterclockwise, the resulting coordinate point will be;
(x, y) - > (y, -x)
From the given triangles, the coordinate points are expressed as
X = (1, 3)
Y = (2, 2)
Z = (3, -1)
If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;
X' = (3, -1)
Y' = (2, -2)
Z' = (-1, -3)
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scientist released 8 rabbits into a new habitat in year 0. Each year, there were twice as many rabbits as the year before. How many rabbits were there after X years? Write a function to represent this scenario.
Answers
Answer:
Step-by-step explanation:
his function will be an exponential function, because the number of rabbits double each year
the basic form for exponential functions is
where s is the starting number, c i s the constant (rate of change like double, triple, etc.) and x is the number repeats (in this case, years)
so in this case, the starting number (year 0) is 8, and the rate of change is 2
therefore, the equation is:
f(X) =8 times 2
hope this helps!
p.s. can i have brainliest?
A conduit of circular cross section has 7 cables all same diameter. Inside diameter of conduit is 30cm. What is the cross sectional area of the conduit not part of the 7 cables
Answers
The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²
What is the cross sectional area of the conduit not part of the 7 cables?It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.
Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;
where radius, r = D/2 = 30/2.
Area = πr² = 3.14 × (30/2)² = 706.5cm²
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a rectangle has horizontal sides of 3 (x-2)ft and vertical sides of 4x-7+(-2x) ft finde the value of x so that the rectangle has a perimeter of 34 ft
Answers
Based on the given horizontal and vertical sides of a rectangle and its perimeter, the value of x in the expression is 6
Perimeter of rectanglePerimeter of rectangle = 2(length + width)
Perimeter of the rectangle = 34 ftLength of the rectangle = 3(x - 2) ft= 3x - 6
Width of the rectangle = 4x - 7 + (-2x)= 4x - 7 - 2x
= 2x - 7
Perimeter of rectangle = 2(length + width)
34 = 2{(3x - 6) + (2x - 7)}
34 = 2(3x - 6 + 2x - 7)
34 = 2(5x - 13)
34 = 10x - 26
34 + 26 = 10x
60 = 10x
x = 60/10
x = 6
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this table shows values that represent an exponential function.
x y
1 7
2 9
3 13
4 21
5 37
what is the average rate of change for this function for the interval from x = 1 to x = 3?
a. 4 b. 2 c. 3 d. 8
Answers
The average rate of change for this function for the interval from x = 1 to x = 3 is 3
How to determine the average rate of change?The average rate of change is calculated as:
m = (f(b)- f(a))/(b - a)
The interval is given as:
x = 1 to x = 3
From the table of values, we have:
f(1) = 7
f(3) = 13
So, we have:
m = (13-7)/(3-1)
Evaluate
m = 3
Hence, the average rate of change for this function for the interval from x = 1 to x = 3 is 3
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WILL GIVE BRAINLIEST!!! If [tex]\frac{a}{b} =2[/tex] what is the value of [tex]\frac{a}{a-b}[/tex]?
Could the answer be D) or is it C)?
A) -2
B) 1
C) 2
D) It cannot be determined from the given information
Answers
Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:
C) 2
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion between a and b is given by:
a/b = 2.
Then:
a = 2b.
The expression is:
[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]
Hence option C is correct.
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Which graph best represents the solution to the system of equations shown below? y = -2x + 14 y = 2x + 2 A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair 8, 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 8, negative 3. A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on ordered pair negative 3, 8.
Answers
The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.
What is the graphical solution of the system big equations?As an alternative, solving the system of equations algebraically, we have;
-2x +14 = 2x +2
x = 3 and by substitution;
y = 8.
On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.
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The following figure shows the entire graph of a relationship.
See attached!
Answers
The correct answer is Yes. The graph represents a function. The function given is: F(x) = y(-5). Note that the value of x is zero.
What is the graph of a function?A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x).
Thus, the correct answer or function represented in the graph is f(x) = y(-5)
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PreCalc work, Need help writing piecewise functions with graphs. Giving brainliest
Answers
Answer:
f(x) = 2 for x < -2
f(x) = -2x + 11 for x > 3