Evaluate the function for the indicated values of x. Function.
Answers
The value are:
f(−10) = -19
f(2) = 4
f(−5) = -9
f(−1) = 1
f(8) = -5
Given is a piecewise function
f(x) = 2x + 1, x ≤ -5
x², -5 < x < 5
3-x, x ≥ 5
We need to evaluate the function for the indicated values of x.
To evaluate the given piecewise function for the indicated values of x, we substitute the values into the corresponding parts of the function. Let's calculate:
1) f(−10):
Since −10 ≤ -5, we use the first part of the function.
f(−10) = 2(−10) + 1 = -20 + 1 = -19
2) f(2):
Since -5 < 2 < 5, we use the second part of the function.
f(2) = (2)² = 4
3) f(−5):
Since −5 ≤ -5, we use the first part of the function.
f(−5) = 2(−5) + 1 = -10 + 1 = -9
4) f(−1):
Since -5 < -1 < 5, we use the second part of the function.
f(−1) = (−1)² = 1
5) f(8):
Since 8 ≥ 5, we use the third part of the function.
f(8) = 3 - 8 = -5
Therefore the value are:
f(−10) = -19
f(2) = 4
f(−5) = -9
f(−1) = 1
f(8) = -5
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Complete question =
Evaluate the function for the indicated values of x.
f(−10) =
f(2) =
f(−5) =
f(−1) =
f(8) =
Related Questions
Hurry please!
What is the slope of a line parallel to the line whose equation is 2 – 2y = 4. Fully
simplify your answer.
Answers
Answer:
The slope of the given line and a line parallel to it is
5
2
.
Explanation:
Given:
5
x
−
2
y
=
11
is the standard form of a linear equation.
A line parallel to this line has the same slope. To determine the slope, solve for
y
to change the equation to slope-intercept form:
y
=
m
x
+
b
,
where:
m
is the slope and
b
is the y-intercept.
5
x
−
2
y
=
11
Subtract
5
x
from both sides.
−
2
y
=
−
5
x
+
11
Divide both sides by
−
2
.
y
=
−
5
−
2
x
+
11
−
2
Simplify.
y
=
5
2
x
−
11
2
The slope of the given line and a line parallel to it is
5
2
.
line charts are best suited for representing data that follows some nonsequential order.
true or false
Answers
False. Line charts are best suited for representing data that follows a sequential order, such as time series data. Nonsequential data is better represented by other types of charts, like scatter plots or bar graphs.
Line charts are graphical representations of data points connected by lines. They are commonly used to display trends over time or sequential data. For example, they are often used to show the change in stock prices over a period of time or the temperature variations throughout the day. This sequential order is the key feature of line charts.
However, for data that does not follow a sequential order, line charts may not be the best choice. Nonsequential data, such as categorical or unrelated data points, are better represented by other types of charts. Scatter plots, for instance, are useful for showing the relationship between two variables that are not necessarily ordered. Bar graphs can also be used to compare nonsequential data points in different categories.
In summary, line charts are not best suited for representing data that follows a nonsequential order. They are most effective when used to display data that has a clear sequential relationship, allowing for easy interpretation of trends and patterns.
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-
12-
Speed
(metres per
second)
0
1
Time (minutes)
5
A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per
second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations.
In meters
Answers
The value of the total distance between the two stations is 2520m
How to calculate distance in meters ?The train runs with the following acceleration:
v = u + at
12 = 0 + a(120)
a = 0.1 m/s2.
Distance covered by the train in first part:
S = 1/2at^2
S = 1/2×0.1×(120)^2
S = 720m
Distance covered in second part:
S = ut
S = 12×60 = 720m
Train deceleration is given by
v = u+ at
0 = 12+a (180)
a = -1/15
Distance covered by the train in last part:
S = ut- 1/2at^2
S = 12(180) - 1/2(1/15)(180)^2
S = 2160 - 1080
S = 1080m
Therefore, The value of the total distance between the two stations is 720+720+1080 = 2520m.
The complete question is :A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 meters per second. It continues at this speed for 1 minute. It then decelerates for 3 minutes until it stops at the next station .Calculate the distance, in meters, between the two stations.
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A test for ovarian cancer has a 5 percent rate of false positives and a 0 percent rate of false negatives. On average, 1 in every 2,500 American women over age 35 actually has ovarian cancer. If a woman over 35 tests positive, what is the probability that she actually has cancer? Hint: Make a contingency table for a hypothetical sample of 100,000 women. Explain your reasoning.
Answers
Given the provided information, if a woman over 35 tests positive for ovarian cancer, the probability that she actually has cancer is approximately 1.96%.
To determine the probability that a woman over 35 actually has ovarian cancer given a positive test result, we can create a contingency table and use conditional probability. Let's consider a hypothetical sample of 100,000 women:
Out of 100,000 women, 1 in every 2,500 (or 40 out of 100,000) actually has ovarian cancer. Since the test has a 0% rate of false negatives, all the women with ovarian cancer will test positive.
The test also has a 5% rate of false positives. This means that out of the remaining 99,960 women who do not have ovarian cancer, approximately 5% (or 4,998) will test positive incorrectly.
Therefore, out of a total of 5,038 positive test results (40 true positives + 4,998 false positives), only 40 are true positives for ovarian cancer. The probability that a woman who tests positive actually has ovarian cancer can be calculated as the ratio of true positives to the total positive tests:
Probability = (True Positives) / (Total Positive Tests) = 40 / 5,038 ≈ 0.00795 ≈ 0.795%
Thus, the probability that a woman over 35 actually has ovarian cancer given a positive test result is approximately 1.96%. This calculation highlights the importance of considering both the prevalence of the disease and the accuracy of the test in interpreting the results correctly.
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PLS ANSWER BRAINLIST AND A THANK YOU WILL BE GIVEN!!!!
Answers
Answer:
\(\huge\boxed{Option \ D}\)
Step-by-step explanation:
4x + 5x = 180 [They are angles on a "straight" line so they will add up to 180 degrees)
Answer:
D
Step-by-step explanation:
The sum of angles that are formed on a straight line is 180.
4x + 5x = 180
I NEED HELP ON 11 PLEASE
Answers
Answer:
1579.5
Step-by-step explanation:
i think ...
81 x 39 =3159 / 2 (because there are 2 sides )=1579.5
x + 6 = -6
please help me pls
Answers
explanation...
−
6
=
6
−
6
+
6
=
6
+
6
add both sides to the equation
and then simplify
Does x equal to -670
Answers
Answer:
i think its no to my best ability
Step-by-step explanation:
A rectangle has a perimeter of 80 cm and its length is 1 cm more than twice its width. Find the dimensions of a rectangle given that its perimeter is 80 cm and its length is 1 cm more than twice its width. Set up your solution using the variables L for the length, W for the width, and P for the perimeter. Part a: Using the definition of the perimeter, write an equation for P in terms of L and W. Part b: Using the relationship given in the problem statement, write an equation for L in terms of W. Solve the equations from parts a and b. Part c: The length is ? Cm. Part d: The width is? Cm.
Answers
Answer: (a) P = 6W + 2
(b) L = 2W + 1
(c) Width = 13cm
Length = 27cm
Step-by-step explanation:
The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:
L = (2 × W) + 1
(b) L = 2W + 1
Therefore, P = 2(L + W)
P = 2( 2W + 1) + 2W
P = 4W + 2 + 2W
(a) P = 6W + 2
Since perimeter is given as 80cm. Therefore,
P = 6W + 2
6W + 2 = 80
6W = 80 - 2
6W = 78
W = 78/6
W = 13
Width is 13cm
Length = 2W + 1
Length = 2(13) + 1
Length = 27cm
The width of the rectangle is 13cm and the length is 27cm.
Description of a rectangleA rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.
The formula for determining the perimeter of a rectangle = 2x (length + width)
P = 2(L + W)
Perimeter = 80 length = 1 + 2w Width = w Determining the values of width and length80 = 2(1 + 2w + w)
80 = 2(1 + 3w)
40 = 1 + 3w
40 - 1 = 3w
39 = 3w
w = 13cm
Length = 1 + 2(13) = 27cm
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here are 5 airplanes ready to depart. runway a and runway d are available. how many ways can 2 planes be assigned to runways without using the same runway?
Answers
Hence, the number of ways be assigned to runways without using the same runway is \(240\) ways.
What is the permutation?
The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.
Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged.
Here given that,
Here are five airplanes ready to depart. runway \(A\) and runway \(D\) are available.
Number of ways to assign \(3\) planes to that runway is
\(^5C_3=^5C_2=10ways\)
Then for each group
Each group of three planes can be arranged in \(^3P_3=3!=6ways\)
Each group of three planes can be arranged in \(^2P_2=2!=2ways\)
So total number of arrangements are
\((2)(10)(6)(2)=240ways\)
Hence, the number of ways be assigned to runways without using the same runway is \(240\) ways.
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Find the future value of the following ordinary simple annuity. The future value is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
Answers
The future value of an ordinary simple annuity depends on the amount of the annuity payments, the interest rate, and the length of the annuity. By using the future value of an ordinary simple annuity formula, we can calculate the future value of the annuity.
To calculate the future value of an ordinary simple annuity, we use the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity,
P is the amount of each annuity payment,
r is the interest rate per period, and
n is the number of periods.
By plugging in the given values into the formula, we can find the future value. Make sure to convert the interest rate and number of periods to match the same time units (e.g., annual interest rate and number of years).
For example, if we have an annuity with $1,000 monthly payments, an annual interest rate of 5%, and a term of 10 years, we would calculate the future value as follows:
P = $1,000
r = 0.05 (5% annual interest rate divided by 12 to match the monthly payments)
n = 10 (number of years multiplied by 12 to match the monthly payments)
Using the formula, we find:
FV = $1,000 * [(1 + 0.05/12)^(10*12) - 1] / (0.05/12)
Calculating this expression would give us the future value of the annuity. Remember to round the final answer to the nearest cent as needed and round all intermediate values to six decimal places.
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if B is the midpoint of AC, and AC = 8x-20, find BC
3X-1
Answers
3(9)-1= 26
Solving steps for x:
Write the equation of the line (in slope-intercept form) that has an x-intercept at -6 and a y-intercept at 2. Provide a rough sketch of the line indicating the given points. [1 mark]. Exercise 2. For the polynomial f(x) = −3x² + 6x, determine the following: (A) State the degree and leading coefficient and use it to determine the graph's end behavior. [2 marks]. (B) State the zeros. [2 marks]. (C) State the x- and y-intercepts as points [3 marks]. (C) Determine algebraically whether the polynomial is even, odd, or neither.
Answers
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.
For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.
To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.
The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
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There are 20 chocolates in a box.
Some of the chocolates contain nuts and the rest do not.
The probability that a chocolate containing nuts is picked at random from the
box is 0.6
How many of the chocolates in the box contain nuts?
Answers
Answer:
12 nutted chocolates
Step-by-step explanation:
0.6 is equal to 60% and 60% 0f 20 is 12.
Simplify: \(\frac{32a^2bc^3}{20abc}\)
Answers
The fractions is simplified to 8ac²/ 5
What is a fraction?A fraction can be described as the part of a whole element, number or variable.
There are different types of fractions, which includes;
Improper fractionsProper fractionsMixed fractionsComplex fractionsSimple fractionsExamples of improper fractions; 5/3, 7/5
Examples of proper fractions; 3/4, 5/6
Examples of mixed fractions; 3 1/2, 4 5/6
Examples of simple fractions; 1/2 , 1/ 4
From the information given, we have that;
\(\frac{32a^2bc^3}{20abc}\)
This is simplified to;
32 × a × a × b × c × c × c/ 20 × a × b × c
Divide the common terms
8ac²/ 5
Hence, the fractions is 8ac²/ 5
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Simplify the following expression.
3(4x + 5) + 2x – 6
Answers
Answer:
14x +9
Step-by-step explanation:
3(4x + 5) + 2x – 6
Distribute
12x +15 +2x - 6
Combine like terms
14x +9
help me plz i have 5 more
Answers
Answer:
1343
Step-by-step explanation:
1/2+3/4+4/5 how to solve it please help me i'm waiting
Answers
Answer:
41/20
Step-by-step explanation:
or 2 1/20
Construct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
Answers
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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A car rental agency charges $15 a day for driving a car 200 miles or less. If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven. Which of the following functions represents the cost to drive a car from this agency miles x a day?
Answers
The function which represents the cost to drive a car from this agency miles x a day is :
C(x) = 15, if 0 ≤ x ≤ 200
= 15 + 0.05x, if x > 200
Given that,
A car rental agency charges $15 a day for driving a car 200 miles or less.
The function can be written as,
C(x) = 15 if 0 ≤ x ≤ 200
If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.
C(x) = 15 + 0.05x, if x > 200
Hence the correct option is D.
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Which is the best definition of iteration?.
Iteration is the process of solving for the value of z0.
Iteration is the process of repeating an operation by using the output of the previous operation as the input for the next operation.
Iteration is the process of solving a function using algebraic methods to determine the value of the unknown.
Iteration is the process of using a recursive function to find an initial value.
Answers
The best definition of the iteration concept is given as follows:
Iteration is the process of repeating an operation by using the output of the previous operation as the input for the next operation.
What is the iteration concept?Iteration of a function is the process of repeatedly applying the function to its own output, using the result of each iteration as the input for the next. In other words, it is the process of taking a number or value, feeding it into a function, and then taking the output and feeding it back into the function repeatedly.
Hence the correct statement in the context of this problem is given by the second option.
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PLEASE HELP!!!!!!!!!!!!!!!
Answers
Answer:
27.6%
Step-by-step explanation:
See the attached worksheet. Find the total number of marbles (29) and then take the green marbles and divide by the total and multiply by 100%. (8/29)*(100%) = 27.6% to the nearest tenth.
78 fifth graders are going on a field trip to the zoo. If each school bus seats 35 students how many buses will be needed?
Will there be extra seats for parents and teachers? If so, how many extra seats?
Answers
Answer:
You will need 3 buses and you will not have any seats left.
find two numbers that multiply to -81 but add to 0
Answers
Answer:
9 and -9
Step-by-step explanation:
9*-9=-81
9+(-9)=0
Answer:
-9 and 9 are the two numbers that you can multiply to get -81 and add to get 0
Step-by-step explanation:
-9 × 9 = -81
-9 + 9 = 0
Hope this helps can you mark my answer as brainliest please?
Air is being pumped into a spherical balloon at the rate of 7 cm³/sec. What is the rate of change of the radius at the instant the volume equals 36n cm³ ? The volume of the sphere 47 [7] of radius r is ³.
Answers
the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.
The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.
We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)
7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³
36 = (4/3)r³
27 = r³
r = 3 Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)
(dr/dt) = 7 / (4π(9))
(dr/dt) = 7 / (36π)
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what times what equals 26,838
Answers
The answer is 200 times 104.19 is 26838
Find the value of x. (2x +4)° 2x-9)°
Answers
Answer: x=3
Step-by-step explanation: 2x +4)° 2x-9)°= 4x 2 +8x−9=3
Pull out like factors :
2x + 4 = 2 • (x + 2) (4 • (x + 2) • x) - 9
4x • (x + 2) - 9
Factoring 4x2+8x-9
The first term is, 4x2 its coefficient is 4 .
The middle term is, +8x its coefficient is 8 .
The last term, "the constant", is -9
Step-1 : Multiply the coefficient of the first term by the constant 4 • -9 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is 8 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5
-6 + 6 = 0
-4 + 9 = 5
-3 + 12 = 9
-2 + 18 = 16
-1 + 36 = 35
x=3
The value of x for the given triangle is 37°.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
The sum of all interior angles of a triangle is 180°.
So,
x + 2x +4 + 2x-9 = 180°
5x - 5 = 180°
x = 37°
Hence "The value of x for the given triangle is 37°".
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Given question is missing an image attached below;
How is speed similar to solving for time?
Answers
To get the speed of something you would have to sole for s=d/t (speed equals distance over time)
cindy bought 7 dresses for $28 each and 2 pairs of shoes for $28 each. she used this expression to calculate the total amount she spent.(7x28) (2x28)what is another expression to calculate the total amount spent?
Answers
Another expression to calculate the total amount spent would be (7+2) x 28.
This expression uses the distributive property, which states that when multiplying a number by a sum, the number can be multiplied by each addend separately and then the results can be added together.
In this case, we are multiplying 28 (the cost of the dresses and shoes) by the sum of 7 (the number of dresses bought) and 2 (the number of shoes bought). This would be the same as (7x28) + (2x28), which is the same as (7x28) (2x28). Therefore, the total amount Cindy spent is (7+2) x 28, which is equal to $392.
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Which of the following expressions is equivalent to 3m(m - 2) - (m^2 + 1)
A. 2m^2 - 1
B. 4m^2 - 1
C. 4m^2 - 6m + 1
D. 2m^2 - 6m - 1