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Determine the intervals where the value of f(x) is negative, when
f(x) = (x + 7)(2x - 3)(x - 5). Choose all that apply.
a. -∞ < x < -7
b. -7 < x < 3/2
c. 3/2 < x < 5
d. 5 < x < ∞
Answers
9514 1404 393
Answer:
a, c
Step-by-step explanation:
There are 3 linear factors, so the function is odd degree (cubic). The coefficients of x are all positive, so the function has the general shape of an increasing function, left-to-right. The three linear factors mean that the curve crosses the x-axis 3 times, changing sign each time.
The x-intercepts are the values of x that make the factors zero: -7, 3/2, 5. The shape of the function tells you it will be negative for x < -7. Between -7 and 3/2, it will be positive, since it changes sign at x=-7. It changes sign again at x=3/2, so will be negative for 3/2 < x < 5.
In short, the function will be negative at any point that has an odd number of function zeros to its right (taking multiplicity into account).
The function is negative on intervals (a) and (c).
Related Questions
What is the product of the rational expressions shown below? Make sure your
answer is in reduced form. X+1/x-4 • 5x/x+1?
Answers
Answer:
5x / (x - 4)
Step-by-step explanation:
(x + 1)/(x - 4) • 5x/(x + 1)
Method 1:
Cancel out x + 1
Leaving 5x/(x - 4)
Method 2:
(x + 1)/(x - 4) • 5x/(x + 1)
Multiply numerator and denominator separately
= 5x(x + 1) / (x - 4)(x + 1)
Cancel out (x + 1) in the numerator and (x + 1) in the denominator
= 5x / (x - 4)
Therefore,
(x + 1)/(x - 4) • 5x/(x + 1) = 5x / (x - 4)
PLEASE HELP ASAP!!!
Describe the graph of the function g by transformations of the base function f.
(Graph and Answers pictured!)
Answers
Answer:
Option (3)
Step-by-step explanation:
Base function in the graph is 'f' and the transformed form of the function 'f' is function 'g'.
Since, the base function 'f' is reflected across the x-axis,
h(x) = -f(x)
Followed by the translation by 3 units downwards,
g(x) = h(x) - 3
= -f(x) - 3
Therefore, function in the form of g(x) = -f(x) - 3 will be the answer.
Option (3) is the correct option.
Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a survey, the favorite sports of respondents are identified as 1 for basketball, 2 for baseball, 3 for football, and 4 for anything else. The average (mean) is calculated for 517 respondents and the result is 1.5.
Answers
Answer:
(a) Nominal data
(b) Calculating the mean is wrong
Step-by-step explanation:
Given
[tex]1 \to[/tex] Basketball
[tex]2 \to[/tex] Baseball
[tex]3 \to[/tex] Football
[tex]4 \to[/tex] Others
Solving (a): The level of measurement
In the given parameters, digit 1 to 4 are used to label each of the given sport.
When such labels are used, the type of data is nominal.
Solving (b): The error
In (a), we identified that the level of measurement is nominal. This implies that, the data are not counted, but instead they are categorized.
And as such, the mean of the data cannot be calculated.
Each time Caroline goes shopping she decides whether or not to buy fruit.
The probability that she does buy fruit is 0.7.
Independently, she then decides whether or not to buy a CD, with a probability of 0.6 that she does buy a CD.
Work out the probability that she buys fruit or buys a CD or both.
Answers
The probability that she buys fruit or buys a CD is 1.3.
The probability that she buys fruit and buys a CD is 0.42.
What are the probabilities?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that she buys fruit or buys a CD = 0.7 + 0.6 = 1.3
The probability that she buys fruit and buys a CD = 0.7 X 0.6 = 0.42
To learn more about probability, please check: https://brainly.com/question/13234031
#SPJ1
A true false test contains 24 questions. In how many different ways can this test be completed. (Assume we
don't care about our scores.)
Answers
Answer:
The total number of ways to give the answer of the question is 16777216.
Step-by-step explanation:
Total number of questions = 24
The number of possibilities so that the answer is given is only 2. It is either true or false.
So, the total number of ways to complete the test is
[tex]2^{24} = 16777216[/tex]
factor x^2-8x-48 completely
Answers
Answer: (X-12)(x+4)
The middle number is -8 and the last number is -48.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -8
Multiply together to get -48
Can you think of the two numbers?
Try 4 and -12:
4+-12 = -8
4*-12 = -48
Fill in the blanks in
(x+_)(x+_)
with 4 and -12 to get...
(x+4)(x-12)
Answer:
(x+4)(x−12)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { (x - 12)(x + 4 )}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] {x}^{2} - 8x - 48[/tex]
[tex] = {x}^{2} + 4x - 12x - 48[/tex]
Taking [tex]x[/tex] as common from first two terms and [tex]12[/tex] from last two terms, we have
[tex] = x \: (x + 4) - 12 \: (x + 4)[/tex]
Taking the factor [tex](x+4)[/tex] as common,
[tex] = (x - 12)(x + 4)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
On a
paper, graph y < -2x Then determine which answer matches
the graph you drew.
Answers
Answer:
theres the graph
Step-by-step explanation:
х
f(x)
What is the initial value of the exponential function
represented by the table?
-2
1
8
e
8
-1
1
4
0
1
2
1
1
1
2
2
2
Answers
Answer:
the answer will be table -1
Step-by-step explanation:
What is the answer to number 5?
Answers
Answer:
Add 6 to the x-axis and 3 to the y-axis.
Step-by-step explanation:
Right and left are x-axis, and up and down are y-axis.
If 5(y-2) - 3(y + 4) = 0, then y
IS
A. -1
B. 3
C. 7
D. 11
Answers
Answer:
Y is -1.
Step-by-step explanation:
If you substitute the values, you find that that's the correct answer.
Which of the following will have 6 at unit place? a.19² b.11² c.24² d.13²
Answers
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26. What is
the solution set of this problem?
0 (-0, -21)
O (-0, -21]
o [-21, +00)
O (21, +00)
Answers
Answer:
5 × (x + 27) ≥ 6 × (x + 26).
Step-by-step explanation:
The solution set of " Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26" is (-∞, -21]
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
For this case, let the number in consideration be 'x', then according to the condition specified, we get:
The sum of a number and 27 = x+27Five times the sum of a number and 27 = [tex]5(x+27)[/tex]The sum of that number and 26 = x + 26Six times the sum of that number and 26 = [tex]6(x+26)[/tex]Also, we get:
Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26 as:
[tex]5(x+27) \geq 6(x+26)[/tex]
Expanding and taking x on one side:
[tex]5x+135 \geq 6x+156\\135-156 \geq x \\\\x \leq -21[/tex]
Thus, the considered statement is true for all the numbers which is smaller or equal to -21. Symbolically, the solution set is: (-∞, -21]
The square bracket shows that the -21 is included in the interval. And the interval (-∞, -21] is set of all real numbers smaller or equal to -21.
Thus, the solution set of " Five times the sum of a number and 27 is greater than or equal to six times the sum of that number and 26" is (-∞, -21]
Learn more about inequalities here:
https://brainly.com/question/27425770
3. What shape is a prism?
Answers
Answer:rectangular
Step-by-step explanation:
Answer:
TRIANGULAR
Step-by-step explanation:
A prism is a triangular-shaped piece of glass. The white light that reaches the prism contains all of the colors of the visible spectrum even though you can’t see them. As the white light passes through the edge or boundary of the prism, the light waves refract. Each of the different wavelengths contained in the white light refracts differently and results in a different color. The white light is broken up by the prism into all the colors of rainbow. The longest wavelength bends (refracts) the least and is red. The shortest wavelength bends the most and is violet.
please help. question in picture
Answers
Answer:
Step-by-step explanation:
c+12<16
what will be the answer
Answers
Answer:
[tex]c < 4[/tex]
Step-by-step explanation:
Move the constant to the right-hand side and change its signs:
[tex]c < 16 - 12[/tex]
Subtract the numbers:
[tex]c < 16 - 12 = c < 4[/tex]
find the equation of line parallel to y=-2x+1 and passing through the point (2,4)
Answers
Answer:
[tex]y=-2x+8[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slopes1) Determine the slope (m)
[tex]y=-2x+1[/tex]
The given line has a slope of -2. Because parallel lines always have equal slopes, we know that the line parallel to this would also have a slope of -2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-2x+b[/tex]
Plug in the given point (2,4) to solve for b
[tex]4=-2(2)+b\\4=-4+b[/tex]
Add 4 to both sides to isolate b
[tex]4+4=-4+b+4\\8=b[/tex]
Therefore, the y-intercept of the line is 8. Plug this back into [tex]y=-2x+b[/tex]:
[tex]y=-2x+8[/tex]
I hope this helps!
What is the mean absolute deviation of Warren’s data?
Warren's Scores Absolute Deviation from Mean Score – individual score
0
25
15
10
20
30
10
15
5
25
20
15
20
5
10
sum of absolute deviations =
Answers
Answer:
6.667
Step-by-step explanation:
I just did the calculations
Find the area of the composite area
Answers
Area of triangle = bxh/2 = 7x7/2= 24.5
Total area= 91+24.5= 115.5 in^2
In a recent year, 31.6% of all registered doctors were female. If there were 53,000 female registered doctors that year, what was the total number of registered doctors?
Answers
Answer:
The total number of registered doctors was 167,722.
Step-by-step explanation:
Total number of doctors:
The total number of doctors is given by x.
31.6% of all registered doctors were female. 53,000 female doctors.
This means that:
[tex]0.316x = 53000[/tex]
What was the total number of registered doctors?
We have to solve the above equation for x. So
[tex]x = \frac{53000}{0.316}[/tex]
[tex]x = 167722[/tex]
The total number of registered doctors was 167,722.
Please answer me the question and find the graph and question number 2 find the area of the surface
Answers
hi pls help me now i'll gibe you brainest,thank you
Answers
Answer:
64 cm^3
Step-by-step explanation:
answer for question no 5
length , breadth and height of the cube are always equal .So
here length = 4 cm
volume of a cube = l^3
=4^3
=64 m^2
Use the limit definition of the derivative to find the instantaneous rate of change of
f(x)=5x^2+3x+3 at x=4
Answers
[tex]f'(4) = 43[/tex]
Explanation:
Given: [tex]f(x)=5x^2 + 3x + 3[/tex]
[tex]\displaystyle f'(x)= \lim_{h \to 0} \dfrac{f(x+h) - f(x)}{h}[/tex]
Note that
[tex]f(x+h) = 5(x+h)^2 + 3(x+h) + 3[/tex]
[tex]\:\:\;\:\:\:\:= 5(x^2 + 2hx + h^2) + 3x + 3h +3[/tex]
[tex]\:\:\;\:\:\:\:= 5x^2 + 10hx + 5h^2 + 3x + 3h +3[/tex]
Substituting the above equation into the expression for f'(x), we can then write f'(x) as
[tex]\displaystyle f'(x) = \lim_{h \to 0} \dfrac{10hx + 3h + 5h^2}{h}[/tex]
[tex]\displaystyle\:\:\;\:\:\:\:= \lim_{h \to 0} (10x +3 +5h)[/tex]
[tex]\:\:\;\:\:\:\:= 10x + 3[/tex]
Therefore,
[tex]f'(4) = 10(4) + 3 = 43[/tex]
Which phrases can be represented by the algebraic expression 2x + 1? Check all that apply.
two times a number plus 1
a number plus 2
twice a number and one
two more than a number and one
twice the product of a number added to 1
Answers
Two times a number plus 1
Twice a number and one
Answer the following questions using what you've learned from this unit. Write your
answers in the space provided. Be sure to show all work.
CLASSIFY and MEASURE TRIANGLES
1. Find angle measures and use angles to classify triangles.
Part I: Find the missing angle measure in each triangle. Show your work.
(3 points, 1 point each)
AAN
50"
В
A
mC
m B
mA
Answers
Answer:
50"
В
A
mC
m B
mA
Step-by-step explanation:
Write down in terms of n, an expression for the nth term
of the following sequences:
a) 6 2 -2 -6 -10
b) -8 -15 -22 -29 -36
Answers
Answer:
[tex]{ \bf{(a).}} \\ { \tt{ {n}^{th} = a + (n - 1)d }} \\ { \tt{ {n}^{th} = 6 + (n - 1) \times - 4 }} \\ {n}^{th} = 10 - 4n \\ \\ { \bf{(b).}} \\ { \tt{ {n}^{th} = - 8 + (n- 1) \times - 7 }} \\ { \tt{ {n}^{th} = -1 - 7n}}[/tex]
Complete each congruency statement and name the rule used. If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "Cannot be determined" in place of the rule. ∆ARE ≅ ∆_____ by _____
Answers
Answer:
add a picture so i can see .
Step-by-step explanation:
13 multiplied by the sum of 4 and11. Now reverse the result and add it to the earliest result and then multiplied it by 13
Answers
Step-by-step explanation:
I am not critically certain but the ways you have jotted down your enquiry..
I assume is13 × (4×11)
13 × 44
=572 - 44= 528
528+13 =541
541 ×13=7033
I am not sure how to approach this problem or where to start? How would I be able to solve this problem?
Answers
Answer:
5.7
Step-by-step explanation:
We can use a proportion to solve the problem:
24 : 100 = 1.37 : x
x = (100 * 1.37)/24 = 137/24 = 5.7
Julie borrowed 3500 for 3years at a seven and a half simple interest rate how much interest rate is that
Answers
Answer:
787.50
Step-by-step explanation:
interest=3500*7.5*3/100
interest=35*7.5*3
interest=787.50
The answer I got for this problem was 10.8 (multiplied 18 and 60 then divided by 100) however, it stated that my answer is incorrect. Did I not round correctly or is my entire answer wrong?
Answers
9514 1404 393
Answer:
30 mL
Step-by-step explanation:
The meaning of 60% solution is ...
alcohol/(total volume) = 0.60
You are told the amount of alcohol is 18 mL, so you have ...
(18 mL)/(total volume) = 0.60
Multiplying by total volume gives ...
18 mL = 0.60 × (total volume)
Then dividing by 0.60, you have ...
(18 mL)/0.60 = total volume = 30 mL
_____
Additional comment
You need to apply what you know about the real world to consider whether your answer makes any sense. If alcohol is a little more than half of the volume, and the amount of alcohol is 18 mL, then the total volume cannot be less than 18 mL. In fact, you expect it to be not quite double 18 mL.
An answer of 10.8 mL makes no sense in this context. You cannot have less total solution than you have of something that makes up a part of the total solution.