The domain and the range of the function is (d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}
The complete questionWhat are the domain and range of the function f(x) = x^2 + 8x + 7/x + 1
The domain of the functionWe have the function to be
[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]
Set the denominator to 0
x + 1 = 0
Solve for x
x = -1
This means that the domain of the function is the set of all real numbers except -1
Hence, the domain of the function is {x ∊ ℝ | x ≠ -1}
The range of the functionWe have the function to be
[tex]f(x) = \frac{x^2 + 8x + 7}{x + 1}[/tex]
Factorize the numerator
[tex]f(x) = \frac{(x + 1)(x + 7)}{x + 1}[/tex]
Simplify
f(x) = x + 7
The function is undefined at x= -1.
So, we have:
f(-1) = -1 + 7
f(-1) = 6
This means that the range of the function is the set of all real numbers except 6
Hence, the range of the function is {y ∊ ℝ | y ≠ 6}
Read more about domain and range at:
https://brainly.com/question/10197594
#SPJ1
Answer:
It is d) D: {x ∊ ℝ | x ≠ -1}; R: {y ∊ ℝ | y ≠ 6}
Step-by-step explanation:
I took the test
What is the solution to the linear equation?
-12 +3b-1-5-b
b=-2
b = -1.5
b = 1.5
b = 2
Answer:
[tex]b = 2[/tex]
Step-by-step explanation:
[tex]( - 12 - 1 - 5) + (3b - b) \\ - 18 + 2b \\ 2b - 18 \\ b = 2[/tex]
Inside the box of every cereal box contains a surprise gift. The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring and inside the other 30 boxes on the shelf contain a different gift. If two cereal boxes are randomly selected from the shelf to purchase, what is the probability that both of them have the secret decoder ring? (Give answer as a decimal correct to least three decimal places.)
The probability that both of them have the secret decoder ring will be 0.1356.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
Inside the box of every cereal box contains a surprise gift.
The store manager assures employees that 18 of the 48 boxes on the shelf have a secret decoder ring.
And inside the other 30 boxes on the shelf contain a different gift.
If two cereal boxes are randomly selected from the shelf to purchase.
Then the probability that both of them have the secret decoder ring will be
The total events will be
Total event = ⁴⁸C₂
Total event = 1128
The favorable events will be
Favorable event = ¹⁸C₂
Favorable event = 153
Then the probability will be
P = 153 / 1128
P = 0.1356
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ1
HELPPP!!! can someone turn 3x−2=13 into a WORD problem. (i already know answer)
The tables represent the functions f(x) and g(x).
Which input value produces the same output value for the two functions?
x = –12
x = –9
x = –6
x = –3
A function assigns the values. The correct option is C, x=-6.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A.) When the value of x is -12,
f(-12) = 2/3(-12) + 7 = -1
g(-12) = 2(-12) + 15 = -9
B.) When the value of x is -9,
f(-9) = 2/3(-9) + 7 = 1
g(-9) = 2(-9) + 15 = -3
C.) When the value of x is -6,
f(-6) = 2/3(-6) + 7 = 3
g(-6) = 2(-6) + 15 = 3
D.) When the value of x is -3,
f(-9) = 2/3(-3) + 7 = 5
g(-9) = 2(-2) + 15 = 11
Hence, the correct option is C, x=-6.
Learn more about Function:
https://brainly.com/question/5245372
#SPJ1
Which of the following graphs shows the solution set for the inequality below?
|x + 2| + 7 > 10
Work Shown:
|x+2| + 7 > 10
|x+2| > 10-7
|x+2| > 3
x+2 > 3 or x+2 < -3
x > 3-2 or x < -3-2
x > 1 or x < -5
The graph for x > 1 has an open circle at 1 and shading to the right.
The graph for x < -5 has an open circle at -5 and shading to the left
Both of these facts combine to describe Choice C
In other words, we have open circles at -5 and 1, with nearly everything shaded except for the region between the open circles.
The open circles are used to exclude those x values mentioned.
Find the equation of a line that contains the points (−2,−4) and (−5,4). Write the equation in slope-intercept form, using fractions when required.
The equation would be y+ 3/8x+9/4.
Lets try to explain in the further steps to calculate the equation,
Slope formula: (y₂ - y₁) / (x₂ - x₁)
First, plug in these values of the two given points.
[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]
Slope = -3/8
To find the equation of the line, (y- y1) = m* (x-x1)
So by putting the values into the above equation we get,
[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]
Hence the equation is [tex]y+ 3/8x+9/4.[/tex]
Learn more about slope intercept equations on:
https://brainly.com/question/1884491
#SPJ10
The accompanying frequency distribution represents the square footage of a random sample of 500 houses that are owner occupied year round. Approximate the mean and standard deviation square footage.
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
The mean and the standard deviation are 233 and 208.95 respectively.
The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.
First, we calculate the class midpoint (x) from the given intervals.
The class midpoint is the average of the intervals. So, we have:
X1 = (0+199)/2 = 99.5
X2 = (200+399)/2 = 299.5
X3 = (400+599)/2 = 499.5
X4 = (600+799)/2 = 699.5
X5 = (800+999)/2 = 899.5
X6 = (1000+1199)/2 = 1099.5
X7 = (1200+1399)/2 = 1299.5
So, the table becomes:
X values Frequency (f)
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean of the distribution is:
This gives:
Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)
Mean = 124832.5/535 = 233
Therefore, Mean = 233
The standard deviation is calculated as follows:
So, we have:
Б =
√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)
Standard Deviation = √(23357155.5)/535
= √43658.23
= 208.95
Б = 208.95
Hence, the mean and the standard deviation are 233 and 208.95 respectively.
Read more about mean and standard deviation at: https://brainly.com/question/14451674
#SPJ10
Help! I need help with this math problem
Answer:
h(-1) is -1, h(-0.5) is 0 and h(1) is 1.
Step-by-step explanation:
functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.
h(-1)In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.
h(-0.5)In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.
h(1)In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.
Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.
know more about functions at brainly.com/question/15912209
#SPJ10
Alex Meir recently won a lottery and has the option of receiving one of the following three prizes: (1) $90,000 cash immediately, (2) $35,000 cash immediately and a six-period annuity of $9,400 beginning one year from today, or (3) a six-period annuity of $17,700 beginning one year from today. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)
1. Assuming an interest rate of 5%, determine the present value for the above options. Which option should Alex choose?
2. The Weimer Corporation wants to accumulate a sum of money to repay certain debts due on December 31, 2030. Weimer will make annual deposits of $180,000 into a special bank account at the end of each of 10 years beginning December 31, 2021. Assuming that the bank account pays 6% interest compounded annually, what will be the fund balance after the last payment is made on December 31, 2030?
Based on the annuities calculated, he should choose option 1.
How to calculate the annuities?Present value = $35,000 + (Annuity amount * Present value of an ordinary annuity of $1)
= $35,000 + ($9,400 * (5%,6))
= $35,000 + ($9,400 * 5.07569)
= $35,000 + 47,711
= $82,711
Present value = (Annuity amount * Present value of an ordinary annuity of $1)
= $17,700 * (5%,6)
= $17,700 * 5.07569
= $89,840
Alex should choose Option 1
Future value annuity = Annuity amount * Future value of an ordinary annuity of $1
= $180,000 * (6%,10)
= $180,000 * 13.1808
= $2,372,544
Learn more about annuity on:
https://brainly.com/question/5303391
#SPJ1
How do I solve this problem? The green dots can be moved
Answer :
Points at (1, 3) and (3, 3) and (2, 1)
Explanation:
The original graph (dashed) is an absolute value function meaning f(x) = |x|
Given: y = 2f(x - 2) + 1
f(x - 2) means you plug in x - 2 for x in f(x) function
the new graph equation is: y = 2|x - 2| + 1
The graph will shift up 1 because +1The graph will shift right because -2The graph has a scale factor of 2The graph is V shaped because it is an absolute value graphLearn more about Absolute Value here: https://brainly.com/question/729268
Visual:
Jacob invests a sum of money in a savings account with an interest rate of 9% compounded
continuously. After 6 years, the balance reaches $11,303.34. What was the amount of the initial
investment?
Answer:
6587
Step-by-step explanation:
Formula is
A= P(1+r/n)^nt
A = 11303.34
r = .09
n = 365 compounded daily
t = 6 years
solve for P
A sphere has a radius of 24 centimeters. What is its volume
Answer:
57905.8
Step-by-step explanation:
Use the formula:Plug in:
V = 4/3 * 24³π
= 4/3 * 13824π
= 18432π
= 57905.83579cm³
Rounded to nearest tenth:
57905.8
Answer: 18,432
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
What mistake did he make ?! I need everybody Anwser
Answer:
he subtracted the wrong coordinates to find the horizontal leg
Step-by-step explanation:
It should be 4-(-3) but he labeled 4-(-1)
what is the area of a triangle (-4,-5),(3,-3),(3,-7)?
i will give brainliest please help quick
The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.
What is the area of the triangle?The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).
Then the area of the triangle will be
Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|
We have
(x₁, y₁) ⇒ (-4, -5)
(x₂, y₂) ⇒ (3, -3)
(x₃, y₃) ⇒ (3, -7)
Then the area will be
Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]
Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]
Area = 1/2[-18 + 4]
Area = 1/2 × 14
Area = 7 square units
More about the area of the triangle link is given below.
https://brainly.com/question/16653962
#SPJ1
If a person is chosen at random in this survey, what is the P(decaf or sugar)?
HELP PLS!
The value of the probability P(decaf or sugar) is 0.41
How to determine the probability?From the table, we have:
P(decaf) = 0.05 + 0.08 + 0.09 = 0.22
P(sugar) = 0.19 + 0.08 = 0.27
P(decaf and sugar) = 0.08
The required probability is:
P = P(decaf) + P(sugar) - P(decaf and sugar)
This gives
P = 0.22 + 0.27 - 0.08
Evaluate
P = 0.41
Hence, the value of the probability P(decaf or sugar) is 0.41
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
Help please I need it asap and thank you
Answer: 2.5
Step-by-step explanation:
The altitude of an equilateral (or isosceles) triangle bisects the side to which it is drawn.
Ms. Mather filled 8 3/4 gallons of gas in her car's fuel tank. The car used up 3 1/2 gallons when she visited a friend in a neighboring town. How many gallons of gas are left in Ms. Mather's fuel tank?
Answer: [tex]5\frac{1}{4}[/tex] gallons are left
Step-by-step explanation:
convert to mixed number...
[tex]8\frac{3}{4} = \frac{35}{4}[/tex]
[tex]3 \frac{1}{2} = \frac{7}{2}[/tex] or [tex]\frac{14}{4}[/tex]
[tex]\frac{35}{4} -\frac{14}{4}=\frac{21}{4}[/tex]
[tex]\frac{21}{4} =5\frac{1}{4}[/tex]
therefore, [tex]5\frac{1}{4}[/tex] gallons are left in Ms. Mather's fuel tank
Answer:
5 1/4 gallons are left... correct
let p be the perimeter of a rectangle, and let one side of the rectangle be x
PLEASE SHOW WORK
That is the length in terms of p and x.
L = p/2 - x
How to get the length of the other side in terms of x and p?
For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W).
Here we know that the perimeter is p, so P = p, and let's say that the width is x.
Then we can write:
p = 2*(L + x)
Solving for L:
L = p/2 - x
That is the length in terms of p and x.
If you want to learn more about rectangles:
https://brainly.com/question/17297081
#SPJ1
Difficult one. Need help with work shown.
Answer:
the length of the fence = 420 ft
The total area = 8000 ft²
Step-by-step explanation:
the fence has the same length as the perimeter of the rectangle
then
the length of the fence = 2×(160+50) = 420 ft
………………………………………………………………
The total area enclosed by the fencing = the area of the rectangle
Then
The total area = 160×50 = 8000 ft²
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) of a rectangle is calculated as
P = 2(length + width)
= 2(160 + 50)
= 2 × 210
= 420 ft ← amount of fencing needed
the area (A) of a rectangle is calculated as
A = length × width = 160 × 50 = 8000 ft²
which of the following are characteristics of the graph of the square root parent function
Answer:
C
Step-by-step explanation:
A Ferris wheel at an amusement park is modeled by (x – 100)2 + (y – 75)2 = 4,900, where the measurements are in feet. A slingshot attraction is modeled by y = –3x2 + 48x – 30. Which attraction reaches a greater height, and what does it represent in terms of the context?
The attraction that reaches a greater height and what it represent in terms of the context is:
The slingshot reaches a greater height at 162 ft, which is the vertex of the parabola.The Ferris wheel reaches a greater height at 145 ft, which is the highest point on the circle.HeightFerris wheel
(x – 100)2 + (y – 75)2 = 4,900
y max= 75+70
y max=145 ft
Sling shot
y = –3x² + 48x – 30
dy/dx=-6+48=0
x=48/6
x=8
Hence:
y max = –3(8)² + 48(8) – 30
y max = –3×64+48(8)-30
y max = –192+384-30
y max =162 ft
Therefore slingshot reaches a greater height at 162 ft and Ferris wheel reaches a greater height at 145 ft.
Learn more about height here:https://brainly.com/question/1739912
#SPJ1
Shawn is collecting money from students at his school for a charity. The table gives the ratios of the number of students who have donated and the amount of money he has collected from them. Complete the table to form equivalent ratios.
In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.
The missing table is given below.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Shawn is collecting money from students at his school for a charity.
The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.
Since 30 is 1/3 of 90, we know the ratio is 1:3.
In order of blank boxes going from left to right then down
1, 9, 5, 75, 35
The complete table is attached below.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ1
In a study designed to examine the association of breakfast intake and body mass index (BMI), the National Heart, Lung, and Blood Institute Growth and Health Study recruited 2,379 adolescent girls. Frequency of breakfast consumption, dietary calcium and fiber, and BMI were recorded over a period of nine years. The study found that girls who ate breakfast more often tended to have a lower BMI [Source: J Am Diet Assoc. (2005) 105(6):938–45].
Which of the following conclusions can you make on the basis of this study?
From the given study, we can tell that the conclusion is; The frequency of eating breakfast is associated with lower BMI in adolescent girls.
How to arrive at statistics conclusions?From the study in the question, we see that a national institute is trying to examine the association of breakfast intake and body mass index (BMI).
Now, in the research we saw that the frequency is being counted about the type of foods being eaten by those surveyed to find out the impact on BMI.
From the study, we see that girls who ate breakfast more often tended to have a lower BMI. Thus, we can say that the conclusion is that The frequency of eating breakfast is associated with lower BMI in adolescent girls.
The missing options are;
A. The frequency of eating breakfast is associated with lower BMI in adolescent girls.
B. There is no relationship between eating breakfast and BMI in adolescent girls.
C. Eating breakfast makes adolescent girls thinner.
D. Skipping breakfast can contribute to obesity in adolescent girls.
Read more about Statistics Conclusions at; https://brainly.com/question/15980493
#SPJ1
Find an equation for the line that passes through the points (-6, -6) and (4,-2)
Answer:
y = 2/5 x - 18/5
Step-by-step explanation:
y = mx + b
m = (y2 - y1)/(x2 - x1) = [-2 - (-6)]/[4 - (-6)] = 4/10 = 2/5
y = 2/5 x + b
-6 = (2/5)(-6) + b
-30 = -12 + 5b
5b = -18
b = -18/5
y = 2/5 x - 18/5
graph g(x) = -8|x| +1
Answer:
look the attachment in the above
Solve for x: |x − 2| + 10 = 12 (1 point)
Answer:
I think that would be 1
Step-by-step explanation:
Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.
Answer:
x = 0 or 4
Step-by-step explanation:
The absolute value function can be resolved into two equations. These one- or two-step equations can be solved in the usual way.
__
negative argument-(x -2) +10 = 12
-x = 0 . . . . . . . . . simplify, subtract 12
x = 0 . . . . . . . . . multiply by -1. Check: 0 -2 is negative.
positive argumentx -2 +10 = 12
x = 4 . . . . . . . . . simplify, subtract 8. Check: 4 -2 is positive.
The two solutions are x=0 and x=4.
What's x ? find the indicated side of the right triangle
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 6}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{The image provided with 2 angles and one side}[/tex]
Find: [tex]\textsf{Solve for the unknown side of x}[/tex]
Solution: In order to determine the length of x we need to use some trigonometric functions. Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees. We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin. Plug in the values and solve for the unknown.
Plug in the values
[tex]\textsf{sin(30) = }\frac{\textsf{opposite}}{\textsf{hypotenuse}}[/tex][tex]\textsf{sin(30) = }\frac{\textsf{3}}{\textsf{x}}[/tex]Multiply both sides by x
[tex]\textsf{sin(30) * x = }\frac{\textsf{3}}{\textsf{x}}\textsf{ * x}[/tex][tex]\textsf{sin(30) * x = 3}[/tex]Divide both sides by sin(30)
[tex]\textsf{sin(30) * x}*\frac{1}{\textsf{sin(30)}}\textsf{ = 3}}*\frac{1}{\textsf{sin(30)}}[/tex][tex]\textsf{x = 3}}*\frac{1}{\textsf{sin(30)}}[/tex]Simplify
[tex]\textsf{x = 3}}*\frac{1}{\textsf{0.5}}[/tex][tex]\textsf{x = 6}[/tex]Therefore, the value of the unknown variable x is 6 units.
Vector g is shown below.
Vector h is parallel to g, in the same direction and
half as long.
Work out h as a column vector.
9
Answer:
h = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
Step-by-step explanation:
g = [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] , then
h = [tex]\frac{1}{2}[/tex] [tex]\left[\begin{array}{ccc}10\\2\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
The figure below is a scatterplot for paired data (x, y), with x values on the horizontal axis and y on the vertical axis. The tick marks are spaced 10 units apart on both axes. (Note that to answer the following questions you don't need the actual values for each tick mark, only differences between them.) 00 00 Oo oo 8 Oo oo (1) What are plausible values for the standard deviations of x and y, respectively? (2) What is a plausible value for the slope of the SD line? (3) Given your answer to part (b), what is a plausible value for the slope of the regression line?
The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.
What is a scatter plot?Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.
We have a scatter plot shown in the table:
1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:
Standard deviation = SD
6SD(x) = 40
SD(x) = 40/6 = 6.67
6SD(y) = 20
SD(y) = 20/6 = 3.37
2) Slope of the line:
= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5
3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.
Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.
Learn more about the scatter plot here:
brainly.com/question/13984412
#SPJ1
what is the equation
Answer:
[tex]y = \sin( \frac{2\pi}{3} x) [/tex]
Step-by-step explanation:
The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:
[tex]y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )[/tex]
