The domain and range of [tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex] is D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2} .
The domain of a function f(x) is set of the value of x for which it is defied and Range of function is set of values f takes .
The rational number [tex]f(x) = \frac{p(x)}{q(x)}[/tex] where p(x) and q(x) are polynomial in terms of x and q(x) ≠ 0 . The domain of rational number is set of values that do not cause denominator equal to zero .
The given function is :
[tex]f(x) = \frac{x^{2}+ 6x+8}{x+4}[/tex]
we need to find domain and range of function,
For domain put denominator equals to zero
x+4 = 0
x = -4
so, domain is every real number except number making it zero
domain = (-∞,-4)∪(-4,∞) and x ≠ -4
For range ,factoring numerator
x²+6x+8 = x²+2x+4x+8
x(x+2)+4(x+2) = (x+4)(x+2)
Putting numerator back,
[tex]f(x) = \frac{(x+4)(x+2)}{x+4}[/tex]
Cancelling factor (x+4) from numerator and denominator
[tex]f(x) = x+2[/tex]
Putting x+2 = 0
[tex]x +2 = 0\\x = -2[/tex]
range = (-∞,-2)∪(-2,∞) and f(x) ≠ -2
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D: {x ∊ ℝ | x ≠ −4}; R: {y ∊ ℝ | y ≠ −2}
I took the test
1 Decide whether the graph shown below is a function or not.
According to the vertical line test, a curve represents a function only if the vertical line drawn at any point intersects the curve atmost once.
Observe that the given curve fails to satisfy this condition.
This concludes that the given curve does not represent a function.
6. Analyze Marc has one dollar, one quarter, one dime, one nickel, and
one penny. He spends 35 cents. How much money does he have left?
A $0.76
B $0.96
$1.06
D $1.16
Which system of inequalities is shown? O Ayx у 2 в ух y2 с. у.х y2 р. уки
First, we need to find the equations of the two dotted lines.
One of the lines is parallel to the x-axis and passes through the point (0, 2), then its equation is:
y = 2
The other line has a slope of 1 and intercepts the y-axis at the point (0,0). Using the slope-intercept form with m = 1 and b = 0, its equation is:
y = mx + b
y = 1*x + 0
y = x
Given that the shaded region is below both lines and the lines are not included in the solution, then we need to use a "<" sign in the inequalities. Finally, the system of inequalities is:
y < x
y < 2
Five students, Stella, Victoria, Alexander, Eva, and Hunter, line up one behind theother. How many different ways can they stand in line?
Permutations formula
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]where n things are chosen r at a time.
In this case, we need to find the number of permutations of n = 5 students chosen r = 5 at a time. That is,
[tex]\begin{gathered} _5P_5=\frac{5!}{(5-5)!} \\ _5P_5=\frac{5!}{0!} \\ _5P_5=\frac{5\cdot4\cdot3\cdot2\cdot1}{1} \\ _5P_5=120 \end{gathered}[/tex]They can stand in line in 120 different ways
What is 6/24 in lowest terms(I’m reporting wrong answers)
The greatest common factor of 6 and 24 is 6.
Divide the numerator and denominator by 6.
6/24 = (6/6) / (24/6) = 1/4
9+7x = -5Which is the following above Addition property of equality Subtraction property of equality Simplify Division property of equality Symmetric property of equality Distributive property
Given:
[tex]9+7x=-5[/tex]To find:
The properties.
Explanation:
Using the subtraction property of equality,
[tex]\begin{gathered} 9+7x-9=-5-9 \\ 7x=-14 \end{gathered}[/tex]Using the division property of equality,
[tex]\begin{gathered} \frac{7x}{7}=-\frac{14}{7} \\ x=-2 \end{gathered}[/tex]Final answer:
The properties used are,
• The subtraction property of equality
,• The division property of equality
A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
A student plays the following game. He tossed three coins. If he gets exactly two heads he wins $5. If he gets exactly one head he wins $3. Otherwise, he loses $2. On the average, how much should he win or lose per play of the game?
we have that
If he gets exactly two heads he wins $5.
the probability is
P=2/8
If he gets exactly one head he wins $3
the probability is
P=1/8
we have that
2/8+1/8=3/8
that means, that the probaility of any other result is 1-3/8=5/8
therefore
he win or lose per play
(2/8)*$5+(1/8)*$3-(5/8)*$2=(10/8)+(3/8)-(10/8)=3/8=$0.375
the answer is
He win $0.375 per gameWhat is the inverse equation for h(x) = 2log(x-3) ?
Given the function:
[tex]h(x)=2log\left(x-3\right)[/tex]To find its inverse:
[tex]\begin{gathered} y=2log\left(x-3\right) \\ x=2log\left(y-3\right) \end{gathered}[/tex]solving for y:
[tex]\frac{x}{2}=log(y-3)[/tex][tex]\begin{gathered} 10^{\frac{x}{2}}=y-3 \\ \\ 10^{\frac{x}{2}}+3=y \end{gathered}[/tex]ANSWER
[tex]h^^{-1}(x)=10^{\frac{x}{2}}+3[/tex]On January 1, 2012 Hector put his life savings of $17,229 into a savings account at Barclays, which was pain 0.9 interest at the time. Over the next year, the inflation rate averaged 1.7%. Now consider the following propositions
Answer:
what propositions?
Step-by-step explanation:
Solve the system of equations x + 2y = 0 Solve the equation for x.
Given the equation :
[tex]x+2y=0[/tex]Solve the equation for x:
[tex]x=-2y[/tex]Final Answer:
x = -2yIn-depth explanation:
Hi! The question is asking us to solve the equation x + 2y = 0 for x.
________________________
To Solve
Rearrange the equation for x.
________________________
All we need to do is subtract '2y' from both sides.
[tex]\implies\sf{x+2y=0}[/tex]
[tex]\implies\sf{x=0-2y}[/tex]
[tex]\implies\sf{x=-2y}[/tex]
∴ Equation: x = -2y
_______________________
AT&T is having a sale on all cell phones. They will give you a loan to pay for the phone. Your phone costs $899 How much will you pay for the phone if they charge you 4.5% interest, and it will take you 24 months to pay it off.
-How do you do this equation?
Answer:
Its a scam AT&T has no such sale going on right now.
Step-by-step explanation:
Two more than the cube root of a number
two more means add 2 , +2
cube root of a number
A number is x
cube root of x :
∛x
Answer:
∛x + 2
Use the following two points to answer parts a - c. (2, 9), (4, - 7) a . Find the slope of the line passing through the two points. b . Write an equation of a line passing through the two points in point-slope form. c Rewrite the equation of the line in slope-intercept form.
slope= m =y2-y1/x2-x1, then
[tex]\begin{gathered} m=\frac{-7-9}{4-2} \\ m=-\frac{16}{2} \\ m=-8 \end{gathered}[/tex]a. slope = -8
6. Examine the two-way frequency table below.Gold Medals Silver Medals Bronze MedalsUSA 201842Spain 2511France 192726Based on the data in the two-way frequency table, what is the probability that a randomly selected player won a bronze medal given that the player represented Spain?22.4%24.4%13.995.5%PREVIOURPREVIOUS6 ofNEXTREVIEWSALSion outINTL
From the table, we can get the total number of players that took part in the games.
See the new table below;
From the table, we got the sum of players from each country, and also the sum of medals won by each player. This gave us a total of 201 when we calculate the total medals collected or the total from all the countries. Hence, the name two-way.
From the table, the number of Spain players that won bronze is 11, hence, the probability is;
[tex]\begin{gathered} \text{Probability = }\frac{n\text{umber of required outcome}}{n\text{ umber of total possible outcomes}} \\ P(\text{Spain player with bronze)= }\frac{n\text{ umber of Spain player that won bronze}}{\text{total n umber of players}} \\ =\text{ }\frac{11}{201} \\ =0.0547 \\ \text{Taking this to percentage, we have it to be 0.0547 x 100} \\ =5.47 \\ =5.5 \end{gathered}[/tex]Therefore, the probability of selecting a Spain player that won a bronze medal at random is 5.5%
What is the equation of the line that passes through the point (5, 3)and has a slope of -4/5
Given:
The slope of the line
[tex]m=-\frac{4}{5}[/tex]The line passes through from the point (5,3).
Required:
Find the equation of the line.
Explanation:
The equation of the line that passes through from the point and has slope m is given by the formula as:
[tex]y-y_1=m(x-x_1)[/tex]Consider
[tex](x_1,y_1)=(5,3)[/tex]Now the equation of the line:
[tex]\begin{gathered} y-3=\frac{-4}{5}(x-5) \\ 5(y-3)=-4(x-5) \\ 5y-15=-4x+20 \\ 4x+5y=35 \end{gathered}[/tex]Final Answer:
The equation of the line passes through from point (5,3) and has a slope -4/5 is 4x + 5y = 35
A town’s population increases at a constant rate. In 2010 the population was 56,000 . By 2012 the population had increased to 81,000 . If this trend continues, predict the population in 2016. The population will be Number in 2016.
Given: A town's population increases at a constant rate. In 2010 the population was 56,000. By 2012 the population had increased to 81,000.
Required: To predict the population in 2016.
Explanation: The population is increasing at a constant rate. In 2 years, the increase in population is-
[tex]81000-56000=25000[/tex]Thus the slope (or rate of change of population per year) is-
[tex]\frac{25000}{2}=12500[/tex]Thus, in 2016 after 6 years, the increase in population will be-
[tex]12500\times6=75000[/tex]Hence, the population in 2016 will be-
[tex]56000+75000=131000[/tex]Final Answer: The population will be 131,000 in 2016.
QUESTION IS IN IMAGE!! DONT SHOW WORK JUST THE ANSWER UNLESS YOU NEED TO
Given:
m∠SPQ = 113 degrees
Let's find the measure of angle RQS, m∠RQS.
By applying the angle-arc relationship, we have:
m∠SPQ = measure of arc SQ = 113 degrees.
Since RQ is the diameter, measure of arc RQ = 180 degrees.
Now, let's find the measure of arc RS:
measure of arc RS = 360 - arc SQ - arc RQ
measure of arc RS = 360 - 113 - 180 = 67 degrees.
To find the m∠RQS, apply angle-arc relationship:
[tex]\begin{gathered} m∠RQS=\frac{1}{2}arcRS \\ \\ m∠RQS=\frac{1}{2}*67 \\ \\ m∠RQS=33.5^o \end{gathered}[/tex]Therefore, the measure of angle RQS is 33.5 degrees.
ANSWER:
m∠RQS = 33.5°
Name the rotation that maps the black triangle onto the red triangle. Explain how you know(See picture below)
We would compare the coordinates of corresponding vertices on the red and black triangles. The vertex at the top of the black triangle and the vertex at the bottom of the red triangle correspond to each other. We would compare them.
For black triangle, coordinate is (1, - 3)
For red triangle, coordinate is (- 1, 3)
If a vertex with coordinate, (x, y) is rotated 180 degrees counterclockwise about the origin, the new coordinate is (- x, - y). By rotating (1, - 3) 180 degrees counterclockwise, it becomes (- 1, - - 3) = (- 1, 3). This corresponds to the coordinate of the corresponding vertex of the red triangle. Thus, the rotation that maps the black triangle onto the red triangle is 180 degrees counterclockwise rotation about the origin
A metallurgist has One alloy containing 49% copper and another containing 62% copper. How many pounds of each alloy must he used to make 51 pounds of a third alloy containing 56% copper?
Explanation
Step 1
a)
Let
x represents the pounds of the 49 % copper alloy
y represents the pounds of the 62 % copper alloy
then,
if we want to make a 51 pounds of a new alloy,
[tex]x+y=51\rightarrow equation(1)[/tex]b)this new allo contains 56% of copper , so
total of cooper = pounds of alloy * percentage
[tex]\begin{gathered} 0.49x+0.62y=51\cdot0.56 \\ 0.49x+0.62y=28.56\rightarrow equation\text{ (2)} \end{gathered}[/tex]Step 2
Solve the equations
a) isolate x in equation (1) and replace in equation(2)
[tex]\begin{gathered} x+y=51\rightarrow equation(1) \\ \text{subtract y on both sides} \\ x+y-y=51-y \\ x=51-y\rightarrow equation(3) \end{gathered}[/tex]Now, replace in equation (2)
[tex]\begin{gathered} 0.49x+0.62y=28.56\rightarrow equation\text{ (2)} \\ 0.49(51-y)+0.62y=28.56 \\ 24.99-0.49y+0.62y=28.56 \\ \text{add like terms } \\ 24.99+0.13y=28.56 \\ \text{subtract 24.99 on both sides} \\ 24.99+0.13y-24.99=28.56-24.99 \\ 0.13y=3.57 \\ \text{divide both sides by 0.13} \\ \frac{0.13y}{0.13}=\frac{3.57}{0.13} \\ y=27.46 \\ \end{gathered}[/tex]now, replace the y value into equation (3) to get x
[tex]\begin{gathered} x=51-y\rightarrow equation(3) \\ x=51-y \\ x=51-27.46 \\ x=23.54 \\ \end{gathered}[/tex]therefore, the answer is
23.54 lb of the 49% copper alloy
27.46 lb of the 62% copper alloy
Which of the functions below could possibly have created this graph?O A. F(x)=x²+x+3O B. F(x)=1.9x +15x² -6O C. F(x)=-x³ + 2x²-3xO D. F(x) = − 3x²¹ +7x² +15x
Solution
Now
Looking at the given graph, It has four values for x
And Option D has four has exponentswhich implies it has four values for x
The final answer
Option DOpa
hello I don't you can help me with this please
Approximately 10 hours
1) Gathering the data
Initial temperature: 79º F
0.8 each hour
84º
2) We can write an exponential function to find that out. So let's do it this way:
[tex]\begin{gathered} T_f=T_0(1+0.8)^h \\ 84=79(1.8)^h \\ \frac{84}{79}=\frac{79(1.8)^h}{79} \\ 1.06=1.8^h \\ \log _{10}1.06=\log _{10}1.8^h \\ h\log _{10}1.8=\log _{10}1.06 \\ h=10.087 \end{gathered}[/tex]Notice that since the temperature is rising, we have to add one to the factor, otherwise, it will decrease it.
Now let's convert that decimal number so that we may have a better approximation:
10 hours and 4 minutes
60 inches =___ feet please and thank you for your help
We know that:
[tex]1ft=12in\text{.}[/tex]Then:
[tex]1in=\frac{1}{12}ft\text{.}[/tex]Therefore:
[tex]60in=60\cdot(\frac{1}{12}ft)\text{.}[/tex]Simplifying the above result we get:
[tex]60\cdot(\frac{1}{12}ft)=\frac{60}{12}ft=5ft\text{.}[/tex]Answer:
[tex]60\text{ inches=5 feet.}[/tex]how do I find the length of x and y?
Which definition best describes a perpendicular bisector?Required to answer. Single choice. A line segment from a vertex of the triangles to the opposite side that divides an angle into two congruent adjacent angles. A line segment from a vertex of the triangles to the midpoint of the opposite side.A line segment from any vertex perpendicular to the line containing the opposite side of a triangle.A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint).
Answer:
A line that is perpendicular to a side of the triangle and also bisects that side of the triangle (it goes through the midpoint)
Step-by-step explanation:
A perpendicular bisector is a line segment perpendicular to and passing through the midpoint, dividing it into two equal segments and creating right angles.
guess this i am less than 10 i am not a multiple of 2 i am a composite number
Composite numbers have a smaller divisor, other than 1 and itself. Hence, the required number is 9.
What is composite number?Any positive integer that may be created by multiplying two other positive integers is referred to as a composite number. It is, in other words, a positive integer that has at least one divisor besides itself and the number 1.
Numbers with more than two elements are known as composite numbers in mathematics. Composite numbers are non-prime numbers that can be divided by more than two other numbers.
Composite numbers below 10 :
4, 6, 8, 9
From the composite numbers given, the value which is not a multiple of 2 is 9.
The values 4, 6, and 8 are multiples of 2.
Hence, the required is 9.
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Lily has 30 Marvel Funko Pops. The number of Marvel Funky Pops in her collection is only 60% of hes total Funko Pops. How many total Funko Pops are in her collection?
Lily has 30 Marvel Pops, they are 60% of the total Pops
How many in total ?
We can say that the realation between 30 an the total is the same relation between 60% and 100%, so we can write:
30/x = 60/100
[tex]\frac{30}{x}=\frac{60}{100}[/tex]Where x is the total number of Pops
Solving this for x:
x = 30(100)/60 = 3000/60 = 50
[tex]x\text{ = }\frac{\text{30(100)}}{60}=\frac{3000}{60}=50[/tex]Answer:
Number of total Funlo Pops in her collection: 50
If the population of a small town satisfies the exponential model A = Aoe^0.015t, where is measured in years, how long will it take for the town's population to increasefrom 5,450 to 10,355? Round your answer to two decimal placesAnswer
ANSWER :
The answer is 42.79 years
EXPLANATION :
From the problem, we have the function :
[tex]A=A_oe^{0.015t}[/tex]Solve for the value of t when A = 10,355 and Ao = 5,450
That will be :
[tex]\begin{gathered} 10355=5450e^{0.015t} \\ \frac{10355}{5450}=e^{0.015t} \\ 1.9=e^{0.015t} \\ \text{ Take the ln of both sides :} \\ \ln(1.9)=\ln(e^{0.015t}) \\ \ln(1.9)=0.015t \\ t=\frac{\ln(1.9)}{0.15} \\ t=42.79 \end{gathered}[/tex]divide decimals by decimals 033 divided by 688
The given numbers are 0.33 divided by 6.88
[tex]\frac{0.33}{6.88}=0.0479[/tex]Answer : 0.0479
Jessica states -79 will make the inequality true.-80 > ? _> -89O FactO Fib
-80>-79>-89
To answer this we have to set a number line.
As we can see in the number line , if we move from left to right, -79 is higher than -80 (-79>-80)
So, the statement is false
A line passes through the points (-21, -22) and (-14, -16). Find this line's equation in point-slope form. Using the point (-21, -22), this line's point-slope form equation is: Using the point (-14, -16), this line's point-slope form equation is:the point slope form has to be simplified
Answer:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4
Explanation:
The point-slope form of a line's equation is:
[tex]y-y_1=m(x-x_1)[/tex]Where (x₁, y₁) is a point in the line and m is the slope.
The slope of a line can be calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x₁, y₁) and (x₂, y₂) are two points in the line. So, replacing (x₁, y₁) by (-21, -22) and (x₂, y₂) by (-14, -16), we get that the slope of the line is:
[tex]m=\frac{-16-(-22)}{-14-(-21)}=\frac{-16+22}{-14+21}=\frac{6}{7}[/tex]Now, using the point (-21, -22), we get that the equation of the line is:
[tex]\begin{gathered} y-(-22)=\frac{6}{7}(x-(-21)) \\ y+22=\frac{6}{7}(x+21) \end{gathered}[/tex]Then, we can simplify the equation as:
[tex]\begin{gathered} y+22=\frac{6}{7}(x)+\frac{6}{7}(21) \\ y+22=\frac{6}{7}x+18 \\ y+22-22=\frac{6}{7}x+18-22 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]On the other hand, using the point (-14, -16), the equation of the line is:
[tex]\begin{gathered} y-(-16)=\frac{6}{7}(x-(-14)) \\ y+16=\frac{6}{7}(x+14) \end{gathered}[/tex]Simplifying, we get:
[tex]\begin{gathered} y+16=\frac{6}{7}x+\frac{6}{7}(14) \\ y+16=\frac{6}{7}x+12 \\ y+16-16=\frac{6}{7}x+12-16 \\ y=\frac{6}{7}x-4 \end{gathered}[/tex]So, the answers are:
Using point (-21, -22): y = (6/7)x - 4
Using point (-14, -16): y = (6/7)x - 4