Answers
In order to calculate f - g, we need to subtract the functions. To do so, we will need to put the fractions in the same denominator.
So we have:
[tex]\begin{gathered} f-g \\ =\frac{x-1}{x+3}-\frac{x-3}{x+1} \\ =\frac{(x-1)(x+1)}{(x+3)(x+1)}-\frac{(x-3)(x+3)}{(x+1)(x+3)} \\ =\frac{x^2-1}{(x+3)(x+1)}-\frac{x^2-9}{(x+3)(x+1)}_{} \\ =\frac{x^2-1-(x^2-9)}{(x+3)(x+1)} \\ =\frac{x^2-1-x^2+9}{(x+3)(x+1)} \\ =\frac{8}{(x+3)(x+1)} \end{gathered}[/tex]Related Questions
1. For each situation below, state the transformation(s) that occur betweenf(x) and g(x).f(x)g(x)Transformation(s)f(x)=4x+5g(x)=-4x+7Reflection across y-axis, andshift up 2 units.f(x)=1/3x-2g(x)=3(x+2)-2f(x)=-2/3x+16g(x)=23(x-3)-16f(x)=14(x-3)+1g(x)=7(x+ 2)+1
Answers
From the image given
For the first case
f(x) = 4x + 5
g(x)= -4x+7
f(x) was:
reflected across the y-axis and shifted up by 2 units
For the second case
f(x)=1/3x-2
g(x)=3(x+2)-2
f(x) was:
Rotated counterclockwise by 90 degrees and reflected over the y-axis
Shifted to the left by 2 units
For the third case
f(x)=-2/3x+16
g(x)=2/3(x-3)-16
f(x) was:
Reflected across the y-axis
shifted to the right by 3 units
shifted downward by 32 units
The area of a rectangle garden is given by the trinomial x^2+2x-48. What are the possible dimensions of the rectangle? Use factoring.
Answers
x^2 + 2x - 48 = (x + 8) (x - 6)
x1 = -8
x2 = 6
b) x^2 + 2x - 8
(x +4 )(x -2)
One ice cream cone costs $2. ron buys m ice cream cones for $24. which equation, when solved, will give the value of m?A. m × 24 = 2B. m + 24 = 2C. m × 2 = 24 D. m + 2 = 24
Answers
Solution:
If one ice cream cone cost $2 and Ron buys m ice creams cones, the total cost for those m ice creams cones are:
2m
now, since buys m ice cream cones for $24, the above equation becomes:
2m=24
so that, we can conclude that the correct answer is:
C. m × 2 = 24
I cant understand function and relation what's the difference and how do I know which is which on a graph
Answers
In order to determine the difference between a relation and a function, consider the following definitions:
In a relation a set of inputs have a corresponding set of outputs that are related in some way.
In a function there is a specific kind of relation in which one input only has one output, that is, in a function, an input can not have two o more outputs, only one.
Hence, the difference is that a function is a relation one-to-one between inputs and outputs, and a relation is more general, here, one input can have two o more outputs.
A deposit of $2000 is invested in an account earning 4.5% interest compounded monthly. How much money will there be in 6 years? Equation:Answer:
Answers
EXPLANATION:
Given;
We are told that a deposit of $2000 is invested in an account that yields an annual interest of 4.5%, but is compounded monthly.
Required;
We are required to calculate how much money will be in the investment in 6 years time.
Step-by-step solution.
The formula for calculating a compound interest is given as;
[tex]A=P(1+r)^t[/tex]The variables in this formula are;
[tex]\begin{gathered} A=amount\text{ }after\text{ }the\text{ }period\text{ }given \\ P=principal\text{ }amount\text{ }at\text{ }the\text{ }beginning \\ r=annual\text{ }rate\text{ }of\text{ }interest \\ t=period\text{ }of\text{ }investment\text{ }in\text{ }years \end{gathered}[/tex]However, when the compounding is done at several periods within a year (for example, monthly, quarterly, half-yearly, etc), the formula is amended to reflect the period of compounding within each year.
The amended formula is what we have been given in this question.
Therefore, from the details provided,
[tex]\begin{gathered} P=2000 \\ r=0.045 \\ t=6 \\ n=12 \end{gathered}[/tex]Please note that n is the number of times compounding takes place per year and in this case its 12 times (monthly).
Therefore;
[tex]A=2000(1+\frac{0.045}{12})^{12\times6}[/tex][tex]\begin{gathered} A=2000(1+0.00375)^{72} \\ \\ A=2000(1.00375)^{72} \\ \\ A=2000\times1.30930310151 \\ \\ A=2618.60620301 \end{gathered}[/tex]Rounded to the nearest hundredth, we now have
ANSWER:
[tex]A=2,618.61[/tex]3) Johann has traveled 15 miles from his station on the train. He will continue onthe train at 80 miles per hour. If he ends up traveling a total of 615 miles, howmuch longer did it take him?
Answers
SOLUTION:
Step 1 :
In the question, we are told that:
Johann has traveled 15 miles from his station on the train.
He will continue on the train at 80 miles per hour.
If he ends up traveling a total of 615 miles,
we are meant to find how much longer did it take him.
Step 2:
Let t represents the time, so that we have the following:
[tex]15\text{ + 80t = 615}[/tex]Solving this, we have that:
[tex]\begin{gathered} 80t\text{ = 615 - 15} \\ 80\text{ t = 600} \\ \text{Divide both sides by 80, we have that:} \\ t\text{ = }\frac{600}{80} \\ \text{ t}=\text{ 7. 5 hours} \end{gathered}[/tex]CONCLUSION:
The final answer is 7. 5 hours
two neighbors in a rural area want to know the distance between their homes in miles. They look at a land map that shows the distance between their homes as . What should the neighbors use as a conversion factor to convert this distance to miles?
Answers
If they look at a land map that shows the distance between their homes as 6,336 feet. What the neighbors should use as a conversion factor to convert the distance to miles is : 6336 feet/1 mile.
What is a conversion factor?A conversion factor can be defined as digit which is used to convert a units into another form of units and this can be done by either multiplying the number by the units or dividing the number by the units.
Now let determine the conversion factor that the neighbor can use to convert or change 6,336 feet into mile
Given data:
Distance = 6,336 feet
Hence,
1 miles = 5,280 feet
Distance to miles = 6,336 feet / 1 miles
Distance to miles = 6,336 feet / 5,280 feet
Distance to miles = 1.2 miles
Therefore we can conclude that the conversion factor is 6336 feet/1 mile..
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The complete question is:
Two neighbors in a rural area want to know the distance between their homes in miles. They look at a land map that shows the distance between their homes as 6,336 feet. What should the neighbors use as a conversion factor to convert the distance to miles?
6336 feet/1 mile
when a force of 70N acts on a certain object the acceleration of the object is 10 m/s^2. If the acceleration of the object becomes 3 m/s^2. what is the force
Answers
First let us find the mass of this objects
F= ma
where m is the mass
a is the acceleration
When F= 70 and a =10
substitute into the formula and solve for m
70 = m(10)
Divide both-side by 10
m = 7
when the acceleration becomes 3
Then substitute m=7 and a = 10 into the formula
F= 7(3)
F= 21 N
Write a system of equations that can be used to find the individual costs of a package of pens and a package of highlighters
Answers
To answer this question, we can proceed as follows:
1. Let p represents the nu of pens and h represents the package
Question 2 of 25Aman (M) is standing halfway between a tree (1) and a lamppost (1). What is the value of x?(10x + 5) mM(5x + 105) mAssesUnit 1
Answers
Since the man (M) is standing halfway between T and L, it means that:
TM = ML
Since :
TM = (10x+5)m
ML = (5x+105)m
(10x+5)m = (5x+105)m
10x+5 = 5x+105
Solving for x:
10x-5x = 105-5
5x=100
x=100/5
x = 20
The hypotenuse of a right triangle is 17.One of the legs is 8.Find the length of the other leg.
Answers
We can use pythagorean theorem to solve for this triangle.
Let , length of other leg of the triangle be "x".
Pythagorean Theorem tells us:
[tex]a^2+b^2=c^2[/tex]where c is the hypotenuse, a and b are the legs
From the question, we can thus write:
[tex]8^2+x^2=17^2[/tex]We can solve for x:
[tex]\begin{gathered} 8^2+x^2=17^2 \\ 64+x^2=289 \\ x^2=289-64 \\ x^2=225 \\ x=\sqrt[]{225} \\ x=15 \end{gathered}[/tex]So, the other side of the triangle is 15
2(-1)^2 why does this equal 2???
Answers
Answer:
2
Step-by-step explanation:
(-1)²= 1
To break down (-1)² you are do -1 * -1 which equals 1
2(1)= 2
Anything times 1 equals its self
Write the equation of the parabola in vertex form.vertex (1,1), point (2,-6)f(x) = 0
Answers
1) Given that we have the vertex at (1,1) and one point (2,6) then we can write
y=a(x-h)²+k
So we can see that this parabola is a<0 due to its point (2, -6)
h = -b/2a = 1
k= -Δ/4a = 1
y=a(x-h)²+k
y=-a(x-1)²+1
2) Let's find the "a" plugging points (2,-6) and (1,1) into the formula:
y=a(x-h)²+k
-6 =a(2-1)² +1
-6= a(1) +1
-6-1=a
a=-7
3) So now we can write our equation:
y= -7(x-1)²+1
I need to find the domain and range on both graphs, I am confused and forgot how to do it
Answers
Using the given graphs, let's find the domain and the range of each function.
• The domain is the set of all possible values of x contained in the graph.
,• The range is the set of all possible values of y contained in the graph.
We have the following:
• Graph 1:
Domain: We can see the line starts with a closed dot on x = 0 and ends with a closed dot on x = 18.
Therefore, the domain will be all numbers from 0 to 18.
Hence, the domain is:
0 ≤ x ≤ 18
Range: The line goes from y =200 to y = 2000
Therefore, the range is:
Range: 200 ≤ y ≤ 2000
• Graph 2:
Domain: The line starts from x = 0 to x = 4
The domain is:
0 < x < 4
Range: Here, the range will be:
0 < y < 160
ANSWER:
• Graph 1:
Domain: {0 ≤ x ≤ 18}
Range: {200 ≤ y ≤ 2000}
• Graph 2
Domain: {0 < x < 4}
Range: {0 < y < 160}
17. The point below best represents which of the following? A 6 7 138 V35 OA O B. V45 48
Answers
Solution
For this case we can see that the point given is a number between 6 and 7 and is closer to 6 than 7
When we analyze the options we see this:
[tex]undefined[/tex]Hello! I need help finding the equation in point slope form. Thank you!
Answers
The point-slope form of the linear equation is
[tex]y-y_1=m(x-x_1)[/tex]m is the slope
(x1, y1) is a point on the line
Since a line passes through the point (-9, 8) and has a slope of -2/3, then
[tex]\begin{gathered} (x_1,y_1)=(-9,8) \\ m=-\frac{2}{3} \end{gathered}[/tex]Substitute them in the form above
[tex]\begin{gathered} y-8=-\frac{2}{3}(x--9) \\ y-8=-\frac{2}{3}(x+9) \end{gathered}[/tex]The equation of the line in the point-slope form is
[tex]y-8=-\frac{2}{3}(x+9)[/tex]Got It? for Part 3 1. Air pressure at sea level on earth is 14.7 pounds per square inch. The top of your head has an area of 7.5 square inches. How many pounds of air pressure are pressing on your head? 2. Is your answer reasonable? Explain. digits Copyright © by Savvas Learning Company LLC. All Rights Reserved
Answers
Solving for F:
[tex]\begin{gathered} F=P\times A \\ F=14.7\times7.5=110.25 \end{gathered}[/tex]F = 110.25in²
The answer is reasonable because the pressure is inversely proportional to the area over which it is exerted, the head area is considerable, so the pressure is low
The length of a rectangle is 2m-5. Width is 4m-2. If the perimeter is 382 inches, find the length and the width.
Answers
Given:
• Length of a rectangle = 2m-5
,• Width of the rectangle = 4m-2
,• Perimeter of the rectangle = 382 Inches
We know that:
[tex]\begin{gathered} Perimeter\; of\; a\; rectangle=2(\text{Length}+Wi\differentialD tth)th).th) \\ \text{Therefore:} \\ 382=2\left(2m-5+4m-2\right) \\ 382=2(2m+4m-5-2) \\ 382=2(6m-7) \\ 382=12m-14 \\ \text{Add 14 to both sides} \\ 382+14=12m-14+14 \\ 396=12m \\ \text{Divide both sides by 12} \\ m=33 \end{gathered}[/tex]A group of 500 art students have three different lecture times for their Introduction seminar . On average, how many students per class will there be
Answers
On average, there will be 167 students in each lecture
Here, we want to get the average number of students that will be in each of the lectures
Mathematically, we proceed to solve this by dividing 500 by 3
Dividing this, we have;
[tex]\frac{500}{3}\text{ = 166.667}[/tex]Since we cannot have a fractional human, we have to round this up to the nearest integer (whole number)
This division to the nearest whole number is 167
Quadrilateral EFGH is the image of ABCD after a transformation or sequence of transformations.
Which could be the transformation or sequence of transformations that maps ABCD onto EFGH?
Answers
The transformation that maps ABCD onto EFGH is: B. a rotation of 180° about the origin.
How to determine the transformation or sequence of transformations?Generally speaking, there are four (4) major types of transformation and these include the following:
RotationReflectionDilationTranslationGiven the following points:
Based on the graph of quadrilaterals EFGH and ABCD, we can logically deduce the following points:
Points at A = (-4, 4)
Points at B = (-3, 7)
Points at C = (1, 6)
Points at D = (-2, 2)
Points at E = (4, -4)
Points at F = (3, -7)
Points at G = (-1, -6)
Points at H = (2, -2)
What is a rotation?In Geometry, a rotation of a geometric figure 180° about the origin in either a clockwise or counterclockwise (anticlockwise) direction would produce a point that has the coordinates (-x, -y) as shown below:
(x, y) → (-x, -y)
Points at A = (-4, 4) → Points at E = (-(-4), -(4)) = (4, -4).
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-3 1/3 x - 1/2 =
11/3 x 3/2
=33/6
simplify it
=11/2
is this correct
Answers
The fractional expression, -3⅓ × -½ is correctly simplified as 5/3 or 1⅔.
How to Simplify Fractions?To multiply fractions that involves mixed numbers, change the mixed number to improper fraction then multiply the denominators of both fractions together, and their numerators together, then simplify in simplest form.
Given the fractional expression, -3⅓ × -½, convert the mixed number to improper fraction:
= -10/3 × -½
Multiply their numerators and their denominators:
= (-10 × -1)/(3 × 2)
= 10/6
Simplify the fraction further
= 5/3 = 1⅔
The correct answer for -10/3 × -½ is 5/3 or 1⅔.
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how to find the volume of a cone?.please include one(1) problem per question with solutions
Answers
• The volume of a cone can be found by using this formula:
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]Where "r" is the radius of the cone, and "h" is the height.
• Problem:
Find the volume of a cone that has a radius of 4 centimeters and a height of 10 centimeters. Round the result to the nearest tenth.
In this case:
[tex]\begin{gathered} r=4\operatorname{cm} \\ h=10\operatorname{cm} \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} V=\frac{\pi(4cm)^2(10\operatorname{cm})}{3} \\ \\ V=\frac{160\pi cm^3}{3} \\ \\ V\approx167.6\operatorname{cm}^3 \end{gathered}[/tex]Therefore, the answer is:
• You can find the volume by using this formula:
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}[/tex]Where "r" is the radius of the cone, and "h" is the height.
• Problem: Find the volume of a cone that has a radius of 4 centimeters and a height of 10 centimeters. Round the result to the nearest tenth.
• Solution:
[tex]V\approx167.6\operatorname{cm}^3[/tex]
y=x – 2 when X = = 3.5
Answers
Answer:
y = 1.5
Step-by-step explanation:
Given equation,
→ x = 3.5
→ y = x - 2
Then required value of y is,
→ y = x - 2
→ y = 3.5 - 2
→ [ y = 1.5 ]
Hence, the value of y is 1.5.
can Someone help me with number 4 i dont understand
Answers
Two lines are parallel if their slopes are equal.
In this case we have the lines:
[tex]\begin{gathered} y-7x=6 \\ y+7x=8 \end{gathered}[/tex]If we rearrange them in slope-intercept form, we get:
[tex]\begin{gathered} a)y-7x=6\longrightarrow y=7x+6 \\ b)y+7x=8\longrightarrow y=-7x+8 \end{gathered}[/tex]As line a has a slope m=7 and line has a slope m=-7, the lines have different slopes so they are not parallel.
[tex]\begin{gathered} m_a=7 \\ m_b=-7 \\ 7\neq-7\longrightarrow\text{not parallel} \end{gathered}[/tex]Answer: The lines are not parallel
I need help with this practice, read below then read the picture The subject is biodiversity index Amy found 6 species in her backyard, she wrote down the names of the species and how many she found for each;Ruby throated hummingbird / 9 individuals Blue jay / 6 individuals Dandelions / 44 individuals Chipmunk / 3 individuals Cooper’s hawk / 3 individuals Red bellied woodpecker / 2 individuals
Answers
Answer:
0.0896
Explanation:
First, calculate the total number of individuals.
[tex]Total=9+6+44+3+3+2=67[/tex]The number of species = 6.
Using the formula given for Biodiversity Index:
[tex]\begin{gathered} \text{ Biodiversity Index}=\frac{\text{Total number of species}}{\text{ Total number of individuals in the area}} \\ =\frac{6}{67} \\ \approx0.0896 \end{gathered}[/tex]The biodiversity index is approximately 0.0896 correct to 4 decimal places.
Find the first four terms of the sequence given by the following.1a₁=5 (4)"-¹, n=1, 2, 3...
Answers
Given the sequence:
[tex]a_n=5(4)^{n-1}[/tex]Therefore, the first four terms are:
n = 1
[tex]a_1=5(4)^{1-1}=5(4)^0=5(1)=5[/tex]n = 2
[tex]a_2=5(4)^{2-1}=5(4)^1=5(4)=20[/tex]n = 3
[tex]a_3=5(4)^{3-1}=5(4)^2=5(16)=80[/tex]n = 4
[tex]a_4=5(4)^{4-1}=5(4)^3=5(64)=320[/tex]Answer: 5, 20, 80, 320
Graph the line with slope -3 through the point -3,3
Answers
Answer:
Explanation:
Here, we want to graph the line with the slope of -3 passing through the point (-3,3)
To graph the line, we need two points
We need the x-intercept (point on the x-axis where y = 0) and the y-intercept (point on the y-axis where x is 0)
The equation of a straight line can be represented as:
[tex]y\text{ = mx + b}[/tex]where m is the slope and b is the y-intercept
Using the equation above, we can write:
[tex]y\text{ = -3x + b}[/tex]We can get b by substituting the coordinates (-3,3: where -3 will be x and 3 will be y)
[tex]\begin{gathered} 3\text{ = -3(-3) + b} \\ 3\text{ = 9 + b} \\ b\text{ = 3-9 = -6} \end{gathered}[/tex]Now we have identified that the y-intercept is at he point (0,-6)
We have the full equation as:
[tex]y\text{ = -3x-6}[/tex]We need to get the x-intercept now.
We can get this by substituting the value 0 for y
Mathematically, we proceed as follows:
[tex]\begin{gathered} 0\text{ = -3x - 6} \\ -3x\text{ = 6} \\ x\text{ = }\frac{-6}{3}\text{ = -2} \end{gathered}[/tex]Thus, we have the x-intercept as (-2,0)
So to graph the line, we locate the points (0,-6) and (-2,0)
Then, we draw a line through these two points
This line will pass through the point (-3,3)
Given the function f(x) = 7x2 - 4x + 7. Calculate the following values: f(-2) = f(-1) = f(0) = f(1) = f(2)=
Answers
To find f(-1), substitute x by -1
[tex]\begin{gathered} f(-1)=7(-1)^2-4(-1)+7 \\ f(-1)=7(1)+4+7 \\ f(-1)=7+4+7 \\ f(-1)=18 \end{gathered}[/tex]To find f(0), substitute x by 0
[tex]\begin{gathered} f(0)=7(0)-4(0)+7 \\ f(0)=0-0+7 \\ f(0)=7 \end{gathered}[/tex]To find f(1), substitute x by (1)
[tex]\begin{gathered} f(1)=7(1)^2-4(1)+7 \\ f(1)=7(1)-4+7 \\ f(1)=7-4+7 \\ f(1)=10 \end{gathered}[/tex]To find f(2), substitute x by 2
[tex]\begin{gathered} f(2)=7(2)^2-4(2)+7 \\ f(2)=7(4)-8+7 \\ f(2)=28-8+7 \\ f(2)=27 \end{gathered}[/tex]Enter the number that makes the equation true.0.4+3/10=?/10+3/10
Answers
Zack is playing a board game. On his next turn he can move his piece to any of the 8shaded squares on the board shown below.What are the chances that he will move his piece to an odd-numbered square?A. 2 out of 8B. 3 out of 8 C. 4 out of 8D.6 out of 8
Answers
Step 1
State the formula for the probability of an event
[tex]Pr(event)=\frac{Required\text{ number of events}}{Total\text{ number of events}}[/tex]Total number of event=8
Required number of events= number of odd numbers between 19,20,21,25,27,31,32 and 33=6
Step 2
Find the required probability
[tex]Pr(chance\text{ of odd-numbered square})=\frac{6}{8}\text{ i.e 6 out of 8}[/tex]Answer; 6 out of 8. option D
