Answers
Given:
f(x) = x^2 + 4x + 4 and g(x) = x^2 - 2x - 8.
we are to find the domain of (f/g) (x)
before we find the domain of the function, its best we know what a domain is.
The Domain of a function is the set of all possible inputs for the function. it can also be seen as the set of input or arguement values for which the function is real and defined.
recall that we have x + 2 as our the simplest form
x - 4
so the domain we wil be looking for is x + 2
x - 4
so we have to take t denominator of the above and compare to zero
x - 4 = 0
x = 4
so this is undefined
the function domain
x < 4 or x > 4
so the domain is:
(- infinity, 4) U (4, infinity)
The correct option is A.
Related Questions
tameka built 1/2 of a shed on monday and 2/5 of the tuesday
Answers
1/10
Step-by-step explanation:
Given,
The part of shed built on Monday = 1/2
The part built on Tuesday = 2/5
Let x be the part built on Wednesday,
If the shed is finished on Wednesday,
Total part of work = 1= -9/10 = 10-9/10 = 1/10
Hence, she built shed on Wednesday.
The Obama family is building a circular swimming pool. If the radius of the pool is 15 feet, What is its circumference? Use I = 3.14 to solve.
Answers
The formula for circumference is given by
C = pi *d where pi = 3.14 and d is the diameter
We can find the diameter from the radius
d = 2*r where r is the radius
C = pi * 2 *r
C = 3.14 * 2 * 15
C =94.2 ft
0.16 whole number , integer, rational number (can be more than one set)
Answers
Answer : 0.16 is a rational number
Rational number is a number such that can be expressed as the quotient or fraction of two integers
An integer is a number that can be written without a fractional component
0. 16 can be written as
16 / 100
16 and 100 are both integers but 0.16 is not an integer but a rational number
16 / 100 = 0.16. This means that fraction of two integers that does does not gives an integer is a rational number
Hence, 0.16 is a ratioanal number
Abby's dog ate 0.75kg of food per day for one week. How much food
did Abby's dog eat?
Answers
Answer:
5.25 kg
Step-by-step explanation:
0.75kgx7(1week)=5.25
Answer:
5.25kg of food
Step-by-step explanation:
From the top of a high diving board to the bottom of a pool is 1,154 centimeters. If the pool is 244 centimeters deep, estimate the distance from the high diving board to the surface of the pool by rounding each number to the nearest hundred.
Answers
So, from the top of the diving board to the bottom of a pool is 1,154. If we subtract this from the depth of the pool, we'll find the distance from the diving board to the surface of the pool.
So, 1,154 - 244 = 910cm. About 9 meters, 900cm.
Also, if we round each number to the nearest hundred, we'll have
1,100 - 200 = 900 cm.
Oliver and Robin have different stride lengths and want to compare them. Oliver uses a table to represent the distance he travels in feet related tothe number of strides he takes. Question 2 Using Robin's graph, how can you find the unit rate?
Answers
The grpah is plotted with the number of strides along the x axis and the distance travelled along the y axis.
So, the slope of the graph gives the distance travelled by Robin per stride or the stride length. The approximate value of slope of the graph is,
[tex]\text{Slope}=\frac{\Delta y}{\Delta x}=\frac{8-0}{3-0}=\frac{8}{3}=2.67[/tex]So, the stride length or the unit rate of Robin is approximately 2.67 feet.
What concentration of mixture would need to be added to protect the cars engine from the coolant boiling away at 230 F
Answers
The mixture should be at a concentration of 65.5% to protect the cars from the coolant boiling away at 230°F .
The given table has the concentration percentages and the boiling points of the antifreeze.
So the coolant boils away at 230F, so we need to find the concertation whose boiling point is higher than 230F .
From the table it is evident that the boiling point of 236 is good to protect the coolant as it is higher and closest to the given temperature.
Corresponding to the temperature we have , the percentage at 65.5%.
As 236F > 230F , so it is evident that we need the concentration of 65.5%.
1. a break will be needed for the x axis.
2. The graph of the table is attached below.
the red line indicates 230F, so the value above it is the required data.
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How do I solve this and what is the answer
Answers
The speed of the vehicle is modeled by
[tex]y=9x+3[/tex]To find the initial value from the linaer function.
If x<0, then the velocity becomes negative. But velocity of a vehicle can not be negative.
Therefore x assumes greater than or equal to 0.
Putting x=0, the value of y is 3.
Therefore, the initial value is 3
Hence the correct answer is (C)
In the diagram shown, it is known that line RP upside-down T line QS and line RP bisects
Answers
Since we know that RP is perpendicular to QS we know that the bisector gives us two right triangles. Furthermore, the bisector divides by two the angle of 104, then the angle SRP is equal to 52°.
Now, we know that the interior angles of any triangle add to 180°. Therefore:
[tex]\begin{gathered} m\angle S+52+90=180 \\ m\angle S=180-52-90 \\ m\angle S=38 \end{gathered}[/tex]points (k,-3) lies on the line whose equation is X-2y=-2 what is the value of k
Answers
(k,-3)
x-2y=-2
replace (x,y ) for (k,-3) and solve for k
k-2(-3)=-2
k+6 =-2
k= -2-6
k=-8
the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2. find the number
Answers
The required number would be 2 which represents "the sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2."
The sum of 4 times a number, and -2 is the same as the sum of five times the number, and -2.
Let's assume the number would be x
As per the given condition, the algebraic form would be as
⇒ 4(x - 2) = 5(x - 2)
Apply the distributive property of multiplication,
⇒ 4x - 8 = 5x - 10
Rearrange the terms of variable x,
⇒ 5x - 4x = 10 - 8
Apply the subtraction operation,
⇒ x = 2
Therefore, the required number would be 2.
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The function f is defined as follows for the domain given. f(x)= 1-3x domain = (-1, 0, 1, 2)(a)Write the range of f using set notation. (b)Then graph f.
Answers
Answer:
(a)Range: {-5, -2 ,1 ,4}
Explanation:
The function f is defined below:
[tex]f\mleft(x\mright)=1-3x[/tex]The domain of f(x) = {-1, 0, 1, 2}.
(a)To find the range of f(x), we evaluate f(x) for each value in the domain.
[tex]\begin{gathered} f\mleft(-1\mright)=1-3\left(-1\right)=1+3=4 \\ f\mleft(0\mright)=1-3(0)=1-0=1 \\ f\lparen1)=1-3(1)=1-3=-2 \\ f\mleft(2\mright)=1-3(2)=1-6=-5 \end{gathered}[/tex]Therefore, the range of f is:
[tex]\{-5,-2,1,4\}[/tex](b)Next, we graph f.
Evaluate the quantity G(-7) given the following function.G(x) = x2 + 4x - 12G(-7)=exact number, no toleranceexact number, no tolerance
Answers
Explanation
Step 1
replace the value of x in the equation with the given value
[tex]\begin{gathered} G(x)=x^2+4x-12 \\ \text{then} \\ G(-7)=(-7)^2+4\cdot-7-12 \\ G(-7)=49-28-12 \\ G(-7)=9 \end{gathered}[/tex]I hope this helps you
Point A is located at coordinates (-4,3). у. А 2 1 -3 -2 2. 3 $ X 1 2 3 What are the coordinates of each point? 1. Point B is the image of A after a rotation of 180° using (0,0) as center. 2. Point C is the image of A after a translation two units to the right, then a reflection using the c-axis. 3. Point D is the image of A after a reflection using the y-axis, then a translation two units to the right.
Answers
1. The rotation of a point in 180 degrees is given by reflecting both of its coordinates. In this case the original point is (-4, 3), so the rotated point will be (4, -3).
2. When we reflect a point around the x-axis we need to invert the signal of the y-coordinate. When we make a translation to the right we need to add the number of units to the x-coordinate of the point, therefore.
Translation:
A' = (-4 + 2, 3) = (-2, 3)
Reflection x-axis:
C = (-2, -3)
3. When we reflect a point around the y-axis we invert the signal of x-coordinate. To perform a translation to the right we add the number of units to the x-coordinates, therefore:
Reflection y-axis:
A'' = (4, 3)
Translation:
D = (4 + 2, 3) = (6,3)
If you vertically compress the absolute value parent function, f(x) = lxl, by afactor of 5, what is the equation of the new function?OA. g(x) = 51x|OB. g(x)=x-51OC. g(x) = 15x|O D. g(x) = x
Answers
When the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
The given function is of the form f(x) = ·|x| .
Therefore we can say that this function will be vertically compressed.
From the properties of transformation of graphs we know that when a function is vertically compressed by a factor of a we get the transformed function as 1/a times the original function.
given function:
f(x) = |x|
vertically compressed by 5.
therefore new function = 1/5 |x|
Hence the transformed function is g(x) .
g(x) = 1/5 |x|
Let us take a few coordinates along the x-axis to get the values of the y and the graph of both modulus function pass through origin .
f(x) = |x|
at x = 10 , f(x) = 10
and g(x) = 2
Here we see that the function is compressed.
Therefore when the parent function f(x) = |x| is vertically compressed by a factor of 5 then we get the transformed function as g(x) = 1/5 |x| .
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Find the length of XY if W is between X and Y, WX = 38 and WY = 16.XY =
Answers
Answer
XY = 54 units
Explanation
We are told that W is in between X and Y. This means that
XY = XW + WY
WX = XW = 38
WY = 16
XY = ?
We just make the necessary substitutions
XY = XW + WY
XY = 38 + 16 = 54 units
Hope this Helps!!!
14 3/4% as a decimal
Answers
ANSWER
14.75
EXPLANATION
To write a fraction as a decimal we have to do the division. In this case we have a mixed number, so we have the whole part of the decimal and we just have to find the decimal part - which is 3/4.
3/4 is 0.75:
So 14 3/4 is:
[tex]14\frac{3}{4}=14+\frac{3}{4}=14+0.75=14.75[/tex]Which of the following is equal to the fraction below?(6)711O A. 7."44O B. 711411O O C. 11.00O D.D.7744
Answers
given the fraction
[tex](\frac{7}{4})^{11}[/tex]power properties
where
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]then
[tex](\frac{7}{4})^{11}=\frac{7^{11}}{4^{11}}[/tex]then te correct answer is option B
In the scenarios you have explored so far, the angle measures were given, and you used trigonometric ratios to find missing side lengths. To determine the angle measures when only the side lengths are given, you can use inverse trigonometric functions. The input of each function is a number, which represents a ratio of two of the sides. The output of each function is an acute angle measure.Inverse sine: If sin A = z is given, then angle A can be determined by sin ¹2 = A.Inverse cosine: If cos A = x, is given, then angle A can be determined by cos ¹ = A.Inverse tangent: If tan A = z, is given, then angle A can be determined by tan ¹ = A.Let's explore this idea using the familiar 45°-45°-90° isosceles right triangle.
Answers
Given:-
A right angled triangle with side length 1.
To find the required angle value.
So now we use different trigonometric ratios such as,
[tex]sin,cos,tan[/tex]So we get,
[tex]sin^{-1}(\frac{1}{\sqrt{2}})=cos^{-1}(\frac{1}{\sqrt{2}})=tan^{-1}(\frac{1}{1})=45[/tex]So the required angle is 45 degree.
Find an equation of the line passing through point (4, -5) and perpendicular to the line whose equation is y= 1/2x + 11/6. *In Slope-Intercept Form
Answers
Explanation:
Given the equation:
[tex]y=\frac{1}{2}x+\frac{11}{6}[/tex]Comparing it with the slope-intercept form: y=mx+b
[tex]\text{Slope,m}=\frac{1}{2}[/tex]Definition: Two lines are perpendicular if the product of the slopes is -1.
Let the slope of the new line = n
[tex]\begin{gathered} \frac{1}{2}n=-1 \\ n=-2 \end{gathered}[/tex]Substitute the slope, -2 and point (4,-5) in the slope-point form:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-2(x-4) \end{gathered}[/tex]We then express it in the slope-intercept form:
[tex]\begin{gathered} y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]The equation of the perpendicular line is y=-2x+3.
Answer:
[tex]y=-2x+3[/tex]Selma and Didi both have parents that live far away. One weekend, both women decide to visit their parents. They each decide to leave for their trips at the same time.
Selma's distance from home is shown in the graph.
Unfortunately, Didi's route has a lot of traffic at the beginning of her trip. Didi's distance from home, in miles, is represented by the function f(x)=12(1.63)x, where x represents the hours she has been traveling.
How do the distances each woman is from home compare during their journeys?
Responses
After 3 hours, Selma is approximately 130 miles from home, and Didi is approximately 52 miles from home.
After 3 hours, Selma is approximately 130 miles from home, and Didi is approximately 52 miles from home.
After 2 hours, Selma is 91 miles from home, and Didi is approximately 20 miles from home.
After 2 hours, Selma is 91 miles from home, and Didi is approximately 20 miles from home.
After 2 hours, Didi is 91 miles from home, and Selma is approximately 20 miles from home.
After 2 hours, Didi is 91 miles from home, and Selma is approximately 20 miles from home.
After 3 hours, Didi is approximately 130 miles from home, and Selma is approximately 52 miles from home.
Answers
After 3 hours, Selma is approximately 130 miles from home and Didi is approximately 52 miles from home
Which of the following numbers is irrational?Select all that apply.(A)8/9(B)pi(C)2.3(Recur)(D)1.5
Answers
Answer:
B) π
Definition
A number is said to be Irrational if it cannot be expressed as a terminating or repeating decimal.
[tex]\begin{gathered} \frac{8}{9}=0.8888888\cdots=0.\bar{8} \\ 2.\bar{3}=2.3333333\cdots \\ \pi=3.1415926535\cdots \end{gathered}[/tex]From the given options
• Option A when converted to a decimal number is a repeating decimal.
,• Option C is also a repeating decimal
,• Option D (1.5) is a Terminating decimal.
Therefore, the only number which is Irrational is π since it neither terminates nor repeats (or recur).
Triangle ABC is similar to triangle DEF. Side AB is the longest side of ABC. It measures 12 centimeters. Side DE is the longest side of DEF. It measures 8 centimeters. What is the scale factor that takes DEF to ABC?
Answers
since these are similar triangles, all sides have a scale factor in order to become the other
since you are being asked for the scale factor from DEF to ABC, the equality should be like this
[tex]8x=12[/tex]solve for x
[tex]x=\frac{12}{8}=\frac{3}{2}[/tex]WHAT WOULD BE THE SCALE FACTOR THAT TAKES ABC TO DEF?
apply same procedure as before, but the initial value should be 12
[tex]\begin{gathered} 12x=8 \\ x=\frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]Choose the option with the proper number of sig figs
Answers
let's break down the expression to get the final result:
[tex]\begin{gathered} \frac{9\text{ }\times10^9}{4.5\text{ }\times10^1}\text{ = }\frac{9}{4.5}\times\text{ }\frac{10^9}{10^1} \\ \frac{9}{4.5}\text{ = }\frac{9\text{ }\times\text{ 10}}{4.5\text{ }\times\text{ 10}}\text{ = }\frac{90}{45} \\ \frac{9}{4.5}\text{ = }2 \\ \\ \frac{10^9}{10^1}\colon\text{ when we divide exponents with same base, } \\ we\text{ take one of the base and combine the exponents by subtracting them:} \\ \frac{10^9}{10^1}=10^{9-1} \\ \frac{10^9}{10^1}=10^8 \end{gathered}[/tex][tex]\begin{gathered} \frac{9}{4.5}\times\text{ }\frac{10^9}{10^1}\text{ = 2 }\times10^8 \\ \\ \text{when dividing decimals, }the\text{ least number of }significant\text{ }figures\text{ in the problem}, \\ \text{ }\det ermines\text{ the significant figures in the answer} \\ 9\text{ = 1 significant, 4.5 = 2 significant} \\ \text{The least significant is 1} \\ \\ \frac{9\text{ }\times10^9}{4.5\text{ }\times10^1}\text{ = 2 }\times10^8 \end{gathered}[/tex]graph the image of the figure after the given rotation. all rotations have a center of rotation at the origin180 degree rotation
Answers
Since all rotations have a center of rotation at the origin, let us first give the coordinates of the vertices of the original figure
If an object M(x, y) is rotated about the origin, the image will have the coordinates M'(-x, -y)
F(-4, 2)
N(-1, -2)
K(3, 0)
P(2, 4)
The coordinates of the new vertices after rotation will be:
F'(4, -2)
N'(1, 2)
K'(-3, 0)
P'(-2, -4)
The graph is shown below:
If you were to make a relative frequency table, which percent would go in the cell for red cars?1. 23.6%2. 27.3%3. 18.2%4. 30.9%
Answers
Answer:
23.6%
Explanation:
A relative frequency table shows the number of times a specific event occurs compared to the total number of events.
First, we calculate the total number of vehicles.
[tex]15+13+10+17=55[/tex]Next, the number of red cars = 13.
Therefore, the relative frequency for red cars will be:
[tex]\frac{13}{55}=0.236=23.6\%[/tex]The percent that would go in the cell for red cars is 23.6%.
find the angle theta with 0°
Answers
To determine the number of trout in a lake, a conversationist catches 141 trout, tags them and trows them back into the lake. Later, 45 trout are caught and 15 are tagged. How many trout would the conversationist expect to be in the lake???
Answers
Find the volume of the circular cone picture below use 3.14 for pie. round your answer to the nearest whole number.
Answers
To find:
The volume of the circular cone whose height is 69 meters and the radius of the cone is 21 meters.
Solution:
The formula used to find the volume of the cylinder with height h and the radius r is given below:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Fro the given question, h = 69 and r = 21. So, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\times3.14\times(21)^2\times69 \\ =31849.02m^3 \end{gathered}[/tex]Thus, the volume of the cone to neart
Find the angles using the diagram below. Line ris // to lines, and line tis I toline s.S3225045tm21= 2m22= 4m3= 5
Answers
To begin answering the question, let us familiarize ourselves with some basic terms
Linear Pairs: Two adjacent angles are a linear pair when their noncommon sides are opposite rays.
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees.
Vertical angles: Vertical angles are a pair of opposite angles formed by intersecting lines.
Vertical angles are equal.
We can now apply this knowledege to find the required angles
To find the measure of angle 1 (m<1)
[tex]\begin{gathered} m<1\text{ and 25}^0\text{ are linear pairs} \\ so\text{ they add up to 180}^0 \\ \end{gathered}[/tex]This means that
[tex]\begin{gathered} m<1+25^0=180^0 \\ m<1=180^0-25^0 \\ m<1=155^0 \end{gathered}[/tex]Thus, m<1 = 155°
To find the measure of angle 2 (m<2)
[tex]\begin{gathered} m<2\text{ and 25}^0\text{ are vertical angles} \\ \text{This means that they are equal} \end{gathered}[/tex]Hence,
[tex]m<2=25^0[/tex]m<2 =25°
To get the measure of angle 3 (m<3)
Given: Line t is perpendicular to s
Wehen two lines are perpendicular to eachother, they meet at right angle
This means that
[tex]m<3=90^0[/tex]Thus,
m<3=90°
Hence, the summary of the solution is shown below
[tex]\begin{gathered} m\angle1\Rightarrow155^0 \\ m\angle2\Rightarrow25^0 \\ m\angle3\Rightarrow90^0 \end{gathered}[/tex]