Answers
The values of the equations that are given will be:
17. b + 9 and -b + 7
18. c - 4 and c + 4
19. a + b - c and a + b + c
20. 5 + 2b and 5 - 2b
21. 4 - h - b and -b + h - 4
22. 2 - b - 2h and b - 2
How to express the equation?Based on the information given, it should be noted that the equations will be expressed thus:
It should be noted that an equation is used to show the relationship between the variables. The equations will be:
17. |b + 1| + 8
= b + 1 + 8
= b + 9
and
|b + 1| + 8
= -b - 1 + 8
= -b + 7
18. 5 - |c + 1|
= 5 - c + 1
= - c + 4
= c - 4
and
5 - |c + 1|
5 + c - 1
= c + 4
19. |a + b|- c
= a + b - c
and
-a - b - c
Multiply through by -
= a + b + c
20. 5 + |2b|
= 5 + 2b
and
5 + |2b|
= 5 - 2b
21. |4 - h| - b
= 4 - h - b
and
-4 + h - b
= -b + h - 4
22. |2 - b - h| - h
= 2 - b - h - h
= 2 - b - 2h
and
-2 + b + h - h
= b - 2
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Related Questions
A kangaroo hops 2 kilometers in 3 minutes. At this rate, how long, in minutes, does it take the kangaroo to hop 5 kilometers? Answer ________________________ minutes At this rate, how far, in kilometers, does the kangaroo travel in 2 minutes? Answer ________________________ kilometers
Answers
Answer:
It takes the kangaroo 7.5 minutes to travel 5 kilometers.
Step-by-step explanation:
It takes the kangaroo 7.5 minutes to travel 5 kilometers.
First step is to formulate
3×5/2
Second step is to determine the time by calculating the product or quotient
Time=3×5/2
Time=15/2
Time=7.5 minutes
Inconclusion how long it takes the kangaroo to travel 5 kilometers is 7.5 minutes.
The height, h, in meters, of a falling object is related to the time, t, in seconds, the object
has been falling, by the formula h= -4.9t² + d, where d is the initial height, in meters, of
the object above the ground. If an object is dropped from a height of 32 meters, how long
does it take the object to hit the ground? Round the answer to the nearest hundredth of a second.
Answers
The amount of time it would take this object to hit the ground is 2.56 seconds.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
What is the maximum value of a function?The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.
The height (h) in meters, of this falling object is related to the time by the following function:
h = -4.9t² + d
Substituting the given parameters into the formula, we have;
0 = -4.9t² + 32
4.9t² = 32
Time, t² = 32/4.9
Time, t² = 6.53
Time, t = √6.53
Time, t = 2.56 seconds.
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I need help!!! I’m taking a test that might feasible my grade
Answers
Answer:
you'll need a graph to answer this
12. The sales tax rate in a certain state is 6%.
Find the total price paid for a pair of pants
that costs $44.
Answers
Answer:
$46.64
Step-by-step explanation:
convert 6% to .06
multiply that by 44
you get 2.64.
add that to 44 to get a final ansewr of 46.64 dollers
A total of 290 people attended the high school play. The admission prices were $14 for adults, $7 for high school students, and $3 for children not yet in high school. The ticket sales totalled $2040 The principal suggested that next year they raise prices to $17 for adults, $8 for high school students, and $4 for children not yet in high school. He said that if exactly the same number of people attend next year, the ticket sales at the higher prices will total $2470
How many adults, high school students, and children not yet in high school attended this year?
Answers
The number of adults, high school students, and children not yet in high school attended this year are respectively; 70, 100, 120
How to solve a system of simultaneous equations?We are told that a total of 290 people attended the high school play.
If x represents number of adults, y represents number of high school students and z represents number of children, then we have;
x + y + z = 290 ---- (1)
The admission prices were $14 for adults, $7 for high school students, and $3 for children not yet in high school. The ticket sales totaled $2040 . Thus;
14x + 7y + 3z = 2040 ---- (2)
The principal suggested that next year they raise prices to $17 for adults, $8 for high school students, and $4 for children not yet in high school. Total cost of $2470. Thus;
17x + 8y + 4z = 2470 ---- (3)
Solving the three equations simultaneously gives;
x = 70, y = 100, z = 120
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Convert 180 pounds to kilograms
Answers
Answer:
"What is 180 lbs to kg?" is the same as "What is 180 pounds to kilograms?" or "What is 180 pounds to kg?" or "What is 180 lbs to kilograms?" Here we will show you how to convert 180 lbs to kg.
There are 0.45359237 kilograms per pound and there are 2.204622622 pounds per kilogram. Therefore, you can get the answer to "180 lbs to kg?" two different ways. You can either divide 180 by 2.204622622 or multiply 180 by 0.45359237. Therefore, the answer is
Step-by-step explanation:
81.6466
Four teenage, who all work at the same rate, can clean a house in 6 hours. How long would it take three of them to clean the same hose.
Answers
If 4 teenagers can clean in 6 hours, 1 teenager will take 4x more time
1 teenager will take 24 hours = k
No. of teenagers (p) is proportional to time (t):
p = k/t
3 = 24/t
t = 24/3 = 8 hours
So it will take 8 hours for 3 teenagers to clean a house.
8 hours
Step-by-step explanation:
teenagers. hours
4. 6
3. ?
it is actually direct multiplication where you multiply the upper numbers,4 × 6 ,then divide by the lower value, 3. This gives 24 /3 which gives you 8 .
Use the image above to identify and explain the relationship between the segments and circles A and B. In your explanation, be sure to include specific vocabulary and definitions for the relationships.
PS
Answers
Circle A and Circle B's connection
Circle A's size is more significant than Circle B's size.
As a result, circle A's radius exceeds circle B's radius.
The connection between segments
1.
Let M be the location where Segment QT and ER intersect.
Additionally, tangents from an outside point to a circle have identical lengths.
QM = ME———— (1)
MT=MR————(2)
Including (1) and (2)
MR + ME = QM + MT
Q T=ER
2.
Tangents from an exterior point to a circle have identical lengths.
We may write the following segments are equal using this property.
UP=U Q
ZC=ZR
VC=VS
NR=NS
KC=K T
What are Tangents?
A line that only touches a circle or an ellipse at one point is said to be divergent in geometry. If a line contacts a curve at point P, that point is referred to as the point of tangency. In other words, it is described as the line that, at that particular location, indicates the slope of a curve. The following methods can be used to find the tangent equation in differential geometry:
As we are aware, the gradient of the curve at any given location on the curve is equal to the gradient of the tangent to the curve. The following is how to determine the tangent equation of the curve y = f(x):
Utilizing the differentiation principles, determine the gradient function's derivative.
To determine the tangent's gradient, the derivative should be changed to include the provided point's x-coordinate
Find the tangent equation by substituting the provided coordinate point and the gradient of the tangent into the straight-line equation (in a slope-point formula).
Circle's Tangent
A closed, two-dimensional form, a circle is also a curve. The radius of the circle or the line from the center O to the point of tangency is always vertical or perpendicular to the tangent line AB at P, i.e., OP is perpendicular to AB as illustrated in the accompanying picture.
Geometric Tangent
Here, "AB" stands for the tangent, "P" for the point of tangency, and "O" for the circle's center. The OP is the radius of the circle.
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suppose 39% of recent college graduates plan on pursuing a graduate degree. twenty one recent college graduates are randomly selected. a. what is the probability that no more than five of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) b. what is the probability that exactly eight of the college graduates plan to pursue a graduate degree? (do not round intermediate calculations. round your final answer to 4 decimal places.) c. what is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree?
Answers
0.6054 is the probability that at least eight but no more than thirteen of the college graduates plan to pursue a graduate degree.
What are examples and probability?
It is predicated on the likelihood that something will occur. The justification for probability serves as the basic foundation for theoretical probability. For instance, the theoretical chance of receiving a head while tossing a coin is 12.this is binomial with parameter n=21 and p=0.39
a)
probability = P(X<=5)= ∑x=0x (nCx)px(1−p)(n-x) = 0.1124
b)
probability = P(X=8)= (nCx)px(1−p)(n-x) = 0.1763
c)
probability = P(8<=X<=13)= ∑x=x1x2 (nCx)px(1−p)(n-x) = 0.6054
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Demuestra las funciones trigonométricas de 45o a partir de un cuadrado con longitud de lado igual a 1.
Answers
The most appropriate choice for trigonometric function will be given by -
sin 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = 1
cot 45° = 1
sec 45° = [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\sqrt{2}[/tex]
What are trigonometric functions?
Trigonometric functions are those functions which shows the relationship between side and angle of a right angled triangle.
There are six trigonometric functions-
[tex]sin \theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin \theta[/tex] = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
[tex]cos\theta[/tex] = [tex]\frac{Base}{Hypotenuse}[/tex]
[tex]tan\theta[/tex] = [tex]\frac{Perpendicular}{Base}[/tex]
[tex]cot\theta[/tex] = [tex]\frac{Base}{Perpendicular}[/tex]
[tex]sec\theta[/tex] = [tex]\frac{Hypotenuse}{Base}[/tex]
[tex]cosec\theta[/tex] = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
Here,
The diagram of the square has been attached with this answer
∠ABC = 90° [Side of a square is 90°}
∠BAC = [tex]\frac{90}{2}[/tex]
= [tex]45[/tex]°
Side of square = 1 unit
Length of diagonal of a square = [tex]\sqrt{2}[/tex] [tex]\times[/tex] side
= [tex]\sqrt{2}[/tex] [tex]\times[/tex] [tex]1[/tex]
= [tex]\sqrt{2}[/tex] units
From [tex]\Delta[/tex] ABC,
sin 45° = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]
= [tex]\frac{BC}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
cos 45° = [tex]\frac{Base}{Hypotenuse}[/tex]
= [tex]\frac{AB}{AC}[/tex]
= [tex]\frac{1}{\sqrt{2} }[/tex]
tan 45° = [tex]\frac{Perpendicular}{Base}[/tex]
= [tex]\frac{BC}{AB}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
cot 45° = [tex]\frac{Base}{Perpendicular}[/tex]
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
sec 45° = [tex]\frac{Hypotenuse}{Base}[/tex]
= [tex]\frac{AC}{AB}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
cosec 45° = [tex]\frac{Hypotenuse}{Perpendicular}[/tex]
= [tex]\frac{AC}{BC}[/tex]
= [tex]\frac{\sqrt{2} }{1}[/tex]
= [tex]\sqrt{2}[/tex]
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Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A.
all of the measurement pairs that could be the dimensions of Rectangle B.
Answers
When Rectangle A measures 9 inches by 3 inches and rectangle B is a scaled copy of Rectangle A, the possible dimensions will be:
3 inches by 1 inches6 inches by 2 inchesHow to express the value?From the information, Rectangle A measures 9 inches by 3 inches. Therefore, the ratio will be:
=Length / Width
= 9 / 3
= 3:1
Therefore, a scaled copy will have an equivalent ratio of 3:1.
This can be 3 inches by 1 inches and 6 inches by 2 inches. Their ratio is:
= 6/2 = 3:1.
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A 10-visit movie pass costs $79.50. What is the unit rate for each visit
Answers
Answer:
$7.95 per visit
Step-by-step explanation:
To find the unit rate, divide dollars by number of visits.
79.5 ÷ 10 = 7.95
Solve question.
I will give you as many points as possible.
Answers
Answer : 3500
Reasoning 2589+2920+3500=9009
Then 9009/3 = 3003
Round 3003 to 3000 and there's your answer
A sandwich store charges $20 to have 3 turkey subs delivered and $26 to have 4 delivered.
Is the relationship between number of turkey subs delivered and amount charged proportional? Explain how you know. (Proportional just means equal)
Answers
A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four. There is no proportionality between the quantity of turkey subs delivered and the amount billed.
Given that,
A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four.
We have to find the relation ship between the quantity of turkey subs delivered and the amount billed.
The reciprocal of the ratio of subs to amount charges is
We get,
3/20 and 4/26
Since,
3/20≠4/26
Therefore, There is no proportionality between the quantity of turkey subs delivered and the amount billed.
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Leily was guessing Joseph’s number. He said that his number was composite, even, and a square number between 15 and 30. What is Joseph’s number?
Answers
The number that Joseph is thinking of that is between 15 and 30 is 16.
What is Joseph’s number?The first step is to determine the squares between 15 and 30. The square of a number is the product of a number with itself. For example, 16 is a square number.
Squares between 15 and 30 = 16, 25
The next step is to determine the even number. An even number is a number that is perfectly divisible by 2. An example of an even number is 4.
The even number that is a square between 15 and 30 is 16.
The last step is to determine the composite number. A composite number is a number that has more than 2 factors.
Factors of 16 = 1, 2, 4, 8, 16
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3. a 95% confidence interval for a slope spans from 10 to 20, but the level of confidence changes to 99%, list a plausible 99% confidence interval for the new slope
Answers
( 8.43 , 21.57) is ist a plausible 99% confidence interval for the new slope.
In algebra, what is an interval?
In mathematics, an interval is expressed in numerical terms. All the numbers between two specific integers are referred to as an interval. All actual values between those two are included in this range. Any form of number you may imagine is a real number.95% of confidence interval = (10 ,20)
x = 10 + 20 /2 = 15
margin of error = 20 - 10 /2 = 10/2 = 5
SE = Margin of error/2 = 5/1.96 = 2.551
99% confidence interval = x ± z/2 * 3E
= 15 ± 2.576 * 3E.
= 15 ± 2.576 * 2551
= 15 ± 6.571376
= (15- 6.571376 , 15 + 6.571376)
= ( 8.43 , 21.57)
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suppose a series system has three components c1, c2, and c3 with the probability that each component functions equal to 0.90, 0.99, and 0.95, respectively. what is the probability that the system operates? (4 decimals)
Answers
0.8465 is the probability that the system operates if the probability that each component functions equals to 0.90, 0.99, and 0.95 respectively.
As the components are in a series system, this means that all the components have to function in order for the system to operate, and the failure of any one of the components to function will result in the system not operating.
Therefore, the probability for the system to operate is the probability that all the components c1, c2, and c3 function together
The probability of multiple events occurring together can be found by multiplying the probabilities of each event by one another.
Therefore;
Probability = 0.90 × 0.99 × 0.95
Probability = 0.84645
Rounding it off to 4 decimals as follows;
Probability = 0.84645 = 0.8465
Therefore, the probability that the system operates is calculated to be 0.8465.
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Kinsley's house is due west of summerfield and due south of hillsdale. summerfield is 6 kilometers from kinsley's house and 10 kilometers from hillsdale. how far is hillsdale from kinsley's house, measured in a straight line?
Answers
The Hillsdale is 8 km from the Kinsley's house
Let Kinsley's house be A
Summerfield be B
Hillsdale be C
The Kinsley's house due west of Summerfield be AB which is 6 km and The distance between Summerfield and Hillsdale is BC which is 10 km
Distance between Kinsley's house and Hillsdale can be calculated using Pythagoras' theorem, which states that the square of the hypotenuse is equal to the sum of the square of the other two sides.
BC² = AB² + AC²
We need AC, so let us rewrite this equation
AC² = BC² - AB²
AC² = 10² - 6²
AC² = 100 - 36
AC² = 64
AC = √64
AC = 8 km
Therefore, Kinsley's house is due south of Hillsdale from 8 km
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As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution.
Answers
As the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.
What is sampling distribution?Regardless of the distribution of the population one samples from, is roughly normally distributed for a large sample size (we shall explain this later). The population will have a mean and standard deviation if it has a mean and one.Regardless of the distribution of the population, the central limit theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases. The CLT is frequently thought to hold for sample sizes equal to or larger than 30.The sample size and variability affect how accurate your statistics are. A tighter confidence interval with a smaller margin of error will be obtained with a bigger sample size or lower variability.Therefore, as the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.
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calculate the volume of air in liters that you might inhale (and exhale) in 8.00 hours. assume that each breath has a volume of 0.475 liters, and that you are breathing 18 times a minute.
Answers
The volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.
What is defined as the unitary method?The unitary method is one that involves determining the value of a single unit and then calculating the value of a required number of units based on that value.The unitary method's formula is to identify the value of a specific unit and then multiply that value by the number of units to arrive at the required value.For the given question;
The volume of air inhale (and exhale) once = 0.475 liters
Number of breathing in 1 minutes = 18 times.
Thus, the volume of air inhaled in 1 minutes is 0.47×18 = 8.46 litres.
This can be written as;
1 minutes ------- > 8.46 litres of air.
For calculating in 8 hours that is 8×60 = 480 minutes, multiply the both side by 480 in above equation;
1× 480 minutes ------- > 480×8.46 litres of air.
480 minutes --------> 4060.8 litres of air.
Therefore. the volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.
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Given: A, B, and C are collinear, AB=BD, and BD=BC
Prove: B is the midpoint of AC
Answers
Using the definition of a midpoint and collinear points, the proof that shows that B is the midpoint of AC is explained below.
What are Collinear Points?If three points are on a straight line, they are defined as being collinear points. That is, three points, A, B, and C are collinear points if they are on a straight line, and B is in the middle of points A and b.
What is the Midpoint of a Segment?When a segment is divided into two equal halves, the point that lies in the middle of the segment where the segment is cut into halves is called the midpoint of the line segment.
The proof that shows that B is the midpoint of line segment AC is shown below:
Statements Reasons
a. A, B, and C are collinear a. Given
AB = BD, BD = BC
b. AB = BC b. Substitution
c. AB ≅ BC c. Definition of congruency
d. B is the midpoint d. AB ≅ BC
Thus, the proof above explains how point B is the midpoint of line segment AC in the image given.
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pic below!! find the surface area of a cube with side lengths of 2 m
Answers
Answer:
24
Step-by-step explanation:
the equation is 6s^2, where s=2. This equals 24
Answer:
Step-by-step explanation: area of one square 2x2 right, then you multiply to get 4 then x6 because of the six sides to a cube then you get 24
2.5, 10, 17, 26...
a Arithmetic, geometric, or neither?
c. Explicit:
b. Recursive:
Answers
Express x2-5x + 8 in the form (x-a)² + b
where a and b are top-heavy fractions.
Answers
Using Complete the Square method, we find out that [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.
It is given to us that the expression is -
[tex]x^{2} -5x+8[/tex] ----(1)
We have to express it in the form of[tex](x-a)^{2}+b[/tex] where a and b are top-heavy fractions.
In order to achieve the required expression in the form of [tex](x-a)^{2}+b[/tex] we have to use "Completing the Square" method.
The given expression from (1) is -
[tex]x^{2} -5x+8[/tex]
This expression is in the form of [tex]ax^{2} +bx+c[/tex]
Adding and subtracting [tex](b/2)^{2}[/tex] terms into the expression, we get
[tex]x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8[/tex] -----(2)
Equation (2) can also be represented as -
[tex](x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8[/tex]
[tex]= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex]------- (3)
We see that equation (3) is in the form of [tex](x-a)^{2}+b[/tex].
So, we can derive that -
[tex]a=\frac{5}{2}[/tex]
and, [tex]b=\frac{7}{4}[/tex].
Thus, [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] through "Complete the Square" method as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.
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exclude leap years from the following calculations. (a) compute the probability that a randomly selected person does not have a birthday on december 9. (b) compute the probability that a randomly selected person does not have a birthday on the 3rd day of a month. (c) compute the probability that a randomly selected person does not have a birthday on the 30th day of a month. (d) compute the probability that a randomly selected person was not born in february.
Answers
Answer:
yes
Step-by-step explanation:
Goggle
A kite is at the end of a string that is 40 meters long. The person
is holding the end of the string 3 meters off the ground, and the
angle of elevation formed by the string is 50°. Which expression
represents how high in meters the kite is off the ground?
Answers
The expression representing height of kite from ground is Height = sin 50° × 40.
The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -
sin theta = perpendicular ÷ hypotenuse
Keep the values in mentioned trigonometric relation to find the expression -
sin 50 = height ÷ 40
Height = sin 50° × 40
Finding the height using formed equation -
Height = 0.77 × 40
Performing multiplication
Height = 30.64 meters
Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.
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if b=5, what is b^3=
Answers
Answer:
15
Step-by-step explanation:
B*3
5*3
15
Answer:
Step-by-step explanation: if b= 5 the the equation will be (5)^3 you multiply and get 15
Function g is a transformation of the parent function f(x) = x2. The graph of g is a translation left 4 units and down 2 units of the graph of f.
Write the equation for g in the form y = ax2 + bx + c.
Answers
f(x) = x^2
write new equation after translation using vertex form;
(x+4)^2 - 2
simplify; convert to standard form
(x+4)(x+4) - 2
x^2 + 8x - 2
The function after translation is g(x) = x²+ 8x - 2.
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
f(x) = x²
Now, g is a translation left 4 units and down 2 units of the graph of f.
So, g(x)= (x+4)² - 2
Then, in the standard form
g(x) = (x+4)(x+4) - 2
g(x) = x²+ 8x - 2
Hence, the function is g(x) = x²+ 8x - 2.
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50pts for this question:)
Answers
Answer: 1: 6√6 = 36
hope this helps, good luck!
f+15+7g terms: coefficients:
Answers
Based on the given expression; there are three terms;
f157gand one coefficient; 7
Terms and coefficientsA term refers to any value (variable or constant) or expression separated from another term by a space or an appropriate character or symbol, in an overall expression.
Coefficient refers to be a constant by which an algebraic term is multiplied.
f + 15 + 7g
There are three terms in the expression;
f157gFrom the task given above,
The coefficient of 7g is 7
Also the coefficient of f is 1.
Therefore, the terms in the expression are f, 15 and 7g.
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