Transformations are used to move a function from one position to another. The function of g(x) is g(x) = x/6
Given:
f(x)=|x|
The rule of a horizontal stretch by factor k is: (x,y) = (x/k, y)
i,e
g(x) = f(x/k)
where k is 6
g(x) = f(x/6)
so, f(x/6) = x/6
Hence g(x) = x/6
What is transformation?In mathematics, a transformation is a function f, usually on some geometric basis, that maps the set X to itself, i.e. f X → X. Examples are linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and certain affine transformations such as rotations, reflections, and translations. Although it is common to use the expression transformation of a set with some function to itself, there is an alternative form of terminology where the expression "transformation" is reserved for conjecture only. If such a narrow definition of a transformation is generalized to partial functions, then a partial transformation is a function f: A → B, where both A and B are subsets of some set X.
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The manager of a restaurant found that the cost to produce 200 cups of coffee is $19.91,
while the cost to produce 500 cups is $47.81. Assume the cost C(x) is a linear function of x,
the number of cups
What’s the c(x) function
The cost function to produce x cups of coffee is C(x) = 0.093x + 1.31
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
A linear function is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
Let C(x) represent the cost to make x cups. If m is the rate of making each cup and b is the initial cost of start up, hence:
The manage produce 200 cups of coffee is $19.91:
19.91 = 200m + b (1)
Also, to produce 500 cups is $47.81:
47.81 = 500m + b (2)
From both equations:
m = 0.093 and b = 1.31
The cost function is C(x) = 0.093x + 1.31
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Tamar has four more quarters than dimes. If he has a total of $1.70, how many quarters
and dimes does he have?
================================================
Work Shown:
d = number of dimes
q = number of quarters
q = d+4 since she has 4 more quarters than dimes
$1.70 = 170 cents
10d = value of all the dimes in cents
25q = value of all the quarters in cents
10d+25q = total value of all the coins in cents
10d+25q = 170
10d+25( q ) = 170
10d+25( d+4 ) = 170 .... plug in q = d+4
10d+25d+100 = 170 .... distribute
35d+100 = 170
35d = 170-100 ..... subtract 100 from both sides
35d = 70
d = 70/35 ... divide both sides by 35
d = 2
He has 2 dimes
q = d+4
q = 2+4
q = 6
He also has 6 quarters
------------------
Check:
1 dime = 10 cents
2 dimes = 20 cents ..... multiply both sides by 2
1 quarter = 25 cents
6 quarters = 150 cents ..... multiply both sides by 6
(2 dimes) + (6 quarters) = (20 cents) + (150 cents) = 170 cents
This confirms the answers.
help meeeeee pwease
The volume of a cone is 13.4m cubed and the radius is 3.2m what is the height
Answer:
The height is 1.25m.
Step-by-step explanation:
Volume = 1/3 πr²h
Given:
V = 13.4 m³
r = 3.2 m
Asked: height (h)
Substitute the formula with the given values then solve
13.4m³ = 1/3π(3.2m)²h
13.4(3) = 10.24πh
40.2 = 10.24πh
h = 40.2/10.24π
h = 1.25m
The height of the cone is 1.25 meters.
We know that the volume of the cone is given by
V = (1 / 3) * π * r ^2 * h................equation 1
where,
V is the volume of the cone.
r is the radius of the cone's base
h is the height
The volume and radius of the cone are given,
V = 13.4 m
r = 3.2m
substituting these values in equation 1 we get,
13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h
on simplifying further
13.4 = 10.717 * h
h = 1.25m
The height of the cone is 1.25 meters.
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at the state fair there is a ferris wheel with 24 kids on it the ratio of kids to adults is 4 to 5 how many total people are on the ferris wheel
Answer:
270
Step-by-step explanation:First, you need to figure out how many times 24 goes into 120 (120 being the number of minutes in a 2 hour period). When you divide 120 by 24, you get 5.
Next, multiply the number of people (54) by the number of minutes (5) to discover that the Ferris wheel can accommodate 270 people in 2 hours.
$53 es un numero
racional
irracional?
0
Matematica
Answer:
racional
Step-by-step explanation:
porque puedes encuentrarlo en el linea de numeros
Irrational es como 3.1415926535... numerosnque no altan
There are 40 pens and 15 pencils in a pot. Write down the ratio of pens to pencils in its simplest form.
Answer:
8:3
Step-by-step explanation:
we can divide each number by 5 and get the answer
3/10=15/50=18/?
Para ya pLis
a sum of money amounting 5.35 consists of dimes and quarters. if there are 28 coins in all, how many are quarters
Answer:
15 quarter is the answer
please help me on the question I attached an image thank you ❤️
Answer:
<
Step-by-step explanation:
6 1/2 is equal to 6.5, which is less than 6.7
Hope this helps :-)
Answer:
<
Step-by-step explanation:
because 6 7/10 is larger than 6 1/2 so therefore greater than would be your answer❤
whats the square root of ³√27??
Answer:
theres a link to the answer
Step-by-step explanation:
√
27
=
9
√
3
Explanation:
If
a
,
b
≥
0
then
√
a
b
=
√
a
√
b
So
3
√
27
=
3
√
3
2
⋅
3
=
3
√
3
2
√
3
=
3
⋅
3
√
3
=
9
√
3
Answer link
that should be a link up there
the sum of a number and three, divided by seven
Answer:
x+3/7
Step-by-step explanation:
i hope that right
A shape is made up of 10 right triangles of equal size.Each right triangle has a base of 5cm and a height of 4cm.What is the total area in square centimeters,of the shape?
Answer:
The area if the shape is 10 cm².
Step-by-step explanation:
First, you have to find the area of each triangle :
[tex]area = \frac{1}{2} \times base \times height[/tex]
[tex]let \: base = 5,height = 4[/tex]
[tex]area = \frac{1}{2} \times 5 \times 4[/tex]
[tex]area = \frac{1}{2} \times 20[/tex]
[tex]area = 10 {cm}^{2} [/tex]
This shape contain 10 similar triangles so you have to multiply by 10 :
[tex]area = 10 \times 10[/tex]
[tex]area = 100 {cm}^{2} [/tex]
The sum of a and b is irrational. Which of the following statements must be true?
A
a is irrational
B
bis irrational.
C
Either a orb is irrational.
D
Both a and bare irrational.
Seven less than nine times a number is negative seven. What is the number?
Answer:
The answer is 0
Step-by-step explanation:
7 - (9x0)
0-7
-7
Determine whether the lines are parallel or perpendicular or neither.
One line passes through points (−2, −7) and (1, 5);
another line passes through points (4, 1) and (−8, 4)
Answer:
Perpendicular (I believe)
Step-by-step explanation:
f(x)=8−4x−x³
g(x)=x²+7x−9
Find f(x)+g(x).
Answer:
-x^3+x^2+3x-1
Step-by-step explanation:
f(x)=8−4x−x³
g(x)=x²+7x−9
f(x)+g(x) = 8−4x−x³ +x²+7x−9
Combine like terms
=-x^3+x^2+3x-1
Answer:
See below
Step-by-step explanation:
[tex]f(x)=8-4x-x^3\\g(x)=x^2+7x-9[/tex]
Once
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex](f+g)(x)=(8-4x-x^3)+(x^2+7x-9)=-x^3+x^2+3x-1[/tex]
[tex]\therefore (f+g)(x)=-x^3+x^2+3x-1[/tex]
which measures 9.75 ft by 8.63 ft and estimate the area
Answer:Cubic Feet . Cubic Feet . Measure . Per 50 Cubic Feet . Per 40 Cubic Feet .
Step-by-step explanation:
Solve for u.
227 = 49-u
Answer:
-178 = u
Step-by-step explanation:
227 = 49-u
Subtract 49from each side
227-49 = 49-49-u
178 = -u
Multiply each side by -1
-178 = u
given f(x)=3/x and g(x)=x^2-5 find f(g(x))
To perform the composition, we need to substitute g(x) for x in f(x).
f(g(x)) = 3/(x^2 - 5)
Mrs. Thomas wants to open a yarn shop. She surveyed a random sample of 100 knitters about their preference of specialty yarn. The table below shows the results.
Which two inferences can be reasonably made based on the data?
a. More knitters use sequin yarns than fuzzy yarns.
b. Most knitters use some kind of specialty yarn.
c. More knitters like boucle yarn than other specialty yarns.
d. Of 500 knitters, about 175 prefer boucle yarn to other specialty yarns.
e. Of 500 knitters, about 50% will say that they prefer metallic yarn to plain yarn.
Based on the given data, we can Reasonably infer that most knitters use some kind of specialty yarn and that there is a higher preference for boucle yarn compared to other specialty yarns among the surveyed knitters.
Based on the given data, we can make the following inferences:
b. Most knitters use some kind of specialty yarn:
Since the total number of knitters surveyed is 100, and each knitter was asked about their preference for specialty yarn, we can infer that most knitters (if not all) use some kind of specialty yarn. This is because all the surveyed knitters were specifically asked about their preference for specialty yarn, indicating that specialty yarn is commonly used among knitters.
c. More knitters like boucle yarn than other specialty yarns:
According to the data, 40 knitters preferred boucle yarn, which is more than the number of knitters who preferred any other specialty yarn. Therefore, we can infer that among the surveyed knitters, there is a higher preference for boucle yarn compared to other specialty yarns.
The other statements cannot be reasonably inferred from the given data:
a. The data does not provide information about the number of knitters using sequin yarns compared to fuzzy yarns. We only have information about the preference for boucle, mohair, and metallic yarns.
d. The data does not provide information about the preference of 500 knitters or the comparison of boucle yarn to other specialty yarns among a larger population.
e. The data does not provide information about the preference for metallic yarn compared to plain yarn among the surveyed knitters. The data only includes information about the preference for boucle, mohair, and metallic yarns.
In conclusion, based on the given data, we can reasonably infer that most knitters use some kind of specialty yarn and that there is a higher preference for boucle yarn compared to other specialty yarns among the surveyed knitters.
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4. If x=4 and y=10, what is the value of the expression 3x²y + y/2 - 6x?
1. 221
2. 461
3. 872
4. 1916
Answer:
2
Step-by-step explanation:
3*4^2*10+10/2 - 6*4
4*4=16 5 24
3*16*10 + 5 - 24 = 19
480 - 19
Pls help will mark brainliest. Click on the photo.
Answer:
1/50
Step-by-step explanation:
divide B by A to give you the denominator. then choose your answer
Answer: D
Plz dont forget brainliest
Sam has $3.30 in quarters and dimes, and the total number of coins is 18. How many quarters and how many dimes?
Answer:
Quarters: 10
Dimes: 8
Step-by-step explanation:
Constraints
value: 0.25q + 0.10d = 3.30
count: q + d = 18
q = 18 - d
0.25(18-d) + 0.10d = 3.30
4.50-0.25d+0.10d = 3.30
4.50-0.15d = 3.30
-0.15d = -1.20
d = 8
q + d = 18
q + 8 = 18
q = 10
Check:
0.25(10) + 0.10(8) = 3.30
2.5+ 0.80 = 3.30
3.30 = 3.30
Please help! Which point represents-2 3/8
Answer:B
Step-by-step explanation:
How you plug this in binomial probability
The Binomial probability of x = 3 for the given parameters is 0.2048
Using Binomial probability conceptThe Binomial probability relation can expressed as :
[tex]P(x) = nCx * p^{n} * q^{n-x}[/tex]
where :
n = number of trials = 17p = probability of success q = 1 - pfor x = 3
We substitute x into the equation thus :
P(x = 3) = 17C3 * (1/8)³ * (1 - 1/8)¹⁴
P(x = 3) = 0.2048
Therefore, the probability of x = 3 in the scenario given is 0.2048
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If Reyan has 10 pieces of pizza,and she gave jane 3 pieces and Reyan ates 2 pieces.How many pieces of pizza left?
Answer:
5 pieces of pizza are left
Step-by-step explanation:
Because 10 - 3 = 7
7 - 2 = 5
Answer:
5 pieces
Step-by-step explanation:
3 + 2 = 5
10 - 5 = 5
Given h(2)
–5x – 1, solve for x when h(x) = -6.
Answer:
x = 1
Step-by-step explanation:
Step 1: Define
h(x) = -5x - 1
h(x) = -6
Step 2: Substitute and Evaluate
-6 = -5x - 1
-5 = -5x
x = 1
Given the graph of a line y=−x.
Write an equation of a line (there are many) which intersects the line, but is not perpendicular.
There are infinitely many possible answers.
===============================================
Explanation:
If m = 1, then y = mx+b would be perpendicular to the original equation. Recall that if two slopes multiply to -1, then the lines are perpendicular. So we ignore cases when m = 1.If m = -1, and b is nonzero, then y = mx+b is parallel to y = -x. Parallel lines have equal slopes and different y intercepts. We'll ignore m = -1 as well.If m is any other value, then y = mx+b will intersect y = -x exactly once. This is why we have infinitely many solutions. In the case of y = 2x, we have m = 2 and b = 0.How can i solve questions like these?
please tell me the steps and keep it simple
i have trouble solving questions like these
Answer:
7. A = 4pi
8. A = 36pi
9. A = pi/16
Look into explanation to know how to solve these
Step-by-step explanation:
I assume C is the circumference
Now, the formula for C is
[tex]C = 2(pi)r[/tex]
and the formula for area is,
[tex]A = pi(r^2)[/tex]
where r is the radius.
We need to find the radius to find the area
Now, since the circumference is given, we can use that to find the radius in the following manner.
[tex]C = 2(pi)r\\r = C/(2pi)[/tex]
And then put that into the area formula.
So, for your questions.
7. C = 4pi
r = (4pi)/(2pi)
r = 2
and then the area will be,
[tex]A = pi(2^2)[/tex]
A = 4pi
8. C = 12pi
then r = (12pi)/(2pi)
r = 6
and area is,
[tex]A = pi(6^2)[/tex]
A = 36pi
9. C = pi/2
r = (pi/2)/(2pi)
r = 1/4
and area will be then
A = pi(1/4)(1/4)
A = pi/16
The areas in terms of π are
1. A = 4π units²
2. A = 36π units²
3. A = π/16 units²
What is area of a circle?A circle is a round-shaped figure that has no corners or edges.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
The area of a circle is expressed as;
A = πr²
where r is the radius.
The circumference of a circle is expressed as;
C = πd
1. C = 4π , therefore d = 4 and r = 2
A = πr² = 2²π = 4π units²
2. C = 12π , therefore d = 12 and r = 6
A = π6² = 36π units²
3. C = π/2 , therefore d = 1/2 , r = 1/4
A = (1/4)²π
= π/16 units²
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