carmela translates f (x) = x2 to create p (x). If p 9 (x) = f (x+3) -10 sketch the graph

Answers

Answer 1

The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.

What are some rules of function transformations?

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over the y-axis, (-x, y).

-f(x) = Reflection over the x-axis, (x, -y).

Given, A function f(x) = x².

Now, p(x) = f(x + 3).

p(x) = (x + 3)² and it is a transformed function to the parent function f(x).

Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.

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Related Questions

The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-17)®
(7x-3)
56°

Answers

The measurement of three angles in the triangle are 43°, 81°, 56°.

What are the angles of a triangle?

A triangle's interior angles always add up to 180°, whereas its exterior angles are equal to the sum of the two interior angles that are not adjacent to it.

Given three angles,

∠A = (5x - 17)°

∠B = (7x - 3)°

∠C = 56°

We know that in a triangle ∠A + ∠B + ∠C = 180°

By substituting values,

(5x - 17) + (7x - 3) + 56 = 180

12x -20 + 56 = 180

12 x + 36 = 180

12x = 180 - 36

12x = 144

x = 144/12

x = 12

By substituting values of x we get,

∠A = (5x - 17)°

     = 5 x 12 - 17

     = 60 - 17

     = 43

∠A = 43°

∠B = (7x - 3)°

     = 7 x 12 - 3

     = 84 - 3

     = 81

∠B = 81°

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Find the LCM of the first five primes

Answers

Answer:

The first 5 prime numbers are 2, 3, 5, 7 and 11. Their LCM is 2310

A container with an open top is to have 10 m3 capacity and be
made of thin sheet metal. Calculate the dimensions of the box if it
is to use the minimum possible amount of metal.

Answers

The dimensions of the box if it is to use the minimum possible amount of metal are,

⇒ 2.714 m, 2.714 m, 1.358 m

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A container with an open top is to have 10 m³ capacity.

Now,

Let the dimensions are x, y and z.

Since, Volume of box = 10 m³

Hence, We get;

⇒ xyz = 10

⇒ z = 10/xy

Since, A container is open in top.

Hence, The surface area = 2xz + 2yz + xy

Substitute z = 10/xy;

⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy

          = 20/y + 20/x + xy

For minimum metal;

⇒ d (S.A)/ dx = 0

⇒ - 20/x² + y = 0

⇒ y = 20/x²  ..(i)

And, d (S.A) / dy = 0

⇒ - 20/y² + x = 0

⇒ x = 20/y²   ..(ii)

Divide equation (i) and ((ii);

⇒ x = y

Hence, We get;

⇒ xyz = 10

⇒ x³ = 10

⇒ x = 2.714

And, y = 2.714

So, The value of z is,

⇒ z = 10/xy

⇒ z = 10 / 2.714×2.714

⇒ z = 1.358 m

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True or False: 10, 8, 6, 4, … is a geometric sequence.

Answers

Answer:

  False

Step-by-step explanation:

You want to know if it is true that 10, 8, 6, 4, ... is a geometric sequence.

Geometric sequence

A geometric sequence has a common ratio between adjacent terms. Here the ratios are ...

  8/10 = 0.8

  6/8 = 0.75

These numbers are different, so there is no common ratio. The sequence is not a geometric sequence. (False)

Is the value of the first 7 ten times as great as the value of the second 7 in 7237

Answers

Answer:

no

Step-by-step explanation:

On a scale, drawing inches equals 10 miles if the length of the road on the scale is 4 inches which of the following could be used to find the length of the road

Answers

On solving the provided question, we can say that - here in equation 10x + =4 = 2

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

the equation we have is  = 10x + =4 = 2

10x = -2

x = -1/5

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If there are estimated to be 10 ^ 11 galaxies in the known universe and 10 ^ 11 stars in each galaxy, how many stars are estimated to be in the universe?​

Answers

Answer: We can use the information given to find the number of stars in the universe by multiplying the number of galaxies by the number of stars per galaxy:

number of stars = (10 ^ 11 galaxies) x (10 ^ 11 stars per galaxy)

This is a simple arithmetic problem and we can find the solution by multiplying the numbers 10^11 and 10^11

10^11 * 10^11 = (10101010101010101010)(101010101010101010*10) = 10^(11+11) = 10^22

So, there are estimated to be 10 ^ 22 stars in the known universe.

Step-by-step explanation:

Polynomial in standard form

1.
7-3x^3+6x^2

2.
2y-3-8y^2

Answers

Answer:

[tex]-3x^3+6x^2+7[/tex][tex]-8y^2+2y-3[/tex]

Step-by-step explanation:

The terms are ordered from greatest to least degree.

parallel abcd is similar to parallelogrem efgh. what is the lenght of gh?

Answers

The value of side GH as shown in the parallelogram is 2 units

What is an parallelogram?

Parallelogram is a polygon that has four sides (quadrilateral) and opposite sides are always equal and parallel to each other

Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are proportional. Also, their corresponding angles are equal to each other.

Parallelogram abcd is similar to parallelogram efgh, hence:

FG/BC = GH / CD

substituting:

7/21 = GH / 6

GH = 6 * 7/21 = 2

GH is 2 in

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Work out 2/3 - 2/5 in its simplest form

Answers

Answer:

It is in its simplest form

Step-by-step explanation:

The answer to this is 4/15

The altitude of the hypotenuse of a right triangle divides the hypotenuse into two segments. If the ratio of lengths of the segments is 1:9 and the length of the altitude is 6 meters, find the lengths of the two segments?

Answers

Answer:

2 m18 m

Step-by-step explanation:

You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.

Geometric mean

The altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...

  6 = √(x(9x)) = 3√x² = 3x

  x = 2 . . . . . . . divide by 3

The length of the shorter segment is 2 m; the longer one, 18 m.

Please answer!!!Thanks


The swim team trains 4 days every week on monday, tuesday and thursday. The swim team spends 1/2 hours in the gym followed by 1 1/4 hours in the pool. On saturday there is no gym but the swim time is doubled. How many hours per week does the swim team train?

Answers

Answer:

6 hours

Step-by-step explanation:

The swim team trains 4 days every week, with 1/2 hour in the gym and 1 1/4 hours in the pool on Monday, Tuesday and Thursday. On Saturday, there is no gym, but the swim time is doubled, so the total swim time is 2 1/2 hours.

Therefore, the total time spent training each week is 6 hours.

1/2 hour in the gym plus 5 1/2 hours in the pool.

Answer: The swim team trains for 7 hours and 45 minutes a week.

Step-by-step explanation:

Since the swim team trains in the gym and the pool (collectively) on Monday, Tuesday and Thursday, subsequently we will be multiplying GYM TIME + POOL TIME, 3 TIMES to get the time taken for training on the three days i.e. 3 ( ½ + 1 ¼ ) and add twice the time taken in pool for Saturday i.e. 2(1 ¼ )

             

                                                                   = 3( ½ + 5/4) + 2(5/4)

                                                                   =31/4

                                = 7 ¾

Multiply ¾ with 60 as 1 hour = 60 minutes to get the answer in time format.

Firstly, convert mixed fractions into improper ones and find the final answer. Then, convert the final answer into Time format i.e. hours and minutes.

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A store buys 14 sweaters for $84 and sells them for $504. How much profit does the store make per sweater?

Answers

Answer:

$30 per sweater is how much profit the store will make

Step-by-step explanation:

The cost of 1 sweater (for the store) is $6.

The store sells the sweater for $36 (504/14).

The store is making $30 per sweater.

Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas. If Lydia uses the same recipe to make 1 pizza, how much cheese is needed?​

Answers

Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.

If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.

Step-by-step explanation:

what fraction of 3 kilograms is 50 grams

Answers

Answer:

50/30

5/0

1.6%

Step-by-step explanation:

What information will be useful to know to answer the main question? How can you get it? How will you use that information

Answers

Answer:

Step-by-step explanation:

Can u give more detail as to what the question is asking pease

It would be helpful to know what the main question is in order to accurately determine what information would be useful to know and how to obtain and use it. Could you please provide the main question?

Refer to the diagram shown.

I need help with this please help me

Answers

Answer: Angle-Side-Angle Theorem

Step-by-step explanation:

The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.

Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.

Which statement could most likely be a description of the org
expression 12 - 3x ?
a. The amount of money, in dollars, Eloise is left with, if she had
$12 and with that, she bought x + 3 flowers.
b. The amount of money, in dollars, Eloise is left with, if she had
$12 and with that, she bought 3x flowers.
c. The amount of money, in dollars, Eloise is left with, if she had
$3 and with that, she bought 12 flowers at $x each.
The amount of money, in dollars, Eloise is left with, if she had
$12 and with that, she bought x flowers at $3 each

Answers

c is the correct answer

Mental Math In a toy​ store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240​ dolls, how many teddy bears are in the​ store? Use pencil and paper. Describe the mental math steps you use to solve this problem.

Answers

Answer:

Step-by-step explanation:

Dolls:240 Teddy Bears:120

120:240

Please Describe the fraction If Possible.

What is the domain of f(x)=[1/2]*

Answers

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

The first thing we need to do is to define the domain of a function.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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When is it best to solve a system of equations using substitution?​

Answers

Answer:

It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.

Step-by-step explanation:

This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution

Answer:

Answer Below

Step-by-step explanation:

It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.

12a-3b squared, when a=9, b=4

Answers

Answer:

60

Step-by-step explanation:

12a - 3b²

12(9) - 3(4)²

108 - 3(16)

108 - 48

60

[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{12a - 3b^2}\\\mathsf{= 12(9) - 3(4)^2}\\\mathsf{= 12(9) - 3(4\times4)}\\\mathsf{= 12(9) - 3(16)}\\\mathsf{108 - 3(16)}\\\mathsf{= 108 - 48}\\\mathsf{= 60}\\\\\huge\text{Therefore, your answer should be: }\\\huge\boxed{\mathsf{60}}\huge\chdckmark[/tex]



[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]


Help if you know how to do this! I’d really appreciate it!

Answers

The value of x is 20 and the value of y is 8 from the given quadrilaterals.

What is a Congruent Polygon?

The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.

Given that, ABCD≅EFGH

We know that, corresponding parts of congruent polygon are equal.

Now, (4y-4)°=28°

4y=32

y=8

(10x-65)°=135°

10x=200

x=20

Therefore, the value of x is 20 and the value of y is 8 from the given quadrilaterals.

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Ann 's car can go 132 miles on 4 gallons of gas. During a drive last weekend, Ann used 5 gallons of gas. How far did she drive? Use pencil and paper. Explain how the problem changes if you were given the distance Ann drove last weekend instead of how much gas she used.

Answers

Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

Rewrite (2x+v)^2 without parentheses and simplify

Answers

Answer:

[tex]4x^2+4vx + v^2[/tex]

Step-by-step explanation:

[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]

Is the relation shown in the table a function?
Input: 4,8,4,8
Output: 1,3,5,4

Answers

keeping in mind that a function does not have any X-Repeats, that is, the 1st coordinate in every pair never repeats, Check the picture below.

write a mutiplcation exprresion that shows ten to the third

Answers

Answer:

10x10x10 or 10*3......

9.
The table shows the number of pools sold by the Allied Pool company over a six month period.
Allied Pool Sales
Month
Number of
Pools Sold
Feb.
11
Mar.
10
Apr.
12
May
16
June
15
July
18


From the above table, what is the range in the number of pools sold during this period?
8 pools

Answers

According to the table, the Range of pools sold during this period is 8.

What is Range?

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, the range could also be defined as the difference between the highest observation and lowest observation. The obtained result is called the range of observation. The range in statistics represents the spread of observations.

Range = Highest Value – Lowest Value

Range = 18 – 10

Range = 8

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2. What are the domain and range for the exponential parent function,
where b is a positive real number not equal to 1 and a > 0?

Answers

On solving the provided question, we can say that - the value of the given polynomials domain will be ( - infinity, 0)

what is domain?

The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.

domain will be ( - infinity, 0)

range = (-infinity, +infinity)

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HELP ASAP PLS
Question 2 of 5
Select all the correct answers.
Which expressions are prime polynomials?

Answers

Answer: There is no picture

Step-by-step explanation:

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