Quiz: 4.12: Step Functions
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#4 How does the graph of g(x)=2⌈x⌉ differ from the graph of f(x)=⌈x⌉?


Multiplying by 2 compresses the graph of ​ g(x)=2⌈x⌉ ​vertically by a factor of 2.

Multiplying by 2 shifts the graph of​ ​ g(x)=2⌈x⌉ ​ up 2 units.

Multiplying by 2 shifts the graph of ​ g(x)=2⌈x⌉ ​ ​down 2 units.

Multiplying by 2 stretches the graph of ​ g(x)=2⌈x⌉ vertically by a factor of 2.


#5 How does the graph of g(x)=⌊x⌋−3 differ from the graph of f(x)=⌊x⌋?


The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted down 3 units.

The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted right 3 units.

The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted left 3 units.

The graph of g(x)=⌊x⌋−3 is the graph of f(x)=⌊x⌋ shifted up 3 units.

The inequality is

[tex]-32> -5+9x[/tex]

We need to isolate x and for that first we need to get rid of 5 by adding 5 to both sides.

[tex]-32+5 +-5+9x+5\\-27>9x\\[/tex]

Now we need to get rid of 9 and for that we divide both sides by 9 .That is

[tex]-\frac{27}{9}>\frac{9x}{9}[/tex]

[tex]-3>x[/tex]

[tex]x<-3[/tex]

Hello...

Tony and his three friends live in Albuquerque, New Mexico, but they all attend college in Boston, Massachusetts. Because they want to have a car at school this year, they are planning to drive Tony's car from Albuquerque to Boston at the beginning of the school year. Although they'll each pay for their own food during the road trip, the friends plan to split the costs for gas and hotels evenly between the four of them.

Estimate the total cost that each friend will have to pay for gas and hotels. Explain how you got your answer. Here are some figures that may help you out:

•Tony's car can travel 28 miles for each gallon of gas.

•The average fuel cost at the time of their trip is $3 per gallon.

•They plan to drive about 650 miles each day.

•They estimate the average cost of a hotel each night is $85.

•They will drive approximately 2,240 miles to get from Albuquerque to Boston.

Solution:

Cost of Gas:

2240 / 28 x 3 = $240

Cost of Lodging:

85 x floor2240 / 650 = $255

Cost of both: $240 +255 = $495.

The cost for a 1/4 share is $495/4 = $123.75.

3 pens  per 1 seconds it is so easy

The formula of a midpoint:

[tex]M_{AB}\left(\dfrac{x_A+x_B}{2},\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have:

[tex]A(7,\ 12)\to x_A=7,\ y_A=12\\B(-1,\ 6)\to x_B=-1,\ y_B=6[/tex]

Substitute:

[tex]\dfrac{7+(-1)}{2}=\dfrac{7-1}{2}=\dfrac{6}{2}=3\\\\\dfrac{12+6}{2}=\dfrac{18}{2}=9[/tex]

Answer:

y = 3x^2+15x-18

Step-by-step explanation:

Parabola has an equation with one variable in degree 2 and other in degree 1.

Given that y=3(x-1)(x+6) is the function.

y is of degree 1 and x of degree 2

Standard form of these types of parabolas would be

y =ax^2+bx+c.

To make the given equation in standard form, we multiply all factors on  the right side

y = 3(x-1)(x+6) = 3(x^2+5x-6)

= 3x^2+15x-18

a=3 b = 15 and c =-18

y = 3x^2+15x-18 is the standard form of the parabola

Answer:

y = 3x^2 + 15x - 18

Step-by-step explanation:

To represent the function y = 3 (x - 1) (x + 6), start by by expanding the equation by multiplying the common factor with each term inside the brackets to get:

y = 3 (x - 1) (x + 6)

y = (3x - 3) (x + 6)

Now multiply both the terms with each other to get:

y = 3x^2 + 18x - 3x - 18

Arrange the like terms together and add them:

y = 3x^2 + 15x  - 18

Hence, y = 3x^2 + 15x - 18 is the standard form of the given function.

2/3 x 12 = 8

8 jelly beans were eaten

You would have to multiply 2/3 and 12 to find out how many jelly beans were eaten. 2/3*12=8

a total of $9500 is invested, part at 10% simple interest and part at 9%

if the total annual return from the two investments is $914.00

Amount invested = 9500

Total amount return means total yield = $914

Let x amount  is invested at 10% simple interest

Interest for first part =  10 % times x = 0.10x

Remaining part invested is 9500 -x

Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)

Total interest yield is 914. Now we frame an equation

0.10x + 0.09(9500-x) = 914

0.10x +855 - 0.09x = 914 (combine like terms)

0.01 x + 855 = 914 (subtract 855)

0.01x = 59 ( divide both sides by 0.01)

So x = 5900

$5900 is invested in 10% simple interest

9500 - 5900 = $3600 is invested in 9% simple interest

Final answer:

To solve the problem, we set up a system of equations based on the provided information. After simplifying and solving the system, we find that $5900 is invested at 10% and $3600 is invested at 9%.

Explanation:

Investment Allocation Problem

Let's denote the amount of money invested at 10% as $x and the amount of money invested at 9% as $y. Since the total amount invested is $9500, we can write the first equation as:

x + y = 9500

The total annual return from the investments is $914. We know that the interest from the first investment is 0.10x and from the second investment is 0.09y. Thus, our second equation, based on the total interest earned is:

0.10x + 0.09y = 914

Now we can solve the system of equations:

x + y = 9500 (Equation 1)

0.10x + 0.09y = 914 (Equation 2)

Multiplying Equation 1 by 0.10 gives us a new equation:

0.10x + 0.10y = 950 (Equation 3)

Now, we subtract Equation 2 from Equation 3:

(0.10x + 0.10y) - (0.10x + 0.09y) = 950 - 914

0.10y - 0.09y = 36

0.01y = 36

y = 3600

Substitute y = 3600 into Equation 1 to find x:

x + 3600 = 9500

x = 5900

Therefore, $5900 is invested at 10% and $3600 is invested at 9%.

Answer:

296

Step-by-step explanation:

111/3 = 37

37 * 8 = 296

Hope this helps :-)

2) angles are vertical so they are congruent- 7x-27= 4x+12 --> subtract 4x from both sides so 3x-27=12 --> add 12 to both sides so 3x=39 (divide both sides by 3) so then x= 13

3) again, vertical angles so 8x-120= 4x+16 --> subtract 4x so that 4x-120=16 --> add 120 to both sides and then 4x=136, divide both by 4 and x= 34

hope this helps:))

CE is equal to 58 units.

To find the length of CE, we'll use the fact that D is the midpoint of CE. The midpoint of a line segment divides it into two equal parts.

If CD is one part and DE is the other, then we can set up an equation:

CD=DE

9X−7=3X+17

Now, solve for X:

6X=24

X=4

Now that we have the value of X, substitute it back into either CD or DE to find the length of each part:

CD=9X−7=9(4) −7=36−7=29

DE=3X+17=3(4) +17=12+17=29

Now, since D is the midpoint, CD and DE are equal.

CD=DE=29

Finally, CE, the total length, is the sum of CD and DE:

CE=CD+DE=29+29=58

So, CE is indeed 58

Answer:

It is 8 3 pointers and 13 2 pointers

Step-by-step explanation:

8 x 3 = 24

13 x 2 = 26

24 + 26 = 50

The bulldogs made 13 2-pt shots and 8 3-pt shots.

Let's assume that the bulldogs made x 2-pt shots and y 3-pt shots. Since each 2-pt shot is worth 2 points and each 3-pt shot is worth 3 points, we can set up the following equations: 2x + 3y = 50 (equation 1) and x + y = 21 (equation 2). To solve this system of equations, we can multiply equation 2 by 2 to get 2x + 2y = 42, and then subtract equation 1 from it. This gives us y = 8. Substituting y = 8 into equation 2, we get x + 8 = 21, which means x = 13. Therefore, the bulldogs made 13 2-pt shots and 8 3-pt shots.

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Answer:

[tex]\displaystyle \frac{dy}{dx} = -4x \sin x^2 \sin (\cos x^2) \cos (\cos x^2)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \sin^2 (\cos x^2)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

A) N +2 = Q which equals

A) N -Q = -2

B) .05N +.25Q = 3.50  multiplying A) by .25

A) .25N -.25Q = -.5  then adding A) and B)

.30N = 3

Nickels = 10 Quarters = 12

*************DOUBLE CHECK ***************

.05 nickels = $0.50  .25 Quarters = $3.00

Melinda has 12 quarters and 10 nickels in her bank, totaling $3.50. By setting up and solving equations based on the values of the coins, we were able to determine the exact number of each type of coin.

Little Melinda has nickels and quarters in her bank, with two fewer nickels than quarters. The total amount of money she has is $3.50. To determine how many coins of each type she has, we need to set up equations based on the values of the coins and the given conditions.

Let's define:
Q = number of quarters
N = number of nickels
Since each quarter is worth 25 cents and each nickel is worth 5 cents, we have the following equations:

1. N = Q - 2 (since she has two fewer nickels than quarters)
2. (5 × N) + (25 × Q) = 350 cents (because the total amount is $3.50)

Substitute the first equation into the second to find the number of each coin:
5(Q - 2) + 25Q = 350
5Q - 10 + 25Q = 350
30Q - 10 = 350
30Q = 360
Q = 12

Then, substitute Q = 12 into the first equation to find N:
N = 12 - 2
N = 10

Therefore, Melinda has 12 quarters and 10 nickels.

The perimeter is 32m add all sides to find perimeter

Final answer:

The expanded form of the decimal 24.56 is 20 + 4 + 0.5 + 0.06, which breaks down each digit by its place value.

Explanation:

The expanded form of the decimal 24.56 is an expression that shows the value of each digit in the number. To write it in expanded form, we break down each digit according to its place value. For the number 24.56, the expanded form would look like this:

Combining these values, the expanded form of 24.56 is:

20 + 4 + 0.5 + 0.06

3s+6 <=  -5(s+2)

3s+6 <=  -5s - 10

8s + 6 <= -10

8s <= -16

  s <= -2

Answer: 4:1

Step-by-step explanation:

Given:- Number of tables in the classroom=6

Number of students on each table = 4

thus number of students in the classroom =6×4=24 students

Now ratio of numbers of students to the tables in the classroom= numbers of students/tables in the classroom=24/6=4/1=4:1

Ratio of numbers of students to the tables in the classroom= 4:1

Answer: -4x + 2y

Step-by-step explanation:

6x - 3y + 5y - 10 x

Group like terms:

= 6x - 10x  - 3y + 5y

Add similar elements :

6x - 10 x = - 4x

- 3y + 5y = +2y

Therefore:

-4x + 2y

Hope that helps!

The simplified form of the equation [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].

Further explanation:

A binomial is an algebraic expression which consists of two terms having operations of addition and subtraction.

Procedure:

The following steps are involved to simplify the algebraic expression.

1) First we collect the like terms from the given algebraic expression.

2) Second we add or subtract the like terms in the algebraic expression.

Given:

The algebraic expression is [tex]6x-3y+5y-10x[/tex].

Calculation:

Step 1:

First we collect the like terms from the given algebraic expression.

The given algebraic expression consists two variables [tex]x[/tex] and [tex]y[/tex].

Clearly, we can see that the given algebraic expression is in the form of binomial.

So, collect the terms of [tex]x[/tex] aside and the [tex]y[/tex] term on other side as follows:

[tex]\boxed{(6x-10x)+(5y-3y)}[/tex]

Step 2:

Now, add the given algebraic expression to simplify it.

[tex]\boxed{(6x-10x)+(5y-3y)=-4x+2y}[/tex]  

The above algebraic expression can be written as,

[tex]\boxed{2y-4x}[/tex]  

The simplified form of the algebraic expression [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].

Thus,  the simplified form of the algebraic expression [tex]6x-3y+5y-10x[/tex] is [tex]\boxed{2y-4x}[/tex].

Learn more:  

1) Learn more about simplification of the expressions with BODMAS rule https://brainly.com/question/365957

2) Learn more about algebraic expression for the word phrase is https://brainly.com/question/1600376

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Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Simplification

Keywords: Addition, subtraction, operation, terms, like terms, unlike terms, variables, binomial, monomial, simplification, collecting the terms, coefficient, constant, value, algebraic expressions.

The cube of the product of 3 and a number is expressed as (3x)³ or 27x³, which involves cubing the numeric part and multiplying the exponent of the variable by 3.

The question is asking about the volume of a cube with sides of length a and also about the process of cubing the product of a number and three. When we cube a product, such as 3 times an unknown number, we are calculating the result of multiplying that product by itself three times.

For example, if our number is x, we would express this as (3x)³ or 27x³. This is because when we cube a product, we cube the numeric part as usual, obtaining 3³ which is 27, and we multiply the exponent of the exponential term by 3, thus x becomes x³.

Answer:

1968

Step-by-step explanation:

I use the following method when it comes about products of big numbers

I grab the longer and put on the first line, below I put the smallest number.

492

x 4

Now, it is time to distribute the product, term by term, remember that when performing a product, if the result is greater or equal than 10, you need to carry a number for the following product.

      492

        x 4

--------------------

   19    6    8

(end) (c3) (nc)

nc means: not carrying anything since 4x2=8 and 8 <10

c3 means: carrying 3 since 4x9= 32 and 32 >10

end means: put the whole number and sum it what you were carrying. 4*4+3=19

The product 492*4=1968

The product of 4 multiplied by 492 equals 1968. To find this, we used a step-by-step approach using basic multiplication and the distributive property.

To determine the product of 4 multiplied by 492, you can execute the following steps:

Therefore, 4 × 492 = 1968.

(64+36)x50= 5,000

Brainliest Please

50(64 + 36) = 5000

Hope this helps

-AaronWiseIsBae

Answer:

 [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]

 [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]

Explanation:

Ratio between [tex]4*10^{15}[/tex] and [tex]8*10^9[/tex] = [tex]\frac{4*10^{15}}{8*10^9} =5*10^5[/tex]

 So [tex]4*10^{15}[/tex] is [tex]5*10^5[/tex] times larger than [tex]8*10^9[/tex]

Ratio between [tex]2*10^{-5}[/tex] and [tex]4*10^{-12}[/tex] = [tex]\frac{2*10^{-5}}{4*10^{-12}} =5*10^6[/tex]

 So [tex]4*10^{15}[/tex] is [tex]5*10^6[/tex] times larger than [tex]4*10^{-12}[/tex]

1 place to the right of a decimal point is the tenths, so you would multiply 7 by 1/10.

2 places to the right of the decimal point is the hundredths place, so you would multiply 23 by 1/100

The correct answer is D.

Answer:

your graph is gonna have a horizontal line crossing the y axis at (0,3)

First the two angles are equal to one another so take note of that.

Now setup the equation which will be

x+90=4x

Now get rid of alike terms

So subtract x from both sides

90=3x

Now divide 90 by 3

x=30

Answer:  The correct option is

(C) x = 30.

Step-by-step explanation:  We are given to find the value of x from the figure shown.

From the figure, we note that the angles with measures (x+90)° and 4x° are vertically opposite angles.

Since the measures of two vertically opposite angles are equal, so we must have

[tex](x+90)^\circ=4x^\circ\\\\\Rightarrow x+90=4x\\\\\Rightarrow 4x-x=90\\\\\Rightarrow 3x=90\\\\\Rightarrow x=\dfrac{90}{3}\\\\\Rightarrow x=30.[/tex]

Thus, the required value of x is 30.

Option (C) is CORRECT.

Follow below steps:

The question is asking to identify how many days will pass before Heather will have both a jelly sandwich and milk again, given that she eats a jelly sandwich every 5th day and drinks milk every 4th day. To find out when Heather will have both on the same day again, we need to find the Least Common Multiple (LCM) of the two numbers, 5 and 4.

The multiples of 5 are 5, 10, 15, 20, 25, and so on. The multiples of 4 are 4, 8, 12, 16, 20, and so on. The first common multiple of both 5 and 4 is 20. Therefore, Heather will have both a jelly sandwich and milk together on every 20th day after today.

So, after today, Heather will wait 19 more days before having both a jelly sandwich and milk on the same day again.

87 Pounds would be the correct answer I believe.

5x=29x

x=3

87 pounds

Since $5 = 29. You can multiply both 5 and 29 to get 15=87 pounds

*I hope this will help*

(3 x 16) + (2 x 21) + 8

3 people made 16, which is 48

2 made 21, making 42

and 1 made 8, making 8

The answer would be c. because there is 3 players with 16 points (3x16) and 2 with 21 points (2x21) so (3x16)+(2x21) and one player scored 8 points so (3x16)+(2x21)+8

I hope this helps     have a nice day

8^14 is the answer.

This is because since they both have the same base, the exponents could be added together if the numbers are multiplied together

Hello Tim!

[tex]8^1^0*8^4[/tex]

First you had to used apply exponent rule.

[tex]8^1^0*8^4=8^1^0^+^4=8^1^4[/tex]

[tex]=8^1^4[/tex]

Answer⇒⇒⇒8¹⁴

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

Final answer:

To find the actual distance from Rose Lake to the hiking trail, a proportion is used based on the given information of the map scale, resulting in an actual distance of 7 miles.

Explanation:

The question involves solving for an actual distance on a map scale, which is a proportional relationship problem in mathematics. To find the actual distance between Rose Lake and the hiking trail, we can set up a proportion using the given distances: if 2 inches on the map equal 3.5 miles in reality, then 4 inches would represent the distance from Rose Lake to the hiking trail (since the relationship between inches on the map and actual miles should be consistent).

Set up the proportion as follows:

2 inches (map) / 3.5 miles (real) = 4 inches (map) / X miles (real)

Now, solve for X, which represents the unknown actual distance in miles. By cross-multiplying and solving for X, we get:

X = (4 inches * 3.5 miles) / 2 inches

Therefore, the actual distance between Rose Lake and the hiking trail is 7 miles.