Express (x + 3)² as a trinomial in standard

radius -15

Surface Area of a sphere =4πr^2

=4x22/7x15x15

=19800/7

=2828.57

The function that is graphed is y = |x -2| + 3. The correct option is D. y = |x -2| + 3

From the question, we are to determine the function for the given graph

From the graph,

When x = 2, y = 3

The equation that satisfy this condition is

y = |x -2| + 3

NOTE: This function satisfies all the points on the graph

Hence, the function that is graphed is y = |x -2| + 3

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Peter:

£2.30 ÷ 6 = £0.38 each sausage

Paul:

£3.50 ÷ 10 = £0.35 each sausage

As you can tell, it is cheaper to buy from Paul because each sausage is £0.35 which is 3 pence less than buying from Peter.

In other words, the best value for money would go to the 10 pack sausage, saving £0.03 per unit of sausage.

However, that doesn't answer the question. You need to find how many packages you can get with your available £10.

£10 ÷ £2.30 = 4.34...

So, you can buy 4 packs of sausage from Peter - meaning you will get 24 sausages in total. This is because each pack contains 6 sausages, and you have 4 of this. (6x4=24)

£10 ÷ £3.50 = 2.85...

So, you can buy 2 packs of sausages from Paul & meaning you will get 20 sausages in toal because each package contains 10 sausages. (2x10 = 20)

Thus, you should buy from Peter because you get 24 sausages, instead of 20 sausages from Paul, in accordance to the £10 you can spend in both shops.

Hope this helps!

we conclude that the store where you can get more sausages is in Peter the Butcher.

You have £10.

Peter the Butcher sells 6 sausages for £2.30

The number of packages that you can buy is:

£10/£2.30 = 4.3

Rounding down to the next whole number, we conclude that here you can buy 4 packages, then:

4*6 = 24 sausages

4*£2.30 = £9.20

So here you can buy 24 sausages for £9.20

In Paul the butcher, you can buy 10 sausages for £3.50

Notice that here you can only buy 2 packages (because the cost of 3 packs would be  £10.50, which is more than the amount you can spend).

Then here you only can get 20 sausages.

Then, we conclude that the store where you can get more sausages is in Peter the Butcher.

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The answers are :

a)

b)

Let's find point A by using g(x). A is clearly the y-intercept so take x = 0.

Points B and C can be found using f(x). As they are the x-intercepts, take y = 0.

As B lies to the left of the y-axis, its x-coordinate is negative.

As C lies to the right of the y-axis, its x-coordinate is positive.

Point D can be found using g(x). D is clearly the x-intercept so take y = 0.

Point E lies at the intersection of f(x) and g(x). So they have to be equated.

Answer:

see explanation

Step-by-step explanation:

(a)

A lies on the y- axis with x- coordinate of zero

substitute x = 0 into either of f(x) or g(x) for y- coordinate

g(0) = 2(0) + 1 = 0 + 1 = 1

then A (0, 1 )

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

B and C lie on the x- axis with y- coordinate of zero

let f(x) = 0 and solve for x , that is

1 - x² = 0 , then

x² = 1 ( take square root of both sides )

x = ± [tex]\sqrt{1}[/tex] = ± 1

then B (- 1, 0 ) and C (1, 0 )

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

D is the point on the x- axis where g(x) crosses

let g(x) = 0 and solve for x

2x + 1 = 0 ( subtract 1 from both sides )

2x = - 1 ( divide both sides by 2 )

x = - [tex]\frac{1}{2}[/tex]

then D (- [tex]\frac{1}{2}[/tex] , 0 )

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

(b)

E is the point of intersection of f(x) and g(x) so equate them, that is

2x + 1 = 1 - x² ( subtract 1 - x² from both sides )

x² + 2x = 0 ← factor out x from each term

x(x + 2) = 0

equate each factor to zero and solve for x

x = 0 ← x- coordinate of A

x + 2 = 0 ⇒ x = - 2 ← x- coordinate of E

substitute x = - 2 into g(x) for corresponding y- coordinate

g(- 2) = 2(- 2) + 1 = - 4 + 1 = - 3

then E (- 2, - 3 )

Answer:

11

Step-by-step explanation:

9 + 12 + 7 + 13 + 21 + 10 + 12 + 4

21 + 20 + 31 + 16

41 + 47

88

88 / 8 = 11

Answer:

9060$ is the final amount because 7060 is the interest

The amount of money after 45 years will be $64,060.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Investments increase exponentially by about 26% every 3 years.

If you made a $2,000 investment.

Then the equation will be

[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{t}{3}}[/tex]

Where t is the number of years.

Then the amount of money after 45 years will be

[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{45}{3}}[/tex]

Simplify the equation, then we have

A = 2000 × (1.26)¹⁵

A = 2000 × 32.03

A = $64,060

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Answer:

(4x+5)

Step-by-step explanation:

4x(5x-3)+5(5x-3)

collecting like terms, first part is (5x-3) hence second part of the equation is (4x+5) from the equation above.

Answer:

Step-by-step explanation:

(20x2 – 12x) + (25x– 15)

4x(5x – 3) + 5(5x – 3)

(( (5x – 3)(4x +5) ))

Answer:

480

Step-by-step explanation:

1/5 of 400 =   1/5 * 400 = 80

  increase 400 by 80   = 480

Answer:

A)  See attached for graph.

B)  (-3, 0)  (0, 0)  (18, 0)

C)   (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}[/tex]

Therefore, the function has two definitions:

When graphing piecewise functions:

First piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies g(3)=(3)^3-9(3)=0 \implies (3,0)[/tex]

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of function

Substitute the endpoint of the interval into the corresponding function:

[tex]\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)[/tex]

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the first piece of the function to zero and solve for x:

[tex]\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}[/tex]

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the second piece to zero and solve for x:

[tex]\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}[/tex]

[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}[/tex]

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation:  (-3, 0) ∪ [3, 18)

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The 10the term of the sequence -1/1, -1/2, -1/9, -1/64....is -1/1,000,000,000

-1/1, -1/2, -1/9, -1/64

This can be written as;

-1/1° , -1/2¹, -1/3², -1/4³, -1/5⁴, -1/6^5, -1/7^6, - 1/8^7, -1/9^8, -1/10^9

So,

First term = -1/1,

Second term = -1/2,

Third term = -1/9,

Fourth term = -1/64,

Fifth term = -1/625,

Sixth term = -1/7,776,

Seventh term = -1/117,649,

Eighth term = -1/2,097,152,

Ninth term = -1 / 43,046,721,

Tenth term = -1/1,000,000,000

Therefore, the 10th term is -1/1,000,000,000

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Answer: [tex]-3x^2+6y^3-9z[/tex]

Step-by-step explanation:

[tex](2x^2-y^3+5z)-(5x^2-7y^3+14z)[/tex]    given

[tex]2x^2-y^3+5z-5x^2+7y^3-14z[/tex]  use distributive property and distribute the -

[tex]-3x^2+6y^3-9z[/tex]          final answer

Answer:

-3x^2 + 6y^3 - 9z

Step-by-step explanation:

(2x^2 - y^3 + 5z) - (5x^2 - 7y^3 + 14z)

open the brackets:

2x^2 - y^3 + 5z - 5x^2 + 7y^3 - 14z

simplify:

=> -3x^2 - y^3 +5z + 7y^3 - 14z               [2x^2 - 5x^2 = -3x^2]

=> -3x^2 + 6y^3 + 5z - 14z                       [ -y^3 + 7y^3 = 6y^3]

=>  -3x^2 + 6y^3 - 9z                               [  5z - 14z = -9z]

The points would be matched with their polar coordinates as follows:

A polar coordinate can be defined as a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

In geometry, the relationship between a polar coordinate (r, θ) and a rectangular coordinate (x, y) based on the conversion rules is given by the following polar functions:

a = rcos(θ)    ....equation 1.

b = rsin(θ)     ....equation 2.

Where:

In Mathematics, a negative vector for a given vector has the same magnitude but acts in an opposite direction while an antiparallel vector for a given vector refers to any vector that acts in an opposite direction.

This ultimately implies that, a negative vector equals to an antiparallel vector, but an antiparallel vector isn't always a negative vector.

In this context, we can infer and logically deduce that the points would be matched with their polar coordinates as follows:

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Answer:

20 minutes

Step-by-step explanation:

Rate x Time = jobs

The rate is 3 jugs/ 4 minutes.

The number of jobs is 15

Use T for time

3/4T = 15  Multiply both sides by 4/3 to get the variable T by itself

(4/3) 3/4 T = 15(4/3)

T = 20 minutes

Answer:

See below

Step-by-step explanation:

237/50   =    4    R 37

37/20     =     1     R 17

17 / 10     =     1     R 7

7 / 1         =     7    R 0

4   50gm's      1     20gm       1   10gm       and   7    1g wts

The required number of weights used in chemical balance to weigh 237g is 4,1,1,7 respectively.

What is mathematical expression?

A mathematical expression expression in mathematical is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, it is given that :

A chemical balance needs to weigh 237g using weights of 50g, 20g, 10g and 1g.

Now, let us find the number of weights for each weight type :

For 50g weight the maximum number of weights needed will be 4 that is :

50g x 4 = 200g

Now, for 20g weight the maximum number of weights needed will be 1 that is :

20g x 1 = 20g

Now, for 10g weight the maximum number of weights needed will be 1 that is :

10g x 1 = 10g

Now, for 1g weight the maximum number of weights needed will be 7 that is :

1g x 7 = 7g

Adding all the weights we get :

200g + 20g + 10g + 7g = 237g;

which is the required weight and the number of weights used is 4,1,1,7 respectively.

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Answer:

Distance = 15

Step-by-step explanation:

4 - (-11) = 4 + 11 = 15

By using the linear function which models the data in the given table, the cost of a textbook with 402 pages is equal to $47.4478.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 0.1057x + 4.9564

If x = 402, then y is given by:

y = 0.1057(402) + 4.9564

y = 42.4914 + 4.9564

y = $47.4478.

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Answer:

What is the expected value when rolling a fair 12-sided die?

132=6.5

Recall the definition of the expected value:

E[X]=∑ni=1xp(x)

Here, we have 12 possible values the die can take on, and the probability of each one is the same: 1/12. So we can just pull the term p(x), the probability of each outcome, out of the summation:

E[X]=112∑12i=1x

A useful trick here is that the sum of the numbers 1..N=N(N+1)2. So:

E[X]=11212(13)2

E[X]=12(13)12(2)

E[X]=132

Step-by-step explanation:

hope it helps you :)

The amount we should charge Tommy is $363.

How much should we charge Tommy:

The amount charged for 1000 words = $110

The amount charged per word = $110/1000

Amount to be charged for 3300 words = $(110/1000) × 3300

= $(0.11) × 3300

= $363

The amount we should charge Tommy is $363.

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The direct variation function is y = 0.3x

The direct variation from y to x is represented as:

y = kx

When y = 1.5 and x = 5, we have

1.5 = 5k

Divide by 5

k = 0.3

Substitute k = 0.3 in y = kx

y = 0.3x

Hence, the direct variation function is y = 0.3x

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The future value interest earned semiannually at a  compound rate of 4% is $7598.89.

To calculate the future value in interest earned, we use the of compound interest

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

Formula:

Where:

From the question,

Given:

Substitute the values above into equation 1

Hence, the future value interest earned is $7598.89.

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[tex]x[/tex] and [tex]3x+5[/tex] are being multiplied to form the expression, and are not being added or subtracted.

Here, x and (3x+5) are given in the form of multiplication, instead of being separated by addition or subtraction. This is why x and (3x+5) are factors of the expression x(3x + 5)² and not terms of the expression.

What are terms and factors in an expression?

Terms of an expression can be a variable, a signed number, or a constant multiplied by one or more variables. On the other hand, the factors are the items that have been multiplied by another items. Any integer, variable, phrase, or lengthier expression can be a factor.

For instance, the expression 2x(y - 5) has three components: 2, x, and (y-3). These three components are its factors, since when multiplied, they produce the same expression. The factors may or may not be comprised of more than one terms.

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The equivalent expression of -14 - 6 is -14 - (+6)

Equivalent expressions are expressions that have the same value when evaluated

The expression is given as:

-14 - 6

Put the terms of the expression in brackets

-14 - (6)

Rewrite 6 as +6

-14 - (+6)

Hence, the equivalent expression of -14 - 6 is -14 - (+6)

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The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.

Hence, option C is the correct answer.

Given the data in the question;

To find the equation, we use the equation of the parabola that opens up or down since the directrix ( y = -13 ) is vertical.

The equation is expressed as;

( x - h )² = 4p( y - k )

First, we find the distance from the focus to the vertex.

|p| is the distance rom the focus to the vertex and from the vertex to the directrix.

p = -9 + 13

p = 4

We substitute the values into the equation;

( x - h )² = 4p( y - k )

( x - (-5) )² = 4(4)( y - (-9) )

( x + 5 )² = 16( y + 9 )

Multiply both side by 1/16

(1/16)( x + 5 )² =  y + 9

Make y the subject of the formula

(1/16)( x + 5 )² - 9 =  y

y = (1/16)( x + 5 )² - 9

The equation of the parabola with the given vertex and directrix in vertex form is y = (1/16)( x + 5 )² - 9.

Hence, option C is the correct answer.

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The first five terms of the sequence representing each bottle scheme for Mike is illustrated below.

From the information given, Mike and Tim are looking to earn a little extra money and the beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle.

For Mike, the price for the first bottle is $0.10.

The price for the second bottle will be:

= 0.10 × 1.02 = 0.102

The price for the third bottle will be:

= 0.10 × 1.02² = 0.10404

The price for the forth bottle will be:

= 0.10 × 1.02³ = 0.10612

The price for the fifth bottle will be:

= 0.10 × 1.02⁴ = 0.10824

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Complete question:

Mike and Tim are looking to earn a little extra money. The beach committee offers them the opportunity of picking up plastic bottles, paying them $0.20 per bottle. Mike realizes as they pick up it will get harder and harder to find more bottles. So as an incentive to keep looking he suggests a different form of payment. He suggests $0.10 for the first bottle and increase the pay by 2% for each bottle after that. Tim thinks Mike is crazy to propose an increase of just 2% per piece. He plans to ask for a one cent increase for every piece, starting at 15 cents for the first bottle. Write the first five terms of the. sequence representing each bottle scheme for Mike.

Answer:

39 pages

Step-by-step explanation:

If 13 pages are read in 1/3 of an hour, we need to multiply 13 by 3 to get the number of pages read in 1 hour. 13*3 = 39 pages

Answer:

4.93

See the discussion below if the number is 4928.

Step-by-step explanation:

Comment

Do you really mean hundred? If you do, the nearest hundred is 0 when the actual value is 4.928

If you mean the nearest hundredth that means that 2 is the value of the hundredth now. Rounded, the answer is 4.93

If the given value is 4928, the hundred's place is the 9. Look at the 10s place (2). Since the 2 is less than 5, the 9 is not changed. 2 zeros are at the end of 49 since the hundreds place is rounded.

4900 is the answer

Hi there,

please see below for solution steps :

__________

Let us revise the rounding rules :

1) if the number you’re rounding to is followed by a number from 0 to 4, you drop that number

2) if the number you’re rounding to is followed by a number equal to 5 or more, you add 1 to that number

________

Now,

Nearest Hundredth => 3 digits after the decimal point

Thus,

4.928 => 4.93

Hope the Answer - and steps - made sense to you,

Happy Studying !!

Frozen Melody

The expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.

According to the task content, it follows that the given expression in the task content is; x⁴z⁵/(xz)⁶.

Hence, the expression can be simplified by means of the laws of indices as follows;

x^(4-6) z^(5-6)

= x-²z-¹

= 1/x²z.

Ultimately, the expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.

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