Solve x2 - 3x = 28 by factoring.

Answer:

24

Step-by-step explanation:

let W represent the number of wins and let P represent the number of plays let T represent profit from each play. from the question, Marcelo played 3 times, this means 3P can represent the first equation He won 7 times, 7W can represent the second equation

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Certainly! Marcelo played the carnival games six times, spending three tokens for each game and winning seven tokens from each. To find the total profit in tokens that Marcello made, we can create two different expressions:

1. The first method involves directly calculating the net tokens won over all the games:
  - We calculate the total tokens won by multiplying the number of tokens won per game (7) by the number of games played (6).
  - Then we calculate the total tokens spent by multiplying the number of tokens spent per game (3) by the number of games played (6).
  - Finally, we determine the total profit by subtracting the total tokens spent from the total tokens won.
  Using this method, the first expression to calculate the total profit (P_1) is:
  \[
  P_1 = (\text{Tokens won per game} \times \text{Games played}) - (\text{Tokens spent per game} \times \text{Games played})
  \]
  \[
  P_1 = (7 \times 6) - (3 \times 6)
  \]
  \[
  P_1 = 42 - 18
  \]
  \[
  P_1 = 24
  \]
  So, using this expression, Marcello's total profit is 24 tokens.
2. The second method is to calculate Marcello’s profit per game and then multiply that by the number of games played:
  - First, we find the profit per game by subtracting the number of tokens spent per game (3) from the number of tokens won per game (7).
  - Then we multiply the profit per game by the total number of games played (6) to find the total profit.
  Using this method, the second expression to calculate the total profit (P_2) is:
  \[
  P_2 = (\text{Profit per game}) \times \text{Games played}
  \]
  \[
  P_2 = (\text{Tokens won per game} - \text{Tokens spent per game}) \times \text{Games played}
  \]
  \[
  P_2 = (7 - 3) \times 6
  \]
  \[
  P_2 = 4 \times 6
  \]
  \[
  P_2 = 24
  \]
  So, using the second expression, Marcello's total profit is also 24 tokens.
In both scenarios, the profit that Marcello makes from playing the six games is 24 tokens. The first expression gives us a direct calculation of the total, while the second expression calculates the profit on a per-game basis and then accumulates it.

Answer:

option B) 62541

Step-by-step explanation:

The given number is 84273.

The number can be written as 80000+4000+200+70+3=84273.

Here in the given number, the digit 2 has value 200.

Given that, value of two in new number is ten times means, 200 x 10=2000.

thus, 2 should  be at thousandth's place, which is only in 62541 in given options.

62541=60000+2000+500+40+1

while others are,

78325=70000+8000+300+20+5

34482=30000+4000+400+80+2

25874=20000+5000+800+70+4 ,

none of which has 2 at thousandth's place.

Answer:

The cost of the can is minimal when r=2 m and h=5 m

Step-by-step explanation:

This is an optimization problem which will be solved by the use of derivatives

We must find an expression for the total cost of the cylindrical can and then find its dimensions to make the cost minimal

Let's picture a cylinder of radius r and height h. Its volume is computed as

[tex]V=\pi r^2h[/tex]

To make the lids we need two circle-shaped pieces of a material which costs $10 per square meter

The area of each lid is

[tex]A_l=\pi r^2[/tex]

The cost of both lids will be

[tex]C_l=(2)(10)(\pi r^2)=20\pi r^2[/tex]

The lateral side of the cylinder can be constructed with a rectangle of material which costs $8 per square meter

The rectangle has a height of h and a width equal to the length of the circumference

[tex]A_s=2\pi rh[/tex]

The cost of the side of the cylinder will be

[tex]C_s=16\pi rh[/tex]

The total cost of the can is

[tex]C=20\pi r^2+16\pi rh[/tex]

We know the volume of the can is [tex]20\pi[/tex] cubic meters

[tex]V=\pi r^2h=20\pi[/tex]

Isolating h we have

[tex]h=\frac{20}{r^2}[/tex]

Using this value into the total cost

[tex]C=20\pi r^2+16\pi r(\frac{20}{r^2})[/tex]

[tex]C=20\pi r^2+\frac{320\pi}{r}[/tex]

Differentiating with respect to r

[tex]C'=40\pi r-\frac{320\pi}{r^2}[/tex]

To find the critical point, we must set C'=0

[tex]40\pi r-\frac{320\pi}{r^2}=0[/tex]

Operating

[tex]40\pi r^3-320\pi=0[/tex]

Solving for r

[tex]r=\sqrt[3]{\frac{320\pi}{40\pi}}=\sqrt[3]{8}[/tex]

r=2

And since  

[tex]h=\frac{20}{r^2}=\frac{20}{2^2}[/tex]

h=5

Differentiating again we find

[tex]C''=40\pi +\frac{640\pi}{r^3}[/tex]

Which is always positive for r positive. It makes the critical point found a minimum

The cost of the can is minimal when r=2 m and h=5 m

J+S=24 and J=S+6 represents the relationship between ages.

John is 15 years old and Sally is 9 years old.

Step-by-step explanation:

Let,

John's age = J

Sally's age = S

According to given statement, the sum of their ages is 24;

[tex]J+S=24[/tex]    Eqn 1

John is 6 years older than Sally means we will add 6 in Sally's age;

[tex]J=S+6[/tex]     Eqn 2

Putting value of J from Eqn 2 in Eqn 1;

[tex](S+6)+S=24\\S+6+S=24\\2S=24-6\\2S=18[/tex]

Dividing both sides by 2

[tex]\frac{2S}{2}=\frac{18}{2}\\S=9[/tex]

Putting S=9 in Eqn 2

[tex]J=9+6\\J=15[/tex]

J+S=24 and J=S+6 represents the relationship between ages.

John is 15 years old and Sally is 9 years old.

Keywords: linear equation, substitution method

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Answer:[tex]\dfrac{5}{24}[/tex]

Step-by-step explanation:

Let [tex]r[/tex] be the rate at which Jaquez completes his test.

Let [tex]x[/tex] part of test be completed by Jaquez in [tex]t[/tex] hours.

Then,

[tex]x=rt[/tex]

Given that Jaquez completed 1/8 of his test in 3/5 hour.

So,[tex]\frac{1}{8}=r\times \frac{3}{5}[/tex]

[tex]r=\frac{5}{24}[/tex]

To know how much he completes in one hour,substitute [tex]1[/tex] in the above equation.

So,[tex]x=r\times 1=\frac{5}{24}[/tex]

Jaquez completes [tex]\frac{5}{24}[/tex] of his test in [tex]1[/tex] hour

Answer:

Option (d)

5/24

Explanation:  

Hour taken to complete 1/8  of his test=3/5 hour

Suppose r is the rate at which Jackuez completes his test

For completing the test in t hours

The equation is

y= r t

where y is the part of test which will be completed in t hour

with the information given

substituting the values

[tex]\frac{1}{8}=r \frac{3}{5}[/tex]

[tex]r=\frac{5}{24}[/tex]

now when t=1 hour

substituting the value

[tex]\mathrm{x}=\frac{5}{24} \times 1[/tex]

[tex]\mathrm{x}=\frac{5}{24}[/tex]

hence at 1 hour his test was completed [tex]\frac{5}{24}[/tex]

Answer:

It is 0.42 repeated, with a line on top of the 4 and the 2.

Step-by-step explanation:

The decimal repeats when she divides into the same number twice.

The cost of the television is $894, and the cost of the DVD player is $298.

Let's denote the cost of the DVD player as x dollars.

Since the cost of the television is three times the cost of the DVD player, we can express the cost of the television as 3x dollars.

According to the given information, the total cost of both items is $1192. Therefore, we can set up the following equation:

[tex]\[ x + 3x = 1192 \]Now, let's solve for \(x\):\[ 4x = 1192 \]\[ x = \frac{1192}{4} \]\[ x = 298 \][/tex]

Now that we have found the cost of the DVD player [tex](\(x = 298\) dollars)[/tex], we can find the cost of the television, which is three times the cost of the DVD player:

[tex]\[ \text{Cost of television} = 3 \times 298 = 894 \][/tex]

Answer:

14

Step-by-step explanation:

2x2=4

10+4= 14

Answer:Yes

Step-by-step explanation:5is the solution

Answer: Option C

Step-by-step explanation: A Positive correlation means that as one variable increases, also does the other variable.

In this case, if we put the data in order we have:

$10 ----- 650 calories

$11 ----- 1250 calores (here we have an increase)

$12 ----- 550 calories (here we have a decrease)

$13 ---- 780 calories (here we have an increase)

The correlation can be calculated with a calculator, and it yields to:

C = (∑(x-x')(y-y'))/√(∑(x-x')^2*∑(y-y')^2) = -0.12924

(where y' and x' are the means of the variables x and y)

So whe can see that the correltion is negative and close to zero, so this is a weak negative correlation.

Answer:

The answer is C. a weak negative correlation

on EDGE

Step-by-step explanation:

2022

Answer:

The monthly percentage rate would be 1.6%

Step-by-step explanation:

Given,

Finance charge = $ 85.50,

Amount of bill in this month  = $ 5,343.75,

Hence, the monthly rate of percentage

[tex]=\frac{\text{Finance charge}}{\text{Amount of bill}}\times 100[/tex]

[tex]=\frac{85.5}{5343.75}\times 100[/tex]

[tex]=\frac{8550}{5343.75}[/tex]

[tex]=\frac{855000}{534375}[/tex]

= 1.6 %

i.e. OPTION A would be correct.

The monthly percentage rate on Jeremy's credit card is [tex]\[ {1.6\%} \][/tex]. So option (a) is correct.

To determine the monthly percentage rate on Jeremy's credit card, follow these steps:

Step 1: Identify the Given Values

Finance charge: $85.50

Average daily balance: $5,343.75

Step 2: Understand the Formula

The following formula is used to determine the finance charge:

[tex]\[ \text{Finance Charge} = \text{Average Daily Balance} \times \text{Monthly Percentage Rate} \][/tex]

Step 3: Set Up the Equation

Let ( r ) represent the monthly percentage rate (in decimal form).

[tex]\[ 85.50 = 5343.75 \times r \][/tex]

Step 4: Solve for the Monthly Percentage Rate

The equation should be rearranged to find ( r ):

[tex]\[ r = \frac{85.50}{5343.75} \][/tex]

Step 5: Perform the Calculation

[tex]\[ r = \frac{85.50}{5343.75} \approx 0.016 \][/tex]

Step 6: Convert the Decimal to a Percentage

[tex]\[ \text{Monthly Percentage Rate} = 0.016 \times 100 = 1.6\% \][/tex]

Therefore, the monthly percentage rate on Jeremy's credit card is:

[tex]\[ {1.6\%} \][/tex].

To solve the equation e3x+6 = 8 for 'x', first take the natural logarithm of both sides (3x + 6 = ln(8)) to isolate 'x', resulting in x = (ln(8) - 6) / 3. If calculated, the approximate answer is x ≈ -0.307.

This question pertains to solving for unknown variable 'x' in an exponential equation. The equation provided is e3x+6 = 8. In solving for 'x', you must first rearrange the equation by taking the natural logarithm (ln) of both sides. This is because the inverse operation for the base of natural logarithm 'e' is natural logarithm 'ln'. Thus, you get 3x + 6 = ln(8). Afterwards, you subtract 6 from both sides and divide by 3 to get x = (ln(8) - 6) / 3. The numerical solution for this can be calculated with a scientific calculator, which yields x as roughly -0.307.

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Answer:6.8

Step-by-step explanation:

Answer:

0.58 pounds per friend

Step-by-step explanation:

divide 5.8 into the 10 friends.

Answer:

Step-by-step explanation:

hour 60 min 2

min of a hour is 60/2

Answer:

[tex]\frac{1}{30}[/tex]

Step-by-step explanation:

There are 60 minutes in 1 hour thus as a fraction

= [tex]\frac{2}{60}[/tex] ← divide numerator/ denominator by 2

= [tex]\frac{1}{30}[/tex]

No, It is not true.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ r + 9 = 42

⇒ r + 9 - 9 = 42 + 9

Now,

Since, The expression is,

⇒ r + 9 = 42

⇒ r + 9 - 9 = 42 + 9

It is not true, because if we subtract 9 then both side subtract as;

⇒ r + 9 - 9 = 42 - 9

⇒ r = 33

Thus, It is not true.

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Answer:

Point S

ST

Step-by-step explanation:

Answer:

[tex]\boxed{\sf point \ S}[/tex]

Step-by-step explanation:

Line QS and ST intersect at one point, the intersection is point S.

Answer:

Number of committees that are possible =210

Step-by-step explanation:

Total names in ballot = 10

Total members to be elected for the committee = 4

So, we need the number of different ways in which 4 names out of 10 can be elected for the committee.

To find the number of ways in which the committee can be elected, we use the combinations which is given as

[tex]aCb=\frac{a!}{(a-b)!b!}[/tex]

where [tex]a[/tex] represents total number of members and [tex]b[/tex] represents total number of members to be elected.

So, [tex]10C4=\frac{10!}{(10-4)!4!}[/tex]

[tex]10C4=\frac{10!}{6!4!}[/tex]

[tex]10C4=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{6\times5\times4\times3\times2\times1\times4\times3\times2\times1}[/tex]

[tex]10C4=\frac{10\times9\times8\times7}{4\times3\times2\times1}[/tex] [Canceling the common numbers]

[tex]10C4=210[/tex]

∴ Number of committees that are possible =210

Using the combinations formula, we will see that 210 different committees are possible.

Here we need to use the combinations function. It says that for a set of N elements, the number of different subsets of K elements (such that K is equal or smaller than N) that we can make is:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case, we have N = 10 and K = 4, replacing that we will get:

[tex]N(10, 4) = \frac{10!}{(10 - 4)!*4!} = \frac{10!}{6!*4!} = \frac{10*9*8*7}{4*3*2} = 210[/tex]

This means that from 10 names, there are 210 different committees of 4 members that can be made.

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Adam burnt 631.6 calories approximately

Given that, Adam swam 1500m in 19 minutes.  

If swimming at a rate of 4.5km/h burns 600 calories,  

we have to find how many calories did adam burn?

Now, let us find his rate of swimming

Distance travelled = speed rate x time taken

[tex]\begin{array}{l}{1500 \mathrm{m}=\text { rate } \times 19 \text { minutes }} \\\\ {1500 \times 1 \mathrm{m}=\text { rate } \times 19 \times 1 \text { minute }}\end{array}[/tex]

We know that 1 hour = 60 minutes and also 1 kilometer = 1000 meter

[tex]\begin{array}{l}{1500 \times \frac{1}{1000} \mathrm{km}=\text { rate } \times 19 \times \frac{1}{60} \text { hour }} \\\\ {\frac{1500}{1000}=r a t e \times \frac{19}{60}} \\\\ {\text { Rate }=\frac{60}{19} \times \frac{3}{2}} \\\\ {\text { Rate }=\frac{30}{19} \times 3} \\\\ {\text { Rate }=\frac{90}{19}=4.736 \mathrm{km} / \mathrm{h}}\end{array}[/tex]

Now, we know that, swimming at a rate of 4.5km/h burns 600 calories,

Let "n" be the calories burnt when adam swam 1500 meter in 19 minutes

[tex]\begin{array}{l}{4.5 \mathrm{km} / \mathrm{h} \rightarrow 600 \text { calories }} \\\\ {\text {Then, } 4.736 \mathrm{km} / \mathrm{h} \rightarrow \text { n calories. }}\end{array}[/tex]

Now, by criss cross multiplication method,

[tex]\begin{array}{l}{4.5 \times n=4.736 \times 600} \\\\ {\rightarrow 4.5 n=2842.1052} \\\\ {\rightarrow n=631.578}\end{array}[/tex]

Hence, adam burnt 631.6 calories approximately.

The answer would be 32/3 or 10.67

Ok, so the formula would be set up like this...

[tex]\frac{(2*4)-(4*3)-(11*2)+(3x-6)}{x+2}[/tex]

then, you can simplify the numerator into

[tex]\frac{8-12-22+3x-6}{x+2}[/tex]

srry but i am just going to assume that you are trying to find what x equals.

if you are, then read on!

so this means that [tex]\frac{8-12-22+3x-6}{x+2}=0[/tex]

now multiply (x+2) on both sides, geting [tex]8-12-22+3x-6=0[/tex]

simplify this, and you got [tex]3x-32=0[/tex] and then [tex]3x=32[/tex]

divide both sides and u got [tex]x=\frac{32}{3}=10.67[/tex]

if the stuff doesn't load, reload the screen hope this helps!

Answer: 160ft.

Step-by-step explanation:

Answer:

Howard's order will contain 15 boxes of hammers and 39 boxes of wrenches.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Price of box of wrenches = US$ 100

Price of box of hammers = US$ 300

Cost of the order = US$ 8,400

2. Let's find the exact amount of boxes of wrenches and hammers

Cost of the order = Price of box of wrenches * Number of boxes of wrenches  + Price of box of hammers * Number of boxes of hammers

Replacing with the real values:

8,400 = 100 * 40 + 300 * Number of boxes of hammers

8,400 = 4,000 + 300 * Number of boxes of hammers

- 300 * Number of boxes of hammers = 4,000 - 8,400

- 300 * Number of boxes of hammers = -4,400

Number of boxes of hammers = -4,400/300 = 14.67 ≈ 15

For making a order without fractions or decimals of a box, it will contain just whole numbers, this way:

15 boxes of hammers + 39 boxes of wrenches

Cost of Howard's order = 15 * 300 + 39 * 100 = 4,500 + 3,900 = 8,400

Howard ordered 18 boxes of wrenches and 22 boxes of hammers. This solution was found by solving the system of equations derived from the total number of boxes and the total cost of the order.

Let's denote:

w  as the number of boxes of wrenches Howard ordered.

h  as the number of boxes of hammers Howard ordered.

Given:

1. Each box of wrenches costs $100.

2. Each box of hammers costs $300.

3. Howard ordered a total of 40 boxes.

4. The total cost of the order is $8400.

We can set up a system of equations based on the given information:

1. The total number of boxes ordered:

w + h = 40

2. The total cost of the order:

100w + 300h = 8400

Now, let's solve this system of equations.

We can use the first equation to express one of the variables in terms of the other:

h = 40 - w

Substitute this expression for h into the second equation:

100w + 300(40 - w) = 8400

Now, let's solve for w:

100w + 12000 - 300w = 8400

-200w = 8400 - 12000

-200w = -3600

w = 3600 ÷ 200

w = 18

Now, we can find h using the first equation:

h = 40 - w

= 40 - 18

= 22

So, Howard ordered 18 boxes of wrenches and 22 boxes of hammers.

Answer:

is this a question or a passage

Answer:

very confused, are you trying to inform us?

Step-by-step explanation:

Answer:

[tex]-\frac{4z}{9}-3[/tex]

Step-by-step explanation:

Combine like terms, [tex]\frac{7}{9}z-\frac{6}{9}z-\frac{5} {9}z= -\frac{4z}{9}[/tex]

and 3-6= -3

There are 21 nickels in the jar

Step-by-step explanation:

Ellie Mae has a jar that contains quarters and nickels

We need to find the number of the nickles in the jar

Assume that the number of nickles is x

∵ There x nickles in the jar

∵ There are 15 more nickels than quarters

∴ The number of quarters = x - 15

∵ 1 nickle = 5 cents

∵ 1 quarter = 25 cents

∵ 1 dollar = 100 cents

∵ The total value is $2.55

- Change the total value to cents

∴ The total value = 2.55 × 100 = 255 cents

∵ 5 x + 25(x - 15) = 255

- Simplify it

∵ 5x + 25x - 375 = 255

- Add like terms

∴ 30x - 375 = 255

- Add 375 to both sides

∴ 30x = 630

- Divide both sides 30

∴ x = 21

There are 21 nickels in the jar

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Answer: $44.50 per hour

Step-by-step explanation:

so easy

6hrs=$267

divide by 6 on both sides

1hr=$44.50

Answer:

4/15 pages per minute

Step-by-step explanation:

10 2/3=32/3

(32/3)/40

(32/3)(1/40)=32/120

simplify

4/15

Answer:

4/15 pages per minute

Step-by-step explanation:

This unit rate is found as follows:

 10 2/3 pages         32/3 pages

----------------------- = ----------------------

   40 minutes           40/1 minutes

To divide 32/3 by 40/1, invert 40/1 and multiply instead:

 32         1

------- * -------

   3        40

Dividing both 32 and 40 by 8, to reduce the fractions, we get:

  4          1

------- * ------- = 4/15 pages per minute

   3         5

Answer:

Step-by-step explanation:

The distributive property:

[tex]a(b+c)=ab+ac[/tex]

[tex](m-3+4n)(-8)=(m)(-8)+(-3)(-8)+(4n)(-8)\\\\=-8m+24-32n[/tex]

Answer:

19 gallons

Step-by-step explanation:

Let x gallons be the amount of water which should be added to 6 gallons of pure acid in order to obtain the 24% acid solution.

Amount of water = x gallons

Amount of pure acid = 6 gallons

Amount of acid solution = x + 6 gallons

Amount of acid in acid solution = 24%

So, there are [tex]0.24(x+6)[/tex] gallons of acid in acid solution.

Hence,

[tex]0.24(x+6)=6[/tex]

Solve this equation. Multiply it by 100:

[tex]24(x+6)=600\\ \\24x+144=600\\ \\24x=600-144\\ \\24x=456\\ \\x=19\ gallons[/tex]

Answer:

19 gallons

Step-by-step explanation:

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hi, i am not giving an explanation because i am trying to get points. Please understand me

The cell phone company made a error in the conversion of cents to dollars in their advertisement. They advertised the cost as 0.02 cents/kilobyte, but they probably meant $0.02/kilobyte.

The cell phone company is advertising their data plan costs at 0.02 cents per kilobyte but it seems like they may have meant $0.02/kilobyte which is different. Understanding the difference requires Mathematics concepts such as understanding of decimals and units conversion. If we take the advertised rate of 0.02 cents/kilobyte, it means for every 1 kilobyte of data, we will only be charged 0.0002 dollars. This is very cheap compared to charging $0.02/kilobyte. The error occurred because the company did not convert cents to dollars correctly, as $1 is equal to 100 cents, not 1 cent.

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