Evaluate the expression given below for x = 3


3(2+5x) = ?​

Answer:

[tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]

Step-by-step explanation:

The straight line BD passes through points B(2a,2b) and D(c,0).

Therefore, the equation of the straight line BD will be given by  

[tex]\frac{y - 2b}{2b - 0} = \frac{x - 2a}{2a - c}[/tex]

⇒ [tex]y - 2b = \frac{2b}{2a - c}x - \frac{4ab}{2a - c}[/tex]

⇒ [tex]y = \frac{2b}{2a - c} x - \frac{4ab}{2a - c} + 2b[/tex]

⇒ [tex]y = \frac{2b}{2a - c} x + \frac{-4ab + 4ab - 2bc}{2a - c}[/tex]

⇒ [tex]y = \frac{2b}{2a - c} x - \frac{2bc}{2a - c}[/tex]

Therefore, third option is correct. (Answer)

We know that the equation of a straight line passing through the points ([tex]x_{1},y_{1}[/tex]) and ([tex]x_{2},y_{2}[/tex]) is given by  

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

Answer:

- 13(x + [tex]\frac{8}{13}[/tex])

Step-by-step explanation:

Given

- 13x - 8 ← factor out - 13 from each term

= - 13(x + [tex]\frac{8}{13}[/tex])

The question asked to factor out -13 from the expression -13x - 8. The steps include dividing each term by -13. Therefore, the expression factored out by -13 is -13(x + 8/13).

In this mathematical problem, we are asked to factor out -13 from the expression -13x - 8. Factoring out in algebra means to divide each term in the expression by that common factor, which in this case is -13. So, we proceed as follows:

Therefore, the expression -13x - 8 factored out by -13 is -13(x + 8/13).

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Answer:

multip[laction and addition

Step-by-step explanation:

Answer:

J would be the answer, my friend.

log2 (24/3) = log5 (x)

log(8)/log(2) = log(x)/log(5)

log(x) = [log(5)][3]

log(x) = log(5^3)

x = 5^3 = 125

Step-by-step explanation:

Answer:

x = 125

Step-by-step explanation:

[tex] \log_2 24 - \log_2 3 = \log_5 x [/tex]

Use the rule of subtracting logs:

[tex] \log_b x - \log_b y = \log_b \dfrac{x}{y} [/tex]

[tex] \log_2 \dfrac{24}{3} = \log_5 x [/tex]

[tex] \log_2 8 = \log_5 x [/tex]

[tex] 3 = \log_5 x [/tex]

Use the definition of log:

[tex] \log_b x = y ~~\Longleftrightarrow ~~ b^y = x [/tex]

[tex] x = 5^3 [/tex]

[tex] x = 125 [/tex]

The right answer is Option B.

Step-by-step explanation:

A unit rate describes how many units of one type of quantity corresponds to one unit of other type of quantity.

A. Trevor spent $49 on 2 theater tickets.

2 theater tickets = $49

1 theater ticket = [tex]\frac{49}{2} = \$24.5[/tex]

B. Sally bought a pack of 5 shirts for $35.

5 shirts = $35

1 shirt = [tex]\frac{35}{5} = \$7\\[/tex]

C. Brandon bought 7 gallons of gas for $14.

7 gallons = $14

1 gallon = [tex]\frac{14}{7}=\$2[/tex]

D . Gina bought nail polish for $5 and a pack of gum for $2.

1 nail polish = $5

1 pack of gum =$2

The pack of 5 shirts for $35 has a unit rate of $7.

The right answer is Option B.

Keywords: unit rate, division

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Answer:

-3 5/6 (-3.83333)

Step-by-step explanation:

(-1x3+2)/3+-(2x6+1)/6

-5/3+-13/6

-5x2/6+-13x1/6

-10/6+-13/6

(-10+-13)/6

-23/6

-(3x6+5)/6

=-3 5/6 or (-3.83333)

Answer: The polynomial is irreducible

Step-by-step explanation:

There is nothing we can subtract between x3-12

For example: you are trying to find the polynomial of x4-6

Options:

A. (x+4)(x-6)

B. (x+1+3)(x-6)

C. None the polynomial is irreducible.

You would chose C because there is no subtraction sign in between the parentheses. If you would choose a right answer, you would rewrite it as:

(x+4)-(6)

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.

An equation has infinitely many solutions if it can be manipulated all the way to an identity (i.e. an equality where the right and left hand side are the same). We have:

A) [tex]12+4x=6x+10-2x \iff 12+4x=10+4x \iff 12=10[/tex]

which is impossible

B) [tex]5x+14-4x=23+x-9 \iff x+14 = x+14[/tex]

which is an equality

C) [tex]x+9-0.8x=5.2x+17-8\iff 0.2x+9=5.2x+9 \iff 0.2x=5.2x\iff x=0[/tex]

which has a unique solution

D) [tex]4x-2x=20 \iff 2x=20 \iff x=10[/tex]

which has a unique solution

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:

(1,K) hope i could help

Step-by-step explanation:

Answer:

[tex](1,K)[/tex]

Step-by-step explanation:

According to the problem, the mixture must contain K ounces of oil for every gallon of gasoline. That is, each gallon of gasoline equals K ounces, this can be expressed as

[tex](1,K)[/tex]

Where [tex]x=1[/tex] expresses each gallon of gasoline and [tex]y=K[/tex] represents ounces of oil.

Therefore, the coordinate on the graph must represent [tex](1,K)[/tex], that is, K ounces of oil per gallon of gasoline.

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:

x^4 -x^3 -9x^2 -11x -4

Step-by-step explanation:

We can use the zero product property

(x-a)  (x-b) (x-c) (x-d)  where a b c d are the roots

(x- -1)(x- -1)(x- -1) ( x-4) since the root -1 is repeated 3 times and 4 is a root

(x+1)(x+1)(x+1) ( x-4)

Foil the first two terms  and the last two terms

(x^2 + 2x+1)( x^2 -3x-4)

Foil again

x^4 -3x^3 -4x^2 +2x^3 -6x^2 -8x +x^2 -3x-4

Combine like terms

x^4 -x^3 -9x^2 -11x -4

Answer:

Step-by-step explanation:

roots = -1, -1, -1, 4

(x + 1)(x + 1)(x + 1)(x - 4) = 0

(x^2 + 2x + 2)(x^2 - 3x - 4) = 0

x^2(x^2 - 3x - 4) + 2x(x^2 - 3x - 4) + 2(x^2 - 3x - 4) = 0

x^4 - 3x^3 - 4x^2 + 2x^3 - 6x^2 - 8x + 2x^2 - 6x - 8 = 0

x^4 - x^3 - 8x^2 - 14x - 8 = 0

Answer:

is this a question or a passage

Answer:

very confused, are you trying to inform us?

Step-by-step explanation:

Answer:

20kg

Step-by-step explanation:

Answer:

6 quarts

Step-by-step explanation:

1 gallon = 4 quarts

1 1/2 gallon * (4 quarts / 1 gallon) =  (1 + 1/2) * 4 = 1*4  + 1/2*4 = 4 +2 = 6 quarts

Answer:

Increasing : [tex]-5<x<-1[/tex]  or [tex]-1<x<1[/tex]

Decreasing : [tex]-8<x<-5[/tex]  or [tex]4<x<7[/tex]

Neither : [tex]1<x<4[/tex]

Step-by-step explanation:

Increasing function : In this function, the y-value increases as the x-value increases.

From the given graph it is clear that the function is increasing on  

[tex]-5<x<-1[/tex]

[tex]-1<x<1[/tex]

Decreasing function : In this function, the y-value decreases as the x-value increases.

From the given graph it is clear that the function is decreasing on  

[tex]-8<x<-5[/tex]

[tex]4<x<7[/tex]

Neither increasing nor decreasing function : In this function, the y-value remains constant as the x-value increases.

From the given graph it is clear that the function is neither increasing nor decreasing on  

[tex]1<x<4[/tex]

To determine if a function is increasing, decreasing, or neither over intervals on a graph, analyze the direction of the graph. If the graph goes up, the function is increasing. If it goes down, the function is decreasing. If it remains flat, the function is neither increasing nor decreasing.

The question asks to determine if the function is increasing, decreasing, or neither over each interval on the given graph. To do this, we need to analyze the direction of the graph. If the graph goes up as we move from left to right, the function is increasing. If the graph goes down, the function is decreasing. If the graph remains flat, the function is neither increasing nor decreasing. Drag the intervals to the appropriate box based on these observations.

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:

13. c,

14. a.

Step-by-step explanation:

13.  The length of a side PQ with coordinates of

      P as (x,y)  and Q as (w,z)

       is: [tex]\sqrt{(x-w)^{2} +(y-z)^{2} }[/tex]

[tex]\sqrt{(5-5)^{2}+(-2+7)^{2}  } =\sqrt{0^{2}+5^{2}  } =5[/tex]

[tex]\sqrt{(5-1)^{2}+(-7+2)^{2}  } =\sqrt{(4)^{2}+(-5)^{2}  } =\sqrt{4^{2}+5^{2}  }[/tex]

[tex]\sqrt{(5-1)^{2} +(-2+2)^{2} } =\sqrt{4^{2} } =4[/tex]

now, the easiest one will be when the vertices are on the coordinate axes.

14. If u see the figure clearly, the lines l and FH are parallel.

the parallel postulate, i.e, the alternate interior angles will always be congruent.

Answer:

Step-by-step explanation:

11x+11y=-5

Those are the factors of 42 c:

(1, 42), (2, 21), (3, 14) and (6, 7).

Answer:

I think your functions are [tex]y=2^{x}[/tex] ,[tex]y=2*5^{x}[/tex] and [tex]y=2+5^{x}[/tex]

If yes then then the third function which is [tex]y=2+5^{x}[/tex].

Step-by-step explanation:

The function [tex]c^{x}[/tex] where c is a constant has

Domain : [tex]c\geq 0[/tex]

Range : ( 0 , ∞ )

The above range is irrespective of the value of c.

I have attached the graph of each of the function, you can look at it for visualization.

Answer:

y = 5∧× + 2

Step-by-step explanation:

Answer:

no, because the hypotenuses must have different lengths.

Step-by-step explanation:

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:

The taken by Rhonda to react before volleyball hits ground is 2.39 seconds

Step-by-step explanation:

Given as :

The upward velocity of the volleyball = 14.5 ft/s

The height of the ball above ground = 4 feet

Consider value of acceleration due to gravity = 9.8 m/s

Let the time for Rhonda to react before ball hits ground = t sec

Now,

S = u t + [tex]\frac{1}{2}[/tex] a t²

where s = height

          u = initial velocity  , a = acceleration due to gravity , t = time in sec

So, 4 = 14.5× t + [tex]\frac{1}{2}[/tex] × 9.8 × t²

or, 4 = 14.5 t + 4.9  t²

or, 4.9  t² + 14 .5 t - 4 = 0

Now, solve for t

 t = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]

or, t =  [tex]\frac{-14.5\pm \sqrt{14.5^{2}-4\times 4.9\times (4)}}{2\times 4.9}[/tex]

Or, t = [tex]\frac{-14.5\pm \sqrt{80.5025}}{9.8}[/tex]

Or, t = - 2.39 , - 2.76

Hence The taken by Rhonda to react before volleyball hits ground is 2.39 seconds . Answer

The right answer is Option B.

Step-by-step explanation:

Pieces of bread produced = 800

Pieces of bread sold = 750

Pieces left = Pieces produced - Pieces sold

Pieces left = 800 - 750 = 50

Percentage of bread left = [tex]\frac{Pieces\ left}{Pieces\ of\ bread\ produced}*100[/tex]

[tex]Percentage\ of\ pieces\ left=\frac{50}{800}*100\\Percentage\ of\ pieces\ left=\frac{5000}{800}\\Percentage\ of\ pieces\ left= 6.25\%\\[/tex]

Rounding off to nearest whole percent;

Percentage of pieces left= 6%

The right answer is Option B.

Keywords: percentage, subtraction

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Answer:

72

Step-by-step explanation:

1 then 7+1=8 8+7=15 15+8=23 23+15=38 38+23=61

Ta Da I have taught you the pattern now you can show your work just in case you have one of those teachers hope this helped

The next number in the pattern 1,7,8,15,23,38,61 is 99. The pattern can be understood by calculating the differences between consecutive numbers, and observing a pattern in these differences.

Let's take a look at the pattern 1,7,8,15,23,38,61 closely. At every step, we're adding an increasing number to get to the next term in the sequence. From 1 to 7, we add 6. From 7 to 8, we add 1. From 8 to 15, we add 7, from 15 to 23, we add 8, from 23 to 38, we add 15 and from 38 to 61, we add 23.

The difference between these numbers (6, 1, 7, 8, 15, 23) reads as follows: 5, 6, 1, 7 and 8. So, the next difference could be 15 (continuing the pattern in the differences). So, the next term would be obtained by adding 15 to previous term's difference (23) and then adding that result to 61.

Finally, we calculate 61 + (23 + 15) = 61 + 38 = 99. So, the next number in this pattern should be 99.

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Answer:

y/x

Step-by-step explanation:

If y is directly proportional to x, then:

y = kx

k is the coefficient of proportionality, or the constant rate of change.  Solving for k:

k = y/x

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