Vito owned 120 shares of a stock before tha corporation instituted a 5 for 3 split. Before the split, the stock was selling at 16 a share. Vito now has 200 shares of te stick that is worth about $26.67 each

Let's rewrite the expression as

[tex] 8x+3ax-5ax = 8-2a \iff 8x - 2ax = 8-2a \iff 2x(4-a) = 2(4-a) [/tex]

So, if [tex] a \neq 4 [/tex], you may divide both sides by [tex] 4-a [/tex], the equation becomes [tex] 2x=2 [/tex], and the only solution is [tex] x=1 [/tex], which means that this is not an identity (an indentity is tautologically true, no matter the value of x).

If instead [tex] a = 4 [/tex], you are multiplying both sides by zero, so the equation becomes

[tex] 2x \cdot 0 = 2 \cdot 0 \iff 0=0 [/tex]

So, it doesn't matter which value for x you choose, because you will always end up with [tex] 0=0 [/tex], which is obviously always true.

Answer:

138 pipe cleaners can make 23 kit

Step-by-step explanation:

6 pipe cleaners = 1 kit

1 pipe cleaner = 1/6 kit

138 pipe cleaners = 1/6 x 138

138 pipe cleaners = 23

Answer:

a_n=a_(n−1)+1.4 , where a_1=4.4

Step-by-step explanation:

Given a sequence as

4.4, 5.8, 7.2, 8.6, 10, …

We find that first term is 4.4

II term = 5.8 = 4.4+1.4

III term = 7.2 = 5.8+1.4

Iv term = 8.6 = 7.2+1.4

V term = 10.0 = 8.6+1.4

i.e. each term is got by adding 1.4 to the previous term.

In other words, this is an arithmetic sequence with I term =4.4 and d = common difference =1.4

I term = a_1 = 4.4

and a_2 = a_1+1.4 and so on.

Hence correct answer is

a_n=a_(n−1)+1.4 , where a_1=4.4

x - length of side of a square

A perimeter of a square: P = 4x

We know:

20 ≤ P ≤ 32

20 ≤ 4x ≤ 32       |divide by 4

5 ≤ x ≤ 8

Answer: b. 5 ≤ x ≤ 8

Answer:

ans in b

Step-by-step explanation:

Answer: k = -1 +/- √769

Step-by-step explanation:

48x - ky = 11

-48x           -48x

         -ky = -48x + 11

         [tex]\frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}[/tex]    

           [tex]y =\frac{48x}{k} - \frac{11}{k}[/tex]

Slope: [tex]\frac{48}{k}[/tex]

*************************************************************************

 (k + 2)x + 16y = -19

- (k + 2)x             -(k + 2)x

                 16y = -(k + 2)x - 19

                  [tex]\frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]

                  [tex]y = -\frac{(k + 2)x}{16} - \frac{19}{16}[/tex]

Slope: [tex]-\frac{(k + 2)}{16}[/tex]

**********************************************************************************

[tex]\frac{48}{k}[/tex] and [tex]-\frac{(k + 2)}{16}[/tex] are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

[tex]-\frac{(k + 2)}{16}[/tex] *  [tex]\frac{k}{48}[/tex] = -1

[tex]\frac{(k + 2)k}{16(48)}[/tex] = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769

Answer:

Maximum revenue = 1000 thousands of dollars.

Explanation:

We have the revenue equation [tex]r(x)=10x - 0.025x^2[/tex], where x is measured in thousands of toys produced, and r(x) is measured in thousands of dollars.

At maximum revenue the derivative of equation is zero

So, [tex]r'(x)=0\\ \\10 - 0.025*2x=0\\ \\ x=10/0.05\\ \\ x=1000/5=200[/tex]

So maximum revenue is when 200 thousands of toys are produced.

Maximum revenue, [tex]r(200)=10*200 - 0.025*200^2\\ \\ r(200)=1000[/tex]

Maximum revenue = 1000 thousands of dollars.

Answer:

  see below

Step-by-step explanation:

The following definitions apply:

  if p, then q . . . . conditional statement

  if q, then p . . . . converse

  if ~p then ~q . . . inverse

  if ~q then ~p . . . contrapositive

You have ...

  p = "it is October 31"

  q = "it is Halloween"

(a) The converse is ...

  If it is Halloween, then it is October 31.

(b) The inverse is ...

  If it is not October 31, then it is not Halloween.

(c) The contrapositive is ...

  if it is not Halloween, then it is not October 31.

ANSWER

The subscription price of $45 provides the maximum revenue for the company

EXPLANATION

When the price is $[tex]40[/tex], the company sells [tex]2000[/tex] quantities.

The total revenue accrued

[tex]=40\times2000[/tex]

[tex]=$80,000[/tex]

When the price increases to $[tex]45[/tex] the quantity sold will decrease by 200 magazines which is [tex]2000-200=1800[/tex]

The total revenue accrued

[tex]=45\times 1800[/tex]

[tex]=81000[/tex] dollars

When the price increases to $[tex]50[/tex] the quantity sold will decrease by 200 magazines again which is [tex]1800-200=1600[/tex]

The total revenue accrued

[tex]=50\times 1600[/tex]

[tex]=80000[/tex] dollars

When the price increases to $[tex]55[/tex] the quantity sold will decrease by 200 magazines which is [tex]1600-200=1400[/tex]

The total revenue accrued

[tex]=55\times 1400[/tex]

[tex]=77000[/tex] dollars

Hence a subscription price of $45 provides the maximum revenue for the company.

Answer:

The remaining child got a fraction of  [tex]\frac{1}{10}[/tex].

Step-by-step explanation:

Lets take the fraction of the money fourth child got is [tex]x[/tex]

Addition of all these fractions should be equal to 1.

⇒[tex]\frac{1}{3} +\frac{1}{6} +\frac{2}{5} +x=1[/tex]

⇒[tex]\frac{10+5+12+30x}{30} =1[/tex] (Taking a common denominator)

⇒[tex]\frac{27+30x}{30} =1[/tex]

⇒[tex]27+30x=30[/tex]

⇒[tex]30x=3[/tex]

⇒[tex]x=0.1[/tex]

Therefore,

The remaining child got a fraction of  [tex]\frac{1}{10}[/tex].

By calculating the combined fractions of the inheritance received by the first three children, we've determined that 27/30 of the inheritance has been allocated. Subtracting this from the whole leaves us with 3/30, which simplifies to 1/10 of the inheritance for the remaining child.

The student has asked about how much the remaining child will receive from a father's inheritance if the first received 1/3, the second received 1/6, and the third received 2/5 of the inheritance. To answer this, let's first add up the portions of the inheritance that the first three children received:

First child: 1/3

Second child: 1/6

Third child: 2/5

Now, we will find a common denominator to add these fractions. The least common multiple of 3, 6, and 5 is 30. Let's convert each fraction:

First child: 1/3 = 10/30

Second child: 1/6 = 5/30

Third child: 2/5 = 12/30

Now, add these fractions:

10/30 + 5/30 + 12/30 = 27/30

Once we add up these portions, we get 27/30 which represents the total part of the inheritance that has been given out to the first three children. To find out the portion for the remaining child:

30/30 (the whole inheritance) - 27/30 (the part given away) = 3/30

Reducing the fraction 3/30 gives us 1/10. So, the remaining child would receive 1/10 of the inheritance.

Explanation:

First we consider ΔABC and ΔBCD,

∠C=∠C  (common)

∠B=∠D=[tex]90\textdegree[/tex]

So, ΔABC ≈ ΔBCD (By AA similarity rule )

So by taking corresponding sides in ratios we get

[tex]\frac{AB}{BD}=\frac{AC}{BC}=\frac{BC}{CD}[/tex]      

Now

[tex]AC.CD=BC.BC\\BC^{2} =AC.CD[/tex]              -------- Eqn (1)

Similarly,

We consider ΔABD and ΔABC

∠A=∠A (Commom)

∠B=∠D=[tex]90\textdegree[/tex]

So,

ΔABD ≈ ΔABC (By AA similarity rule )

So by taking corresponding sides in ratios we get

[tex]\frac{BC}{BD}=\frac{AC}{AB}=\frac{AB}{AD}[/tex]  

Now,

[tex]AB.AB=AC.AD\\AB^{2} =AC.AD[/tex]              --------Eqn (2)

By Adding both the equation we get

[tex]AB^2+BC^2=AC.CD+AC.AD\\AB^2+BC^2=AC(CD+AD)\\AB^2+BC^2=AC.AC\\AB^2+BC^2=AC^2[/tex]

Hence, we proved the pythagorean theorem by using similarity of triangle.

94

for her average to be at least 90 then letting x be the score she requires on her next test, then

[tex]\frac{85+89+92+x}{4}[/tex] = 90 ( solve for x )

multiply both sides by 4 to eliminate the fraction

85 + 89 + 92 + x = 360

266 + x = 360 ( subtract 266 from both sides )

x = 94

Answer:

If a polygon has not got four right angles then it is not a square.

Step-by-step explanation:

Contrapositive is

if A implies B then not B implies not A.

One inch is greater than centimeter

There is a certain pattern:

As x is increased by 1/4 every time, y is increased by 3 every time. You can make a proper ratio and set up proportions with these numbers.

Every 3 Parrots there will be 5 Birds

3/5

Answer:

Every 3 Parrots there will be 5 Birds

3/5

Step-by-step explanation:

Answers:

Explanation:

The given model provides a function that allows to approximate the population of Italy from 1990 through 2008 and predict the populations for other years, assuming validity of the same model over the coming years.

You only need to convert the year into the variable t and subsitute in the model.

1.  Calculate t for every year of your interest:

Year        t = year - 1990

1990             1990 - 1990 = 0 (initial value)

2000            2000 - 1990 = 10

2008            2008 - 1990 = 18

2015             2015 - 1990 = 25

2020            2020 - 1990 = 30

2. Calculate the population as per the model:

         [tex]p = 56.8e^{0.0015(10)}=57.7[/tex]

        [tex]p = 56.8e^{0.0015(18)}=58.4[/tex]

         [tex]p = 56.8e^{0.0015(25)}=59.0[/tex]

        [tex]p = 56.8e^{0.0015(30)}=59.4[/tex]

The answer is b. I see you got it. You are welcome.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have (-6, -8), (12, 7).

Substitute:

[tex]m=\dfrac{7-(-8)}{12-(-6)}=\dfrac{7+8}{12+6}=\dfrac{15}{18}=\dfrac{5}{6}[/tex]

The slope-point form:

[tex]y-y_1=m(x-x_1)[/tex]

We have m = 5/6 and (12, 7).

Substitute:

[tex]y-7=\dfrac{5}{6}(x-12)[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

[tex]y-7=\dfrac{5}{6}(x-12)\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{6}\cdot12}\\\\y-7=\dfrac{5}{6}x-\dfrac{5}{1}\cdot2\\\\y-7=\dfrac{5}{6}x-10\qquad|+7\\\\y=\dfrac{5}{6}x-3[/tex]

26 is a multiple of 2 but 39 isn't

39 is a multiple of 3 but 26 isn't

Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11

Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13.  26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.

Answer:

You were the 35th caller.

Step-by-step explanation:

For one minute, every 5th caller will win a music player and every 7th caller will win concert tickets.

If you were just the first caller to win both a music player and concert tickets, that means we need to find a least number which is divisible by both 5 and 7.

Actually we will find the LCM(Least common multiple) of 5 and 7.

[tex]5=1*5\\ \\ 7=1*7\\ \\ So, LCM = 1*5*7=35[/tex]

That means, you were the 35th caller.

Answer:

35

Step-by-step explanation:

Tomas will make 10 equal payments of $10.89 each to pay off the total cost of the trumpet which is $108.90.

This question involves simple division, the process of sharing an amount equally. Here, Tomas is dividing the total cost of a trumpet, which is $108.90, into 10 equal payments.

To find the amount of each payment, you simply divide the total cost by the number of payments. So, $108.90 divided by 10 gives us $10.89. Therefore, each payment Tomas will make for his trumpet is $10.89.

For more such questions on payments, click on:

https://brainly.com/question/25792915

#SPJ2

Final answer:

Tomas will make 10 equal payments of $10.89 each to pay for the trumpet that costs $108.90 in total.

Explanation:

Tomas buys a trumpet for $108.90 and plans to make 10 equal payments to pay off the full amount. To find the amount of each payment, we divide the total cost by the number of payments. So, we calculate $108.90 ÷ 10, which results in each payment being $10.89. Therefore, each payment Tomas will make is $10.89.

LCM(2, 3, 4) = 12

LCM(x, y, z) = xyz

therefore

LCM(2x, 3y, 4z) = 12xyz

the LCM is 4xyz.

The Least Common Multiple (LCM) of expressions 2x, 3y, and 4z is calculated by finding the smallest power of each individual variable and prime number base that can be divided evenly by each of the expressions. In this case, we have different variables and numerical coefficients. We must take the highest power of each distinct variable and multiply it by the highest coefficient from the numbers given to find the LCM.

Since 2, 3, and 4 are the coefficients, the highest among them is 4. We will use this and multiply by each of the variables x, y, and z. So, the LCM is 4xyz.

It would be subtraction because 2-1 would result into 1 multiplied by 4 would make 4 your answer. And then 6-3 would equal to 3, multiply 3 by 2, you would get 6. Then finally when you add both 4 and 6, you would get the final answer of 10.

 1 inch :  3 meters

x 4          x 4        

4 inch :  12 meters

Answer: 12 meters

Answer:

a1= -2/9

a2= 4/3

a3= 6

Step-by-step explanation:

[tex]a_n = 3a_{n - 1} + 2[/tex]

a_4= 20

lets plug in 4 for n

[tex]a_4 = 3a_{4 - 1} + 2[/tex]

[tex]20= 3a_3+ 2[/tex]

Subtract 2 from both sides and then divide by 3

18 = 3a_3

[tex]6=a_3[/tex]

lets plug in 3 for n and use a3=6 to find a2

[tex]a_3 = 3a_{3 - 1} + 2[/tex]

[tex]6= 3a_2+ 2[/tex]

Subtract 2 from both sides and then divide by 3

4 = 3a_2

[tex]\frac{4}{3}=a_2[/tex]

lets plug in 2 for n and find out a1

[tex]a_2 = 3a_{2 - 1} + 2[/tex]

[tex]\frac{4}{3}= 3a_1+ 2[/tex]

Subtract 2 from both sides and then divide by 3

[tex]\frac{-2}{3}= 3a_1[/tex]

[tex]\frac{-2}{9}=a_1[/tex]

Answer:

37.5

Step-by-step explanation:

x= time not spent on the internet while on the computer

5/6 = 45/x

45*6/5 = x

This is the equation you should use

One question before I give my answer , Where did it say she stopped?

Answer:

ohhhh cool i go to the same school

Step-by-step explanation: