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At a bargain store, Tanya bought 5 items that each cost the same amount. Tony bought 3 items that each cost the same amount, but each was $2.5 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?

(a) Write an equation. Let x represent the cost of one of Tanya's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.

Answer:

x = - 1

Step-by-step explanation:

3(x + 2) = 2x + 5 ← distribute parenthesis on left side by 3

3x + 6 = 2x + 5 ( subtract 2x from both sides )

x + 6 = 5 ( subtract 6 from both sides )

x = - 1

Answer:

21

Sorry if not correct

But I think this is the answer

The number of rows in the considered theater which has 3 more seats that seats that the previous row, with first row having 15 and last row having 78 seats is given by: Option D: 22

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

[tex]a, a + d, a + 2d, ... , a + (n+1)d, ...[/tex]

Its nth term is

[tex]T_n = a + (n-1)d[/tex]

(for all positive integer values of n)

And thus, the common difference is

[tex]T_{n+1} - T_n[/tex]

for all positive integer values of n

For this case, we can use arithmetic sequence as the number of seats in each next row is 3 more than previous row, so there is constant difference.

Now, the first number is 15, so we have: a = 15,d = 3 (increasing, so positive).

Let there are 'n' row in the theater.

Then the nth term of the arithmetic sequence having a = 15 and d = 3 should be 78 (as the nth row from first to last is the last row, having 78 seats).

Thus, we get:

[tex]T_n = a + (n-1)d\\78 = 15 + (n-1)3\\78-15 =3n - 3\\\\n = \dfrac{63+3}{3} = 22[/tex]

Thus, the number of rows in the considered theater which has 3 more seats that seats that the previous row, with first row having 15 and last row having 78 seats is given by: Option D: 22

Learn more about arithmetic sequence here:

https://brainly.com/question/3702506

Answer:

-19

Step-by-step explanation:

-7+4×-3

-7-12

-19

Maybe it's correct

Answer:

Hope this helps

Step-by-step explanation:

Answer:

slope of the line is =y2-y1/x2-x1

=2-6/6+2

=-4/8

=-1/2

=-(1/2)

Answer:

a = 36

Step-by-step explanation:

6 = [tex]\frac{a}{4+2}[/tex] , that is

6 = [tex]\frac{a}{6}[/tex] ( multiply both sides by 6 to clear the fraction )

36 = a

Answer:

Step-by-step explanation:

a  and d  are in standard form.

b and c are in factored form

ax² + bx + c  ---> this is the standard form.

If the equation is written as product of two terms then it is in factored  form.

Based on the given information, Michael's age is 13, and Gabrielle's age is 26.

Let's represent Gabrielle's age as G and Michael's age as M.

Given that Gabrielle's age is two times Michael's age, we can express this relationship as:

G = 2M.

We also know that the sum of their ages is 39:

G + M = 39.

Now, we can substitute the value of G from the first equation into the second equation:

2M + M = 39.

Combining like terms:

3M = 39.

To isolate M, we divide both sides of the equation by 3:

M = 39 / 3.

Simplifying further:

M = 13.

Therefore, Michael's age is 13.

To confirm this result, we can substitute M = 13 back into the equation G = 2M:

G = 2(13).

G = 26.

So, Gabrielle's age is 26.

For similar question on age.

https://brainly.com/question/30994122  

#SPJ8

Answer:

a, b, d, e, f

Step-by-step explanation:

only c is incorrect

Answer:

is good

Step-by-step explanation:

Answer:

y = 3x - 8

Step-by-step explanation:

m = slope

slope = y2 - y1 / x2 - x1

4 - 1 / 4 - 3 = 3/1 = 3

m = 3

b = y-intercept

b = -8

y = mx + b

y = 3x + (-8)

y = 3x - 8

Answer:

1/10?

Step-by-step explanation:

I dont really understand what you are aasking here.

Line segments can be divided into sub-segments.

The value of DF is 18

The given parameters are:

[tex]\mathbf{BE = 3x + 6}[/tex]

[tex]\mathbf{DF = 7x + 4}[/tex]

We have:

[tex]\mathbf{BE + DF = 30}[/tex]

So, we have:

[tex]\mathbf{3x + 6 + 7x + 4 = 30}[/tex]

[tex]\mathbf{10x + 10 = 30}[/tex]

Subtract 10 from both sides

[tex]\mathbf{10x = 20}[/tex]

Divide both sides by 10

[tex]\mathbf{x = 2}[/tex]

Substitute [tex]\mathbf{x = 2}[/tex] in [tex]\mathbf{DF = 7x + 4}[/tex]

[tex]\mathbf{DF = 7 \time 2 + 4}[/tex]

[tex]\mathbf{DF = 14 + 4}[/tex]

[tex]\mathbf{DF = 18}[/tex]

Hence, the value of DF is 18

Read more about line segments at:

https://brainly.com/question/17313387

Answer:

Step-by-step explanation:

[tex]11. \: \: - 2.5(4x - 4) = - 6 \\ - 2.5(4x) - 2.5(4) = - 6 \\ - 10x + 10 = - 6 \\ - 10x + 10 - 10 = - 6 - 10 \\ - 10x = - 16 \\ \frac{ - 10x}{ - 10} = \frac{ - 16}{ - 10} \\ x = 1.6 \\ [/tex]

[tex] \frac{1}{6} (x - 5) = \frac{1}{2} (x + 6) \\ \frac{1}{6} \times x + \frac{1}{6} ( - 5) = \frac{1}{2} \times x + \frac{1}{2} \times 6 \\ \frac{x}{6} - \frac{5}{6} = \frac{x}{2} + \frac{6}{2} \\ \frac{x - 5}{6} = \frac{x + 6}{2} \\ 2(x - 5) = 6(x + 6) \\ 2x - 10 = 6x + 36 \\ - 10 - 36 = 6x - 2x \\ - 46 = 4x \\ \frac{ - 46}{4} = \frac{4x}{4} \\ \frac{ - 23}{2} = x \\ - 11 \frac{1}{2} = x[/tex]

Step-by-step explanation:

=total pay=(8x30)+20

=240+20=£260

=Total pay=(8x34)+bonus

300-272+bonus

300/-272 -272/-272 +bonus

bonus=£28

Answer:

Step-by-step explanation:

b  - 7x = (-4) - 7*2

          = -4 - 14      {both numbers have same sign, so add and put the - sign for the result}

         = -18

Answer:

10 feet

Step-by-step explanation:

to solve, multiply 2 by 5;

2*5=10

Hope this helps! :)

Answer:

11)The unknown answer is 24

So sorry I couldn't solve the remaining ones

Answer:

Angle A +Angle B=180

67+B=180

B=113°

Step-by-step explanation:

given,

JIMMY bought,

no. of daylillies = 4

no. of shrubs = 9

total cost of all material he bought = $80

TED bought,

no. of daylillies = 12

no. of shrubs = 4

total cost of all material he bought = $148

let daylillies be x and shrubs be y

the equation is,

4x + 9y = $80 -----------(1)

12x + 4y = $148 -----------(2)

now, multiply (1) by 3 we got,

12x + 27y = $240 -----------(3)

now, subtract (2) from (3) we got,

23y = 92

→ y = 92/23 = 4

→ y = 4

therefore cost of shrubs are $4.

so, cost of daylillies,

→ 12x + 4(4) = 148

→ 12x = 148 - 16 = 132

→ x = 132/12 = 11

→ x = 11

Hence, cost of daylillies are $11 and shrubs are $4.

hope this answer helps you dear......take care and may u have a great day ahead!

Answer:

Step-by-step explanation:

Hey ! I beleive this is the answer: 27.5/100=.275

Answer:

15 and 7 Im almost certain

Step-by-step explanation:

1. figure 4 would be 81

Explanation:

from figure 1 wich is 3, if you keep multiplying 3 until figure 4. the shaded triangle would be 81

1x3 - 3

3x3 - 9

9x3 - 27

27x3 - 81

2. figure 10 would be 59,049

Explanation:

from figure 1 wich is 3, if you keep multiplying 3 until figure 10. the shaded triangle would be 59,049

1x3 - 3

3x3 - 9

9x3 - 27

27x3 - 81

81x3 - 243

243x3 - 729

729x3 - 2,187

2,187x3 - 6,561

6,561x3 - 19,683

19,683x3 - 59,049

3. it would be figure 8 wich is 6,561

Explanation:

1x3 - 3

3x3 - 9

9x3 - 27

27x3 - 81

81x3 - 243

243x3 - 729

729x3 - 2,187

2,187x3 - 6,561

Answer:

[tex]good \: luck \: and \: enjoy \: it[/tex]

Answer:

−[tex]x^{2}[/tex] + [tex]x^[/tex] − 1

Answer:x=2

Step-by-step explanation:

hope it helps

Answer:

x^2/3, this the correct answer.

Step-by-step explanation:

It's simple!

=x^1/6+1/6+1/6+1/6

=x^4/6

=x^2/3