A leather coat costs $120 and the sales tax is 7.25%. What is the TOTAL cost of the coat?

[tex]\rule{200}4[/tex]

Answer : The required ratio is (14m-6):(8m+23) .

[tex]\rule{200}4[/tex]

Here we are given that the ratio of sum of first n terms of two AP's is (7n + 1):(4n + 27) .

That is.

[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{7n +1}{4n +27} \\[/tex]

As , we know that the sum of n terms of an AP is given by ,

[tex]\small\sf\longrightarrow \pink{ S_n =\dfrac{n}{2}[2a +(n-1)d]} \\[/tex]

Assume that ,

Using this we have ,

[tex]\small\sf\longrightarrow \dfrac{S_1}{S_2}=\dfrac{\dfrac{n}{2}[2a + (n-1)d]}{\dfrac{n}{2}[2a' +(n-1)d'] } \\[/tex]

[tex]\small\sf\longrightarrow \dfrac{7n+1}{4n+27}=\dfrac{2a + (n -1)d}{2a' + (n -1)d' } . . . . . (i) \\[/tex]

Now also we know that the nth term of an AP is given by ,

[tex]\longrightarrow\sf\small \pink{ T_n = a + (n-1)d}\\[/tex]

Therefore,

[tex]\longrightarrow\sf\small \dfrac{T_{m_1}}{T_{m_2}}= \dfrac{ a + (n-1)d }{a'+(n-1)d'}. . . . . (ii)\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{T_1}{T_2}=\dfrac{2a + (2n-2)d}{2a'+(2n-2)d'} . . . . . (iii)\\[/tex]

From equation (i) and (iii) ,

[tex]\longrightarrow\sf\small n-1 = 2m-2\\[/tex]

[tex]\longrightarrow\sf\small n = 2m -2+1 \\[/tex]

[tex]\longrightarrow\sf\small n = 2m -1 \\[/tex]

Substitute this value in equation (i) ,

[tex]\longrightarrow \sf\small \dfrac{2a+ (2m-1-1)d}{2a' +(2m-1-1)d'}=\dfrac{7(2m-1)+1}{4(2m-1) +27}\\[/tex]

Simplify,

[tex]\longrightarrow\sf\small \dfrac{ 2a + (2m-2)d}{2a' +(2m-2)d'}=\dfrac{14m-7+1}{8m-4+27}\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{2[a + (m-1)d]}{2[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]

[tex]\longrightarrow\sf\small \dfrac{[a + (m-1)d]}{[a' + (m-1)d']}=\dfrac{ 14m-6}{8m+23}\\[/tex]

From equation (ii) ,

[tex]\longrightarrow\sf\small \underline{\underline{\blue{ \dfrac{T_{m_1}}{T_{m_2}}=\dfrac{ 14m-6}{8m+23}}}}\\[/tex]

[tex]\rule{200}4[/tex]

Answer:

1/3

Step-by-step explanation:

The slope of a line represents the variation in height per variation in length.

In our case, for every square you move up, you have to move 3 horizontally. The slope is thus

m= (vertical change) / (horizontal change) = 1/3

Answer:

1/3

Step-by-step explanation:

Answer:

x should be eliminated

hope it helps

Answer:

102in2

Step-by-step explanation:

The formula for surface area is 2(wl+hl+hw). So plug in the measurements of the prism into the formula to get 102.

Answer:

Hey bro ur answer is 5-10g +20h

Step-by-step explanation:

5(1-2g+4h)=5 x 1- (5 x 2g) + ( 5 x 4h) = 5-10g +20h

Answer/Step-by-step explanation:

Explain the role of the GCF in factoring a polynomial.

The role of the GCF in factoring a polynomial is the largest monomial that divides evenly into each term. GCF is a factor that is shared by all terms within a polynomial. For instance, if we have a polynomial of the form A*B + A*C, the GCF is A since both terms have A as a factor.

Where is the GCF placed after factoring the GCF?

After factoring out the GCF, it's placed outside the parentheses, in front of the rest of the polynomial. Like the sample we previous use A*B+A*C = A(B+C).

How do you verify factoring is correct?

To Verify factoring is correct distributing the GCF to the polynomial within the parentheses.

~Learn with Lenvy~

Answer:

119.32 m

Step-by-step explanation:

[tex]\textcolor{violet}{\text{Circumference of circle = 2πr = πd}} [/tex]

In the formula above, r is the radius and d stands for diameter.

Circle's circumference

= 3.14(38)

= 119.32 m

Answer:

no idea

Step-by-step explanation:

Answer:

  800 cm³

Step-by-step explanation:

The volume is the product of the base area and the "height" of the prism. Here, the base can be considered to be a 10 cm × 12 cm rectangle with a 4 cm × 5 cm cutout. Its area will be ...

  A = (10 cm)(12 cm) -(4 cm)(5 cm) = 120 cm² -20 cm² = 100 cm²

The product of this base area and the 8 cm height of the prism is ...

  V = Bh = (100 cm²)(8 cm) = 800 cm³

The volume of the prism is 800 cm³.

Answer:

2. b) New amount = £6200

Same ratio → Jon : Bon = 3 : 7

6200 ÷ (3 + 7) = 620

⇒ 620 × 3 : 620 × 7

⇒ 1860 : 4340

Jon = £1860

Bon = £4340

3.

  Tom : Thom : Thomas

= 2 : 3 : 5

= 2x: 3x : 5x

Given Tom received £2400:

⇒ 2x = 2400

⇒ x = 1200

   2x: 3x : 5x

⇒ (2 × 1200) : (3 × 1200) : (5 × 1200)

⇒ 2400 : 3600 : 6000

Tom = £2400

Thom = £3600

Thomas = £6000

4.

  cats : dogs

= 1 : 5

= 1x : 5x

Given there are 8 cats:

⇒ 1x = 8

⇒ x = 8

   1x : 5x

⇒ (1 × 8) : (5 × 8)

⇒ 8 : 40

Therefore, there are 40 dogs

Answer:

80% of 75 = 60

Step-by-step explanation:

first make 80% a decimal so 0.8 because 80/100 = 0.8

the multiply 0.8 by 75

this will give you 60

Therefore Helen's necklace has 60 blue beads

The graph of the direct variation passes through the origin

From the graph, we have the following points

(x.y) = (0,0) and (2,10)

Where:

x represents the number of revolutions

y represents the distance in feet

The revolution per foot of travel (r) is then calculated as:

[tex]r = \frac{x_2 -x_1}{y_2 -y_1}[/tex]

This gives

[tex]r = \frac{2 - 0}{10 - 0}[/tex]

[tex]r = 0.2[/tex]

This means that, the revolution per foot of travel is 0.2

This is the reciprocal of the revolution per foot of travel

In (a), we have:

[tex]r = 0.2[/tex]

So, the slope is:

[tex]Slope = \frac 1{0.2}[/tex]

[tex]Slope = 5[/tex]

Hence, the slope of the graph is 5

Read more about direct variation at:

https://brainly.com/question/6499629

Answer:

15+15+40+40+40= 150

Step-by-step explanation:

Triangle x2]

(5 x 6) / 2

15

Rectangle x3]

(8 x 5)

40

only for a triangle, we divide by 2

Your answer is 150cm square.

But you do not have that option so I would pick the closes one if I were you. Have a good day.

[tex]\left[Hello!\;Answer\;- > \;Below:][/tex]

Answer:

Decimal Form: 16.25

Fraction Form :16 1/4

Step-by-step explanation:

Given:

James Grows Corn 1/4 of his land

Note: 1/4 = .25

Question:

If he has 65 acres of land, how much of the land is used for growing corn?

Solve:

Thus;

65 x 1/4 or 65 x .25

which given you the answer;

16 1/4 or 16.25

[RevyBreeze]

Answer:

She will ride 13 miles in one hour

Step-by-step explanation:

(8 2/3) / (2/3) = x / 1....8 2/3 miles to 2/3 hr = x miles to 1 hr

cross multiply

(2/3)(x) = (8 2/3)(1)

2/3x = 26/3

x = 26/3 * 3/2

x = 26/2...which equals 13....she will ride 13 miles in 1 hr

Answer:

26

Step-by-step explanation:

[tex]5^{2}[/tex] = 5 · 5 = 25

then add 1

Answer:

26

Step-by-step explanation:

(5 x 5) + 1

25 + 1

26

Have an amazing day!!!

PLEASE RATE AND MARK BRAINLIEST!!!

Answer:

x < 6

Step-by-step explanation:

Step 1: Subtract 12 from both sides.

Therefore, the answer is x < 6.

Answer:

Sis 97,U is 30,Tis19,R is 21and m is 37

Answer:

E = 27.125

Step-by-step explanation:

Hope this helps you.

Answer:

e=56

Step-by-step explanation:

since the denominator is 8, what can you divide by 8 to get something that you can add to 23 and get 30.

30-23=7

56//8=7

Step-by-step explanation:

yo question doesn't make sense.

Answer:

I believe the answer is A.

Step-by-step explanation:

Hope that helps!

Answer:

See below.

Step-by-step explanation:

28x^2yz and 16xy^2

GCF of 28 and 16: 4

GCF of x^2yz and xy^2: xy

The GCF is 4xy.

5x^2y^4, 10x^3y^5, and 15xy^2

GCF of 5, 10, and 15: 5

GCF of x^2y^4, x^3y^5, and xy^2: xy^2

The GCF is 5xy^2.

-hope it helps

Hi! Hope you're enjoying your day!

First of all, the G.C.F. stands for

Greatest Common Factor

So we need to find the Greatest Common Factor of the polynomials.

And yea, polynomials have Greatest Common Factors as well.

So, let's find all the Greatest Common Factors. :)

First, we have

[tex]\bold{28x^2yz}[/tex] and [tex]\bold{16xy^2}[/tex]

What are the common factors of these polynomials?

Well, there are plenty of them, like 2, 2x, y...

What is the Greatest Common factor?

Is it Option A, 12xy?

No, because neither 28 nor 16 is divisible by 12.

So we cross out Option A.

Is it Option B, 8xy?

No, because 28 isn't divisible by 8, and remember, if a number is evenly divisible by another number, then that number is a factor.

Example: 8 is a factor of 16 (16÷8=2); 8 is not a factor of 28, because

28÷8=3.5 (a decimal, not a whole number)

Is it Option C, 4xy?

Yeah, it seems like Option C is the right option.

[tex]\huge\checkmark[/tex]Both 28 and 16 are divisible by 4

[tex]\huge\checkmark[/tex]Both polynomials have an x and a y in them

[tex]\rule{250}{2}[/tex]

Find the GCF:

[tex]\bold{5x^2y^4,\:10x^3y^5, \:and\:15xy^2}[/tex]

Once again, is it Option A, 5x^3y^5?

No, because

✘ 5 and 10 aren't divisible by 3

✘ None of the 3 polynomials has a 3y term

In other words, Option A is wrong.

How about Option B?

You should see right off the bat that 5 and 15 aren't divisible by 10.

So now we have 2 options left.

Is it Option C, 5xy²?

Well,

✓All 3 polynomials are divisible by 5

✓ All 3 polynomials have a y² term

✓ All 3 polynomials have an x term.

Hence, the answers are

[tex]\boxed{\boxed{\bold{1. \;Option\;C; 2.\;Option\;C.}}}[/tex]

Hope everything is clear.

If you have any questions, please comment.

#LearningIsFun

[tex]\rule{200}{2}[/tex]

Answer:

$4825.80

Step-by-step explanation:

Answer:

The answer is

→ 9

Step-by-step explanation:

[tex]3+5+7-6=9[/tex]

Therefore, 9 is your answer.

Answer:

=5x5x5

Step-by-step explanation:

5x5^2

=5x(5x5)

=5x5x5

Answer:

625

Step-by-step explanation:

5×5 to the power of 2

25 to the power of 2

25×25 = 625

Answer:

[tex]-\frac{27(-\frac{20t}{10}+x)^{n} }{50} +2.56[/tex]

Step-by-step explanation:

Answer:

(2x + 14)° + (7x + 13)° = 180°

(2x + 14)° = 48°

(7x + 13)° = 132°

All 3 statements are true

Step-by-step explanation:

Answer: 2nd option: 9-i

Step-by-step explanation:

We can add the numbers and the terms with i separately.

12 - 5i - 3 + 4i = (12 - 3) + (-5i + 4i)

= 9 + (-i)

*Adding a negative is essentially subtracting a positive*

= 9-i

Answer:

108 : 1

Step-by-step explanation:

1 foot = 12 inches

81 foot = 81 * 12 = 972 inches

Scale factor = 81 feet  : 9 inches

                    = 972 : 9

                    = 972 ÷ 9  : 9÷9

                    = 108 : 1

Answer:

12x+4x-7y+45b+78a-44b+1a+1z+0d+1.1a+1.1a+2+2+2