Convert 6 10/36 to an improper fraction in lowest terms

14 = 2y/5 | *5

70 = 2y | :2

35 = y

Test :

14 = 2*35/5 TRUE

Answer:

y=35

Step-by-step explanation:

[tex]\frac{2y}{5}=14\\2y=14*5\\2y=70\\y=\frac{70}{2}\\y=35\\\\Checking\\\frac{2(35)}{5} \\\frac{70}{5} \\=14[/tex]

Answer:

Step-by-step explanation:

General Solution

Left hand side

tan(30) + 1 / tan(30

tan^2(30) + 1

============

tan 30

but tan^2(30) + 1 = sec^2(30)

sec^2(theta) / tan(30) Let theta = 30o. This will work for any angle between 0 and 90

[tex]\dfrac{sec^2(theta)}{tan(theta)} = \dfrac{sec^2(theta)}{\dfrac{sin(theta)}{cos(theta)}} = \dfrac{1}{\dfrac{cos^2(theta)*sin(theta)}{cos(theta)}}[/tex]

Cancel out cos(theta) and one of cos^2(theta)

leaving your with

[tex]\dfrac{1}{sin(theta)*cos(theta)}[/tex]

which is exactly what the right hand side is.

This is the way this problem should be done. If you want to show what happens with 30o then

Thirty degree angle

tan(30) = 0.5774

Left hand side

0.5774 + 1/(0.5774) = 2.3093

Right hand side

1/(sin(30)*cos(30))

1/(0.5 * 0.8660)

1/(0.4330

2.3094

Which is about as close as you will get when you round.

The value of the equation A = 837.2 / 1.3 is A = 644

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be p

The value of p = 837.2

Let the second number be q

The value of q = 1.3

Now , the equation A = p/q

Substituting the values in the equation , we get

A = 837.2 / 1.3

On simplifying the equation , we get

A = 644

Therefore , the value of A is 644

Hence , the equation is A = 644

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Answer:

21 inches

Step-by-step explanation:

May had just over 6 inches of rain, June had just about 9 inches of rain, and July had just under 6 inches of rain. Together, these months had 9 + 6 + 6 = 21 inches of rain.

Answer:

see explanation

Step-by-step explanation:

(a)

Consider the factors of the coefficient of the y² term ( - 12) which sum to give the coefficient of the xy- term (- 4)

The factors are - 6 and + 2

since - 6 × 2 = - 12 and - 6 + 2 = - 4, hence

x² - 4xy - 12y² = (x - 6y)(x + 2y)

----------------------------------------------------

(b)

Consider the factors of + 12 which sum to give + 8

The factors are + 2 and + 6, hence

x² + 8x + 12 = (x + 2)(x + 6)

[tex]36 \times r = 21 \times 12 \\ 36r = 252 \\ r = 252 \div36 \\ r = 7[/tex]

The question asks to solve a proportion 36/42 = 24/r. By cross-multiplication and solving the resulting equation for r, it is found that r = 28. Therefore, the correct value of r in this instance is 28.

To solve the mathematical problem 36/42 = 24/r for the value of r, you should cross-multiply and then solve for r. Cross-multiplication means you multiply 36 by r and 42 by 24, which results in the equation 36r = 42 * 24. When you divide both sides by 36, you get r = 42 * 24 / 36 as the final form of the equation. After calculating the products and divison, you will find that r = 28.

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Answer:

2)    (1,1.5)

4) Not enough information

Step-by-step explanation:

2) If you look along at the intersection point of the two lines it's (1,1.5).

4) Since only one equation is graphed, we can't tell anything.

Answer:

You must be no older than 13 to play a game.

Step-by-step explanation:

≤ this sign means equal to or less than in this case it is 13

The situation that should be modeled by the inequality g ≤ 13 is option b.

Inequality function g ≤ 13

We know that ≤ this sign represent that it is equal or lower than So here it should be no older than 13 for playing the game.

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Answer:

3 1/6

Step-by-step explanation:

To find the highest value, we have to evaluate each term individually,

1)  1 1/6 = 7/6 = 1.167

2) 3 1/6 = 19/6 = 3.16

3) 3/8 = 0.375

4) 5/8 = 0.625

Therefore, second data value (3 1/6) is highest.

Answer:

c.200

Step-by-step explanation:

Answer:

= -7

Step-by-step explanation:

6 ⁹ ×6^x = 6²

From the laws of indices;

aⁿ × aⁿ = a^2n

Therefore;

6 ⁹ ×6^x = 6^(9+x)

6^(9+x) = 6²,

Since the bases are the same then the exponents are equal;

9+x = 2

x = -7

Answer:

x=-7

Step-by-step explanation:

[tex]6^9 \cdot 6^x = 6^2[/tex]

Apply exponential property to solve for x

[tex]a^m \cdot a^n = a^{m+n}[/tex]

[tex]6^9 \cdot 6^x = 6^{9+x}[/tex]

So the given equation becomes

[tex]6^{9+x}= 6^2[/tex]

Both sides of the equation has same base 6

So we equate the exponent and solve for x

[tex]9+x= 2[/tex]

Subtract 9 from both sides

[tex]x=-7[/tex]

The subject of this question is Mathematics.

As a tutor, I would need more information about the specific question or problem you are working on to provide a detailed answer. Mathematics encompasses a wide range of topics including algebra, geometry, statistics, and calculus, among others. If you can provide more details about the specific topic or concept you are struggling with, I can provide a step-by-step explanation to help you understand.

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Answer:

Step-by-step explanation:

It's geometric.

You are starting with -2 and multiplying each successive term by - 2

r = - 2

a1 = -2

tn = ar^(n - 1)

So to try it out, let n be the 4th term

t4 = -2 * (-2)^(4 - 1)

t4 = - 2 * (-2)^3

t4 = - 2 * -8

t4 = 16 just as the series indicated.

Answer:

0.4

Step-by-step explanation:

0.4 as a percentage is 40%

25% is obviously 25%

10 is also obviously 10%

Answer:

(a - 7)(3 - x)

Step-by-step explanation:

Given

3(a - 7) - x(a - 7) ← factor out (a - 7) from both terms

= (a - 7)(3 - x)

Answer:

The answer is D.

Step-by-step explanation:

Count how many l's there are, how many h's there are, and how many w's there are.

Answer:

[tex]\large\boxed{B.\ S.A.=2lw+2lh+2wh}[/tex]

Step-by-step explanation:

It's the net of a rectangular prism.

The formula of a surfave area of a rectangular prism:

[tex]S.A.=2lw+2lh+2wh[/tex]

We have two rectangles l × w, two rectangles l × h and two rectangles w × h.

Answer:

Option B.

Step-by-step explanation:

Let

s-----> the number of songs that Eva downloaded

we know that

The linear equation that represent the situation is

[tex]1.29s=11.61[/tex]

Solve for s

Divide by 1.29 both sides

[tex]s=11.61/1.29[/tex]

[tex]s=9\ songs[/tex]

therefore

Ari's work is correct

Answer:

answer b

Step-by-step explanation:

i took test

The Answer Is J.14.50

Answer: $14.50

Step-by-step explanation:

Multiply $5.95 by 2.

Multiply $0.65 by 4.

Add both of the answers to the multiplying problems

Your final answer... I hope I was able to help!

Answer:

a = 9.632  and b is 10

9.632*10^10 in^3  scientific form

96,320,000,000   in^3  standard form

Step-by-step explanation:

To find volume of a rectangular prism

V = l*w*h

   = 1.4 * 10^4   ( 4.3 * 10^3)   (1.6* 10^3)

When multiply powers of 10, we multiply the numbers out front

1.4*4.3*1.6 =9.632

Then we add the powers of 10

10^(4+3+3)

10^10

The volume is 9.632*10^10 in^3

a = 9.632  and b is 10

In standard form we move the decimal 10 places to the right.  If there are not enough numbers we add zeros

9.632*10^10 in^3

96,320,000,000   in^3

Answer:

x would equal -4

Step-by-step explanation:

Present age of Selma = s

Present age of Joyce = j

Selma is now 3 times as old as joyce

s=3j........(1)

Four years ago,

s-4=j-4

then

Selma was 4 times as old as joyce

s-4=4(j-4)

s-4=4j-16

s=4j-16+4

s=4j-12.............(2)

Put the value of s in (2) from (1)

3j=4j-12

3j-4j=-12

-j=-12

Multiply by -1 both sides

j=12

Put the value of j in (1)

s=3j

s=3(12)

s=36

Present age of Selma = s = 36 years old

Present age of Joyce = j = 12 years old

Answer:

C

Step-by-step explanation:

The sum to infinity of a geometric series is

[tex]\frac{a_{1} }{1-r}[/tex] ( - 1 < r < 1 ) ← substitute values

S( ∞ ) = [tex]\frac{5}{1-\frac{1}{3} }[/tex] = [tex]\frac{5}{\frac{2}{3} }[/tex] = [tex]\frac{15}{2}[/tex]

The sum of the infinite geometric series is [tex]\frac{15}{2}[/tex]

The sum of all the terms of a geometric sequence is called infinite geometric series.

If a, ar, a[tex]r^{2}[/tex], ...., a[tex]r^{n-1}[/tex], .... is a geometric series, then  a+ar+a[tex]r^{2}[/tex]+ ....+a[tex]r^{n-1}[/tex]+.... is the corresponding infinite geometric series.

where a is the 1st term & r is the common ratio between consecutive terms of the series.

Sum of infinite geometric series = [tex]\frac{a}{1-r}[/tex] ; |r|<1

Given, 1st term ([tex]a_{1}[/tex]) of the infinite geometric series = 5

Common ratio (r) = 1/3

∴ Sum of infinite geometric series = [tex]\frac{a_{1} }{1-r}[/tex]

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

                                                         = [tex]\frac{5}{\frac{2}{3} }[/tex]

                                                         = [tex]\frac{15}{2}[/tex]

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200,000/52 weeks in a year =$3846.153846 each week

Her weekly paycheck is 3835.82

As we know that there are 52.14 weeks in a year

So weekly paycheck will be 200,000 / 52.14 = 3835.82

Since she gets weekly check so her weekly paycheck is 3835.82

Answer:

The discount is $109.50

The sale price is $255.50

Step-by-step explanation:

step 1

Find the discount

we know that

The discount is equal to the original price multiplied by the percentage rate of discount

we have

The original price is $365

The percentage of discount is equal to 30%

30%=30/100=0.30

so

the discount is equal to

0.30*($365)=$109.50

step 2

Find the sale price

The sale price is equal to the original price minus the discount

so

$365-$109.50=$255.50

Answer:

I think its 14. If not, check other options. Bye!

Step-by-step explanation:

The estimated length of a paperback book is "8 inches".

The paperback also called a paperback or softback, is a sort of book with a thick paper or paperboard cover that is often held together along with glue rather than stitches or staples.

Hardcover or hardcover books, but at the other extreme, are bonded with cardboard covered in linen, plastic, or leather.

Since 4 inches is far too short, and "14 and 18 " inches is longer than a ruler.

Therefore, the answer is "8 inches".

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Answer:

128 fluid ounces

Step-by-step explanation:

There are 8 fluid ounces in 1 cup.

There's 1 cup in 8 fluid ounces

16 cups x 8 = 128 fluid ounces

There are 20 male students.

Hope this helps.