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3 years ago

The ratio of 1.4/7 in the simplest form

1 answer:

3 0

If you want to convert 1.4 into a fraction, you can do it like this:

1 equals to 1/1 and 0.4 equals to 4/10 which simplifies to 2/5.
The result is 1 2/5.

If you want to write the ratio of 1.4/7 in the simplest form, you can do this using the following steps:

1.4/7 = 1 2/5 / 7 = 7/5 / 7 = 7/5 * 1/7 = 1/5 = 0.2

The correct result would be 1/5.

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A certain project can be completed by 28 men in 90 days. the numbers of men needed varies inversely to the time needed to comple

leva [86]

ANSWER

C. 35 men

EXPLANATION

Let m represent the number of men needed and d represent the number of days.

From the question,the number of men needed varies inversely to the time needed to complete the project.

We can write the inverse variation equation.

$m = \frac{k}{d}$

where k is the constant of variation.

When m=28, d =90.

We substitute these values into the variation equation to determine the value of k.

$28 = \frac{k}{90}$

$k = 90 \times 28$

$k = 252$

Now the equation becomes:

$m= \frac{2520}{d}$

When d=72,

$m = \frac{2520}{72}$

$m = 35$

Therefore he needs to have 35 men working.

3 0

3 years ago

The side length of a square is represented by the expression 2x + 5. Which expression represents the difference between the area

musickatia [10]

Answer:

$4x^2 + 22x + 15$

Step-by-step explanation:

The side length of a square is represented by the expression 2x + 5.

The area of a square is given as:

$A = a^2$

where a = length of side of the square

The area of the square is therefore:

$A = (2x + 5)^2\\\\A = (2x + 5)(2x + 5)\\\\A = 4x^2 + 20x + 25$

The perimeter of a square is given as:

$P = 4a$

The perimeter of the square is therefore:

$P = 4(2x + 5) \\\\P = 8x + 10$

The difference between the area of the square and the perimeter of the square is:

$4x^2 + 30x + 25 - (8x + 10)\\\\4x^2 + 30x + 25 - 8x - 10\\\\4x^2 + 30x - 8x + 25 -10\\\\4x^2 + 22x + 15$

The expression that represents the difference between the area and the perimeter of the square is:

$4x^2 + 22x + 15$

7 0

3 years ago

Solve, then write, each equation in slope intercept form.

djyliett [7]

Answer:

1) (3,5)

2) (4,-7)

3) (6,4)

4) (-4,-3)

Step-by-step explanation:

Subtract y from both sides of the equation.

x = 8 − y

x − y = −2

Replace all occurrences of x in x − y = −2 with 8 − y.

x = 8 − y

(8 − y) − y = −2

Subtract y from −y.

x = 8 − y

8 − 2y = −2

Solve for y in the second equation.

x = 8 − y

y = 5

Replace all occurrences of y in x = 8 − y with 5.

x = 8 −(5)

y = 5

Simplify 8 −(5).

x = 3

y = 5

Slope = (3,5)

Multiply each term by 2 and simplify.

2x+y=12

y+6=−x−4

Move all terms containing variables to the left side of the equation.

2x+y=1x+2

y+6=−4

Move all terms not containing a variable to the right side of the equation.

2x+y=1x+2

y=−10

Multiply each equation by the value that makes the coefficients of x opposite.

2x+y=1(−2)⋅

(x+2y)=(−2)(−10)

Simplify.

2x+y=1−2x−4

y=20

Add the two equations together to eliminate x from the system.

2x+y=1+−2x−4

y=20−3

y=21

Divide each term by −3 and simplify.

y = −7

Substitute the value found for y into one of the original equations, then solve for x.

x = 4

slope (4,-7)

Subtract y from both sides of the equation.

2x−y=8x−y=2

Multiply each equation by the value that makes the coefficients of y opposite

2x−y=8(−1)⋅

(x−y)=(−1)(2)

Simplify. 2x−y=8

−x+y=−2

Add the two equations together to eliminate y from the system.

2x−y=8 + −x+y=−2x=6

Substitute the value found for x into one of the original equations, then solve for y.

y=4

slope (6,4)

Simplify 2(x+1).

y−3=2x+2

y=−3(x+5)

Simplify −3(x+5)

y−3=2x+2

y=−3x−15

Move all terms containing variables to the left side of the equation.

−2x+y−3=2

y=−3x−15

Add 3x to both sides of the equation.

−2x+y−3=2

y+3x=−15

Move all terms not containing a variable to the right side of the equation.

−2x+y=5

y+3x=−15

Reorder the polynomial.

−2x+y=5

3x + y=−15

Multiply each equation by the value that makes the coefficients of y opposite.

−2x+y=5(−1)⋅

(3x+y)=(−1)(−15)

Simplify.

−2x+y=5

−3x−y=15

Add the two equations together to eliminate y from the system.

−2x+y=5 + −3x−y=15−5x=20

Divide each term by −5 and simplify.

x=−4

Substitute the value found for x into one of the original equations, then solve for y.

y=−3

slope (-4,-3)

4 0

3 years ago

Three friends were running at a track as shown here.there postions on the track after 3 sec are shown who is running the slowest

Gennadij [26K]

rEMOVE...NO CONTEXT!

8 0

3 years ago

Suppose that a and b are integers, a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ) . Find the integer c with 0 ≤ c ≤ 12 such that: c ≡ 9 a

g100num [7]

Answer:

A) For c ≡ 9 a ( mod 13 ) ; C is 10

B) For c ≡ 11 b ( mod 13 ) ; C is 8

C) For c ≡ a + b ( mod 13 ); C is 0

D) For c ≡ a² + b² ( mod 13 ); C is 6

E) For c ≡ a² − b² ( mod 13 ) ; C is 0

Step-by-step explanation:

This is a modular arithmetic problem where a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ).

And 0 ≤ c ≤ 12.

A) c ≡ 9 a ( mod 13 )

Substituting the value of a to obtain;

c ≡ 9 x4 ( mod 13 ) = 36 mod 13

To find 36 mod 13 using the Modulo Method, we first divide the Dividend (36) by the Divisor (13).

Second, we multiply the whole part of the Quotient in the previous step by the Divisor (13).

Then finally, we subtract the answer in the second step from the Dividend (36) to get the answer. Here is the math to illustrate how to get 36 mod 13 using Modulo Method:

36 / 13 = 2.769231

2 x 13 = 26

36 - 26 = 10

Thus, the answer to "What is 36 mod 13?" is 10

So C = 10

B) c ≡ 11 b ( mod 13 ) = 11 x 9 ( mod 13 ) = 99 ( mod 13 )

Using the same method as above,

99 ( mod 13 );

99 / 13 = 7.6155

7 x 13 = 91

99 - 91 = 8

So, C = 8

C)c ≡ a + b ( mod 13 ) = 4 + 9 (mod 13) = 13 (mod 13)

Thus;

13 / 13 = 1

1 x 13 = 13

13 - 13 = 0

So, C = 0

D)c ≡ a² + b² ( mod 13 ) = 4² + 9²( mod 13 ) = 16 + 81 ( mod 13 ) = 97 ( mod 13 )

Thus;

97 / 13 = 7.46154

7 x 13 = 91

97 - 91 = 6

So, C = 6

E)c ≡ a² − b² ( mod 13 )= 4² - 9²( mod 13 ) = 16 - 81 ( mod 13 ) = - 65 ( mod 13 )

Thus;

-65 / 13 = - 5

-5 x 13 = - 65

-65 - (-65) = 0

So, C = 0

3 0

3 years ago