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3 years ago

If M has the value of 35 What is 5mx2

Mathematics

2 answers:

Amiraneli [1.4K]3 years ago

8 0

Substitute 35 in place of m
5 x m x 2

5 x 2 = 10
10 x m
10 x 35 = 350

adoni [48]3 years ago

6 0

The value of m=5*35*2=350

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For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4

Elina [12.6K]

Answer:

C. $(5-\frac{1}{2})^6$

Step-by-step explanation:

Given

$15(5)^2(-\frac{1}{2})^4$

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

$Sum = 2 + 4$

$Sum = 6$

Each term of a binomial expansion are always of the form:

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

Where n = the sum above

$n = 6$

Compare $15(5)^2(-\frac{1}{2})^4$ to the above general form of binomial expansion

$(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......$

Substitute 6 for n

$(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......$

[Next is to solve for a and b]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

By direct comparison of

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

and

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

We have;

$^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4$

Further comparison gives

$^nC_r = 15$

$a^{n-r} =(5)^{6-4}$

$b^r= (-\frac{1}{2})^4$

[Solving for a]

By direct comparison of $a^{n-r} =(5)^{6-4}$

$a = 5$

$n = 6$

$r = 4$

[Solving for b]

By direct comparison of $b^r= (-\frac{1}{2})^4$

$r = 4$

$b = \frac{-1}{2}$

Substitute values for a, b, n and r in

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

$(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

Solve for $^6C_4$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......$

Check the list of options for the expression on the left hand side

The correct answer is $(5-\frac{1}{2})^6$

3 0

3 years ago

3. Here is a diagram of a softball field:

Crank

a. Length of the fence around the field = perimeter of quarter circle = 892.7 ft.

b. The area of the outfield is about 39,584 sq. ft..

<h3>What is the Perimeter of a Quarter Circle?</h3>

Perimeter of circle = 2πr

Perimeter of a quarter circle = 2r + 1/4(2πr).

a. The length of the fence around the field = perimeter of the quarter circle fence

= 2r + 1/4(2πr).

r = 250 ft

Plug in the value

The length of the fence around the field = 2(250) + 1/4(2 × π × 250)

= 892.7 ft.

b. Size of the outfield = area of the full field (quarter circle) - area of the infield (cicle)

= 1/4(πR²) - πr²

R = radius of the full field = 250 ft

r = radius of the infield = 110/2 = 55 ft

Plug in the values

Size of the outfield = 1/4(π × 250²) - π × 55²

= 49,087 - 9,503

= 39,584 sq. ft.

Learn more about perimeter of quarter circle on:

brainly.com/question/15976233

4 0

2 years ago

TO get a certain shade of green paint, Melissa decides to mix 3 gallons of blue paint with 2 gallons of yellow paint. How much b

Harlamova29_29 [7]

You have a fraction of 3/2. 3/2=1.5
Therefore, she needs 1.5 gallons of blue paint per 1 gallon of yellow paint.

7 0

3 years ago

Find csc x if sin x + cot x cos x =√3.

Oksi-84 [34.3K]

Answer:

The answer is (d) ⇒ cscx = √3

Step-by-step explanation:

∵ sinx + (cotx)(cosx) = √3

∵ sinx + (cosx/sinx)(cosx) = √3

∴ sinx + cos²x/sinx = √3

∵ cos²x = 1 - sin²x

∴ sinx + (1 - sin²x)/sinx = √3 ⇒ make L.C.M

∴ (sin²x + 1 - sin²x)/sinx = √3

∴ 1/sinx = √3

∵ 1/sinx = cscx

∴ cscx = √3

7 0

3 years ago

On Fridays, Jerry stops at Steak & Taco Shack before he goes home. This week

Vika [28.1K]

Answer:

Steak sandwich = x = 4

Cheese fries = y = 1.75

Taco salad = z = 2

Step-by-step explanation:

Let :

Steak sandwich = x

Cheese fries = y

Taco salad = z

This week:

x + 2y + 2z = 11.50 - - - - (1)

Last week :

2x + 3y + z = 15.25 - - - (2)

Two weeks ago :

x + 4y + z = 13 - - - - - (3)

Taking (1) and (2)

x + 2y + 2z = 11.50 ___(1)

2x + 3y + z = 15.25 ___(2)

Multiply (1) by 2 and (2) by 1 and subtract

2x + 4y + 4z = 23

2x + 3y + z = 15.25

_______________

y + 3z = 7.75 - - - - (4)

Taking (2) and (3)

2x + 3y + z = 15.25 - - (2)

x + 4y + z = 13 - - - - - (3)

Multiply (2) by 1 and (3) by 2 and subtract

2x + 3y + z = 15.25

2x + 8y + 2z = 26

______________

-5y - z = - 10.75 - - - - - (5)

Lets solve (4) and (5)

y + 3z = 7.75 - - - - (4) - - - multiply by 5

-5y - z = - 10.75 - - - - - (5) - - - multiply by 1

Then add the result :

5y + 15z = 38.75

-5y - z = - 10.75

____________

14z = 28

z = 28 / 14

z = 2

To find y ; put z = 2 in (4)

y + 3z = 7.75

y + 3(2) = 7.75

y + 6 = 7.75

y = 7.75 - 6

y = 1.75

From equation 3 ;

x + 4y + z = 13 - - - - - (3)

x + 4(1.75) + 2 = 13

x + 7 + 2 = 13

x + 9 = 13

x = 13 - 9

x = 4

Hence,

Steak sandwich = x = 4

Cheese fries = y = 1.75

Taco salad = z = 2

5 0

3 years ago