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Harrizon [31]
3 years ago
7

What is the length of the rectangle?

Mathematics
1 answer:
gregori [183]3 years ago
4 0

Step-by-step explanation:

area \: of \: rectangle \:  = 60 \:  {yards}^{2}  \\  \therefore \: (w + 4) \times \: w = 60\\  \\  \therefore \:  {w}^{2}  + 4w -60 = 0 \\  \\  \therefore \: {w}^{2}  + 10w - 6w -60 = 0 \\  \\   \therefore \: w({w} + 10) - 6(w  + 10)= 0 \\  \\  \therefore \: ({w} + 10) (w- 6)= 0 \\ \therefore \: {w} + 10 = 0 \: or \: w- 6 = 0 \\  \therefore \: {w}   = -  10  \: or \: w =  6  \\  \because \: sides \: of \: rectangle \: cant \: be \: negative \\  \therefore \: w \neq \:    - 10 \\  \\ \therefore \: w = 6 \\  \\ \therefore \: w + 4 = 6 + 4 = 10 \\  \\ length \: of \: rectangle \:  = 10 \: yards.

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Write a polynomial in standard form with the zeros -4,0, 1, and 4.
gavmur [86]

Answer: x^4-x^3-16x^2+16x

Step-by-step explanation:

Factor theorem : If x=a is a zero of a polynomial p(x) then (x-a) is a factor of p(x).

Given: Zeroes of polynomial : -4,0, 1, and 4.

Then Factors = (x-(-4)), (x-0), (x-1) and (x-4)   [By factor theorem ]

=(x+4), (x-0), (x-1) and (x-4)

Multiplying these factors to get polynomial in standard form.

(x+4)\times(x-0)\times(x-1)\times(x-4)  \\\\= x(x+4)(x-4)(x-1)\\\\= x(x^2-4^2)(x-1)\\\\= x(x^2-16)(x-1)\\\\= x(x^2-16)(x-1)\\\\=x(x^2x+x^2\left(-1\right)+\left(-16\right)x+\left(-16\right)\left(-1\right))\\\\= x(x^3-x^2-16x+16)\\\\=x^4-x^3-16x^2+16x

Hence, B is the correct option.

8 0
3 years ago
Solve a + b + c = 55, b+c= 13, and a + c = 45 for c.
Amanda [17]

Answer:

answer is 10

Step-by-step explanation:

a+c+b+c=55

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6-4x=6x-8x+2<img src="https://tex.z-dn.net/?f=6-4x%3D6x-8x%2B2" id="TexFormula1" title="6-4x=6x-8x+2" alt="6-4x=6x-8x+2" align="
e-lub [12.9K]
6-4x=6x-8x+2 \\&#10;6-4x=-2x+2 \\&#10;-4x+2x=2-6 \\&#10;-2x=-4 \\&#10;\underline{\underline{x=2}}
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3 years ago
A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches.
Vinvika [58]

Answer:

The baseball's volume will be less than the number of cubic inches in the display case. The cube's edge will be 8.

2. If a sphere fits snugly inside this cube, what is its volume?

the volume of a cube is the side^3, 512^(1/3)=8. 3. 4/3pi(r^3)/512,  

3. What fraction of the cube is taken up by the sphere? What percentage is this? Explain or show your reasoning.= the radius will be 4 since the edge of the cube is 8. 4/3pi(4^3)/512, so pi/6 when simplified or 52.3598%.

Step-by-step explanation:

6 0
3 years ago
How many different ways are there to make 30 cents with pennies nickels dimes or quarters?
never [62]
There is 1 way to make 30 cents using only pennies. (i.e. 30 pennies = 30 cents)

There is 1 way to make 30 cents using only nickels. (i.e. 6 nickels = 30 cents)

There is 1 way to make 30 cents using only dimes. (i.e. 3 dimes = 30 cents)

There are 5 ways to make 30 cents using only pennies and nickels. (i.e. 25 pennies + 1 nickel = 30 cents, 20 pennies + 2 nickels = 30 cents . . . )

There are 2 ways of making 30 cents using only pennies and dimes. (i.e. 20 pennies + 1 dime = 30 cents, 10 pennies + 2 dimes = 30 cents)

There is 1 way of making 30 cents using only pennies and quarters. (i.e. 5 pennies + 1 quarter = 30 cents)

There are 2 ways of making 30 cents using only nickels and dimes. (i.e. 4 nickels + 1 dime = 30 cents, 2 nickels + 2 dimes = 30 cents)

There is 1 way of making 30 cents using only nickels and quarters. (i.e. 1 nickel + 1 quarter = 30 cents)

There are 4 ways to make 30 cents using only pennies, nickels and dimes. (i.e. 15 pennies + 1 nickel + 1 dime = 30 cents, 10 pennies + 2 nickels + 1 dime = 30 cents . . . )

Adding all the possible combinations therefore, there are 18 <span>different ways are there to make 30 cents with pennies nickels dimes or quarters.</span>
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3 years ago
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