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stich3 [128]
3 years ago
14

What is 7.75 equivalent to

Mathematics
1 answer:
nevsk [136]3 years ago
3 0
<span> 7.75 = 7 3/4
or
</span><span> 7.75 = 775/100</span>
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John drives to the beach which is 270 miles away. In 2 hours he drives 10 miles. If he continues at the speed, how long will it
Digiron [165]
1 hr = 5 miles
270 ÷ 5 = 54 hrs
8 0
3 years ago
Carlos buys 3 gallons of juice for a party. What is the greatest number of cups of
gtnhenbr [62]

Answer:

48

Step-by-step explanation:

1 gallon=16 cups. So, 3x16=48 cups.

3 0
2 years ago
How do you do this problem
Ainat [17]

You divide (1354.5 kg of potatoes) by (12 stores in the Bronx).

The quotient is  ________ kg of potatoes per store in the Bronx.

The division is easy to do with your pencil or your calculator.

7 0
3 years ago
Write the polynomial f(x)=x^4-10x^3+25x^2-40x+84. In factored form
Verizon [17]
<h2>Steps:</h2>

So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is \pm \frac{p}{q}, with p = the factors of the constant and q = the factors of the leading coefficient. In this case:

\textsf{leading coefficient = 1, constant = 84}\\\\p=1,2,3,4,6,7,12,14,21,28,42,84\\q=1\\\\\pm \frac{1,2,3,4,6,7,12,14,21,28,42,84}{1}\\\\\textsf{Potential roots =}\pm 1, \pm 2,\pm 3,\pm 4,\pm 6, \pm 7,\pm 12,\pm 14,\pm 21,\pm 28,\pm 42,\pm 84

Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:

f(1)=(1)^4-10(1)^3+25(1)^2-40(1)+84\\f(1)=1-10+25-40+84\\f(1)=60\ \textsf{Not a root}\\\\f(2)=2^4-10(2)^3+25(2)^2-40(2)+84\\f(2)=16-10*8+25*4-80+84\\f(2)=16-80+100-80+84\\f(2)=80\ \textsf{Not a root}\\\\f(3)=3^4-10(3)^3+25(3)^2-40(3)+84\\f(3)=81-10*27+25*9-120+84\\f(3)=81-270+225-120+84\\f(3)=0\ \textsf{Is a root}

Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:

  • 3 | 1 - 10 + 25 - 40 + 84
  • _________________

Firstly, drop the 1:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓
  • _________________
  •     1

Next, multiply 3 and 1, then add the product with -10:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3
  • _________________
  •     1  - 7

Next, multiply 3 and -7, then add the product with 25:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3  - 21
  • _________________
  •     1  - 7 + 4

Next, multiply 3 and 4, then add the product with -40:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3  - 21 + 12
  • _________________
  •     1  - 7  +  4  - 28

Lastly, multiply -28 and 3, then add the product with 84:

  • 3 | 1 - 10 + 25 - 40 + 84
  •     ↓ + 3  - 21 + 12  - 84
  • _________________
  •     1  - 7  +  4  - 28 + 0

Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format ax^3+bx^2+cx+d . In this case, our quotient is x^3-7x^2+4x-28 .

So right now, our equation looks like this:

f(x)=(x-3)(x^3-7x^2+4x-28)

However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:

f(x)=(x-3)(x^2(x-7)+4(x-7))

Now it can be rewritten as:

f(x)=(x-3)(x^2+4)(x-7)

<h2>Answer:</h2>

Since the polynomial cannot be further simplified, your answer is:

f(x)=(x-3)(x^2+4)(x-7)

6 0
2 years ago
98x24(100-2)x24 using the distributive property
boyakko [2]

Answer:

98 x 24 = 2352

2352 x 2400 = 5,644,800

2352 x (-48) = - 112,896

5,644,800 - 112,896 = 5,531,904

5,531,904 x 24 = 132,765,696

Step-by-step explanation:

8 0
3 years ago
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