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4 years ago

What is a real world problem with 1/4 divided by 1/8

1 answer:

7 0

Diana is painting statues. She has 1/4 of a gallon of paint remaining. Each statue requires 1/8 of a gallon of paint. how many statues can she paint?

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Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

4 0

3 years ago

Robert gets a loan from his bank.

Goryan [66]

Answer:

£10,200

Step-by-step explanation:

Simple interest = principal × rate × time

Principal = £6000

Rate = 7% = 0.07

Time = 10 years

Simple interest = principal × rate × time

= £6000 × 0.07 × 10

= £4,200

Total = simple interest + principal

= £4,200 + £6,000

= £10,200

He would have to pay back a total of £10,200 in 10 years

5 0

3 years ago

Given that the images represent 4 steps in the construction of a line segment congruent to a given line segment, which is step 3

Evgen [1.6K]

Answer:

Adjust the compasses' width to the point Q. The compasses' width is now equal to the length of the line segment PQ.

Step-by-step explanation:

Start with a line segment PQ that we will copy. Mark a point R that will be one endpoint of the new line segment. Set the compasses' point on the point P of the line segment to be copied. Adjust the compasses' width to the point Q. The compasses' width is now equal to the length of the line segment PQ.

8 0

3 years ago

A diver descend 15 feet below sea level. She then ascends 7 feet. What is the depth of the diver in terms of sea level

Angelina_Jolie [31]

8 feet below sea level because -15+7=-8

5 0

3 years ago

Suppose the teacher begins recording on a digital camera with an hour available. Show that there is enough time to record everyo

kogti [31]

22. Suppose that the teacher started recording on a digital camera with an hour available. She gives 15 minutes introduction. Thus 60 minutes – 15 minutes is 45 minutes. She still have 45 minutes remaining, now the question is how many minutes will remain if she uses 1 minutes per students. Since the number of students is not given. It depends on how many students will be there. For example 25 students thus that’s equals to 25 minutes also. So she has a 20 minutes remaining.,

5 0

3 years ago