Find the 168th term of arithmetic sequence {a_{n}, n = 1, 2, 3, . . .} with common ifference d = 1.5 and first term a_{1} = 2.

Answers

Answer 1

Answer: $a_1=2;\ d=1.5\n\na_n=a_1+(n-1)d\n\na_n=2+(n-1)\cdot1.5=2+1.5n-1.5=0.5+1.5n\n\na_(168)=0.5+1.5\cdot168=0.5+252=252.5$

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What can be said about the discriminant of the graph below?

Answers

Answer:

C. The discriminant is negative, so there are no solutions.

Step-by-step explanation:

We see that the given figure is a graph of a parabola.

The equation of the given parabola is $y=(x-3)^(2)+1$ .

Simplifying the equation in quadratic form, we get,

The equation is $y=(x-3)^(2)+1$ i.e. $y=x^(2)+9-6x+1$ i.e. $y=x^(2)-6x+10$ .

We know that the discriminant of a quadratic equation $ax^(2)+bx+c=0$ is given by $D=b^(2)-4ac$

So, from the equation $x^(2)-6x+10=0$ , we have,

a = 1, b = -6 and c = 10

Thus, the discriminant is $D=(-6)^(2)-4* 1* 10$

i.e. $D=36-40$

i.e. $D=-4$

So, the discriminant is -4 i.e. negative.

Hence, as the discriminant is negative, there are no solutions.

A contraction crew has just finished building a road . The road is 10 kilometers long if the crew worked for 3 3/4 days how many kilometers of road did they build each day

Answers

Answer:

The crew built a 10-kilometer road in 3 3/4 days. To find out how many kilometers of road they built each day, we can divide the total length of the road by the number of days they worked.

First, we need to convert the mixed number of days to an improper fraction:

3 3/4 = (4 x 3 + 3) / 4 = 15/4

Now we can divide the length of the road by the number of days:

10 km ÷ (15/4) days = (10 km) x (4/15 days) = **2.67 km/day**

Therefore, the crew built approximately **2.67 kilometers** of road each day.

I hope this helps!

Step-by-step explanation:

Facrorize TI un²k - 1/4 an²Q