Explanation

Car A:

• Time = 3 hours 20 minutes = $3 + frac{20}{60} = 3.33$ hours

• Distance = 300 km

Car B:

• Time = 2 hours 80 minutes = 2+80/60​=3.33 hours

• Distance = 280 km

Total Distance

$$300 , text{km} + 280 , text{km} = 580 , text{km}$$

Total Time

$$3.33 + 3.33 = 6.66 , text{hours}$$

Average Speed Formula:

$$text{Average speed} = frac{text{Total Distance}}{text{Total Time}} = frac{580}{6.66} approx 87.09 , text{km/h}$$Total Time=580/ 6.66​≈87.09km/h

$$$$
boxed{87.1 , text{km/h (approx)}}

Explanation

If $\sin A=\sin B$, then:

A=B+360∘n or A=180∘−B+360∘n, where n ∈ Z

Let’s solve:

Case 1:

60∘+X=60∘⇒X=0∘

Case 2:

$$60^circ + X = 180^circ - 60^circ = 120^circ Rightarrow X = 60^circ$$

Possible values of X:

$$X = 0^circ quad text{or} quad X = 60^circ$$

Explanation

We are given:

• $x+y=6$

• $xy=5$

We are asked to find:
$x^2 + y^2$

Step-by-step solution:

Use the identity:

x^2+y^2=(x+y)^2−2xy

Substitute the given values:

$$$$x^2+y^2=(6)^2−2(5)=36−10=26

Explanation

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant.

Let’s check each option:

B. 72, 73, 75, 78
Differences: +1, +2, +3 → Not arithmetic

A. 31, 32, 33, 34
Common difference: +1 → Arithmetic

C. 11, 15, 17, 23

Differences: +4, +2, +6 → Not arithmetic

Explanation

• A. √16 = 4 → Rational

• B. √4 = 2 → Rational

• C. √9 = 3 → Rational

• D. √11 ≈ 3.316624... → Not a perfect square → Irrational

Correct answer: D. √11

Explanation

Quadratic equations have roots that can be:

• Real and distinct
• Real and equal
• Imaginary
• Rational or irrational

“Cubic” relates to degree 3, not to root types.

Explanation

Explanation

Explanation

$$abc=?\text{and }ac=2$$

You want to find the value of $b$ in terms of $a$, assuming:.

$$abc\text{ is implied to be known, or }abc=someexpression.$$

If we assume:

$$abc = a cdot b cdot c quad text{and} quad ac = 2,$$

Then:

$$abc=a\cdot b\cdot c=b(ac)=b\cdot 2=2b$$

So:

$$$$
abc = 2b Rightarrow b = frac{abc}{2}

Explanation

We are asked to find the value of $b$.

Step 1: Start with the given

$$abc = a^2 quad text{and} quad ac = 2$$

Step 2: Substitute
$ac=2$ into the first equation

abc=a^2 ⇒b(ac)=a^2⇒b(2)=a^2

Step 3: Solve for b

$$$$
2b=a^2⇒b=a^2/2​