What is the ratio of 12 puppies to 36 kittens? SHOW YOUR WORK PLEASE I NEED THE GRADE AT SCHOOL!

A train travels train travels 288 kilometre at a uniform speed. If the speed had been 4 kilometre per hour more it would have ta

PIT_PIT [12445]

Answer:

Let the train's speed be denoted as x km/h.

Scenario 1:

Distance = 288 km

Speed = x km/h

Time = Distance divided by Speed

= 288/x hours

Scenario 2:

Distance = 288 km

Speed = (x + 4) km/h

Time = 288/(x + 4) hours

As 288/x is greater than 288/(x + 4)

288/x - 288/(x + 4) = 1

288[1/x - 1/(x + 4)] = 1

[x + 4 - x] / [x(x + 4)] = 1/288

[4 / (x^2 + 4x)] = 1/288

x² + 4x = 1152

x² + 4x - 1152 = 0

x² + 36x - 32x - 1152 = 0

x(x + 36) - 32(x + 36) = 0

(x + 36)(x - 32) = 0

x + 36 = 0, x - 32 = 0

x = -36, x = 32

x = -36 is not valid as speed cannot be negative.

Conclusively, the train's speed = 32 km/h

4 0

2 months ago

A special shape is 2.02 m long and 1.22 m wide. A double row of tiles makes a border . Each tile is 2cm by 2cm. How many tiles a

Svet_ta [12734]

Response:

6.48

Detailed explanation:

The calculation required to determine the number of tiles for the border is presented below:-

$= 2 \times (length + breadth)$

Here,

The length measures 2.02 m

And the width is 1.22

Substituting these dimensions into the formula provided above

Consequently, the total number of tiles necessary to create the border is

$= 2 \times (2.02 + 1.22)$

$= 2 \times 3.24$

= 6.48

Hence, to find the tiles required for the border, we utilized the aforementioned formula.

3 0

2 months ago

There is a safety fence around a circular pool with a gate. The gate is 150 cm wide. What is the length of the fence not includi

zzz [12365]

Response:

The fence's length is expressed as 6.28x - 150 cm.

Detailed Breakdown:

Assuming the circular pool has a radius (r) of x cm.

As the pool is circular, its circumference represents the length of the fence. Additionally, subtracting the 150 cm for the gate gives us the actual length of the fence.

Length of fence = Circumference of pool – gate's width.

Length of fence = 2 π r – 150

Length of fence = 2 × 3.14 × x – 150

Therefore, the fence length is 6.28x – 150 cm.

4 0

3 months ago

Segment JK has a length of 4.5 units. If segment LM has end points of L (3,1) and M (-1,4), how much longer than segment JK is s

Leona [12618]

Distance formula:
$d= \sqrt{ (x_{2}-x_{1}) ^{2}+( y_{2} - y_{1} )^{2}}\\ d= \sqrt{ (3-(-1)) ^{2}+(1 - 4 )^{2}}\\ d= \sqrt{ (4) ^{2}+(-3)^{2}}\\ d=\sqrt{16+9}\\ d=\sqrt{25}\\ d=5$

5 units-4.5 units=0.5 units

Segment LM exceeds segment JK by 0.5 units.

4 0

2 months ago

Read 2 more answers

Two of the steps in the derivation of the quadratic formula are shown below. Step 6: StartFraction b squared minus 4 a c Over 4

babunello [11817]

Explanation:

Step-by-step clarification:

Referring to step 6

(b² — 4ac) / 4a² = (x + b/2a)²

The mistake in the question is that it should be (x + b/2a)²

According to step 7

±√(b² —4ac) /2a = x + b/2a

The error in the question is that it should be divided by 2a, not 1a.

1. The transition from step 6 to step 7 involves taking the square roots of both sides

(b² — 4ac) / 4a² = (x + b/2a)²

Taking the square of both sides

√(b²—4ac) / √4a² = √(x + b/2a)²

√(b²—4ac) / 2a = x + b/2a

This forms step 7 correctly.

Next, subtracting b/2a from both sides

√(b²—4ac) / 2a - b/2a= x + b/2a -b/2a

√(b²—4ac) / 2a — b/2a = x

(√(b²—4ac) — b)/2a = x

x = [—b ± √(b²—4ac)] / 2a

This gives the desired formula.

The discriminant is D = b²—4ac.

6 0

3 months ago

Read 2 more answers