rationalise the following 1/√7

Answer:

3.5 hours

Step-by-step explanation:

Paul:

Mary:

Since the distance is same, we have:

Answer: Paul's travel took 3.5 hours

Answer:

[tex]-5x^2-5x[/tex]

Step-by-step explanation:

[tex]-5x\left(x+1\right)\\\\-5x\left(x+1\right)=-5xx-5x\cdot \:1\\\\=-5xx-5x\cdot \:1\\\\=-5x^2-5x[/tex]

Answer:

-5x^2 -5x

Step-by-step explanation:

-5x(x+1)

Distribute

-5x*x  +-5x*1

-5x^2 -5x

Answer:

240 m^3

Step-by-step explanation:

It's a cuboid with a volume=l*b*h, where l, b, h are the dimensions of the shape.

Volume=5*12*4=240 m^3

Answer:

V =240 m^3

Step-by-step explanation:

The volume is given by

V = l*w*h  where l is length w is width and h is height

V = 12*4*5

V =240 m^3

Answer:

12.5 hours

Step-by-step explanation:

budget: 200

fix cost: 50

hourly rate: 12

hours: ?

----

First we deduct the fix 50 dollars cost from the total budget.

Then we divide the remaining amount with the hourly rate

( 200 - 50 ) / 12 = ?

? = 12.5 hours

[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49y^2x^2[/tex]

[tex]\\ \sf\longmapsto 256x^2y^2-x^2y^2+49x^2y^2[/tex]

[tex]\\ \sf\longmapsto (256-1+49)x^2y^2[/tex]

[tex]\\ \sf\longmapsto 304x^2y^2[/tex]

Answer:

2

Step-by-step explanation:

In the above question, we are given the following information:

Total member in the club = 15

Rugby = n(R) = 7

Soccer = n(S) = 6

Neither Rugby nor Soccer = 4

Rugby and soccer = n( R ∩ S) = (Unknown)

Total number of club members = n(R) + n(S) - n( R ∩ S) + Neither Rugby nor soccer

15 = 7 + 6 - n( R ∩ S) + 4

15 = 17 - n( R ∩ S)

15 - 17 = - n( R ∩ S)

-2 = - n( R ∩ S)

n( R ∩ S) = 2

Therefore, the number of people that played both rugby and soccer is 2

Answer:

anything raised to the power of zero= 1

(1+1/4^½)²

(1 + 1/2)²

(3/2)²

9/4

=2.25

Answer:

6 and 7

Step-by-step explanation:

Answer:

y = -3x + 2

Step-by-step explanation:

y2 - y1 / x2 - x1

-1 - 8 / 1 - (-2)

-9/3

= -3

y = -3x + b

-1 = -3(1) + b

-1 = -3 + b

2 = b

Answer:

[tex]\boxed{\sf a) \ 15.9}[/tex]

Step-by-step explanation:

The triangle is a right triangle.

We can use trig functions to solve for x.

cos θ = adj/hyp

cos(51) = 10/x

x = 10/cos(51)

x = 15.89015729

Answer:

Consecutive terms are numbers which follow each other in order, without gaps, from smallest to largest.

Example:

12, 13, 14 and 15

or

2, 24, 26, 28 and 30 (Even Consecutive)

or

40, 45, 50 and 55 (Consecutive Multiples of 5)

SOURCE/GOOGLE

Answer:

Consecutive numbers are numbers that follows one other in their counting order. Each number in the order will be higher than the previous number by 1.

They are always ordered from the smallest to the largest value.

Step-by-step explanation:

Example :

7, 8, 9, 10 are consecutive numbers.

23, 24, 28, 29 are not consecutive numbers.

Use the formula given. R is half the diameter

R = 14/2 = 7 inches.

Area = 3.14 x 7^2

Area = 153.86 inches^2

Answer:

Does the answer help you?

Answer:

115

Step-by-step explanation:

5 - 4(30)

5 - 120

115

Answer:

-115

Step-by-step explanation:

Since anything in between those two lines (absolute value) always comes out positive and the five inside there is already positive, we don't need to worry about it.

First let's look at what's inside the parenthesis.

5 - 4(32 - 2)

= 5 - 4(30)

Next, we'd multiply. (I'm going by PEMDAS)

5 - 120

Now that we've done that we just need to subtract. Generally, 120-5=115, so, we just need to make it negative.

Hope this helps!! <3 :)

Answer:

the stone fell in the air for 7 sec and fell in the water for 5 sec

Answer:

Let time taken in air be 'a'

And the time taken in water be 'b'

a+b=12

Distance covered in air = 16a

′′′′′ ′′″″ water= 3b

16a + 3b = 127

Solve the two equations simultaneously

a= 7 secs

b= 5 secs

Answer:5

Step-by-step explanation:30/600×100

Answer:

Step-by-step explanation:

[tex]\frac{30}{600} \times 100\\\\= \frac{3000}{600}\\ \\= 5\%[/tex]

Answer:

The square root is around 1.414, so yes, it is between 1.4 and 1.5.

Step-by-step explanation:

Answer:

1) -∠B ≅ ∠D

2) -Interior angles on the same side of a transversal are supplementary

3) -∠A ≅ ∠C

Step-by-step explanation:

1) Given that ∠A and ∠B are supplements and ∠A and ∠D are supplements, we have; ∠B ≅ ∠D

2)  Given that ABCD is a parallelogram, therefore ∠A and ∠B,  ∠A and ∠D and ∠B and ∠C  are interior angles on the same side of a transversal and are therefore supplementary

3) Given that ∠A and ∠B and ∠B and ∠C are supplementary, therefore, ∠A ≅ ∠C.

B is the midpoint of DC.

Answer:

7

Step-by-step explanation:

Given line a with 6 points on it, and line b with 4 points on it. Line a is parallel to line b, such that the two lines do not meet at any point even when extended.

Join the first point on line a to that on b, then back to the second point on a, return back to the second point on b, and continue till the line stops at the 5th point on line a. This forms triangles with vertices at the given points on the lines. The possible number of triangles that can be formed is 7.

Answer:

The answer is below

Step-by-step explanation:

To find the maximum amount of cargo the truck can carry, we need to find the volume of the truck.

Volume = length × width × height.

Firstly 1 feet (1') = 12 inches (12"),

For the extra ledge that sticks out, the height = 7'8" = 7.667 feet, the width = 16'9" - 14'3" = 16.75 - 14.25 = 2.5 feet, the length = 2'7" = 2.583 feet

Volume of extra ledge = length × width × height = 2.583 × 2.5 × 7.667 = 49.5 feet³

For the truck, the height = 7'8" = 7.667 feet, the length = 14'3" = 14.25 feet, the width = 6'6" = 6.5 feet

Volume of truck = length × width × height = 14.25 × 6.5 × 7.667 = 710.16 feet³

The maximum volume = volume of extra ledge + volume of truck = 49.5 + 710.16 = 759.66 feet³

[tex]3 \times 3 \times 2 - 7 \times 2 \times 2 \\ 18 - 28 \\ - 10[/tex]

Answer:

115

Step-by-step explanation:

(3x)^2 – 7y^2

Plug in:

(3×3)^2 – 7×2^2

9^2 - 14^2

81 - 196

115

Hope this helped.

Answer:

The digits arranged in order from least to largest is 3.011, 3.09, 3.9, 9.3

Step-by-step explanation:

The arrangement of decimals in order from smallest to largest can be done by  taking note of the  digit in the unit portion, the tenths, hundredths and thousandths.

The numbers are;

9.3

3.09

3.9

3.011

The largest number is the 9.3

Of the three numbers with 3 as unit, the lowest hundredths is 0.011, therefore, we have;

Therefore, the least (lowest) number = 3.011

The next is the 3.09 as 0.09 is larger than 0.011

Then the second number is 3.9

The digits arranged in order from least to largest is then 3.011, 3.09, 3.9, 9.3.

Step-by-step explanation:

For example:

Ex: 2:3 :: 6:9

In this question, the means are 3 and 6.

The extremes are 2 and 9.

We use this method to find whether the two ratios are equal or not.

We multiply the means and the extremes, and if there products are same, then these two ratios are proportional.

If these two ratios are proportional, their "means" = "extremes"

=> Means = Extremes

=> 3 x 6 = 2 x 9

=> 18 = 18

So, these two ratios are proportional.

Hope this helps you.

Answer:

  x = 1/2 or 2

Step-by-step explanation:

You can factor this as ...

  2x^2 -4x -x +2 = 0 . . . rewrite the middle term to enable factoring

  2x(x -2) -1(x -2) = 0 . . . . factor by grouping

  (2x -1)(x -2) = 0 . . . . factor out (x -2)

  x = 1/2, 2 . . . . . . values of x that make the factors zero

Answer:

Step-by-step explanation:

We can see:

This is a linear relationship. Use point-slope form to find the equation:

Answer:

16

Step-by-step explanation:

Distribute 7 into x and 2, which gets you 7x+14. Then distribute 6 into x and 5, which is 6x+30. 7x-6x= x, 30-14=16 so there’s your answer.

Answer:

Step-by-step explanation:

7x + 14 = 6x + 30

x + 14 = 30

x = 16

Answer:

(x+30)+(x-30)=180

2x=180

x=90

x+30=y+20

90+30=y+20

y=100°

There for z = -10