please give an answer Rationalise the denominator and find the values of a and b. 7−4√3/7+4√3 = a + b √3

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▹ Answer

49

▹ Step-by-Step Explanation

Substitute:

13 + 6(6)

Solve:

6 * 6 = 36

13 + 36 = 49

Hope this helps!

CloutAnswers ❁

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Answer: 49

Step-by-step explanation: To evaluate 13 + 6y if y = 6,

we start by substituting 6 in for y.

So we have 13 + 6(6).

Remember to use parentheses when

substituting numbers in for variables.

Now, we use the order of operations to simplify from here.

Since multiplication comes before addition, our next step is

to multiply 6(6) to get 36, and we have 13 + 36, which is 49.

Answer:

This expression has no factors

Step-by-step explanation:

You can't factorize it because it has no factors.

If 14 were sqrt-able then there would have been a factor

Answer:

-17x

Step-by-step explanation:

(2x^3 - x^2) - (3x^3 - 2x^2)

(8x - 2x) - (27x - 4x)

6x - 23x

-17x

(I haven't seen many questions like this before, but I think that this may be the answer.)

Answer:

The other person is correct he should get brainliest!

Hope this helps!

Answer:

2(7n+2m)

2(7n+(5m-3m))

answer: 2(7n+2m)

Answer:

The way to solve the question is:

Depth = Volume/ (Width x Length)

Volume = Depth x Length x Width

=> Volume = 12 x 15 x 5

=> Volume = 12 x 75

=> Volume = 900

Depth= 900 / (Width x Length)

=> Depth = 900/ 5 x 15

=> Depth = 900/75

=> Depth = 12

Answer:

165

Step-by-step explanation:

let the number of boys be x and girls be y.

But there are 175 more girls than boys, so y = x + 175

sum of boys and girls is 505

x + y = 505

and y = x + 175

x + x + 175 = 505

2x = 330

x = 165

I hope this helps! :)

The answer is 120 degree

Pls mark as brainliest

Answer:

Simple 1 part 120 degrees

Step-by-step explanation:

The system is:

[tex]\frac{x}{y}=2x + 4[/tex]

[tex]\frac{x-3}{y-3}=\frac{2}{3}[/tex] (y musn't be 3).

Solving for y in the first equation gives you:

[tex]y=\frac{x}{2x+4}[/tex]

Simplify the second equation to:

[tex]2(y-3)=3(x-3)[/tex]

Insert y you solved in first equation to second equation to get:

[tex]\frac{x}{x+2}-6=3x-3[/tex]

Further simplification gets you to quadratic equation:

[tex]x=(3x+3)(x+2)\implies x=3x^2+9x+6[/tex] [tex]3x^2+8x+6=0[/tex].

Solving quadratic equation using quadratic formula gives you two solutions of x in complex plane:

[tex]x_1=\boxed{-\frac{8}{6}+\frac{\sqrt{8}}{6}i}[/tex]

[tex]x_2=\boxed{-\frac{8}{6}-\frac{\sqrt{8}}{6}i}[/tex]

Insert the found x-es into first equation to find the y-s:

[tex]y_1=\boxed{-\frac{1}{2}+\frac{\sqrt{2}}{2}i}[/tex]

[tex]y_2=\boxed{-\frac{1}{2}-\frac{\sqrt{2}}{2}i}[/tex]

So there are two solutions (points) [tex]P_1(x_1,y_1),P_2(x_2,y_2)[/tex] both in [tex]\mathbb{C}[/tex] plane.

And the two fractions are:

[tex]\frac{-\frac{8}{6}+\frac{\sqrt{8}}{6}i}{-\frac{1}{2}+\frac{\sqrt{2}}{2}i}[/tex].

[tex]\frac{-\frac{8}{6}-\frac{\sqrt{8}}{6}i}{-\frac{1}{2}-\frac{\sqrt{2}}{2}i}[/tex].

Hope this helps.

Answer:

The mean and standard deviation of the number of correct answers is 3 and 1.55 respectively.

Step-by-step explanation:

We are given that a quiz consists of 15 multiple choice questions, each with five possible answers, only one of which is correct.

Let X = the number of correct answers

The above situation can be represented through binomial distribution;

[tex]P(X = x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,......[/tex]

where, n = number of samples (trials) taken = 15 multiple choice questions

            r = number of success

            p = probability of success which in our question is probability of

                  one correct answer out of 5, i.e; p = [tex]\frac{1}{5}[/tex] = 0.2

So, X ~ Binom(n = 15, p = 0.2)

Now, the mean of the number of correct answers is given by;

         Mean of X, E(X) = [tex]n \times p[/tex]

                                    = [tex]15 \times 0.2[/tex] = 3

And the standard deviation of the number of correct answers is given by;

       Standard deviation, S.D.(X) = [tex]\sqrt{n \times p\times (1-p)}[/tex]

                                                     = [tex]\sqrt{15 \times 0.2\times (1-0.2)}[/tex]  = 1.55

Answer:

71/8

8.875

8 7/8

Step-by-step explanation:

5,000,000,000

600,000,000

10,000,000

4,000,000

700,000

80,000

9,000

200

30

6

Answer:

5.614789236​ x 10^9.

Step-by-step explanation:

The exponent is 9 because there are 9 digits after the 5.

Answer:

[tex]\Large \boxed{8\frac{3}{4} }[/tex]

Step-by-step explanation:

35 ÷ 4 = 8 R3

The quotient is 8.

The remainder is 3.

The divisor is 4.

Rewrite as a mixed fraction.

[tex]\displaystyle \sf quotient \frac{remainder}{divisor}[/tex]

35 divided by 4 gives the mixed fraction 4 3/8.

We have,

35 divided by 4 = 8 R3

When we divide 35 by 4, the result is:

35 ÷ 4 = 8 with a remainder of 3.

Or, in the form of mixed fraction we can write as

Divisor x quotient / Remainder

Then, 4 3/8 is the mixed fraction.

Thus, 35 divided by 4 gives the mixed fraction 4 3/8.

Learn more about Mixed fraction here:

https://brainly.com/question/29019463

#SPJ6

Answer:

-10.50 is NOT an integer

Step-by-step explanation:

-10.50 is not an integer number, it includes half of the unit (0.50)

Answer:

384 sq mm

Step-by-step explanation:

Remember that the diagonals of a rhombus are perpendicular bisectors of each other.

So, one side of the rhombus, half the longer diag and half the shorter diag form the 3 sides of a right triangle

with the rhombus side being the hypotenuse.

In this case, let the shorter diagnoal be x mm. In the right triangle,

Hypotenuse = 20

One side = 32/2 = 16

Other side = x/2

Applying Pythagoras principle,

[ check the file attatched ]  (taking only the positive square root)

So the shorter diagonal = 12*2 = 24 mm

Area of the rhombus is given by the formula (1/2)*d1*d2 where d1, d2 are the 2 diagonals.

Here, the area = (1/2)*32*24 = 32*12 = 384 sq mm

Answer:

-43

Step-b-y-step explanation:

f(x)= -x^2+7x-13  so

f(-3)= - (-3)^2 + 7(-3) - 13

= -9 - 21 - 13

= -43.

Answer: The km need to be over the mi.

Step-by-step explanation: The kilometers in this equation are supposed to be used as the denominator, and the miles as the numerator.

Km/mi

Answer:

Option D. 11√6/2

Step-by-step explanation:

We'll begin by calculating the side opposite to angle 60°.

This is illustrated below:

Angle θ = 60°

Opposite =?

Hypothenus = 11

Using the sine ratio, we can obtain the side opposite to angle 60° as follow:

Sine θ = Opposite/Hypothenus

Sine 60 = Opposite /11

Cross multiply

Opposite = 11 × Sine 60

Sine 60 = √3/2

Opposite = 11 × √3/2

Opposite = 11√3/2

Finally, we shall determine the value of x as follow:

Angle θ = 45°

Opposite = 11√3/2

Hypothenus = x

Using the sine ratio, we can obtain the value of x as shown below:

Sine θ = Opposite/Hypothenus

Sine 45° = 11√3/2 /x

Cross multiply

x × Sine 45° = 11√3/2

Sine 45° = 1/√2

x × 1/√2 = 11√3/2

x/√2 = 11√3/2

Multiply through by √2

x = √2 × 11√3/2

x = 11√6/2

Answer:

6+8

a negative minus a negative equals a positive and x minus a negative is addition

Answer:

6+8

Step-by-step explanation:

6 minus (negative 8)

6 - (-8)

We know that subtracting a negative is like adding

6+8

Answer:

The correct answer is True.

Step-by-step explanation:

Altitude: vertical distance either between the top and bottom of something or between a base and something above it.

Answer:

[-8, 7]

Step-by-step explanation:

The range is the set of values used for the y-coordinates of the all the points of the function.

The highest value of the function is at point (8, 7), so the greatest value y has is 7.

The lowest point of the function is at point (-3, -8), so the least value of y is -8.

Range: [-8, 7]

Answer:

[7, -8]

Step-by-step explanation:

Hello!

The range of a graph is found from looking at the graph from top to bottom

The highest point is 7 and the lowest point is -8

The range would be [7, -8]

Hope this helps!

Answer:

-1

Step-by-step explanation:

2 * -1 = -2

Then, -2 / 2  = 1

Answer:bend

Step-by-step explanation:s s

Answer:

The answer is

Step-by-step explanation:

x² + 12x - 64

To factorize the expression write 12x as a difference

That's

x² + 16x - 4x - 64

Factor out x from the expression

That's

x( x + 16) - 4x - 64

Factor out - 4 from the expression

That's

x( x + 16) - 4 ( x + 16)

Factor out (x + 16) from the expression

We have the final answer as

Hope this helps you

Answer:

137°

Step-by-step explanation:

Total angle of a triangle:

a + b + c = 180°

35 + 8 + c = 180°

c = 180° - 43° = 137°

Answer:

3x^2-7

-7 is the constant

3 is the coefficient

x is the variable

Step-by-step explanation:

(3x^2)+(-7)

Step-by-step explanation:

The problem statement says λ<1.  If this is true, then the cannonball is slower than the boat, and it will never reach the boat.  So I assume it's actually λ>1.

If we say t is the amount of time, then the boat travels south a distance of ut, and the cannonball travels a distance of λut.

v = λut

ut = v/λ

Using Pythagorean theorem:

d² + (ut)² > v²

d² + (v/λ)² > v²

λ²d² + v² > λ²v²

λ²d² > (λ² − 1) v²

λ² / (λ² − 1) > (v/d)²

Answer:

answer in attachment

Step-by-step explanation:

Answer:

See bolded for each part below.

Step-by-step explanation:

Attachment 1. (a) The range is 400 dollars, as her greatest balance was 400 dollars, so her domain would be 3 weeks.

( b ) Remember that B(0) models the balance over the course of 0 days. As you can see that starting mark is about half of the greatest balance on the graph, 400 dollars. Therefore you can estimate B(0) to be $200.  

(c) B(12) models the balance over the course of 12 days. It mentions that at B(12) the balance reaches $0, so in function notation that would be B(12) = 0.

(d) Segment 4 would represent that information. As you can see on the graph, the only time period with which the balance became 0 is represented by the fourth segment.

Attachment 2. (a) As you can see on the graph, Ebony reached $400 on day 4, and stayed as such throughout day 8 (modeled by line segment 2). Therefore B(5) = 400 = B(6) = B(7).

(b) We also know that B(0) = ( About ) 200, B(4) = 400. Therefore B(1) = 250, B(2) = 300, B(3) = 350. The slope changes by a rate of 50.

(c) Jade is incorrect. By looking at the graph you can see that the rate from day 8 to day 12 is greater than the rate from day 0 to day 4.

Attachment 3. (a) I would say the amounts she deposited were less than $100 per day. Remember that from day 0 to 4 the slope is about 50. The slope of the line segment that models this situation, line segment 6, has about the same slope, 50.

(b) On day 21 she had 300 dollars, as it seems that this marking is between the starting amount (200) and 400. There are 5 days between 16 and 21. On day 16 she deposited 100 dollars. From then on she apparently deposited 50 dollars,

100 + 50 * 4 = 100 + 200 = 300 ✓