How would the fraction
5/1-√3
be rewritten if its denominator is rationalized
using difference of squares?​

Answer:

x = -3 ± 2√2

Step-by-step explanation:

x² + 6x + 1 = 0

Let's solve by completing the square.

Add -1 and 9 on both sides.

x² + 6x + 9 = 8

Factor left side.

(x + 3)² = 8

Take square root on both sides.

x + 3 = ±√8

Add -3 to both sides.

x = -3 ± 2√2

Answer:

Step-by-step explanation:

Let x and y represent amounts to be taken to Indianapolis and Ft. Wayne, respectively. Then you have ...

  x + y = 1000 . . . . . . 1000 bushels are to be divided between 2 markets

  x ≥ 100 . . . . . . . . . . Indianapolis needs at least 100 bushels

  y ≥ 300 . . . . . . . . .  Fort Wayne needs at least 300 bushels

Answer:  x + y = 1000   This could be x + y ≤ 1000 depending on how you interpret the distribution. (The markets might not need all )

x ≥ 100 We'll say this is Indianapolis needing a minimum of 100 bushels

y ≥ 300 This is Ft.Wayne needing a minimum of 300 bushels

Step-by-step explanation:

The distribution could be anything within the darkest shaded area in the attached graph.

For example, if Indianapolis takes only 100 bu, Ft.Wayne could get up to 900bu. If Ft. Wayne takes 300bu, Indy could get up to 700bu.

Or they could each take 500, and the farmer has none left, or they could each take their minimum plus 100 (200 + 400) and the farmer has 600bu left

Answer:

[tex]\boxed{105}[/tex]

Step-by-step explanation:

∠DAB = ∠BAC = 105 degrees

This is because opposite angles of a parallelogram are congruent.

Answer:

105

Step-by-step explanation:

∠DAB = ∠BAC = 105

Answer:

6.61387 stones

Step-by-step explanation:

Answer:

6.6 stones

Step-by-step explanation:

1 kg= 2.2 pounds

1 stone =14 pounds ⇒ 1 pound= 1/14 stone

42 kg= 42*2.2 pounds= 92.4 pounds  

92.4 pounds = 92.4 * 1/14 stone= 6.6 stones

Answer:35 cars in 7 hours.

Step-by-step explanation:15/3=5 per hour. 5x7=35.

Answer:

35 cars in 7 hrs

Step-by-step explanation:

Steve's rate of work is (15 cars) / (3 hrs), or 5 cars/hr.

In 7 hrs he can wash

5 cars

---------- * 7 hrs = 35 cars in 7 hrs

   hr

Answer:

Option B is the correct answer

Step-by-step Explanation:

[tex] \sin 45 \degree = \frac{x}{2} \\ \\ \frac{1}{ \sqrt{2} } = \frac{x}{2} ..( \because \: \sin 45 \degree =\frac{1}{\sqrt 2}) \\ \\ \huge \purple{ \boxed{ x = \frac{ \sqrt{2} }{2}}} \\ \\ [/tex]

Using the trigonometric ratio sine, we find that x = [tex]\sqrt{2}[/tex], making option D to be correct.

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). These trigonometric ratios deduce a relationship between angles of right angle triangle ( other than the right angle ) and the sides of the triangle : base, perpendicular, hypotenuse.

We have used trigonometric ratio sine here.

sin[tex]\theta[/tex] = [tex]\frac{perpendicular}{hypotenuse}[/tex]

In the given question,

from the point of view of angle 45° which is marked in the figure,

base = y

perpendicular  = x

hypotenuse = 2

Using, sin[tex]\theta[/tex] =  [tex]\frac{perpendicular}{hypotenuse}[/tex]

sin 45 = [tex]\frac{2}{x}[/tex]

[tex]\frac{1}{\sqrt{2} } = \frac{x}{2} \\\\x = \frac{2}{\sqrt{2} } = \sqrt{2}[/tex]

Learn more about trigonometric ratios here

https://brainly.com/question/23130410

#SPJ2

Answer:

The sum of the polynomials in the equation is 3x² - 2x - 3

Step-by-step explanation:

(3 - 4x + 8x²) + (-6 + 2x - 5x²)

Distribute the positive sign to (-6 + 2x - 5x²). So all of these terms will stay the same and maintain their original signs.

3 - 4x + 8x² - 6 + 2x - 5x²

Combine like terms.

- 3 - 2x + 3x²

Now put the equation in standard form. This means that the exponential numbers will be ordered in descending order.

3x² - 2x - 3

Answer:

3x^2 -2x -3

Step-by-step explanation:

Combine like terms

3-4x+8x^2-6+2x-5x^2

Put the numbers that are squared in the front

8x^2 -5x^2 =3x^2

Put the numbers with x only next

-4x + 2x= -2x

Then the normal numbers

3-6=-3

Put them together in simplified form of the equation

Thus your answer is 3x^2 - 2x -3

Hope this helps please mark brainliest!

Answer:

y = -2

Step-by-step explanation:

Put x as -19 and solve for y.

2(-19) - 5y = -28

Multiply.

-38 - 5y = -28

Add 38 on both sides of the equation.

-5y = -28 + 38

-5y = 10

Divide both sides by -5.

y = 10/-5

y = -2

Answer:

2x - 5y = -28

when x = - 19

Substitute the value of x into the equation

That's

2(-19) - 5y = -28

-38 - 5y = -28

-5y = -28 + 38

-5y = 10

Divide both sides by - 5

We get

y = 10/-5

y = -2

Hope this helps

Answer:

x=8

Step-by-step explanation:

Those angles are supplementary so:

140+5x=180

5x=40

x=8

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ ≤ 5.4

For the alternative hypothesis,

H1: µ > 5.4

This is a right tailed test

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 48

Degrees of freedom, df = n - 1 = 48 - 1 = 47

t = (x - µ)/(s/√n)

Where

x = sample mean = 5.23

µ = population mean = 5.4

s = samples standard deviation = 0.56

t = (5.23 - 5.4)/(0.56/√48) = 2.1

We would determine the p value using the t test calculator. It becomes

p = 0.021

Since alpha, 0.01 < the p value, 0.021, then we would fail to reject the null hypothesis. Therefore, At a 1% level of significance, there is no significant evidence that the mean red blood cell count of each person is greater than 5.4 cells per​ microliter.

Since 5.4 is the upper limit, it means that result of the sample group is acceptable.

Answer:

area of trapezoid= 1/2 × ( a + b ) × high

75cm² = 1/2 × (8+17) × h

75. = 1/2 × 25 × h

75. = 12,5 × h

75. = 12,5h

h = 75 ÷ 12,5

h. = 6 ( B )

Answer:

53

Step-by-step explanation:

We know the first term and common difference so we can write the explicit formula. The formula is:

aₙ = a₁ + (n - 1)d

aₙ = 8 + (n - 1) * 3

aₙ = 3n + 5

This means that a₁₆ = 3 * 16 + 5 = 53

by using the formula for arithmetic sequence, the 16th term of the progression can be obtained. Given A1 = 8 and d = 3,

A16=A1 + (n-1) d

A16=8 + (16-1) (3)

A16 = 53

I hope I helped! Be safe!

Answer:

  H.  48

Step-by-step explanation:

Let p represent the number of coins Pamela has. Then 3p is the number Samantha has. After 6 days of adding coins, we have ...

  2(p +3·6) = 3p +2·6

  2p +36 = 3p +12

  24 = p . . . . Pamela has 24 coins; Samantha has 72.

Now, we can find the number of days (d) before the coin count is the same.

  24 +3d = 72 +2d . . . . coin counts are the same after d days

  d = 48 . . . . . subtract 24+2d

In 48 days from now, Pamela and Samantha will have the same number of coins.

Well for the activity we can do a game.

In a game you start with 50 coins and everytime you kill a monster "x" you get 2 more coins.You need 100 coins to level up.

We can make the following inequality,

2x + 50 ≥ 100

So to find x we single it out,

2x + 50 ≥ 100

-50 to both sides

2x ≥ 50

Divide 2 by both sides

x ≥ 25

For the number line look at the image below ↓

The solution in the number line is the number of monsters killed in order to level up.

Hope this helps :)

Answer:

(D)250 ft

Step-by-step explanation:

Circumference of Circle O [tex]= 250\pi ft[/tex]

For a circle of diameter d, Circumference = [tex]\pi d[/tex]

Therefore:

[tex]\pi d = 250 \pi\\d \approx 250$ ft[/tex]

The approximate length of the diameter, d is 250 ft.

The correct option is D.

Answer:

centre: (0, 0)

radius: 3√5 ≈ 6.71

Step-by-step explanation:

The equation of a circle is denoted by:

[tex](x-x_1)^2 +(y-y_1)^2=r^2[/tex], where [tex](x_1,y_1)[/tex] is the centre and r is the radius

Here, we see that x1 and y1 are each 0, which means the centre is (0, 0).

We also see that r² = 45, which means the radius is r = √45 = 3√5 ≈ 6.71.

Therefore, we want to draw a circle with radius 6.71 and centre at (0, 0). See attached.

~ an aesthetics lover

Answer:

8 flowers in each bunch

Step-by-step explanation:

From this information, we can make the equation:

[tex]23b-46=138[/tex]

Where [tex]b[/tex] is the number of flower in each bunch.

[tex]23b-46=138[/tex]

Add 46 to both sides

[tex]23b=184[/tex]

Divide both sides by 23

[tex]b=8[/tex]

There are 8 flowers in each bunch.

Answer:8

Step-by-step explanation:

Answer: 18 animals

Step-by-step explanation:

3 out of 20 pet owners get their pet from a breeder.

To find how many animals have been bought from a breeder, you need to find 3/20 of the 122 animals.

3/20 = 0.15

122 * 0.15 = 18.3

18.3 rounds down to 18

There are 18 animals who have been bought from a breeder.

Answer: Associative Property: (40+(12+18)+27. Evaluate: 97

Answer:

  b.  For every x value, there is only one y value - a function

Step-by-step explanation:

If any x-value is repeated, the relation is not a function. The above answer choice explains that.

Answer:

Step-by-step explanation:

1) We would determine the cube root of 27 and find its square.

Cube root of 27 = 3

3² = 9

Solution = 9

2) 36³ = 46656

√36³ = √46656 = 216

3) we would find the 5th roof of - 243 and find its cube

5th root of - 243 = - 3

- 3³ = - 27

Solution = - 27

4) Looking at the expression, 40⅔, we can see that

a = 2

b = 3

c = 40

Answer: 1) We would determine the cube root of 27 and find its square.Cube root of 27 = 33² = 9Solution = 92) 36³ = 46656√36³ = √46656 = 2163) we would find the 5th roof of - 243 and find its cube5th root of - 243 = - 3- 3³ = - 27Solution = - 274) Looking at the expression, 40⅔, we can see that a = 2b = 3c = 40

Step-by-step explanation:

this my first time to ues this app the answer is right, hope you got it

Answer:

m=4

Step-by-step explanation:

6.33 × 10^9 / 1.79 × 10^5=3.54 × 10^m

Find m

6.33 × 10^9 / 1.79 × 10^5 =3.54 × 10^m

Divide the multipliers

6.33/1.79

=3.54

Divide the other multipliers

10^9/10^5

Division in scientific notation with superscript with the SAME base requires subtraction of the superscript using one of the bases

10^9/10^5

= 10^9-5

=10^4

Therefore,

6.33 × 10^9 / 1.79 × 10^5 = 3.54 × 10^4

m = 4

Answer:

4 :)

Step-by-step explanation:

Answer:  The graph becomes narrower

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k   where

A vertical stretch means the curve gets narrower.

A vertical shrink/compression means the curve gets wider.

Answer:

Cos E= 24/25

Step-by-step explanation:

Length of hypotenuse: 7^2+24^2=625. 625 square root=25

Thus, DE is 25.

Sin D= 24/25, so that is false.

Tan D= 24/7, so that is false.

Cos E= 24/25, so that is true

Sin E= 7/25, so that is false.

Answer: Pls brainliest this took forever, but was really fun :)

Step-by-step explanation:

Imagine you are looking at the structure from the front or the side.  What would you see?  If you want a detailed explanation on orthogonal drawings, just ask :)

Answer:

  [tex]\dfrac{2xy+x}{3y+2}[/tex]

Step-by-step explanation:

Factor numerator and denominator and cancel common factors.

  [tex]\dfrac{3x-12xy^2}{6-3y-18y^2}=\dfrac{-3x(4y^2-1)}{-3(6y^2+y-2)}=\dfrac{x(2y-1)(2y+1)}{(2y-1)(3y+2)}\\\\=\boxed{\dfrac{2xy+x}{3y+2}}[/tex]

Answer:

B.  y ≤ 1/2x + 3

Step-by-step explanation:

Well we can start by finding the y-intercept which is the point on the line that touches the y-axis in this case it’s 3.

And by looking at the shade it is facing down and the line is solid so the inequality starts with y ≤,

So we can cross out answer choices C. and D.

And the slope is 1/2 because that’s how far away each points are from each other.

So the inequality is y ≤ 1/2x + 3

Look at the image below.

Answer:

Total number of side of regular polygon = 36

Step-by-step explanation:

Given:

Angle of rotation (regular polygon) = 10°

Find:

Total number of side of regular polygon

Computation:

Total number of side of regular polygon = 360° / Angle of rotation (regular polygon)

Total number of side of regular polygon = 360° / 10°

Total number of side of regular polygon = 36

Answer:

Adults = 61

Students = 92

Children = 122

Step-by-step explanation:

a adults

x students

c children

a + c + x = 275

c / a = 2

5c + 7x + 12a = 1986

Simplify and solve the system.

a + 2a + x = 275

3a +x = 275

x = 275 - 3a. and c= 2a

The revenue equation can be written in terms of just one variable, a.

5(2a) + 7(275-3a) + 12a = 1986

Solve for a

a = 61

use it to find x and c.

c = 2a = 2 x 61 = 122

x = 275-a-c

x = 275 - 61-122

x = 92