Mathematics High School

why
[tex] \frac{1}{ \sqrt{3 } - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1} = \frac{1 + \sqrt{3} }{2} [/tex]
why not 1+✓3 ?

​

Why [tex] \frac{1}{ \sqrt{3 } - 1} \times \frac{ \sqrt{3} + 1}{ \sqrt{3} + 1} = \frac{1 + \sqrt{3} }{2}

Answers

Answer 1

Answer:

Hey there!

When multiplying fractions, we multiply the numerator by the numerator, and denominator by denominator.

1 x [tex]\sqrt{3}+1[/tex] = [tex]\sqrt{3}+1[/tex]

[tex]\sqrt{3} -1 (\sqrt{3} +1)[/tex] = 2

Thus, the answer is ([tex]\sqrt{3}+1[/tex])/2

Let me know if this helps :)

Related Questions

3a - 6a + 20 = 8a + 24 - 5a - 4

Answers

Step-by-step explanation:

-3a + 20 = 3a + 20

-6a + 20 = 20

-6a = 0

a = 0

Answer: a=0

Step-by-step explanation:

Given

3a-6a+20=8a+24-5a-4

Combine like terms on both sides

-3a+20=3a+20

Subtract 3a on both sides (subtractive property of equality)

-6a+20=20

subtract 20 on both sides (subtractive property of equality)

-6a=0

Divide -6 on both sides (division property of equality)

a=0

Hope this helps!! :)

Please let me know if you have any question or need further explanation

f(x)=x2-x find f (3)

Answers

Answer:

f(3) =6

Step-by-step explanation:

[tex]f(x) =x^2 -x\\\\f(3) = ?\\\\f(3) = (3)^2 -3\\f(3) = 9-3\\f(3) =6[/tex]

Answer:

[tex]\huge \boxed{\sf{f(3)=6}}[/tex]

Step-by-step explanation:

[tex]\sf f(x)=x^2-x[/tex]

For f(3), the input or x value is 3.

[tex]\sf f(3)=3^2-3[/tex]

Evaluate the expression.

[tex]\sf f(3)=9-3[/tex]

[tex]\sf f(3)=6[/tex]

A car covers a distance of 200 m. If its velocity is 20 m/s, calculate the
time taken.​

Answers

Answer:

10 seconds

Step-by-step explanation:

Distance = 200 m

Velocity = 20m/s

Time =?

[tex]time = \frac{distance}{velocity} \\ time = \frac{200m}{20m/s} \\ time = 10 \: seconds[/tex]

What is the slope of
3y = -4x + 6

Answers

Answer:

Hey there!

3y=-4x+6

y=-4/3x+2

Thus, the slope is -4/3.

Hope this helps :)

Answer:

the slope is -4/3

Step-by-step explanation:

3y = -4x + 6

y=-4/3 x +6/3

y=-4/3 x+2

the slope is -4/3

please solve quick as posible

Answers

Answer:

m+p/2=n

Step-by-step explanation:

You can't get any other multiplication factor, so the only way is to isolate n, by adding p to m and dividing by 2

hi, please help me out :)) thank you

Answers

Answer:

d =32

Step-by-step explanation:

[tex]\sqrt{7d+1}-4=11\\\\\mathrm{Add\:}4\mathrm{\:to\:both\:sides}\\\sqrt{7d+1}-4+4=11+4\\\\Simplify\\\sqrt{7d+1}=15\\\\\mathrm{Square\:both\:sides}:\quad 7d+1=225\\7d+1=225\\\\\mathrm{Solve\:}\:7d+1=225:\\\quad d=32[/tex]

Answer:

d = 32

Step-by-step explanation:

[tex]\sqrt{7d-1} -4+4=11+4[/tex]

[tex]\sqrt{7d-1} =15[/tex]

[tex]7d+1=15 *15[/tex]

[tex]7d+1=225[/tex]

[tex]7d=225-1[/tex]

[tex]7d=224[/tex]

[tex]d=\frac{224}{7}[/tex]

[tex]d=32[/tex]

A group of boys went on a camping trip. They spent the night in 5 tents and 4 cabins. There were 9 boys in each tent and 7 boys in each cabin. How many boys went on the trip?

Answers

Answer:

Step-by-step explanation:

In a tent, there are nine boys.

There were five tents.

5 tents containing 9 boys can equal 45 boys.

(5 x 9 = 45)

In a cabin, there are seven boys.

There were four cabins.

4 cabins containing 7 boys can equal 28 boys.

(4 x 7 = 28)

Now, to find all the boys, add the numbers together.

28 boys with 45 boys will equal 73 boys.

Please check my answer for no one, not even me is right.

Good luck :)

I need help with geometry one my question is construct AD congruent to JK​

Answers

Answer:

  use your compass to copy the length to a new line

Step-by-step explanation:

To make a line segment that has the same length as another, set your compass width to the length of the one you want to copy, and use that to mark the length on the line where you want your copy.

Use a straightedge to draw a line longer than JK.

Label a point on that line A.Set your compass to the length JK.Mark that length from point A on the line you drew. Label the mark D.

AD is congruent to JK.

Liset ran 17 miles in 204 minutes. How long would you except it to take her run 8 miles?

Answers

Answer:

96 minutes.

Step-by-step explanation:

17 miles = 204 minutes

1 mile = ?

204/17 = 12 minutes

1 mile = 12 minutes

8 miles = ?

8 × 12 = 96 minutes

It would take Liset 96 minutes to run 8 miles.

The square of a whole number is between 6400 and 7000. The number must be between ?

Answers

Answer:

80 and 83.6660026534

Step-by-step explanation:

The square root of 6400 is 80 and the square root of 7000 is 83.6660026534 so it would be between these two.

Who is estimated at 250 people would attend the movie but 255 people actually attended what is the percent error to the nearest percent of the estimate

Answers

Answer:

Percent error = 2%

Step-by-step explanation:

Given:

Expected value = 250

Actual value = 255

Find:

Percent error

Computation:

Percent error = [(Actual value - Expected value)/Expected value]100

Percent error = [(255 -250) / 250]100

Percent error = 2%

Answer:

Its 6% because |E−T||T|×100

=(250−235)|235|×100

=15235×100

=0.0638298×100

=6.38298%

=6.38298%error

Step-by-step explanation:

find the average rate of change for the interval 2,4​

Answers

Answer:

8

Step-by-step explanation:

It went from 7 to 15?

1.414 is an ? for the square root of 2

Answers

Answer:

1.999396

Step-by-step explanation:

square of 1.414=1.999396

square root of 1.999396=1.414

In the given figure <abc = 90 degree and CA=2BC.Find the measure of <BAC​

Answers

Answer:

the value of <BAC= 30° ...

What number is 0.72 more than 0.971?

Answers

Answer:

1.691

Step-by-step explanation:

.971 + .72

Answer:

1.691

Step-by-step explanation:

What number is 0.72 more than 0.971?

To solve your question, you're gonna have to add the two numbers together.

[tex]0.72+0.971[/tex]

  0.971

+0.72

_______

          1

  0.971

+0.72

_______

        91

  0.971

+0.72

_______

     691  

  1

  0.971

+0.72

_______

   1.691

So your answer is

[tex]1.691[/tex]

Hope this helped!

 

Pete is purchasing a smart phone for $249.30 he gives the sales clerks 3 fifty-dollar bills 4 twenty-dollar bills, and 4 five-dollar bills. how much should he receive in change

Answers

3 • 50 = 150
4 • 20 = 80
4 • 5 = 20
150 + 80 + 20 = 250
250 - 249.30 = 0.70

So Pete should receive $0.70 in change.
The answer would be 0.7

what is the sum of the arithmetic series: s10 = -20, d = 4, a1 =? ​

Answers

Answer:

first term a1 is -40.

Step-by-step explanation:

in an arithmetic series,

sum of first term terms (S10) = -20

Common difference (d) = 4

first term (a)= ?

number of terms (n)= 10

now,

S10 =( n÷2) [a1 +(n-1) d]

or, -20 = (10÷2) [a1 + (10-1) 4]

or, -20 = 5 ( a1 + 36)

or, -4 = a1 + 36

or, a1 = -40

Step-by-step explanation:[tex] \green\star[/tex] Given

[tex]\blue\star[/tex]s10 = -20

[tex]\blue\star[/tex]n = 10

[tex]\blue\star[/tex] an = -20

[tex] \green\star[/tex] solution

[tex] \green\star[/tex]s10 = n\2 [a+(n-1)d]

[tex] \green\star[/tex]-20 = 10a2[a+(10-1)4]

[tex] \green\star[/tex]-4 = a +36

[tex] \green\star[/tex]a1 = -40

[tex]\small\boxed{a = -40}[/tex]

Hope it helps.

Hope it helps

What is the difference between 6^ and ^ 6 ?

Answers

I think it’s 6 to the exponential power or a number vs a number to the power of 6

Average Weight Animal At Birth (g) Adult Female(g) Adult Male (g) Hamster 2 120 110 Guinea pig 65 800 1,030 Rat 7 265 470 On average, a hamster at birth weighs 2 3 the weight of a gerbil at birth. Enter and solve an equation to find the average weight of a gerbil at birth. Let g represent your variable. The equation is . The average weight of a gerbil at birth is g.

Answers

Answer:

The answer is below

Step-by-step explanation:

An equation is a mathematical statement that shows the equality between two expressions.

From the table, the average weight of the hamster at birth is 2 grams. The average weight of gerbil at birth is 2/3 of that of hamster. Let g represents the weight of the gerbil at birth, hence the weight can be gotten by solving the equation:

2/3 of hamster weight at birth = Average weight of gerbil at birth

2/3 × 2 grams = g

g = 2/3 × 2 grams = 4/3 grams = 1.33 grams

The average weight of gerbil at birth = 1.33 grams

Really struggling with this one. Can someone help please?​

Answers

Answer:

12

Step-by-step explanation:

M is in the middle between S and T we know 2x+6 has to be the same as 3x+3 if 3x is one more x then 2x then we do 6-3 that eqauls 3 so X=3 and 2*3=6 and 6+6= 12.

Hey there! :D

Answer:

[tex]\huge\boxed{SM = 12}[/tex]

SM = 2x + 6

MT = 3x + 3

M is the midpoint of SM

Write an expression to represent the length of ST:

ST = SM + MT

ST = 2x + 6 + 3x + 3

Combine like terms:

ST = 5x + 9

Since ST = 2(SM), set up another equation:

5x + 9 = 2(2x + 6)

5x + 9 = 4x + 12

Isolate the "x" variable:

5x - 4x = 12 - 9

x = 3.

Substitute in this value of "x" into the equation for SM:

2(3) + 6 = 12.

Elliott put 7 cups of tea in to a jar. How many more cups of tea does he need to fill up the jar? Capacity: 4 quarts (1 quart = 4 cups)​

Answers

Answer:

9 cups

Step-by-step explanation:

1 quart= 4 cups

4 quart= ? cups  (crisscross)

4 quart=16 cups

16-7= 9 cups

4) Given that x is an integar
find the three greatest value
of x which satisfies the lines
inequality 7x < 2x - 13
​

Answers

Answer:

The three greatest are -3, -4, -5

Step-by-step explanation:

7x < 2x - 13

Subtract 2x from each side

7x-2x < 2x-2x - 13

5x < -13

Divide by 5

5x/5 < - 13/5

x < - 2 3/5

Since x is an integer

-3 is the largest integer that fits the inequality

The three greatest are -3, -4, -5

side length of 216 cubic yards

Answers

Answer:

6 yards

Step-by-step explanation:

a³ = 216

a = ∛ 216

    = 6 yards

Answer:

6 yards

Step-by-step explanation:

The volume of a cube can be found using the following formula.

[tex]v= s^3[/tex]

We know the volume is 216 cubic yards, so we can substitute 216 yd³ in for v.

[tex]216 yd^3=s^3[/tex]

We want to find the side length. Therefore, we must isolate the variable, s, on one side of the equation.

s is being cubed. The inverse of cubed is the cube root. Take the cube root of both sides of the equation.

[tex]\sqrt[3]{216 yd^3}=\sqrt[3]{s^3}[/tex]

[tex]\sqrt[3]{216yd^3}=s[/tex]

[tex]6yd=6[/tex]

The side length of the cube is 6 yards.

Which properties can be used to solve 7y − 15 = −29? Select all that apply.

Answers

Answer:

addition property of equality

inverse property of multiplication

Step-by-step explanation:

7y − 15 = −29

Add 15 to each side using the addition property of equality

7y -15+15 = -29+15

7y = -14

Divide each side by 7 using the inverse property of multiplication

7y/7 = -14/7

y =2

Answer:

[tex]\Large \boxed{\mathrm{Addition \ Property \ of \ Equality}} \\\\\\ \Large \boxed{\mathrm{Inverse \ Property \ of \ Multiplication}}[/tex]

Step-by-step explanation:

[tex]\sf 7y-15=-29[/tex]

Using the additive property of equality, we add 15 to both sides of the equation.

[tex]\sf 7y-15+15=-29+15[/tex]

[tex]\sf 7y=-14[/tex]

Using the inverse property of multiplication, we divide both sides of the equation by 7.

[tex]\displaystyle \sf \frac{7y}{7} =\frac{-14}{7}[/tex]

[tex]\sf y = -2[/tex]

How many oranges equal 6 cups of juice?

Answers

Answer:

1/3

Because 1/3 if divide into two, it'll be 0.5/3 but if the question says that the answer have to be in whole number, that means it must be 1/6.

Answer:12

Step-by-step explanation:

because it will take 2 to make a cup

The sum of 2 and the square of a number r

Answers

Answer:

[tex] {r}^{2} + \: 2[/tex]

Step-by-step explanation:

Let the no. be r . It's square will be r^2 .

When r^2 is added with 2 , then it's sum is r^2 + 2

∠A and ∠B are two supplementary angles such that ∠A= x° and ∠B= (2x+30)°. Find the measure of ∠B.

Answers

Answer: 130°

Step-by-step explanation:

supplementary angle: ∠A+∠B=180°

x+(2x+30)=180

x+2x+30=180

   3x+30=180

          3x=150

            x=50

2(50)+30=100+30=130°

Hope this helps!! :)

Please let me know if you have any question

Max drove 460 miles in 8 hours at a constant speed. How long would it take him to drive 661.25 miles at that speeds?

Answers

Answer:

106

Step-by-step explanation:

Sksjwisjsjsoansnsan just to get points so give it a thanks thing ty

Answer:

x=11.5hours

Step-by-step explanation:

661.25miles÷57.5mph=11.5hours

Se quieren repartir 21 chocolates entre 4 chicos en partes iguales y sin que sobre nada, cuantos chocolates recibira cada uno?

Answers

Answer: Cada chico recibira 5.25

write the polynomial the product and sum of whose zeroes are -9/2 and-3/2

Answers

Answer:

y = 2x² + 3x - 9

Step-by-step explanation:

Given αβ = - [tex]\frac{9}{2}[/tex] = [tex]\frac{c}{a}[/tex]

and α + β = - [tex]\frac{3}{2}[/tex] = - [tex]\frac{b}{a}[/tex]

Then a = 2, b = 3 and c = - 9, thus

y = 2x² + 3x - 9

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