<img src="https://tex.z-dn.net/?f=6%20%5Csqrt%7B.4" id="TexFormula1" title="6 \sqrt{.4" alt="6 \sqrt{.4" align="absmiddle" class

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iren [92.7K]

3 years ago

="latex-formula">

Mathematics

1 answer:

ss7ja [257]3 years ago

3 0

The first step for solving this expression is to convert the decimal number into a fraction.
6 $\sqrt{ \frac{2}{5} }$
Remember that in order to take a root of a fraction,, you must take the root of the numerator and denominator separately. This will look like the following:
6 × $\frac{ \sqrt{2} }{ \sqrt{5} }$
Now calculate the product.
$\frac{6 \sqrt{2}}{ \sqrt{5} }$
Lastly,, rationalize the denominator to find your final answer.
$\frac{6 \sqrt{10} }{5}$
Let me know if you have any further questions.
:)

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the sides of a square each have a length of 11x inches write an expression for the perimeter of the square in inches

notsponge [240]

Answer:

P = 44x

Step-by-step explanation:

Given

a = 11x

Perimeter of a square is:

P = 4a

Substitute the value:

P = 4(11x) = 44x

4 0

3 years ago

For 0 ≤ θ < 2 π what are the solutions to sin^2(θ) =2sin^2(θ/2)

gregori [183]

Recall the half-angle identity for sine,

sin²(x/2) = (1 - cos(x))/2

Then the given equation is identical to

sin²(θ) = 1 - cos(θ)

Also recall the Pythagorean identity,

sin²(θ) + cos²(θ) = 1

Then we rewrite the equation as

1 - cos²(θ) = 1 - cos(θ)

Factoring the left side, we have

(1 - cos(θ)) (1 + cos(θ)) = 1 - cos(θ)

and so

(1 - cos(θ)) (1 + cos(θ)) - (1 - cos(θ)) = 0

and we factor this further as

(1 - cos(θ)) (1 + cos(θ) - 1) = 0

which gives

cos(θ) (1 - cos(θ)) = 0

Then either

cos(θ) = 0 or 1 - cos(θ) = 0

cos(θ) = 0 or cos(θ) = 1

[θ = arccos(0) + 2nπ or θ = -arccos(0) + 2nπ]

… or [θ = arccos(1) + 2nπ or θ = -arccos(1) + 2nπ]

(where n is any integer)

[θ = π/2 + 2nπ or θ = -π/2 + 2nπ] or [θ = 0 + 2nπ]

In the interval 0 ≤ θ < 2π, we get three solutions:

• first solution set with n = 0 ⇒ θ = π/2

• second solution set with n = 1 ⇒ θ = 3π/2

• third solution set with n = 0 ⇒ θ = 0

So, the first choice is correct.

6 0

3 years ago

A high school sports team is ordering sports drinks online from a company. The price of sports drinks varies, based on the numbe

Elena-2011 [213]

The amount of drinks is a linear function of the number of drinks. The maximum amount that can be purchased is 100 soft drinks.

Let

$y \to$ amount of drinks

$x \to$ number of drinks

For drinks not more than 50

$y = 10 + 0.8x$

For drinks more than 50.

$y = 15 + 0.7x$

For a purchase of $85, it means that:

$y = 85$

So, we solve for x in both equations.

$y = 10 + 0.8x$

$85 = 10 + 0.8x$

Collect like terms

$0.8x = 85-10$

$0.8x = 75$

Divide through by 0.8

$x = 93.75$

$x = 94$ --- approximated

$y = 15 + 0.7x$

$85 =15 + 0.7x$

Collect like terms

$0.7x = 85 - 15$

$0.7x = 70$

Divide by 0.7

$x = 100$

By comparing both values:

$x = 100$

$x = 94$

$100 > 94$

Hence, the maximum amount that can be purchased is 100

Read more about functions at:

brainly.com/question/20286983

5 0

3 years ago

Read 2 more answers

Pls answer these 2 questions show your work

salantis [7]

Multiply 64% (0.64) x 75 =48 tiles
Multiply 85% (0.85) x 40 = 34 emails

4 0

3 years ago

what is the quotient when x3 − 5x2 2x 5 is divided by x − 2? x2 − 3x − 4 x2 − 7x 16 x2 − 3x − 4 − 3 over the quantity of x minus

nekit [7.7K]

The correct answer is: 
x²-3x-4 - $\frac{3}{x-2}$ .

Explanation: 
To divide these polynomials, the dividend, x³-5x²+2x+5, goes under the box, and the divisor, x-2, goes outside of the box.

We first want to find what we multiply x by to make x³; x*x²=x³, so we write x² over -5x² in the box.

Now we multiply our divisor, x-2, by x²: 
x*x²=x³
-2*x²=-2x².

This goes under x³-5x² in the box.

Now we subtract: 
(x³-5x²)-(x³-2x²)=-3x².

This goes below the 2x² we wrote, and we bring down 2x.

Now we see what we multiply x by to make -3x²;
x*-3x=-3x², so we write -3x beside x² in the quotient (at the top).

We multiply our divisor, x-2, by -3x: 
x*-3x=-3x²
-2*-3x=6x.

We write -3x²+6x under our -3x²+2x and subtract:
(-3x²+2x)-(-3x²+6x)=-4x.

Write this below 6x. Bring down +5.

Now we see what we multiply x by to make -4x;
x*-4=-4x, so write -4 beside -3x in the quotient.

Multiply our divisor, x-2, by -4: 
x*-4=-4x;
-2*-4=8;

write -4x+8 below -4x+5 and subtract:
(-4x+5)-(-4x+8)=-3.

This gives us the quotient x²-3x-4 with a remainder of -3, so we write our full answer as x²-3x-4-(3/x-2).

3 0

4 years ago

Read 2 more answers