Several paint mixtures are made by mixing blue paint and white paint. Paint Colors Blue Paint White Paint Mixture A 5 cups 12 cups Mixture B 6 cups 6 cups Mixture C 4 cups 12 cups Mixture D 5 cups 6 cups Which mixture has the highest ratio of blue paint to white paint? mixture A mixture B mixture C mixture D

Answer:

A

Step-by-step explanation:

First, simplify the numerator:

[tex]\frac{3 }{\sqrt{3} + \sqrt{x} } \\[/tex]

Next, multiply the numerator and denominator by the opposite of the denominator to rationalize the expression.

[tex]\frac{3}{\sqrt{3}+\sqrt{x} }*\frac{\sqrt{3}-\sqrt{x} }{\sqrt{3}-\sqrt{x}}[/tex]

Finally, evaluate the denominator by multiplying them together.

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {(\sqrt{3}+\sqrt{x})(\sqrt{3}-\sqrt{x})}[/tex]

Simplify:

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {3-x}[/tex]

And done! :)

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

properties to be used here :

[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]

[tex]\large \textsf{Question : 1} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\large \textsf{Question : 2} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\large \textsf{Question : 3} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

35

Step-by-step explanation:

R × S = 15 could be 5 × 3 = 15, 3 × 5 = 15

                               15 × 1 = 15, 1 × 15 = 15

S ×T =3 From our previous step we can see that S could be 1 or 3 or 5 or 15.

            Given that S×T =3, will make sense that S is 1 or 3

            If S is 1 then T is 3 and if S is 3 then T is 1, so multiplied will give 3.

T×V=7 From previous step we see that T could be 1 or 3.

           Since T×V = 7 it will make sense that T is 1, and therefore V is 7.

T ×V = 7,  S ×T =3, R × S = 15, R × V = ??

1 × 7 = 7,  S ×1 = 3, R × 3 = 15, 5 × 7 = ??

               3 ×1 = 3,  5 × 3 = 15, 5 × 7 = 35

Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.

According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.

Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.

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The angles at which the fences will meet is 27 , 38 ,114 degree.

A triangle is  a polygon with three sides , three angles and three vertices.

It is given that the triangle has sides

1.1 miles * 1.5 miles * 2.2 miles

The law of cosines can be used to calculate the angle

a² = b² + c² -2bc cosA

1.1²  = 1.5² + 2.2² -2 *1.5 *2.2 cosA

A = 27.01 degree

Similarly

b² = c² +a² -2ac cosB

1.5²  = 2.2² +1.1²  -2 * 2.2*1.1 cos B

B = 38.27 degree

By angle sum property

Angle C = 180-38.27-27.01

C = 114.72 degree

Therefore , the angles at which the fences will meet is 27 , 38 ,114 degree.

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Answer:

See attached file for answers and explanation.

Step-by-step explanation:

See attached image.

Answer:

Step-by-step explanation:

One equivalent can be obtain by distributing multiplication with 3 over subtraction 5-2i

3(5-2i) =

3·5 -3·2·i =

15 -6i or -6i +15

To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.

From the information given about the probability, the goal here is to design a simulation for this situation.

In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.

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For every meter there are 3.281 feet. The perimeter of the yard is 188ft. Divide 188 by 3.281 and you get 57.3 (rounded to 1dp). Round that up to the nearest meter and you get 58. So, Mr Smith needs 58 meters of fencing for his yard.

Answer: 0.68 or 13.92

Step-by-step explanation:

If the height is 47 meters, then the height, h, is equal to 47.

[tex]47=73t-5t^2\\\\5t^2 - 73t+47=0[/tex]

Using the quadratic formula,

[tex]t=\frac{-(-73) \pm \sqrt{(-73)^{2}-4(5)(47)}}{2(5)}\\\\\\t=\frac{73 \pm \sqrt{4389}}{10}\\\\\\ t=\frac{73+\sqrt{4389}}{10}, \frac{73-\sqrt{4389}}{10}\\\\\boxed{t \approx 0.68, 13.92}[/tex]

Answer:

Law of sines

Explanation:

The law of sines states that the ratios of the sines of angles and their opposite sides are equal for all angles inside a triangle.

Step-by-step explanation:

hope you can understand

Answer:

(n/m) - p

Step-by-step explanation:

Image attached

Answer:

First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

Step-by-step explanation:

This question deals with Slope of a line.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet

Thus, slope =  6/4 = 3/2 ≈ 1.5

For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet

Thus, slope=   10/6 = 5/3 ≈ 1.66

Thus,

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

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Answer:

$5.50

Step-by-step explanation:

For one water bottle you divide the 55 dollars by 10

55/10= 5.5

Answer:

$5.50

Step-by-step explanation:

We must divide to solve so lets do that now :)

55/10 = 5.50

Each bottle will cost 5 dollars and 50 cents :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

Step-by-step explanation:

Comment

This is an arithmetic series. It has the following givens.

a = 27     The first term

d = - 2       The difference between one term and the one behind it.

n = quite small

Tn = a + (n - 1)*d

tn = 27 - 2n  + 2

tn = 29 - 2n

Answer:

18.18%

Step-by-step explanation:

(65000-55000)/55000×100

From calculations, we can say that the given tiles will not fit together perfectly.

If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.

Expression for the measure of the interior angle of a polygon,

Interior angle of a polygon = [(n - 2) * 180]/n

Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°

Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°

Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°

To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°

Sum of all interior angles = 108° + 120° + 135° = 363°

Therefore, given tiles will not fit together perfectly.

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By the binomial theorem,

[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]

where

[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]

is the so-called binomial coefficient.

The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have

[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]

but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]

Answer:

C

Step-by-step explanation:

The horizontal line, y=2, is solid and shaded above, so it represents

[tex]y \geqslant 2[/tex]

The slanted line, y=x is dashed and shaded below, so it represents y<x.

Answer

Answer is A

Step-by-step explanation:

Answer:

1.5kg

Step-by-step explanation:

The mean for the packages on day 1 will be:

= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8

= 47/8

= 5.875

The mean for day 2 will be:

= (47 + 12)/8

= 59/8

= 7.375

The increase in mean:

= 7.375 - 5.875

= 1.5

Answer:

In the circle, the measure of the arc AC is 21°.

Step-by-step explanation:

Concept: We can use the Inscribed Angle theorem to get the measure of AC.

Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.

Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

3x - 1.5 = 0.5(3x + 9)

6x - 3 = 3x + 9

3x = 12

x = 4

Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,

intercepted arc AC is 21°.

Hence the intercepted arc AC is 21°.

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The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

As per the law of cosine, the measure of angle x can be written as,

[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]

Hence, the value of x is 117.8°. thus, the correct option is A.

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Answer:

460

Step-by-step explanation:

if you look at the values you'll notice the next month is just half their value

7360 / 2 = 3680

3680 / 2 = 1840

1840 / 2 = 920

so

920 / 2 = 460 which should be month 5

The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.

We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:

Plug in the values into the equation of the function

0 = -16t² + 400

Solve for t

0 - 400 = -16t²

-400 = -16t²

-400/-16 = t²

400/16 = t²

√(400/16) = t

20/4 = t

5 = t

t = 5

The number of seconds it takes is: 5 seconds.

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Answer:

Step-by-step explanation:

The diagonal of a square is given as, √2 × side. Rearranging this formula to calculate the side of the square, we get, side = diagonal/√2 = (√2 × diagonal)/2 . Thus, the perimeter of the square can be calculated using the formula, P = 2√2 × diagonal.

Diagonal = 5 * 2 = 10

P = 2√2 * 10

P = 20√2

Answer:

[tex]3x-1[/tex]

Step-by-step explanation:

The formula to find the area of a triangle:

[tex]A = \frac{bh}{2}[/tex]

Here, [tex]A[/tex] is the area, [tex]b[/tex] is the base and [tex]h[/tex] is the height.

However, we are looking for height, so let's rearrange the equation for [tex]h[/tex]:

[tex]A = \frac{bh}{2}\\2A = bh\\h = \frac{2A}{b}[/tex]

Now we know the formula to find the height, let's do so:

[tex]h = \frac{2(18x-6)}{12}\\\\h = \frac{36x-12}{12}\\\\h = 3x - 1[/tex]

Therefore, our final answer is [tex]3x-1[/tex].