Solve for x: 12x2 – 6 (a2 + b2)x + 3a2b2 = 0

The unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

Unit rate is the rate of a quantity in terms of another quantity per unit.

Unit rate(books per hour) = Number of books / Number of hours

= 1/4 ÷ 1/3

= 1/4 × 3/1

= (1×3) / (4×1)

= 3/4 books per hour

Therefore, the unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

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Answer:

the answer is 1,2,4,5 and 7.

Answer: The answer is A,B,D,E,G

Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.

Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

Let the dimension of the rectangle be x and y m.

According to the given question.

The area of the rectangle is 1728 square meter.

⇒ x × y = 1728

⇒ x = 1728/y

Since, the perimeter of the rectangle is the sum of the length of its boundary.

Therefore,

Perimeter of the recatngle with dimensions x and y is given by

Perimeter of the rectangle, P = 2(x + y)

⇒ P = 2(1728/y + y)

⇒ P = 3456/y + 2y

Differentiate the above equation with respect to y

⇒ [tex]P^{'} = -\frac{3456}{y^{2} } + 2[/tex]

For the minimum(small) perimeter equate the above equation to 0.

⇒ [tex]-\frac{3456}{y^{2} } + 2 = 0[/tex]

⇒ [tex]2y^{2} =3456[/tex]

⇒ [tex]y^{2} = \frac{3456}{2}[/tex]

⇒ y^2 = 1728

⇒ y = √1728

⇒ y = 41.56 m

Therefore,

x = 1728/41.56

⇒ x = 41.57 m

Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

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The power output is  = 5W

Correct option is B.

Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power

Power is characterized as the rate at which a thing performs labor.

P = W/T ..... (1)

Work is calculated as the product of force applied to an item and the distance that object has traveled.

W = F.s

When we plug this value into the equation above, we get:

P = (F. s)/t

where,

power = P =?W

F = 10N Force Exercised

s = Displacement = 400cm = 4m  (1 meter = 100 centimeters).

t = Time required = 8s

Using the values in the equation above, we obtain

P = (10 x 4)/8

P = 5W

Hence, the correct option is Option b.

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I understand that the question you are looking for is :

Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.

What is his power output? (Power: P = W/t)

a. 1.25 W

b. 5 W

c. 40 W

d.500 W

Answer:

Step-by-step explanation:

Comment

The sum of the remote interior angles = The exterior angle not connected to them

What that means is that

<C + <D = <KEB

Givens

<C = 60

<KED = <C + <D

Solution and answer

<KED = <C + <D                      Substitute the givens into this equation

100 = 60 + <D                         Turn this around

<60 + <D = <100                     Answer first equation

Subtract 60 from both sides

<60-<60 + <D = <100 - 60

<D = <40                                   Answer second Equation

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

Given:

▪ [tex]\longrightarrow \sf{KED = 100^\circ}[/tex]

▪ [tex]\longrightarrow \sf{\angle ECD = 60^\circ}[/tex]

[tex]\leadsto[/tex] According to the triangle angle sum theorem, the sum of interior angles of a triangle is 180°.

[tex]\leadsto[/tex] We can find the value of ∠E if we know the sum of two supplementary angles is equal to 180°

[tex]\longrightarrow \sf{m \angle E+ m \angle K=180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E+ 100^\circ =180^\circ}[/tex]

[tex]\longrightarrow \sf{m \angle E= 80^\circ}[/tex]

As we find the value of ∠E, we can replace it in the initial formula. [tex]\downarrow[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex]\bm{m \angle C + m \angle \boxed{\bm D} = m \angle \boxed{\bm E}}[/tex]

[tex]\bm{m \angle D= \boxed{\bm{ 40^\circ}}}[/tex]

Answer:

B

Step-by-step explanation:

because i said so

The probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5 is 0.0494.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Probability of an event P(E) = Number of favourable outcomes/Total number of outcomes.

Calculation for the given condition;

Either 1 or 3 must be present if a given integer is odd and smaller than 5.

The likelihood that it was picked from a set of nine numbers is (2/9).

The probability that the first integer is 1 is 50/50.

If it is and their combined number is less to 5, the second number will either be 1, 2, or 3.

The likelihood that it was picked out of the nine numbers is (3/9).

Additionally, there is a 50/50 probability that the first digit will be 3.

A second number is 1 if it is and the sum would be less than 5.

It was selected with a 1 in 9 chance of being one of the other 8 numbers.

The total probability is;

= (2/9)  times  [ (0.5 x 3/9)  +  (0.5 x 1/9) ]

= (2/9)  times  [ (1.5/9)  +  (0.5/9) ]

= (2/9)  times  [ 2/9 ]  =  4/81

= 0.0494

Therefore,  the probability that the sum of the two numbers malik picks is less than 5 is 0.0494.

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Answer:

See image

Step-by-step explanation:

Plato

Answer:

Rs.11,111.11 (2 d.p.)

Step-by-step explanation:

The original price of the mobile is 100% of the price.

Therefore, the price of the mobile after a discount of 10% is 90% of the original price.

Let x be the original price.

If the price of the mobile after the discount is Rs.10000 then:

⇒ 90% of x = Rs.10000

⇒ 0.9x = 10000

⇒ x = 10000 ÷ 0.9

⇒ x = 11111.11  (2 d.p.)

M.P. =Rs 11111.1111

Answer:

Solution Given:

Selling price (S.P.) = Rs 10,000.

Discount =10%

Marked Price (M.P.)=?

we have

M.P. = S.P. + discount% of M.P.

keeping M.P. on same side

M.P. - discount% of M.P=S.P.

substituting value

M.P. - 10% of M.P.= Rs 10,000

taking common M.P.

M.P.(1-10%)=Rs. 10,000

we know that %=1/100

M.P.(1-10/100)=Rs 10,000

(9/10)M.P.= Rs 10,000

M.P.= Rs 10,000*10/9

M.P.=Rs11111.1111

The complete proofs are:

Proof 1

Proof 2

Proof 1

Lines a & b and c and d are given as parallel lines.

So, we have

a || b; c || d ⇒ Given

From the question, we have:

∠5 is supplementary to ∠4

So, we have

∠5 + ∠4 = 180

This is so because supplementary angles add up to 180

Corresponding angles are equal.

So, we have:

∠2 = ∠4

By the substituting ∠2 for ∠4 in ∠5 + ∠4 = 180, we have

∠5 + ∠2 = 180

Hence, angles ∠5 and ∠2 are supplementary angles

Proof 2

Line BD bisects angle ABC; lines AD & BC and AB & CD are given as parallel lines.

So, we have

BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given

From the question, we have:

∠3 ≅ ∠4 ⇒ Definition of congruent angles

∠1 ≅ ∠3 ⇒ Definition of corresponding angles

Substitute ∠1 ≅ ∠3 in ∠3 ≅ ∠4

∠1 ≅ ∠4

Hence, the angles 1 and 4 are congruent

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Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Reference angle (∅) = 60

Adjacent = 4√3

Opposite = ?

tan 60 = opp/adj

tan 60 = Opp/4√3

√3 = opp/4√3

Opposite = √3 × 4√3

Opposite = 12

Reference angle (∅) = 60

Adjacent = 4√3

Hypotenuse = ?

cos 60 = adj/hyp

cos 60 = 4√3/hyp

hyp = 4√3/cos 60

hyp = 4√3/1/2

hyp = 4√3 × 2

hyp = 8√3

Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

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By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

According to linear algebra, a point lies in a line segment if its vector is a multiple of the vector that generates the line segment itself, that is:

AB = k · AP        (1)

The vector that generates the line segment is:

AB = (2, 6) - (- 2, 3)

AB = (4, 3)

And the vectors related to each point are:

Case A

AP = (- 2, 12) - (- 2, 3)

AP = (0, 9)

Case B

AP = (6, 12) - (- 2, 3)

AP = (8, 9)

Case C

AP = (- 6, 0) - (- 2, 3)

AP = (- 4, - 3)

Case D

AP = (- 6, 6) - (- 2, 3)

AP = (- 4, 3)

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

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Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

The linear function of best fit for the information on the graph is:

f(x) = 200x + 100.

A linear function is modeled by:

y = mx + b

In which:

The function on the graph goes through points (3,700) and (4,900), that is, when x changes by 1, y changes by 200, which means that the slope is of 200 and the function is:

f(x) = 200x + b.

When x = 3, f(x) = 700, hence we use it to find b.

700 = 200(3) + b

b = 100.

Hence the function is:

f(x) = 200x + 100.

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The area of a rectangle is the amount of space it would cover on a 2-Dimensional plane. The required value of the width is 25 feet.

A rectangle is a plane shape with equal opposite sides. Its area can be determined by;

Area of a rectangle = length x width

Considering the given question, let the length of the plot be represented by l and its width as w. Given that the width of the plot should be longer than its length by 5, then we have;

w = l + 5

But,

Area of the plot = length x width

500 = l x (l + 5)

       = [tex]l^{2}[/tex] + 5l

This implies that,

500 = [tex]l^{2}[/tex] + 5l

[tex]l^{2}[/tex] + 5l - 500 = 0

Applying the quadratic formula, we have;

l = (-b  ± [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a

a = 1, b = 5, c = -500

= (-5  ±  [tex]\sqrt{5^{2} - (4*1*-500)}[/tex]/ 2

 = (-5  ± 45) / 2

l =   (40) / 2 OR l =  (-50) / 2

l = 20 OR l = - 25.5

So that,

l = 20

Therefore, the length of the plot is 20 feet.

Thus the width of the plot can be determined as;

w = l + 5

   = 20 + 5

w = 25

The width of the plot is 25 feet.

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Answer:

So, having "hold-out" data allows you to have a nonpartisan set of data (so to speak) for you to refer to later, once you have made use of the "train" and "test" sets. That way you can make a fair assessment as to the difference between the new and old ('hold-out") sets.

Or if you need to repeat the experiment or model again - then you can refer to the "hold out data"

Using the normal distribution, it is found that:

a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.

b. 5.7% of male sailors requires custom uniform pants.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 32.6, \sigma = 1.3[/tex]

For item a, the percentile is the p-value of Z when X = 34.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (34.1 - 32.6)/1.3

Z = 1.15

Z = 1.15 has a p-value of 0.875.

Hence 87.5th percentile.

For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:

X = 36:

Z = (36 - 32.6)/1.3

Z = 2.62

Z = 2.62 has a p-value of 0.996.

X = 30:

Z = (30 - 32.6)/1.3

Z = -2

Z = -2 has a p-value of 0.023.

0.996 - 0.023 = 0.943.

Hence the proportion who requires an special order is:

1 - 0.943 = 0.057.

5.7% of male sailors requires custom uniform pants.

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Based on the orbital period of the planet in earth years, and the distance it is rotating, the mass of the star that the planet is orbiting is 3 solar masses.

Because the sun is so heavy, it needed to have a special unit that could adequately reflect this mass.

Solar masses was the term that scientists came up with. In terms of the Earth's mass, a single solar mass means that the body is 333,000 times the mass of the Earth.

When given the orbital period of a planet, and the distance it is orbiting around a sun, you can find the solar mass by the formula:

= Distance planet is rotating³ - Orbital period²

Solving gives:

= 1.2³ / 0.76²

= 2.99

= 3 solar masses

In conclusion the mass of the star is 3 solar masses

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Answer:

3 solar masses

Step-by-step explanation:

just did it and got it right

The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).

The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.

Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].

[tex]$\mathrm{y}=x^{2} / 8[/tex]

General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]

where (a, b) exists the coordinates of the vertex.

For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]

The vertex of the given parabola exists at (0, 0).

Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).

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Answer:

[tex]x = 3.5[/tex]

[tex]y\approx1.666666667[/tex]

Step-by-step explanation:

To solve simultaneous equations, at least one of our variables must have the same coefficient. We can easily multiply the first equation by 4 to get 12y on both sides, so let's do that:

[tex]8x + 12y = 8[/tex]

No let's subtract the second equation from the first equation to get the third equation:

[tex]2x = 7[/tex]

Solve:

[tex]x = 3.5[/tex]

Now, we can substitute this value into one of the original equations - let's use the second one:

[tex]21 + 12y = 1[/tex]

Solve:

[tex]12y = - 20[/tex]

[tex]y = - \frac{ - 20}{12} = \frac{ - 10}{6} = - \frac{5}{3} \approx - 1.66666666667[/tex]

The rate of change for the function on the table is; 15 grapes eaten per minute.

It follows from the complete question that the table given indicates that;

On this note, it is conclusive that the rate of change of the function represented by the table is; 15 grapes eaten per minute.

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Answer:

2 x 3 x 3 x 5 x 5 x 5 x 5

Step-by-step explanation:

see picture

Step-by-step explanation:

....................

The new mixture exists 56.5% peanuts.

The first batch of 9 lb of mixed nuts possesses 40% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 40/100 = 3.6 lb

The second batch of 9 lb of mixed nuts possesses 73% peanuts.

This means the quantity of peanuts exists:

9 [tex]*[/tex] 73/100 = 6.57 lb

The total quantity of peanuts in the mix exists

3.6 lb + 6.57 lb = 10.17 lb

There exist 9 lb + 9 lb = 18 lb of mix.

Therefore, the percent of peanuts in the mix exists:

10.17 / 18 [tex]*[/tex] 100 = 56.5%

The new mixture exists 56.5% peanuts.

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The matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

In this question,

The angle is -π/3 = -60°

Clockwise rotations are denoted by negative numbers.

Matrix for counter-clockwise direction for an angle α is

[tex]\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right][/tex]

Then, matrix for clockwise direction for an angle α

Put α = -α in the above matrix,

⇒ [tex]\left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right][/tex]

Now substitute α = 60°

Then matrix becomes,

⇒ [tex]\left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex]

Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

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Answer: Mean = 23

Step-by-step explanation:

Given information:

35, 40, 12, 16, 25, 10

Given formula:

[tex]Mean~=~\frac{Sum~of~terms}{Number~of~terms}[/tex]

Substitute values into the formula

[tex]Mean~=~\frac{35~+~40~+~12~+~16~+~25~+~10}{6}[/tex]

Combine like terms

[tex]Mean~=~\frac{75~+~28~+~35}{6}[/tex]

[tex]Mean~=~\frac{103~+~35}{6}[/tex]

[tex]Mean~=~\frac{138}{6}[/tex]

Simplify the fraction

[tex]\Large\boxed{Mean=23}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

51.617

Step-by-step explanation:

tythe answer is 51.617 hope it helps

Explanation: The thousandths place is 51.6172 (Underlined is the thousandths) and since 2 is closest to zero we get an answer of 51.617.

Answer: 51.617

:)

Answer: $200

Step-by-step explanation:

       We will find 66⅔% of $300 to see how much Jay received. A percent divided by 100 becomes a decimal.

               66⅔% / 100 ≈ 0.667

               0.667 * $300 = $200

Answer:

6

Step-by-step explanation:

Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.

[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]

The length of AC is simply x, therefore 6