The sum of three numbers is 100. The second number is 2 times the third. The third number is 8 less than the first. What are the numbers?

The expression, the  fifth term of the binomial expansion is y^4

Binomial expansion is a means of expanding expressions into terms

Given the expression (x+y)^4, according to the theorem, as the power of x is decreasing, the power of y will be increasing up till the power of the expression.

Expand (x+y)^4

(x+y)^4 = x^4y^0 + x^3y^1 + x^2y^2 + xy^3 + x^0y^4

Include the coefficients according to the Pascal triangle to have:

(x+y)^4 = x^4y^0 + 4x^3y^1 + 6x^2y^2 + 4xy^3 + x^0y^4

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

From the expression, the  fifth term of the binomial expansion is y^4

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Answer:

h = -14

Step-by-step explanation:

-7πh = 98π

⇔ -7h = 98   (Just Divide both sides by π)

⇔ h = 98 ÷ (-7) = -14

Hi :)

We should find h. All it takes is some algebra skills ^•^

First off, you can see than we have π on both sides. So, why not divide both sides by π and get it out of the way?

We end up with

[tex]\boldsymbol{-7h=98}[/tex]

Super! Now all we have to do is divide both sides by -7

We end up with

[tex]\boldsymbol{h=-14}[/tex]

[tex]\tt{Learn~More;Work~Harder}[/tex]

:)

He will be left no money after buying 25 copies because he has 1900 rupees less.

Given that Usman buys 8 books that cost Rs. 120/ each, he will be left Rs. 140.

The cost of 1 books is Rs 120.

The cost of 8 book is 120×8=960.

The cost of 25 books is 120×25=3000

To find the money usman will left with him is the difference between the total money and the cost of 25 books.

Total money=960+140=1100

money left=Total money -cost of 25 books

money left=1100-3000

Usman have less money to buy 25 books. He has 1900 rupees less to buy 25 books.

Hence, Usman does leave any money with even he has less money to buy 25 books

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1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle. This can obtained by using the formula of Area of a Triangle with 2 Sides and Included Angle.

Area of a triangle is obtained using the formula of Area of a Triangle with 2 Sides and Included Angle.

If in a triangle ΔABC,

Here it is given that,

67 feet and 48 feet are the sides of the triangular space and angle 72° is the included angle.

By using the formula of Area of a Triangle with 2 Sides and Included Angle,

Area of the cheetah area = 1/2 × bc × sin(A)

Area of the cheetah area = 1/2 × (67)(48) × sin(72°)

sin(72°) = 0.951056516

Area of the cheetah area = 1608 × 0.951056516

Area of the cheetah area = 1529.29888 ≈ 1529.3 square unit

Hence 1529.3 square unit is the area of the cheetah area at a zoo is designed in a triangular fashion, surrounded on all three sides by sidewalks, given that the property has 67 feet of frontage on one sidewalk, and 48 feet of frontage on another; these two sidewalks intersect at a 72° angle.

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The pair of words that describe the given system of equations is: consistent and dependent.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

It demonstrates the equality of the relationship between the expressions written on the left and the right.

Given equations:

3y=9x-6

2y-6x=4

The first equation can be simplified and written as: y=3x-2

Similarly, the second equation can be written as: y-3x=2

It can be seen that the two equations are the same. Thus, the given system of equations is consistent and dependent.

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Answer: Interior Angle

Step-by-step explanation:

The angle BAD is fully enclosed, it is on the inside

The magnitude of -1-5i is √26.

Given the complex expression; -1 - 5i

To find the magnitude, we use the formula;

| a+bi | = √[ a² + b² ]

| a+bi | = √[ a² + b² ]

| -1-5i | = √[ (-1)² + (-5)² ]

| -1-5i | = √[ 1 + 25 ]

| -1-5i | = √26

Therefore, the magnitude of -1-5i is √26.

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sorry its a little messy!! not good at drawing with a finger haha. all you need to do is follow pedmas and isolate, knowing that a right angle=90°. hope this helps!<3<3

Answer: [tex]\Large\boxed{x=12}[/tex]

Step-by-step explanation:

Given information

∠1 = x + 42°

∠2 = 3x°

Total Angle = 90° (Right Angle)

Derived formula from the given information

∠1 + ∠2 = Total Angle

Substitute values into the given formula

(x + 42) + (3x) = (90)

Combine like terms

x + 3x + 42 = 90

4x + 42 = 90

Subtract 42 on both sides

4x + 42 - 42 = 90 - 42

4x = 48

Divide 4 on both sides

4x / 4 = 48 / 4

[tex]\Large\boxed{x=12}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

since there are 365 days in a year, so 180 days is really just 180/365 of a year, so

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1295\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\to \frac{180}{365}\dotfill &\frac{36}{73} \end{cases} \\\\\\ I = (1295)(0.07)(\frac{36}{73})\implies I\approx 44.7[/tex]

Step-by-step explanation:

if we are taking in terms of domain.. is d set of number that we can put to the function with get division by zero .. squaroot of negative number,log of zero e.t.c

A) p(x)/m(x)= 1/squaroot(x) ÷ x²-4 which we know that x²-4 must not be equal to zero

because if is equal to zero we will have division by zero, which have contradicted the hypothesis of law of domain

x²-4 =! 0

(x-2)(x+2)=!0

x=!2 or x=!-2 because if is equal to that it's has contradicted d hypothesis

the answer is all real number except -2 and -

2

B)p(m(x))=p(x²-4) =1/squaroot of x²-4

note they are two things involve we must not get division by zero and root of negative number

we have all real number expect from -2 to 2

C)m(p(x))=m(1/root of (x))=(1/root of (x))²_4)

we have 1/x-4

so the answer is all real number expect zero

Answer:

6

Step-by-step explanation:

Solve for y:

[tex]y/8=9/12[/tex]

Multiply both sides by 8:

[tex]y=72/12[/tex]

Solve fraction

[tex]y=6[/tex]

Answer: Ans. Option c As the price of basket in England is $15, which is less than the world

The volume of a cylinder is 197.82 yards³ and the surface area of ​​a cylinder is 188.4 yards².

Given a cylinder has a height of 7 yards and a radius of 3 yards.

(a) We first find the volume of the cylinder using the formula V=πr²h, where π=3.14, r=3 yards and h=7 yards.

Substitute the values ​​in the formula and we get

V=π(3)²×7

V=3.14×9×7

V = 197.82 yards³

(b) We will now find the surface area of ​​the cylinder using the formula S=2πr²+2πrh, where π=3.14, r=3 yards and h=7 yards.

Substitute the values ​​in the formula, we get

S=2π(3)²+2π×3×7

S=2×3.14×9+2×3.14×21

S=56.52+131.88

S = 188.4 square yards

Therefore, the volume and area of ​​a cylinder with a height of 7 meters and a radius of 3 meters is 197.82yards³ and 188.4 yards².

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Circle A has center of (6, 7) and a radius of 4, and circle B has a center of (2, 4) and a radius of 16. Now, in order to show that circle A is similar to circle B, we will have to dilate circle A by a scale factor of 4. We can use transformations like dilation and translation to make two circles similar.

Given Information:

For circle A,

Center, C1(x, y) = (6, 7)

Radius, r1 = 4

For circle B,

Center, C2(x, y) = (2, 4)

Radius, r2 = 16

Showing the Two Circles Similar

Now, to make circles A and B similar, we will have to make their centers coincide. It can be done by following the steps listed below:

Hence, we can now see that circle A is similar to circle B.

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Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the values of the parameters are given by:

p = 0.3, n = 6.

The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595

0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.

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Compute the first two derivative.

[tex]f(x) = x \sqrt{16 - x^2} = x (16 - x^2)^{1/2}[/tex]

[tex]f'(x) = x \dfrac{d}{dx} (16 - x^2)^{1/2} + (16 - x^2)^{1/2} \dfrac{d}{dx} x \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} \dfrac{d}{dx} (16-x^2) + (16 - x^2)^{1/2} \\\\ ~~~~ = \dfrac x2 (16 - x^2)^{-1/2} (-2x) + (16 - x^2)^{1/2} \\\\ ~~~~ = (16-x^2)^{-1/2} \left(-x^2 + (16 - x^2)\right) \\\\ ~~~~ = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}}[/tex]

[tex]f''(x) = \dfrac{(16-x^2)^{1/2} \frac d{dx} (16-2x^2) - (16-2x^2) \frac{d}{dx} (16-x^2)^{1/2}}{\left((16-x^2)^{1/2}\right)^2} \\\\ ~~~~ = \dfrac{(16-x^2)^{1/2} (-4x) - (8-x^2) (16 - x^2)^{-1/2} \frac{d}{dx} (16-x^2)}{16 - x^2} \\\\ ~~~~ = \dfrac{-4x (16-x^2) - (8-x^2) (-2x)}{(16 - x^2)^{3/2}} \\\\ ~~~~ = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}}[/tex]

Take note of the domain of [tex]f(x)[/tex]. We must have [tex]16-x^2\ge0[/tex] for the square root to be defined, so

[tex]16 - x^2 \ge 0 \implies x^2 \le 16 \implies |x| \le 4[/tex]

and [tex]f(x)[/tex] exists only for [tex]-4 \le x \le 4[/tex].

Intercepts

Set [tex]x=0[/tex] to find the [tex]y[/tex]-intercepts. The only one is (0, 0), since

[tex]f(0) = 0 \sqrt{16-0^2} = 0[/tex]

The first intercept you listed is not a valid intercept. One or both coordinates must be 0.

Set [tex]f(x)=0[/tex] and solve for [tex]x[/tex] to find [tex]x[/tex]-intercepts. We already found (0, 0); there are two others at (-4, 0) and (4, 0).

[tex]f(x) = x \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } \sqrt{16 - x^2} = 0 \\\\ x = 0 \text{ or } 16 - x^2 = 0 \\\\ x = 0 \text{ or } x^2 = 16 \\\\ x = 0 \text{ or } x = \pm4[/tex]

The instructions say to list these in order from smallest to largest by [tex]x[/tex]-coordinate first, then by [tex]y[/tex]-coordinate. So the proper order of the intercepts would be (-4, 0), (0, 0), and (4, 0).

Relative minima/maxima

Find the critical points. We have [tex]f'(x) = 0[/tex] when

[tex]f'(x) = \dfrac{16 - 2x^2}{(16 - x^2)^{1/2}} = 0 \\\\ 16 - 2x^2 = 0 \\\\ x^2 = 8 \\\\ x = \pm2\sqrt2 \approx \pm 2.83[/tex]

and [tex]f'(x)[/tex] is undefined when

[tex](16 - x^2)^{1/2} = 0 \\\\ 16 - x^2 = 0 \\\\ x^2 = 16 \\\\ x = \pm4[/tex]

Check the sign of the second derivative at the first two critical points.

[tex]f''(-2\sqrt2) = 4 > 0 \implies \text{rel. min. at }  f(-2\sqrt2) = -8[/tex]

[tex]f''(2\sqrt2) = -4 < 0 \implies \text{rel. max. at } f(2\sqrt2) = 8[/tex]

For posterity, we should also check the value of [tex]f(x)[/tex] at the endpoints of the domain.

[tex]f(-4) = f(4) = 0[/tex]

So [tex]f(x)[/tex] has a relative minimum at (-2.83, -8) and a relative maximum at (2.83, 8).

Inflection points

We have [tex]f''(x) = 0[/tex] for

[tex]f''(x) = \dfrac{2x^3-48x}{(16 - x^2)^{3/2}} = 0 \\\\ 2x^3 - 48x = 0 \\\\ 2x (x^2 - 24) = 0 \\\\ 2x = 0 \text{ or } x^2 - 24 = 0 \\\\ x = 0 \text{ or } x = \pm2\sqrt6\approx\pm4.90[/tex]

The two non-zero solutions fall outside the domain, so the only inflection point is (0, 0).

Could you try reposting the question clearly

Answer:

plane HNA, HMB, ANG ...

Step-by-step explanation:

Any combination of three points on plane K will work unless all three are on the same line.

The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].

In this problem we have a function in implicit form, that is, an expression of the form: f(x, y, c) = 0, where c is a constant. Then, we should apply implicit differentiation twice to determine the second derivative of the function:

Original expression

x · y - 1 = 2 · x + y²

First derivative

y + x · y' = 2 + 2 · y · y'

(x - 2 · y) · y' = 2 - y

y' = (2 - y) / (x - 2 · y)

Second derivative

y' + y' + x · y'' = 2 · (y')² + 2 · y · y''

2 · y' - 2 · (y')² = (2 · y - x) · y''

y'' = 2 · [y' - (y')²] / (2 · y - x)

y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]]

The second derivative of the implicit function x · y - 1 = 2 · x + y² is equal to y'' = [2 / (2 · y - x)] · [(2 - y) / (x - 2 · y)] · [1 - [(2 - y) / (x - 2 · y)]].

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The size of the second application given the size of the first application and the expression ( x - 3.45 mb) for the size of the second application is 293.55 MB.

Let

For instance,

if the size of the first application is 297 MB

Size of the second application= x - 3.45 mb

= 297 MB - 3.45 MB

= 293.55 MB

Therefore, the size of the second application given the size of the first application and the expression for the size of the second application is 293.55 MB

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Answer:

350

Step-by-step explanation:

Let the number of adult tickets be x, then the number of student tickets sold would be (x–54).

We now have

x+(x–54)=646

2x=700

x=350

Therefore, 350 adult tickets were sold.

The three dimensional shape formed by the net shown below is a cube.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

The cube is a a three-dimensional solid object bounded by six square faces.

The three dimensional shape formed by the net shown below is a cube.

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The Elements can be defined as a mathematical treatise which comprises 13 books that are attributed to the ancient Greek mathematician who lived in Alexandria, Ptolemaic Egypt c. 300 BC and called Euclid.

Basically, the Elements is a collection of the following geometric knowledge and observations:

Based on my experiences so far, an approach to geometry which I prefer is Euclidean geometry because it's much easier than analytical geometry.  Also, an approach that is easier to extend beyond two-dimensions is Euclidean geometry because it can be extended to three-dimension.

A situation in which one approach to geometry would prove to be more beneficial than the other is when dealing with flat surfaces. In Euclidean geometry, a correspondence can be established between geometric curves and algebraic equations.

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The number of three-digit positive integers that have three different digits and at least one prime digit are 7960.

The only two components in prime numbers are 1 and the number itself.

Any whole number greater than one is a prime number.

It has exactly two factors—1 and the actual number.

There is just one 2-digit even prime number.

Every pair of prime numbers is always a co-prime.

The product of prime numbers can be used to represent any number.

Three-digit positive integers that have three different digits and at least one prime digit = 3!*4!*10*9 = 7960

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Answer:

x = 1.086

Step-by-step explanation:

Formula

6^x = 7                     Take the log of both sides.

Solution

log 6^x = log 7         Bring the power down You are now dealing with log 6

x * log 6 = log 7        Divide by log 6

x = log 7/log 6

x = .8451 / .7782       Divide

Answer

x = 1.086

Answer:

  B.  y = x +3

Step-by-step explanation:

The fastest way to find this answer is to substitute offered values of x and y into the given equations to see if they are true.

Using the first line in the table, (x, y) = (2, 5), we have ...

  A  5 = 2(2) . . . . false

  B  5 = 2 +3 . . . . true

  C  5 = 3(2) . . . . false

  D  5 = 2 +1 . . . . false

__

Additional comment

Checking answer choices against the problem statement is one of many possible strategies for answering multiple-choice questions.

Answer:

Below

Step-by-step explanation:

Using the given law of cosines    c = 26   a = 50   b = 29

      and cos c   is  cos x  

26^2 = 50^2 + 29^2 - 2(50)(29) cos x

-2665 = -2900 cos x

cos x = 2665/2900

x = arc cos ( 2665/2900) = 23.2°

The probability that a randomly selected member did not volunteer for the recent activity is 19/43.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability that a randomly selected member did not volunteer for the recent activity = 1 - ratio of randomly selected members that volunteered

1 - 24/43

(43/43) - (24/43) = 19/43

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