Simplify.
2[(8 ÷ 4)-(-5)] + 6

Answer:

81

Step-by-step explanation:

If a number is divisible by 11, then you can make those numbers by multiplying 11 by any number. Like 33 is divisible by 11 because 3×11 is 33.

Of course, 33 is too small, we are looking for 3-digit numbers...

see image.

Answer:

y = - [tex]\frac{1}{3}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, 4) ← 2 points on the line

m = [tex]\frac{4-5}{3-0}[/tex] = [tex]\frac{-1}{3}[/tex] = - [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = - [tex]\frac{1}{3}[/tex] x + 5 ← equation of line

The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]

The correct simplification of 8x2(5x 2x2 − 3).

[tex]8x^{2} (5x+2x^{2+1} -3)=8*2x^{2+2} -8*3x^{2}[/tex]

                                [tex]=40x^{3} +16x^{4} -24x^{2}[/tex]

Rearranging the above expression in descending order of power, we get:[tex]16x^{4} +40x^{3} -24x^{2}[/tex]

The correct simplification of 8x2(5x 2x2 − 3) is [tex]16x^{4} +40x^{3} -24x^{2}[/tex]

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Answer:

31. (98,765 x 9) + 3 = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2

42.  1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

hope this helps

Answer:

see the step-by-step explanation

Step-by-step explanation:

31. (98,765 x 9) + 3 = = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41.3+9+27+81 +243 = 3(243-1)/2

42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

Answer:  [tex]h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6[/tex]

Work Shown:

[tex]h(\text{x}) = f(\text{x}) - g(\text{x})\\\\h(\text{x}) = ( 8\text{x}^2 - 2\text{x} + 3) - ( 12\text{x}^2 + 4\text{x} - 3 )\\\\h(\text{x}) = 8\text{x}^2 - 2\text{x} + 3 - 12\text{x}^2 - 4\text{x} + 3 \\\\h(\text{x}) = (8\text{x}^2-12\text{x}^2) + (- 2\text{x} - 4\text{x}) + (3 + 3) \\\\h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6 \\\\[/tex]

The probability for at least 1 page is 0.667 .

Probability is the department of arithmetic concerning numerical descriptions of the way likely an event is to occur, or how probable it is that a proposition is actual. The probability of an event is a number between 0 and 1, where, roughly speaking, zero shows the impossibility of the event, and 1 suggests truth.

Possibility = the wide variety of methods of achieving success. The whole wide variety of possible outcomes. As an example, the opportunity of flipping a coin and its being heads is ½ because there's 1 way of having a head and the total quantity of viable outcomes is 2 (a head or tail). We write P(heads) = ½.

The form opportunity is from old French probability (14 c.) and at once from Latin probabilities (nominative probabilitas) "credibility, possibility," from probabilistic (see likely). The mathematical sense of the time period is from 1718.

As there's an average of 1 misprint in line with the web page, the possibility of a minimum of 5 misprints is 1 - P(0, 1, 2, 3, or 4 misprints)

P(0) = e-1/0!

P(1) = e-1/1!

P(2) = e -1/2!

P(3) = e-1/3!

P(4) = e-1/4!  

P(0, 1, 2, 3, or 4 misprints) = e-1(1 + 1 + half of + 1/6 + 1/24) = 2 17/24 e-1 = .99634

Then, P(5 or more misprints) is 1 - .99634 = .00366

Then, the P(at the least 1 page in a 300-page ebook has at least 5 misprints) = 1 - P(0 pages have at least 5 misprints).

P(0 pages have at the least 5 misprints) = P(300 of 300 pages have 0, 1, 2, 3, or 4 misprints) =.99634 300

(you could view this as C(300, 300) p300 in case you desire) = 0.332881690573629

Then, P(1 or greater pages have at least 5 misprints) = 1 - 0.332881690573629 = 0.667118309426371

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The function f(x) = ∛x - 3 is positive at the interval (3, oo)

The function is given as:

f(x) = ∛x - 3

The function is positive when the function value is greater than 0

This is represented as:

f(x) > 0

So, we have the following inequality expression

∛x - 3 > 0

Take the cube of both sides

x - 3 > 0

Add 3 to both sides

x > 3

Express as an interval notation

(3, oo)

Hence, the function f(x) = ∛x - 3 is positive at the interval (3, oo)

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Answer:

7/6π, 1/6π

Step-by-step explanation:

We know that tan is sine/cosine, so cot is cosine/sine.

In this case, we know cotθ = √3

As the number is positive, using the unit circle, we now can say that the two solutions are in quadrants I and III.

Taking a look at the unit circle, we can finalize our answer.

Considering the definition of an inequality, the number of people who can go to the amusement park is 3.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "p" the number of people who can go to the amusement park, the inequality that expresses the previous relationship is

$9.75 + $16.25×p ≤$65

Solving:

$16.25×p ≤$65 - $9.75

$16.25×p ≤$55.25

p ≤$55.25÷ $16.25

p≤ 3.4

Finally, the number of people who can go to the amusement park is 3.

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Answer:

m<DCF = 155°

Step-by-step explanation:

m<DCF = m<D + m<E

m<DCF = 72° + 83°

m<DCF = 155°

Answer:g(x)

Step-by-step explanation:1/5 g (x)

Answer:

Step-by-step explanation:

The rational root theorem tells you any rational roots of the expression will be found from the constant and the leading coefficient:

  rational roots = ±{divisor of 25} / {divisor of 3}

The list of divisors in each case is pretty short, so this is ...

  rational roots = ±{1, 5, 25) / {1, 3} = ±{1/3, 1, 5/3, 5, 25/3, 25}

We find the only actual rational root is x = 5/3 when we graph the function.

(Factoring out that root, we find the remaining roots are ±i√5, irrational imaginary values.)

Answer:  [tex]35 cm^2[/tex]

Step-by-step explanation:

Area of trapezium =

2X = 2 + 2 = 4 cm

2Z = 5 + 5 = 10 cm

Y = 5 cm

[tex]\dfrac{ \left( 4+10 \right) }{ 2 } \times 5[/tex]

                 |

                 |--------> 35 [tex]cm^2[/tex]

There are 27720 strings.

Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 = 531,441 ternary strings of length 12.

There are

C(12,3) = 12! / (9! 3!) = 12 * 11 * 10/ 3 * 2 = 220 possible combinations of positions for the three 0s.

Of the 9 remaining positions, there are

C(9,4) = 9! / (5! 4!)

= 9 * 8 * 7 * 6/ (4 * 3 * 2 * 1)

= 126 possible combinations of positions for the four 2s.

The remaining 5 places are, of course, occupied by the five 1s.

So there that contain exactly three 0s, five 1s, and 4 2s are 220 * 126= 27720 such strings.

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The parallel sides AB, PQ, and CD, gives similar triangles, ∆ABD ~ ∆PQD and ∆CDB ~ ∆PQB, from which we have;

[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]

From the given information, we have;

According to the ratio of corresponding sides of similar triangles, we have;

[tex] \frac{x}{z} = \mathbf{\frac{BD}{QD} }[/tex]

[tex] \frac{y}{z} = \frac{BD}{ BQ} [/tex]

Which gives;

[tex] \mathbf{\frac{y}{z}} = \frac{BD }{ BD - Q D} [/tex]

[tex] \frac{z}{y} = \frac{BD - QD }{ BD } = 1 - \frac{Q D }{ BD}[/tex]

QD × x = BD × z

BD × z = (1 - QD/BD) × y = y - (QD × y/BD)

Therefore;

BD × z = y - (QD × y/BD)

BQ × y = y - (QD × y/BD)

BQ × y = y - (z × y/x) = y × (1 - z/x)

(1 - z/x) = BQ

BD × z = y × (1 - z/x)

BD = (y × (1 - z/x))/z

Therefore;

QD × x = y × (1 - z/x)

(BD-BQ) × x = y × (1 - z/x)

(BD-(1 - z/x)) × x = y × (1 - z/x)

BD = (y × (1 - z/x))/x + (1 - z/x)

BQ + QD = (1 - z/x) + (y × (1 - z/x))/x

BD = BQ + QD

(y × (1 - z/x))/x + (1 - z/x) = (y × (1 - z/x))/z

(1 - z/x)×(y/x + 1) =(1 - z/x) × y/z

Dividing both sides by (1 - z/x) gives;

y/x + 1 = y/z

Dividing all through by y gives;

(y/x + 1)/y = (y/z)/y

Therefore;

[tex] \frac{1}{x} + \frac{1}{y}= \frac{1}{z}[/tex]

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Answer:

9.72 lb

Step-by-step explanation:

Yield = the amount or quantity produced or returned.

Given:

To determine how many pounds of eggplant you will be able to use, calculate 81% of the amount of eggplant purchased.

[tex]\begin{aligned}\sf 81\% \: of \: 12 \: lb & = \sf \dfrac{81}{100} \cdot 12\\\\& = \sf \dfrac{81 \cdot 12}{100}\\\\& = \sf \dfrac{972}{100}\\\\& = \sf 9.72\:lb\end{aligned}[/tex]

Therefore, you will be able to use 9.72 lb (nearest hundredth).

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Purchase=12lb

Amount to be used

You will be able to use 9.72pounds

The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].

To find the values of x:

Given equation: [tex](x+7)(x-9)=25[/tex]

Then: [tex]x(x-9)+7(x-9)=25[/tex]

Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]

[tex]x^{2} -9x+7x-63=25[/tex]

Combine like terms:

[tex]x^{2} -2x-63=25[/tex]

Subtract 25 from both sides and obtain:

[tex]x^{2} -2x-88=0[/tex]

Using completing square form:

Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:

[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]

Add 89 to both sides we have:

[tex](x-1)^{2} =89[/tex]

Taking square roots on both sides, obtain:

[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]

Add 1 to both sides we have:

[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]

Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].

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The complete question is given below:

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

[tex]r = \frac{15}{7} [/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{Keep in mind that \boxed{of} means multiplication in mathematics and}\\\large\text{percentages run out of 100.}[/tex]

[tex]\mathsf{3\%\ of\ x = 10}[/tex]

[tex]\mathsf{\dfrac{3}{100}\ of\ x = 10}[/tex]

[tex]\mathsf{\dfrac{3}{100}\times x = 10}[/tex]

[tex]\mathsf{\dfrac{3}{100}x = 10}[/tex]

[tex]\textsf{Find the reciprocal of }\mathsf{\dfrac{3}{100}}\textsf{ and multiply that particular number on both sides.}[/tex]

[tex]\mathsf{\dfrac{3}{100}= \dfrac{100}{3}}[/tex]

[tex]\textsf{So, that means we have multiply by }\mathsf{\dfrac{100}{3}}\textsf{ to both of your sides.}[/tex]

[tex]\mathsf{\dfrac{100}{3}\times\dfrac{3}{100}x = 10\times \dfrac{100}{3}}[/tex]

[tex]\textsf{Cancel out: }\mathsf{\dfrac{100}{3}\times\dfrac{3}{100}}\textsf{ because it gives you 1}[/tex]

[tex]\textsf{Keep: }\mathsf{10\times\dfrac{100}{3}}\textsf{ because it gives you the value of x or simply understanding of}\\\textsf{the \boxed{\mathsf{x-value}}\ .}[/tex]

[tex]\mathsf{x = \dfrac{100}{3}\times10}[/tex]

[tex]\mathsf{x = \dfrac{100}{3}\times\dfrac{10}{1}}[/tex]

[tex]\mathsf{x = \dfrac{100\times10}{3\times1}}[/tex]

[tex]\mathsf{x = \dfrac{1,000}{3}}[/tex]

[tex]\mathsf{x\approx 333 \dfrac{1}{3}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = }\frak{\dfrac{1,000}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 15

Step-by-step explanation:

First step is to find the slope of the line given

y = -x - 2

y = mx + c where m is the slope of the line so the slope of the line is -1

If 2 lines are perpendicular to one another, the product of the slopes is -1 so the slope of the perpendicular line is -1/-1 = 1

y = 1x + c or y = x + c

As the line passes through the coordinate (-5,10), we can substitute the x and y value of the coordinates into the equation

10 = -5 + c

c = 15

So the equation of the line is y = x + 15

Answer:

20 pounds

Step-by-step explanation:

i took the test trust me i got 2 points

Answer:cost(weight)

Step-by-step explanation:

The term "altitude" is the same as "height of a triangle". It is perpendicular to the base. Since we can rotate the triangle to have any side be horizontal, there are effectively 3 possible bases. Hence, there are 3 heights. It all depends how you look at it.

Let h1, h2, and h3 be the three altitudes or heights.

Without loss of generality, we'll focus on the first two heights h1 and h2. Their respective bases are b1 and b2.

If we use b1 as the base, then the area is...

area = 0.5*base*height = 0.5*b1*h1

Similarly, the other base gives the area of:

area = 0.5*b2*h2

------------------------

Since both formulas refer to the same area (because we're working with the same triangle), we can set the expressions equal to one another

0.5*b1*h1 = 0.5*b2*h2

b1*h1 = b2*h2

Let's see what happens when b1 = b2, so,

b1*h1 = b2*h2

b1*h1 = b1*h2

b1h1 - b1h2 = 0

b1(h1 - h2) = 0

b1 = 0 or h1 - h2 = 0

b1 = 0 or h1 = h2

If the bases b1 and b2 were equal, then either those bases must be 0 which isn't possible, or the altitudes must be equal. However, the initial premise is that the heights must be different from one another.

Therefore, the bases b1 and b2 can't be the same length.

We could follow the same steps and logic to conclude that if the altitudes h1 and h3 were different, then the bases b1 and b3 can't be the same. Similarly, we would conclude that b2 and b3 can't be the same. This is where the "without loss of generality" kicks in.

In other words, we only need to focus on one subcase to extend the logic to the other cases, without having to actually do every single step. That would be a bit tedious busywork.

In conclusion, we've shown that if the heights are different, then their respective bases must be different. This leads to wrapping up the proof that we have a scalene triangle.

Side note: I used an indirect proof or proof by contradiction. I assumed that a non-scalene triangle was possible and it led to a contradiction of h1 = h2.

Answer:

$613.04

Step-by-step explanation:

Compound Interest Formula:

   [tex]A = P(1+\frac{r}{n})^{nt}[/tex]

   n = number of compounds

   t = time

   r = interest rate

   P = principle amount (original amount)

   A = final amount

Since it's compounded quarterly, that means there will be 4 compounds per year, so n=4. The interest rate has to be converted to the decimal value, and this is done by simply dividing it by 100 to get r=0.06.

Plug Values into equation:

[tex]A = 300(1+\frac{0.06}{4})^{12*4}[/tex]

Simplify inside parenthesis

[tex]A = 300(1.015)^{48}[/tex]

Calculate exponent

[tex]A \approx 300(2.043478)[/tex]

Multiply values

[tex]A \approx 613.04348[/tex]

Round

[tex]A = 613.04[/tex]

Answer:

[tex] {x}^{4} [/tex]

Step-by-step explanation:

[tex] { {( - x}^{2} )}^{2} = ( - {x}^{2} )( - {x}^{2} ) = {x}^{4} [/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression when simplified is equal to x⁴.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as shown below,

(-x²)²

= (-x × -x)²

Since the product of two negatives is always positive, therefore, we can write,

= -x² × -x²

As per the rule of exponents, the expression can be written as,

= x⁴

Hence, the value of the given expression when simplified is equal to x⁴.

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The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

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The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.

Especially, he has been credited with proving the following five theorems:  a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same;  the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.

In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.

In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a  theorem and is maximum extensively used in the domain of science.

2-1and interval = [4]

since function text is continuous in a given interval. And also

+(4) = 42+4 = 4-1

20 = 6667

$(5/4) = ($145/2

stone-1

= 5.833

simple, f(4) > $(5/2), hence Intermediate

Theorem & applies to the indicated proved.

Now,

= 6 C-1

C-5c +6 = 0

C=2 or c=3

1=3 or

C= 2, 3

<= 2

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

A function should be one - to - one and onto in order to have inverse.

and to find the point on its inverse function we swap the value of x - coordinate and y - coordinate.

like (x , y) becomes (y , x)

The only way we get (y , x) is by taking image of point (x , y) about line : y = x

[tex] \qquad \large \sf {Conclusion} : [/tex]

we can conclude that the graph of a function and it's inverse is symmetric about equation (line) : y = x

The amount of stone in each sidewalk is 3/16

The given parameters are

Stones = 3/4 tons

Side walks = 4

The amount of stone in each sidewalk is calculated using

Amount = Stones/Side walks

Substitute the known values in the above equation

Amount = 3/4 / 4

Evaluate the quotient

Amount = 3/16

Hence, the amount of stone in each sidewalk is 3/16

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330 ways can the instructor choose the first group of four education students.

What is probability in math?

Given:

12 students

3 groups consisting of 4 students.

Mark can't be in the first group.

The combination formula that I used is =  n! / r!(n-r)!

where: n = number of choices ; r = number of people to be chosen.

This is the formula I used because the order is not important and repetition is not allowed.

Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.

numerator: n! = 11! = 39,916,800

denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960

Combination = 39,916,800 / 120,960 = 330

Therefore, There are 330 ways that the instructor can choose 4 students for the first group.

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