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The length of the shorter leg of a 30-60-90 Special Right Triangle is 17 yd long. How long is the longer leg of the triangle?
1) 17yd
2) 17√2yd
3) 17√3yd
4) 34yd

There are several hypotheses regarding how 0 was created. The idea of utilising 0 as a numeric value is thought to have originated in India. According to legend, Aryabhatta invented zero by using it as a placeholder number in the fifth century.

However, the idea of zero was not always present. Although the idea of nothingness or emptiness existed, applying it numerically had a profound effect on mathematics. The principles for zero were laid forth by Brahmagupta in the seventh century.

In America, the Mayans developed the idea of zero as a placeholder in the 4th century. But though being skilled in mathematics, they never thought the idea of using it in equations.

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The required function obtained after solving f(g(x)) will be equal to 15x³ + 16. Hence, option C is correct.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the functions given in the question,

f(x) = 3x² + 16

g(x) = √5x³

Now, find the function f(g(x)).

f(g(x)) = f(√5x³),                     [g(x) = √5x³]

f(g(x)) = 3( √5x³)² + 16           [f(x) = 3x² + 16]

So,

f(g(x)) = 3(5x³) + 16

f(g(x)) = 15x³ + 16

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Answer:

f(g(x)) = 15x^3 + 16 dollars / hour

I answered the quiz and it's correct

Answer:

D. x=2, -2

Step-by-step explanation:

I think you're asking for the correct answer to the problem because all of the values for x won't work for the equation.

So all we have to do is simplify the equation to isolate x.

[tex]2x^2-8=0[/tex] (original problem)

[tex]2x^2=8[/tex] (add 8 to both sides)

[tex]x^2=4[/tex] (divide both sides by 2)

[tex]x=2, x=-2[/tex] (find the square root of both sides)

Note that x = ±2 and note just 2 because both [tex]2^2[/tex] and [tex](-2)^2[/tex] [tex]=4[/tex].

Hope this helped :D

Tool dividing beats into two, three or four parts is called a simple meter.

A simple meter is a tool in music which divides beats into a number of two, three or four parts. A simple meter is of three types :

1. Duple - a meter which helps to divide a beat into 2 (i.e. into two parts).
2. Triple - a meter which helps to divide beats into 3(i.e. into three parts)

3. Quadruple - a meter which helps to divide beats into 4(i.e. into four parts).
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Duple - a meter which helps to divide a beat into 2 (i.e. into two parts).

Triple - a meter which helps to divide beats into 3(i.e. into three parts)

Quadruple - a meter which helps to divide beats into 4(i.e. into four parts).

The equation of the ellipse with foci at ​(39​,0) and ​(-39​,0) and a constant difference of 30 is given as follows:

x²/39² + y²/9² = 1.

The equation of an ellipse of center (h,k) is given by the rule presented as follows:

(x - h)²/a² + (y - k)²/b² = 1.

In which:

The coordinates of the foci are given as follows:

​(39​,0) and ​(-39​,0).

The center is the midpoint of these two coordinates, hence:

The coefficient a is given as follows:

a = |39 - 0| = |0 - 39| = 0.

Considering the constant difference of 30, the constant b is given as follows:

b = a - 30 = 39 - 30 = 9.

Thus the equation of the ellipse is given as follows:

x²/39² + y²/9² = 1.

The problem asks for the equation of the ellipse with the given features.

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The solution of simultaneous equations 5x-3y=8 and 3x+Y=2 is (1,-1)

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form y=mx+c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

The given equations are:

5x-3y=8  ------(1)

3x+y=2   -------(2)

By solving the equations we get the points

Multiply equation(1) by 3 and equation (2) by 5 then we get

15x-9y=24

15x+5y=10

By solving the above equations we get x and y values.

-14y=14

y=-1

substitute y=-1 in equation(1) we get x value.

5x-3(-1)=8

5x=5

x=1

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Total Productive Maintenance (TPM) practices ensure D. equipment downtime is maximized

According to TPM, operators are in charge of sanitizing, enhancing, and maintaining their workstations to guarantee quality and safety throughout production cycles. The objective of TPM is to maintain equipment in top working order to ensure that production processes go without hiccups or delays.

Through the optimization of equipment availability and performance, TPM seeks to increase overall productivity and quality. The 5S methodology, a method of workforce organization that aids in streamlining and standardizing facility procedures, is the foundation on which TPM is based.

Therefore, the correct option is D.

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Answer:

f(x)= √(x-a) +b

Step-by-step explanation:

parent function is y=√x. This has a domain and range of [0, ∞). The question asks what function transformations will move the domain to [a, ∞) and the range to [b, ∞).

Function transformations

To move the domain from [0, ∞) to [a, ∞) requires the function be translated 'a' units to the right. That transformation is accomplished by replacing x with (x-a) in the function definition.

To move the range from [0, ∞) to [b, ∞) requires the function be translated upward by 'b' units. This is accomplished by adding 'b' to every function value.

The net effect of these transformations is ...

  f(x) = √x   ⇒   f(x) = √(x -a) +b

The leading coefficient is positive. So, the parabola is downward. Then the maximum value of vertex form will be negative 4.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The equation is given below.

y = − x² + 2x − 5

Convert the equation into a vertex form. Then we have

y = − x² + 2x − 5

y = − x² + 2x − 1 − 4

y = − (x² − 2x + 1) − 4

y = − (x − 1)² − 4

The leading coefficient is positive. So, the parabola is downward. Then the maximum value of vertex form will be negative 4.

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The complete question is given below.

How do you find the maximum value of vertex form?

y = − x² + 2x − 5?

Answer:

  at least 5

Step-by-step explanation:

You want to know the number of cups needed to contain 7/8 pitcher of water when each cup holds 3/16 pitcher.

The number of cups can be found by dividing the water quantity by the amount each cup holds:

  (7/8 pitcher)/(3/16 pitcher/cup) = 14/3 cups = 4 2/3 cups

Eve needs at least 5 cups to hold the amount of water in the bottle.

__

Additional comment

If every cup is filled to capacity, then the 5th cup will be 2/3 full. The number of cups can be any number greater than or equal to 5.

If you want, you can write an inequality relating the capacity of the cups to the amount of water:

  n(3/16) ≥ 7/8

  n ≥ 4 2/3 . . . . . . . . . where n is a counting number

  n ∈ {5, 6, 7, ...}

This more clearly shows that the number is not restricted to 5.

Using the provided function and finding the values of input for which it will provide valid output values we can find the domain.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Yes. For instance, the set of all real numbers is the domain and range of the cube root function.

Choose the input values.

Exclude any real numbers that produce a negative value in the radicand because there is an even root. Solve for x by setting the radicand to be greater than or equal to zero.

The domain of the function is the solution(s). If at all possible, format your response as an interval.

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The previous water level is -9.9 feet. The correct option is B.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols.

The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression. They can also denote the operation order and other properties of the logical syntax.

Given that after a heavy storm, the water level of a river is −3.7 feet. This level is 1/2 times 2.5 feet more than the previous water level.

The previous water level is calculated as,

1/2 ( x + 2.5 ) = -3.7

x + 2.5 = -7.4

x  = -7.4 - 2.5

x = -9.9

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Step-by-step explanation:

Let's solve this problem step by step. The current water level is -3.7 feet, which is 1/2 times 2.5 feet more than the previous water level. Let's call the previous water level "x".

So, we can write an equation to represent this relationship:

-3.7 = x + (1/2) * 2.5

Now, let's solve for x:

-3.7 = x + 1.25

x = -3.7 - 1.25

x = -4.95

So, the previous water level was **-4.95 feet**.

Out of the answer choices you provided, the closest value to the correct answer is **-4.9**.

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Inverse proportion is expressed by the equation x y = k or x = k/y. As a result, you can utilize the known values to get the constant k's value before applying this formula to determine all the other values.

Inverse Proportional Method Solutions

As one pair is always given, we may employ the equation to discover the unknown terms and so solve the problem.

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A quadratic inequality of the form

y>a[tex]x^{2}[/tex]+bx+c

(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola .

A quadratic inequality of the form

y>a[tex]x^{2}[/tex]+bx+c

(or substitute <,≥ or ≤ for > ) represents a region of the plane bounded by a parabola .

To graph a quadratic inequality, start by graphing the parabola. Then fill in the region either above or below it, depending on the inequality.

If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line.

Otherwise, if the inequality symbol is < or > , the parabola should be drawn with a dotted line to indicate that the region does not include its boundary.

Example:

Graph the quadratic inequality.

y≤[tex]x^{2}[/tex]−x−12

The related equation is:

y=[tex]x^{2}[/tex]−x−12

First we notice that a , the coefficient of the x2 term, is equal to 1 . Since a is positive, the parabola points upward.

The right side can be factored as:

y=(x+3)(x−4)

So the parabola has x -intercepts at −3 and 4 . The vertex must lie midway between these, so the x -coordinate of the vertex is 0.5 .

Plugging in this x -value, we get:

y=(0.5+3)(0.5−4)

y=(3.5)(−3.5)

y=−12.25

So, the vertex is at (0.5,−12.25) .

We now have enough information to graph the parabola. Remember to graph it with a solid line, since the inequality is "less than or equal to".

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Out of 82, 58 tickets were sold to students and 24 tickets were sold to the adults for the musical.

How to solve an equation for x?

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.

According to the given question:

Let the tickets sold to students be x.

Since total number of sold tickets are 82, the number of tickets sold to families will be 82 - x (that is 82 minus number of tickets sold to students)

Cost for one ticket for students is $3

So, the amount after selling tickets to students = 3x ---- 1)

Similarly, cost of one ticket for an adult is $5

Hence the amount after selling tickets to adults = 5(82 - x) ----- 2)

Total sales from selling tickets is $294

From equation 1) and 2)

3x + 5(82 - x) = 294

Solving for the value of x

3x + 410 - 5x = 294

2x = 410 - 294

2x = 116

x = 58

Therefore, out of 82, 58 tickets were sold to students and (82 - 58) = 24 tickets were sold to adults.

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1 Indexed means that the array elements are numbered starting at 0.

Array can be defined as a collection of elements of the same type placed in contiguous memory locations that can be individually referenced by using an index to a unique identifier also An array is a user defined data type consisting of an ordered set of elements of a single data type

Therefore add 1 to the array suppose an array contain elements  of 1, 2, 3, 4 then the array represents decimal number 1234 and hence adding 1 to this would result 1235.

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The percentage of children allergic to peanuts is 17.5%

The term 'per cent' means 'out of a hundred'. In mathematics, percentages are used like fractions and decimals, as ways to describe parts of a whole. When you are using percentages, the whole is considered to be made up of a hundred equal parts.

Given here, 200 children out of which 35 are allergic thus in percentage terms we have (35/200)×100 =17.5%

Hence, The percentage of children allergic to peanuts is 17.5%

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A null set is a set that contains no elements in mathematics, that is it is empty. It is also called empty set or void set.

It is denoted by the Greek letter Ф (phi). It is expressed as {}.

A null set is formed by intersection of two disjoint sets. For example, a set of odd numbers, say A = {1, 3, 5, ...} and set of even numbers say B = {0, 2, 4, ...}. A set of number of both odd and even is a null set as these sets A and B doesnt have any element in common, that is they are disjoint set.

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Answer: 15 years

Step-by-step explanation:

6000 x 1.05^x = 12000

1.05^x=2

log(1.05^x)=log(2)(Take log of both sides)

x*(log(1.05))=log(2)

x= log(2)

log(1.05)

x=14.206699

15 years

The  probability is 102.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Moderate Success     0.3 102.0 120 208.0

Failure                        0.4 102.0 10.0 100

Now, the probability

E(x) = [tex]\sum^3_i[/tex]= [tex]S_iP_i[/tex]

      = 102 x 0.3 + 102 x 0.3 + 102 x 0.4

      = 30.6 + 30.6 + 40.8

      = 102

Hence, the probability is 102.

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The equation with values that will result in infinitely many solutions is 7x + 2(x + 5) = 7x + 2(x + 6)

From the question, we have the following parameters that can be used in our computation:

7x+2(x+5)=

Rewrite properly

So, we have

7x + 2(x + 5) =

For the equation to have infinitely many solutions, then the variable part must be the same, while the constant part  must be different

So, we have

7x + 2(x + 5) = 7x + 2(x + k)

By comparison, we have

k = 5

This means that the value of k can be any real number except 5

So, we can make use of 7x + 2(x + 5) = 7x + 2(x + 6)

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If three angles of one triangle are congruent to three angles of another triangle then by the AAA similarity theorem, the two triangles are similar. Actually, you need only two angles of one triangle being congruent to two angle of the second triangle.

How to prove AAA Theorem?

Specifying three angles A, B, and C does not uniquely define a triangle, but any two triangles with the same angles are similar. Specifying two angles of a triangle automatically gives the third since the sum of angles in a triangle sums to 180 degrees (pi radians), i.e.,

C = π - A - B .

Prove:

Triangles ABC and DEF such that ∠A = ∠D; ∠B = ∠E; ∠C = ∠F

Δ ABC ~ ΔDEF

Construction : We mark point P on the line DE and Q on the line DF such that AB = DP and AC = DQ, we join PQ.

There are three cases :

Case ( i ) : AB = DE, thus P coincides with E.

⇒ AB = DE, BC = EF and AC = DF

Consequently, Q coincides with F.

AB BC CA

---- = ------ = ------

DE EF FA

Since the corresponding angles are equal, we conclude that Δ ABC ~ Δ DEF.

Case( ii ) : AB < DE. Then P lies in DE

In triangles ABC and DPQ,

Statements ------ Reasons

1) AB = DP- 1) By construction

2) ∠A = ∠D -2) Given

3) AC = DQ -3) By construction

4) ΔABC ≅ ΔDPQ -4) By SAS postulate

5) ∠B = ∠DPQ 5) CPCTC

6) ∠B = ∠E- 6) Given

7) ∠E = ∠DPQ- 7) By transitive property

( from above)

8) PQ || EF -8) If two corresponding angles are congruent then the lines are parallel

9) DP/DE = DQ/DF -9) By basic proportionality theorem

10) AB/DE = BC/EF- 10) By construction

11) AB/DE = AC/DF- 11) By substitution property

12) Δ ABC ~ Δ DEF - 12) By SAS postulate

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Answer:

x^2 + 4x - 2

Step-by-step explanation:

x - 4 = 0

x = 4

Use synthetic division:

4    |    1    0    -18    8   ==> 1=x^3,     0=0x^2,     -18=-18x

              +4   +16   -8

          1    4     -2,    0  ==> x^2 + 4x - 2 with no remainder

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After covering a distance of 160-mile rental cost of both company will become same.

Mathematical expressions with the symbols >,<, ≥ and ≤  are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. Inequalities are resolved using graphs and algebra. It is imperative that you practice the techniques described here a lot so they become second nature if you want to master them.

An inequality still exists if the same amount is added to both sides. The inequality still holds true if the same amount is subtracted from each side. An inequality still holds true if both sides are multiplied or divided by the same positive value. However, if both sides of an inequality are multiplied or divided by a negative value, the inequality is no longer valid. In actuality, the inequity is turned around.

Solving according to ques,

Let us represent distance covered be X miles.

$100+($0.30) X = $20 + ($0.80) X

subtracting $20 and ($0.30) X from both sides, we get

$80 = ($0.50) X

X = 160 mile.

So, rental costs for company will be same when bot the trucks will cover a distance of 160 mile.

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Negative infinity is an abstract concept used to describe a value that is lower than any other real number. It is not a direction, but rather an idea of an unlimited amount of negative numbers.

Negative infinity is an abstract concept used to describe a value that is lower than any other real number. It is not a direction, but rather an idea of an unlimited amount of negative numbers. Although it does not have a physical direction, it can be thought of as a direction that is always negative and decreasing without bound. This concept is often used in mathematics to compare values and calculate limits. For example, when graphing a function, negative infinity is often used as the lower bound on the x-axis. Negative infinity is also used to describe the behavior of certain equations when a variable approaches a certain value or when a denominator approaches zero. In these cases, the equation would approach negative infinity. Negative infinity is not a real number and cannot be used in calculations, but it can be used to compare values and describe the behavior of certain equations.

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Answer:

1/13

Step-by-step explanation:

There are 4 cards that are a "3" in a deck of cards

3 of hearts, 3 of spades, 3 of clubs, 3 of diamonds

P( 3) = number of cards that are a "3" / total number of cards

P(3) = 4/52 = 1/13

Answer:

[tex]\frac{1}{13}[/tex] (one thirteenth)

1/13

Step-by-step explanation:

There's 4 of the card 3 in a deck. (3 of hearts, 3 of diamonds, 3 of clubs, 3 of spades.)

This means 4 of 52 cards are a 3, which makes the fraction [tex]\frac{4}{52}[/tex]. This is the probability.

This fraction can be simplified to [tex]\frac{1}{13}[/tex] by dividing the top and bottom by four. This is the final answer, since it is in the simplest form.

Answer:

As far as I know, in math, Δ means:

Examples:

ΔABC ≅ ΔDEF

Δ = [tex]\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

To rectify the errors using a suspense account, the following journal entries can be made:

i. Rs 3,000 received from a customer as an advance against order was credited to sales account.

To correct this error, we can make the following journal entry:

Debit Suspense Account 3,000

Credit Sales Account 3,000

ii. A sum of Rs 800 written-off as depreciation on machinery, were not posted to depreciation account.

To correct this error, we can make the following journal entry:

Debit Depreciation Account 800

Credit Suspense Account 800

iii. Purchase of a scooter was debited to conveyance account Rs 16,000. Firm charges 10% depreciation on vehicles.

To correct this error, we can make the following journal entries:

Debit Suspense Account 1,600

Credit Conveyance Account 1,600

Debit Depreciation Account 1,600

Credit Suspense Account 1,600

iv. Payment of Rs 500 to Mohan and Rs 600 to Sohan was made but Mohan was debited with Rs 600 and Sohan with Rs 500.

To correct this error, we can make the following journal entries:

Debit Suspense Account 100

Credit Mohan 600

Debit Sohan 500

Credit Suspense Account 100

v. Sales to X Rs 500 were posted to Y’s account

To correct this error, we can make the following journal entries:

Debit Y 500

Credit Suspense Account 500

Debit Suspense Account 500

Credit X 500

Answer:

this answer can't be solved because there are two variables we need at least value of at least one variable

Answer:

y/x=2-x/y+2

Step-by-step explanation: