A worker spent 2 hours and 40 minutes making 20 products. If he works at the same productivity, how long will it take the worker to make 30 units? ​

Answer:

x²+2x

x(x+2)

Step-by-step explanation:

take x common and thats it either tou gave incomplete question or wrong ans

Answer:

See below

Step-by-step explanation:

This should be your expressions: [tex]\displaystyle{x^2+2x-24}[/tex], this can be factored by applying in the form of:

[tex]\displaystyle{x^2+(\alpha + \beta)x+\alpha \beta = (x+\alpha)(x+\beta)}[/tex]

This simply means you have to find two numbers that add up or subtract and obtain the middle term, and that two numbers must also satisfy the last terms as well. (Hence, two numbers adding up to middle term and multiply to last term.)

We can check by seeing into the factor of 24 which are:

These numbers have product of 24. Next, we find the middle term -- since the middle term is positive value. This means that the highest value is in positive.

From factors that we list, we can cancel off the followings:

Therefore, the only factors left are 4 and 6. These two also make 2 (6-4), so we will have [tex]\alpha[/tex] = 6 and [tex]\beta[/tex] = -4. Therefore:

[tex]\displaystyle{x^2+(6-4)x+6(-4) = (x+6)(x+(-4))}\\\\\displaystyle{x^2+2x-24= (x+6)(x-4)}[/tex]

And there you have it, the factor of x² + 2x - 24

ABCD is an isosceles triangle

A segment drawn from a vertex to the midpoint of the opposite side is the correct option.

Lines that cross each other at a correct angle are considered to be perpendicular. Examples are the ends of a horizontal ladder and the opposing sides of a rectangle. the symbol that denotes two parallel lines In geometry, a pair of lines that meet or intersect with right angles (90°) are said to be perpendicular.

Drawing the dotted line for the specified measurement is the first step in the line segment construction process. Then, make a mark at that location on the line and set the compass at that location. Now, draw an arc across each side of the indicated line. Draw another arc without adjusting the compass.

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Answer:the a would be 10

and the b would be 6

Step-by-step explanation:

No, 36 is not a prime number. Because the number 36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, 36.  

A prime number is a natural number more than 1 that has no positive divisors aside from 1 and itself. Prime numbers have several important properties and applications in mathematics, such as the fundamental theorem of arithmetic, which states that every positive integer can be written as a unique product of primes. They are also used in number theory, cryptography, and coding theory.

In addition, prime numbers are of interest in studying patterns and properties in the distribution of numbers, such as the distribution of twin primes and Mersenne primes. They play a crucial role in number theory, which is a branch of mathematics that studies the properties of integers. Prime numbers are infinite in number, and it is an open question whether there are infinitely many prime pairs or twin primes, which are pairs of prime numbers that differ by 2.

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Answer:

Sum of Interior Angles = (8-2) * 180 = 1080 degrees

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

Step-by-step explanation:

The sum of the interior angles in a polygon can be found using the formula (n-2)*180, where n is the number of sides in the polygon.

In the case of an octagon (8 sides), the sum of the interior angles is (8-2)*180 = 1080 degrees.

The measure of the eighth interior angle can be found by subtracting the sum of the known interior angle measures from the total sum of the interior angles.

So,

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

In short,

Sum of Interior Angles = (8-2) * 180 = 1080 degrees

Eighth interior Angle = 1080 - (103 + 175 + 155 + 158 + 169 + 157 + 55) = 1080 - 817 = 263 degrees

The value x = 0 is zero of function p(x) = x²

Consider given function  p(x) = x²

We know that from the definition of zeros of function, the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.

To find the zeros of function p(x), we need to equate p(x) to zero then solve it for x.

Here we need to check whether x = 0 is zero of function p(x)

If for x = 0, p(x) = 0 then x = 0 is zero of function p(x).

Substitute x = 0 in given function p(x)

⇒ p(x) = x²

⇒  p(0) = 0²

⇒ p(0) = 0

Thus x = 0 is a zero of given function.

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The complete question is:

Is x = 0 a zero of p(x)=x² ?

The perimeter of your new patio is 52.

Given that,

In order to match the shape of your backyard, your family has decided to build a rectangular patio there. The dimensions of your backyard are 20 feet wide by 45 feet long. Your new patio measures 18 feet in length.

To find :  The perimeters of your backyard and of the patio.

The dimensions of the yard are length 45 and width 20.

The patio is going to have the same shape, only smaller.

The length of the patio is 18 feet.

The ratio of the length of the patio to the length of the yard is 18/45.

Since the patio and the yard are to have the same shape, then that same ratio of 18/45, applied to the width of 20, gives you a patio width of 18/45* 20 = 8

Therefore, The perimeter of your new patio is 2 * (18 + 8) = 2 * 26 = 52.

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The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.

A. Let "r" be the number of state representatives and "s" be the number of state senators. We know from the problem that:

r + s = 181 (the sum of the number of representatives and senators is 181)

r - s = 119 (the difference of the number of representatives and senators is 119)

So the system of equations is:

r + s = 181

r - s = 119

B. To solve this system of equations, you can use the first equation to solve for one of the variables in terms of the other. Let's solve for "r" in terms of "s":

r = 181 - s

Now we can substitute this expression for "r" into the second equation:

(181 - s) - s = 119

Simplifying, we get:

181 - 2s = 119

2s = 62

s = 31

So there are 31 state senators in the Texas State Legislature. To find the number of representatives, we can use the first equation and substitute in the value of "s" that we just found:

r + 31 = 181

r = 150

So there are 150 state representatives in the Texas State Legislature.

Therefore, The system of equations is: r + s = 181 and r - s = 119. There are 31 state senators and 150 state representatives in the Texas State Legislature.

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Correct option is A, The foci of the hyperbola is (0,±√17).

A hyperbola is a plane curve that is produced by a point that is moving so that the difference between the distances from two fixed points is constant. It is created when a double right circular cone intersects with a plane that cuts through both ends of the cone.

The difference in distances between a group of points that are situated in a plane and two fixed points—which is a positive constant—is what is referred to as the hyperbola.

Given the equation of hyperbola is [tex]\frac{y^2}{12} - \frac{x^2}{5} = 1[/tex]

In this equation,

a² = 12

b² = 5

Using the relation c² = a² + b²

c = √(12 + 5)

c = √ 17

As, the hyperbola is vertical,

The value of foci will be (0,±√17)

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The equation A = 2x²y + 4x²y² is a polynomial

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2x²y + 4x²y²   be equation (1)

On simplifying the equation , we get

A = 2xy ( x + 2xy )

Now , it is a mathematical expression with variables and coefficients

Hence , the equation A = 2x²y + 4x²y² is a polynomial

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Answer:

x⁴-2x³-x²+2x = (x²-2x+2)(x²+2x+1)

Answer:

x(x-2)(x+1)(x-1)

Step-by-step explanation:

just add and subtract the second term to the expression and factor by grouping

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The number of regular sodas served is 12.

Percentage is the fraction of an amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. Percentage is a measure of frequency.

Number of regular sodas served = percentage of regular sodas served x number of sodas served

= 25% x 48

= 25/100 x 48 = 12

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Divide the numerator by denominator. Carry the quotient as a whole number and the remainder as the numerator of the proper fraction, maintaining the denominator the same.

A mixed fraction is a type of fraction described as having a fraction and a whole number.

Let's take an example to understand the process completely.

For example, 3(1/7), where 3 is a whole number and 1/7 is a fraction.

Step 1: Divide the Fraction’s numerator by the denominator, i.e. 22/7.

Step 2: The integer portion of the answer will be the integer portion for a mixed fraction, i.e. 3 is an integer.

Step 3: The Denominator will be the same as the original fraction, i.e. 7.

Step 4: So, the improper fraction 22/7 is changed to a Mixed fraction as 3 (1/7).

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The conjecture regarding a number and it's absolute value being always opposites is incorrect.

The counterexample is that the absolute value of any positive number is always the own number.

The absolute value of a number is the number without the signal, representing the difference between the number and zero.

For example:

|-2| = |2| = 0.

Hence the conjecture is false, as the absolute value of any positive number is always the own number.

The conjecture would be true if it stated this only for negative numbers, then the absolute value of a negative number is in fact always the opposite of the number.

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Answer:

283.5 square inches

Step-by-step explanation:

W = L ÷ 2 - 3

width  = 27 ÷ 2 - 3

width  = 13.5 - 3

width = 10.5

Area = length · width

Area = 27 · 10.5

Area = 283.5

The additive inverse of 7/5 will be -7/5.

The additive inverse of any numeral is the opposite of that numeral. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

7/5

So, the additive inverse of 7/5:

⇒7/5 + Additive inverse = 0

⇒Additive inverse = -7/5

Thus the additive inverse of is 7/5 is -7/5.

--The given question is incorrect; the correct question is

"What will be the additive inverse of 7/5?"--

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The solutions of the quadratic equation 3x^2 + 14x + 5 = 0 can be found by factoring the equation into the product of two binomials, which are equal to zero.

3x^2 + 14x + 5 = (3x+1)(x+5) = 0

To find the solutions, we set each factor equal to zero and solve for x:

3x+1 = 0 or x+5 = 0

x = -1/3 or x = -5

Therefore, the solutions of the quadratic equation 3x^2 + 14x + 5 = 0 are x = -1/3, x = -5.

Alternatively, you can use the Quadratic formula to find the solutions.

The Quadratic formula is: x = (-b ± √(b^2-4ac))/(2a)

Where a,b and c are the coefficients of the equation.

x = (-14 ± √(14^2-435))/(2*3) = (-14 ± √(196-60))/6 = (-14 ± √(136))/6

It's worth noting that both solutions x = -1/3 and x = -5 are correct.

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Step 1: The greatest common factor (GCF) in this equation is x^3. So we can factor it out:

y = x^3(x - 343)

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Step 2: We can not take root of a³ and b as there is no square term in the equation.

Step 3:

a= x^3

b= - 343

Step 4: Plugging in a and b into the original equation, we get

y = x^3(x - 343)

This is the simplified form of the equation.

So, the equation is a polynomial equation of degree 4, with the leading coefficient a = x^3 and the constant term b = -343, and it can be written as y = a(x-b) which is y = x^3(x-343)

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The equation 3x - 5y = 12 could be used to represent the function y = f(x), which is NOT one-to-one.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given that function f(x) is not one-to-one

That means the given equation will have only one solution for the one value of x,

Since Quadratic equations have two values at the one value of x that means option a would not satisfy

option c also makes an exponential graph which means it also has more than one value at x

Since Option (b ) 3x - 5y = 12 has a linear function and linear functions do not have more than one value at a value of x

Therefore, the function y = f(x) is NOT one-to-one, the equation could represent f(x) as 3x - 5y = 12.

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The dividend is influenced by both the quotient and the divisor when the remainder is zero.

Any integer that divides a different number is the divisor. A factor, on the other hand, is a divisor that completely divides a number and leaves no remainder. Therefore, all factors are also divisors of a number. But not every divisor will also be a factor. The factors of 20 in the aforementioned case are 4 and 5.

We are left with a value after division if a number (dividend) cannot be divided entirely by another number (divisor). The term "remainder" refers to this amount.

When the remainder is zero, the dividend is affected by both the quotient and the divisor. When the remainder does not equal zero, neither the quotient nor the divisor are dividend factors.

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Answer:

200.96

Step-by-step explanation:

Pi(8 to the power of 2)

The probability of forgetting iClicker device in each class = 1/4 = 0.25 = p

The probability of remembering iClicker device in each class = 1-p = 0.75

(a) Given that she is sure she has the iClicker device after leaving the first class.

The probability that she left it in second class = 1(0.25) = 0.25

The probability that she left it in third class = 1(0.75)(0.25) = 0.1875

The probability that she left it in fourth class = 1(0.75)(0.75)(0.25) = 0.1406

The probability that she left it in fifth class = 1(0.75)(0.75)(0.75)(0.25) = 0.1055

The total probability that she left iClicker given that she is sure she has the iClicker device after leaving the first class is:

0.25 + 0.1875 + 0.1406 + 0.1055 = 0.6836

Given that she is sure she has the iClicker device after leaving the first class, the probability that she left it in the 5th class is:

0.1055/0.6836 = 0.154

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Answer:

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side.

Step-by-step explanation:

Answer:

1 kilogram

Step-by-step explanation:

A triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.

No, a triangle is not 90 degrees. In geometry, a triangle is a three-sided polygon with three angles. The sum of the angles in a triangle is always 180 degrees.

This can be proved using the fact that a straight line is 180 degrees. If we draw a straight line, and divide it into two angles, which are supplementary angles. Therefore, these angles add up to 180 degrees. In a triangle, we can draw one straight line and divide it into three angles, which are supplementary angles, therefore the sum of the angles in a triangle is always 180 degrees.

For example, if a triangle has angles of 90 degrees, 60 degrees, and 30 degrees, the sum of these angles is 180 degrees (90+60+30=180).

Therefore, In short, a triangle is a three-sided polygon whose sum of all the angles is always 180 degrees, not 90 degrees.

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"Segment GT is congruent to segment PD on the number line." this statement is True.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

The number line is used to represent the coordinates G, T, Y, B, M, P, D, W.

The point of G is -10 and the point of T is -9.

To get the measurement subtract G from T -

= -9 - (-10)

= -9 + 10

= 1

The point of P is 5 and the point of D is 6.

To get the measurement subtract P from D -

= 6 - 5

= 1

The measurement of GT and PD both is 1.

Therefore, segment GD is congruent to segment PD on the number line.

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Answer:

Because the plane is flying due east, it has to turn 90º to face south, before it turns the extra 35.31º to fly towards the airport. 90° + 35.31° = 125.31º It actually turns through the exterior angle of the triangle :

Step-by-step explanation:

hope this helps B)

Answer:

  55°

Step-by-step explanation:

You want to know the additional angle a plane must turn through to be going south after it took off going east, then turned right 35°.

The initial bearing angle was 90° (straight east). After turning right 35°, the airplane now has a heading of (90+35)° = 125°. To be going south (180°), the bearing must increase by ...

  180° -125° = 55°

The airplane will have to turn 55° more to be heading due south.

Answer:

Choose whichever format you want to give the answer

[tex]\boxed{\dfrac{2}{9} \textrm{ hour}}[/tex]

[tex]\boxed{0.2222 \textrm{ hour}}[/tex]

[tex]\boxed{13.3333 \textrm{ minutes}}[/tex]

Step-by-step explanation:

[tex]\sf{Travel\: time = \dfrac{Distance}{Speed}}[/tex]

The time taken to travel the first 600 km

[tex]= \dfrac{600}{90} = \dfrac{20}{3}\; \sf{hours}[/tex]

This leaves 200 km which was travelled at a speed of 100 km/hr

Time taken for this stretch = 200/100 = 2 hours

If the entire trip were driven at 90 km/h, it would take the same time as the first case. Therefore we only need to be concerned about the last 200km

If the last 200km were traveled at 90 km/h instead of 100 km/h, time taken

[tex]=\dfrac{200}{90} = \dfrac{20}{9}\\\\[/tex]

The difference in time then would be:
[tex]=\dfrac{20}{9} - 2\\\\\\= \dfrac{20}{9} - \dfrac{18}{9}\\\\=\dfrac{2}{9}\; hour[/tex]

= 0.22 hour in decimal

= 13.33 minutes

Complex numbers are those whose representation is given by the notation a+ib, where a, b are real numbers and I is a made-up expressions called a "iota." I'm equal to (-1).

If complex numbers are required to answer an equation, it is considered complex. Complex numbers are made up of both imaginary and real parts. This is how it is stated: The letters A and B in the preceding equation both represent numerical values. A complex number is something like 4+3i.

In order to attain vague goals that cannot be met through conventional actions, complex issue solving is a collection of self-regulated psychological processes and activities. It takes a variety of tactics and inventive knowledge combinations.

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