Four times a number is 45 less than the square of that number. Find the negative solution

Answer: x = 19

Step-by-step explanation:

Let's start with what we know. The area of a trapezoid is:

(B1 + x) * H /2 = Area

So here we have:

(25 + x)* 7 /2 = 154.

We multiply by 2 on both sides:
(25 + x)*7 = 308

Divide by 7 on both sides:
25 + x = 44

Subtract 25 from both sides:
x = 19.

So x = 19.

Answer: 19 inches

Step-by-step explanation:

The shape is a trapezium. (You can tell as there is one pair of parallel sides.) Therefore, to find the area, the following formula is needed:

Area of a trapezium =  [tex]\frac{a + b}{2} * h[/tex]

a and b represent the parallel sides

Next, plug in the given values:

[tex]154 = \frac{x + 25}{2} * 7[/tex]

Rearrange the equation to get x on its own:

[tex]154 = \frac{x+25}{2} * 7\\\\\frac{154}{7} = \frac{x+25}{2} \\\\22 = \frac{x+25}{2} \\\\22*2 = x + 25\\\\44 = x + 25\\\\44-25 = x\\\\x = 19\\\\[/tex]

Therefore, the answer is 19 inches. Remember your units!

In general, linear equations have one solution. However, they can have infinitely many solutions in some cases.

A linear equation in mathematics is an equation that can be written in the form

ax + b = 0

The values of x that make this equation true are the solutions to the equation. Generally speaking, linear equations have one solution, which means that there is only one value of x that will make the equation true. However, in some cases, linear equations can have infinitely many solutions. For example, if a = 0 and b = 0, then any value of x will make the equation true.

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Answer:

1/90

Step-by-step explanation:

The wait time required for 200 people are in line would be 40min.

Given that:

wait time to ride the ferris wheel for 75 people is 15 minutes.

we have given 200 people that are in line to ride.

for each person in line from the beginning is an additional 0.2 wait time.

so, the number of people in line n times = 0.2 = wait time.

Therefore,

                 [tex]\frac{15\ min}{75 \ people}=0.2\frac{min}{people} \\\\wait \ time = n*0.2\frac{min}{people} \\\\wait\ time = (200)*0.2\frac{min}{people}\\\\wait\ time = 40 min[/tex]

Hence, The wait time required for 200 people are in line would be 40min.

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The percent equation in the form of p = percent x whole is

p = 1.25 x 24

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Number of members in the club = 24

Number of members in the club next year = 125% of 24

The percent equation of 125% of 24.

p = 125/100 x 24

p = 1.25 x 24

p = 5/4 x 24

p = 5 x 6

p = 30

Thus,

The percent equation is p = 1.25 x 24

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Answer:

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

It is assumed the provided numbers are the zero's of the polynomial function.

We know complex zero's come in pairs if function has rational constants.

So we should have zero's: 8, 3, -i and i.

Find the polynomial:

Answer:

[tex]x^{1}[/tex]=[tex]\frac{-3-\sqrt{7} }{2}[/tex] [tex]x^{2}[/tex]=[tex]\frac{-3+\sqrt{7} }{2}[/tex]

Step-by-step explanation:

1) collect like terms and move everything to the left

2[tex]x^{2}[/tex]2+3x-3+3x+4=0

2[tex]x^{2}[/tex]2 +6x-3+4=0

2) find the coefficients so you can plug them into the quadratic formula

a=2, b=6, c=1

3) plug these into the quadratic formula

4) use a calculator to solve both the positive and negative equations

The value of x in the solution to this system of equations y + 2x = -1 and y=x+4 is 3.

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients. To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given,

Equations:

y + 2x = -1

y = x + 4

y - x = 4

Using elimination method,

y + 2x = -1

y - x = 4

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

x = 3

The value of x in the solution to this system of equations y + 2x = -1 and y=x+4 is 3.

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If the probability of a dancing lady accepting an invitation to dance is 0.18.The accepted number of ladies asked before is 7.14 .

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

According to the above discussion:

P{x(bar) (0.18)} = 0.07142371

                       = 7.14%

Therefore, the expected number is 7.14%.

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Answer:

A and B

Step-by-step explanation:

The triangle is labeled that all three sides are equal and all three angles are equal; thus, it is an equilateral triangle and “B” is correct.

Acute triangles have all acute angles. Understanding that the triangle is equilateral, equilateral triangles have all equal angles, and the total of all three angles in a triangle is 180, we can determine that all three angles are acute and the triangle is acute, so “A” is right. (one angle = x; three angles are equal and add up to 180 —> 3x = 180; x = 60; all angles are acute).

The  difference between addition and subtraction of polynomials is that addition involves like terms  and subtraction  involves taking one polynomial away from another.

A polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as addition, subtraction, multiplication, and division (No division operation by a variable).In addition to polynomials, the like terms are included whereas, in subtraction, the like terms are subtracted. The addition of polynomials involves combining like terms to form a single expression, while subtraction involves taking one polynomial away from another. In addition, when subtracting polynomials, the sign of each term in the second polynomial needs to be changed (from positive to negative, or from negative to positive).

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The solution to given problem is  since E(Wu) < Wr, there will be no migration from rural areas .

The subject of probability in mathematics is concerned with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, with 1 typically signifying certainty and 0 typically signifying impossibility.

Here,

Since ,the rural wage is $2 per day. Urban modern sector employment can be obtained with .24 probability and pays $4 per day. The urban traditional sector pays $1 per day.

As long as the rural pay (Wr) differs from the anticipated urban wage (E(Wu)), according to the Harris-Todaro model, there will be movement between rural and urban areas.

Here, Wr equals $2.00.

Determine the anticipated urban wage now.

E(Wu) = p

*Wum+(1-p)

*Wut

Where p is the likelihood of finding employment in the urban modern sector, which is 0.25, and Wum is the wage for such employment, which is $4.00.

Wut = $1.00 in wages for jobs in the typical urban sector.

Hence, E(Wu) = 0.24*$4.00+0.76*$1.00 = $1.72

Since E(Wu) < Wr, there will be no migration from rural areas .

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It will take 27 minutes 30 seconds to complete eleven questions.

When two values are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage, direct proportionality is represented by a straight line and it equation is of the form -

y = kx

k = y/x

where [k] is the constant

Given is that the number of questions [y] completed and time [x] it takes to complete them are proportional to each other.

The number of questions [y] completed is proportional to the time [x] it takes to complete them.

That means,

y ∝ x

y = kx, where k is constant.

k = y/x

So, we can write;

y₁/x₁ = y₂/x₂

According to the question:

Let  y₁= 6, x₁= 15, y₂= 11.

Substituting the values,

6/15 = 11/x₂

x₂ = 11 x 15 / 6

x₂ = 11 x 5 / 2

x₂ = 55 /2

x₂ = 27. 5

x₂ = 27 minute and 30 seconds.

Therefore, it will take 27 minutes 30 seconds to complete 11 questions.

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Answer: i believe it is

x-intercept(s): (−3,0) y-intercept(s): (0,3)

and

Step-by-step explanation:

substitute in 0 for y and solve for x and do that for the other just 0 for x and solve for y

The equation of the line through [tex](1,2)[/tex] which make equal intercepts on the axis [tex]x+y=3[/tex]

The equation of the line through (1,2) makes an equal intercept on the axis

The formula of the intercept form is

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

If they make an equal intercept

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

Put the value of the point in the axis, and we get.

[tex]1+2=a\\a=3[/tex]

Put the value in the equation, and we get.

[tex]x+y=3[/tex]

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The required measurement of each interior angle of the animal pen

An  interior angle is a point inside a shape. The polygons are the shut shape that has sides and vertices. A standard polygon has generally its interior angle equivalent to one another. For instance, a square has generally its  interior angle equivalent to the right point or 90 degrees.

The question expects us to track down the inside point of a customary heptagon.

To do this initially compute the outside angle of that polygon.

The amount of outside angle is 360°. A heptagon has 7 sides.

Along these lines, one exterior angle = 360°/7 = 51.4°

inside angle+exterior angle=180°

Interior angle = 180-51.4 = 128.6°

Thus, required interior angle is 128.6°.

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Answer:

18b-45

Step-by-step explanation:

9(2b-5)

9*2b-9*5

18b-9*5

18b-45

Answer:

9(2b - 5)

Distribute

9(2b - 5)

18b - 45

Solution

18b - 45

The quotient of given polynomials division is x+2. So, the correct answer is option A.

A quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Given that, (x²+3x+2)÷(x+ 1)

x²+3x+2 can be written as

x²+1x+2x+2 (Splitting of middle term)

= x(x+1)+2(x+1)

= (x+1)(x+2)

Now, (x+1)(x+2)÷(x+1)

= [(x+1)(x+2)]/(x+1)

= (x+2)

Therefore, option A is the correct answer.

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What is the quotient of the following division problem (x²+3x+2)÷(x+ 1).

a. x+ 2

b. x +1

c. x²+3x +2

d. 0

Answer:

B

Step-by-step explanation:

The median is the mid point value. Basically the median is whatever number is in the middle.

The class mean and standard deviation of the distribution used should be of most concern.

What is mean and standard deviation?

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The missing number of the algebraic expression is; x = 15

We are given the algebraic expression that we should find the number x, If 11/3 of x is 55.

This can be expressed as;

(11/3)x = 55

Multiply through by 3 to get;

(11/3)x * 3 = 55 * 3

11x = 165

Divide both sides by 11 to get;

11x/11 = 165/11

x = 15

Which we conclude that 15 is the missing number.

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The cost of each apple is equal to $0.23.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=8x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=8 and b=3.

The question gives:

You should convert the data into an equation:

15A+2.75=6.20

15A=6.20-2.75

15A=3.45

A=3.45/15

A=0.23

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By using the concept of probability, it can be calculated that -

Probability that a two-card hand from a standard deck of 52 cards contains exactly 2 face cards (a face card is a king, queen, or jack) = [tex]\frac{11}{221}[/tex]

What is probability?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur.

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Number of face card = 12

Total number of cards = 52

Probability that a two-card hand from a standard deck of 52 cards contains exactly 2 face cards (a face card is a king, queen, or jack) = [tex]\frac{{12 \choose 2}}{{52 \choose 2}}[/tex]

                                                                                                = [tex]\frac{66}{1326}[/tex]

                                                                                                = [tex]\frac{11}{221}[/tex]

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To calculate the number of cycles we need above 3 options

Stop Watch Time Study:

Stop Watch Time Study is one of the equipment used for Time Study. It is employed for measuring the time taken by an operator to complete the work. Stop watch used for time study purpose should be very accurate and preferably be graduated in decimals so that it can recover even up to 0.01 minute.

A large hand in the stop watch is revolved at a speed of one revolution per minute. The dial of the stop watch is divided into 100 equal divisions. The small hand inside the stop watch revolves at a speed of one revolution in 30 minutes.

Given that

In a stopwatch time study, the number of cycles that must be timed is a function of:

options are

(i) the variability of observed times.

(ii) the desired accuracy for the estimated job time.

(iii) the desired level of confidence for the estimated job time

To calculate the number of cycles we need above 3 options

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Answer:

-17/8

Step-by-step explanation:

-10-7         -17

----------  = -------

4-(-4)          8

The example of the function equation is f(x+3) = x² + 8x + 16 .

In the question ,

we have been asked to give an example of the function equation .

The Function Equation is defined as equations where the unknowns are functions, rather than a traditional variable.

For Example :

If f(x+3) = x² + 8x + 16 , then what is f(x)?

the above question is an example of function equation .

to find the solution ,

we let ,y = x + 3; then x = y - 3 .

Substituting the value of x in f(x+3) we get ,

f(y) = 2y² + 2y + 1 .

hence f(x) = 2x² + 2x + 1  that is = (x + 1)²  .

Therefore , the example is  f(x+3) = x² + 8x + 16  .

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The amount of a good that is demanded will decrease as its price rises

According to the Law of Demand, there is an indirect correlation between a good or service's price and the amount of that good or service that customers are willing and able to purchase .In other words, if an item's price increases, people are less able and willing to buy it, and vice versa.

According to the law of demand, the demand curve demonstrates the inverse relationship between the amount of items sought and price.

The amount of a good that is demanded will decrease as its price rises. The demand curve will therefore have a negative slope if the law of demand and its underlying assumptions are true.

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The products result in a sum or difference of cubes are

(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).

What is sum or difference of cubes?

The term "sum of cubes" refers to a polynomial with the formula a^3 + b^3. The term "difference of cubes" refers to a polynomial with the form

a^3 - b^3.

The formulas for sum of cubes and difference of cubes are given:

Sum of cubes: (a + b)(a²-ab + b²) = a³ + b³

Difference of cubes: (a-b)(a² + ab + b²)=a³-b³

We have to check which products result in a sum or difference of cubes.

Consider,

(1) (x - 4)(x^2 + 4x - 16)

(x - 4)(x^2 + 4x - 16) = x^3 - 8x^2 + 32x - 64

It is not a sum or difference of cubes.

(2) (x-1)(x²-x+1)

(x - 1)(x² - x + 1) = x^3 - 2x^2 + 2x - 1

It is not a sum or difference of cubes.

(3) (x - 1)(x² + x + 1)

(x - 1)(x² + x + 1) = x^3 - 1

This is the difference of cubes.

(4) (x + 1)(x^2 + x - 1)

(x + 1)(x^2 + x - 1) = x^3 + 2x^2 - 1

It is not a sum or difference of cubes.

(5) (x + 4)(x² - 4x + 16)

(x + 4)(x² - 4x + 16) = x^3 + 64

This is the sum of cubes.

(6) (x + 4)(x^2 + 4x + 16)

(x + 4)(x^2 + 4x + 16) = x^3 + 8x^2 + 32x + 64

It is not a sum or difference of cubes.

Hence, the products result in a sum or difference of cubes are

(x - 1)(x² + x + 1) and (x + 4)(x² - 4x + 16).

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The function is linear when the highest degree the the function is 1 .

In the question ,

we have been asked about when a function is called as linear .

By the definition ;

the Linear function is the function that has the highest degree as 1 and

On the coordinate plane the linear function represents the straight line .

the general form of the linear function is f(x) = mx + d ,

the slope is "m" and the y intercept is "d" .

The Examples of Linear Function are

f(x) = 3x + 2 ,

f(x) = -6x + 7

f(x) = 8 .

Therefore , the characteristic for the function to be linear is explained above.

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