You will be writing a short essay on how you can apply the processes you have learned in this unit to solve one of those questions.
Option 1: Solving by Factoring
Please explain in detail the strategy, Solving by Factoring, discussed in the lesson Quadratic in Form Polynomials. Include an example with this explanation to clearly explain the process.

Hope it helps.

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Step-by-step explanation:

the funny thing with equations is we can transform them (as long as we do every operation in both sides), and we can even add them up or subtract from each other to get new equations that are maybe simpler to solve.

to eliminate x i would recommend to multiply the first equation by 4, and the second equation by 5 and then subtract equation 2 from equation 1 (comparable term by comparable term).

5x - 2y = 10

4x - 3y = 15

would then turn into

20x - 8y = 40

- 20x - 15y = 75

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

0 7y = -35

y = -35/7 = -5

now we can pick any original equation to solve for x.

e.g.

5x - 2×-5 = 10

5x + 10 = 10

5x = 0

x = 0

Answer: The scale of the billboard is 1 foot = 8 inches, so to find the actual height of the woman, we need to multiply the height on the billboard by 8.

8 3/8 feet x 8 inches/foot = 66 inches (8 x 8) + (3 x 8) = 66

So the woman's actual height is 66 inches.

Step-by-step explanation:

The x-intercepts and the y-intercept of the cubic function f(x) = x³ - 9·x² + 20·x - 12 for which (x - 6) is a factor are;

A function is a rule that uniquely maps each value from the set of input variables to exactly one value in the set of the output variables.

The specified cubic function is; f(x) = x³ - 9·x² + 20·x - 12

A factor of f(x) = x - 6

The x-intercepts are the points on the graph of the function, where the value of the function, f(x) = 0, which are found as follows;

At the x-intercept, f(x) = x³ - 9·x² + 20·x - 12 = 0

x³ - 9·x² + 20·x - 12

Dividing the cubic function by the factor (x - 6), we get;

          x² - 3·x + 2

(x - 6) | x³ - 9·x² + 20·x - 12

   [tex]{}[/tex]       x³ - 6·x²

[tex]{}[/tex]                 -3·x²

[tex]{}[/tex]                 -3·x² + 18·x

                    [tex]{}[/tex]       2·x  

[tex]{}[/tex]                            2·x - 12

[tex]{}[/tex]                                      0

The other factor of the cubic function is; x² - 3·x + 2

x² - 3·x + 2 = (x -2)·(x - 1)

Therefore;

f(x) = x³ - 9·x² + 20·x - 12 = (x - 6)·(x - 2)·(x - 1)

From which at the x-intercepts, we get;

f(x) = (x - 6)·(x - 2)·(x - 1) = 0

x = 6, x = 2, and x = 1

The y-intercept are the points the x-values is zero, therefore, at the y-intercepts, we get;

f(0) = 0³ - 9·0² + 20·0 - 12 = -12

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Using the mathematical operations of addition and subtraction, the weight of the bag of grapefruit is 3¹¹/₁₆.

The basic mathematical operations we have studied so far include addition, subtraction, division, and multiplication.

In addition operation, two or more addends are added to obtain a result known as the sum or total.

Using subtraction operation, the minuend, subtrahend, and difference are the major parts, including the subtraction operator (-).

There are two ways of solving this problem, we can add the fractional weights of apples and bananas and subtract the sum from the total weight of fruits Lynne bought.

We can also subtract each fractional weight from the total weight of fruits to arrive at the fractional weight of the bag of grapefruit.

The total weight of Lynne's purchases = 7¹/₂ pounds

The weight of apples = 1⁵/₈ pounds

The weight of bananas = 2³/₁₆ pounds

The weight of grapefruit = x

= 7¹/₂ - 1⁵/₈ - 2³/₁₆

= 3¹¹/₁₆

Add fractional weights:

1⁵/₈ + 2³/₁₆ = 3¹³/₁₆

Subtract the sum of the fractional weights from the total weight:

7¹/₂ - 3¹³/₁₆ = 3¹¹/₁₆

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Answer:

Step-by-step explanation:

Solution:- this is question of subtraction , so 18712-9412=9300(Answer)

Answer:

let's see jssjsjnsjsjsjsjsjsjsjsjsjs

Check the picture below.

The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.

A linear equation is an algebraic equation where the highest exponent of the variable is one. There are linear equations with one, two, or three variables, but not all linear systems have three equations. Typically, a system of linear equations has a single solution, but occasionally there is no solution or an infinite number of solutions.

A relationship in which the value of one variable, say "x," depends on the value of the other variable, say "y," is described by a two variables linear equation. A linear equation's graph will be a straight line if there are only two variables.

Given that cost for 5 tickets is $174.45

Let x be the cost of each ticket and y be the processing fee

5x + y = 174.45

And for the cost for 8 tickets is $271.95

8x + y = 271.95

Subtract the terms

 8x + y = 271.95

- 5x + y = 174.45

 3x + 0 = 97.5

If 3x = 97.5

Then,

x = 97.5/3

x = 32.5

Each ticket costs $32.5 then processing fees

5(32.5) + y = 174.45

y = 174.45 - 162.5

y = 11.95

8(32.5) + y = 271.95

y = 271.95 - 260

y = 11.95

Thus, The linear equation for this situation is ax + y = Total cost, where is no. of ticket, x = $32.5, is cost of ticket and y = $11.9 is processing fee.

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Part (a)

Reason:

There are 7 items inside set A. The notation n(A) counts the number of elements in a set.

==========================================

Part (b)

It's not clear what your teacher is asking. It seems this part is incomplete. Please revise.

Answer:

90

Step-by-step explanation:

15 to first 20

so 120 = 6*20

so 6*15 =90

Answer: A irregular

b. irregular

c neither

d. Regular

e. regular

Step-by-step explanation: Regular polygons have all sides equal in length but an irregular polygon does not have all sides equal.

Answer:

A: Irregular polygon

B: Irregular polygon

C: Neither

D: Regular polygon

E: Regular polygon

Step-by-step explanation:

To start off with, we can eliminate C for being a polygon (neither), because being a polygon states the shape must be closed with a finite number of line segments (a circle has an infinite amount of line segments).

A regular polygon states that it must have an equal distance on all sides. We can find this by looking at what shapes have a line (which represents that it has the same length) on all sides. The only polygons that fit this requirement are D and E.

From here we can see that the remaining polygons of A and B are in fact irregular polygons by process of elimination.

Answer:

4+3=7

-2+3=7

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

2^2+11^2=c^2

4+121=c^2

125=c^2

c=125 square root

they expect to discard everyday 288.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, given that,

they must discard 3 out of 100 wheels because they are defective.

the factory produces 1200 wheels per hour in each 8 hr day.

total per day = 9600

so, they expect to discard everyday =9600 * 3%

                                                            =288

hence, they expect to discard everyday 288.

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The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of  -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, [tex]\sqrt{x^2-11}[/tex] , This in word phrase can be written the square root of the difference between a square of a number and 11.

-2x/11 can be written as twice the number multiplied by the reciprocal of -11

√2x + 11 can be written as sum of square root of twice the number and 11

Hence, The correct statement is- the square root of the __difference__ of a _the polynomial x²_ and 11 → √x² - 11 the __product__ of _-2x_ times a number and reciprocal of  -11 → -2x/11 the sum_ of the __square root__ of two times a number and 11 → √2x + 11.

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Answer: To solve this problem, we can use algebra. Let x be the smaller page number. Then, the larger page number is x + 1, since the pages are facing each other. We know that the sum of these two numbers is 553, so we can set up the equation:

x + (x+1) = 553

Next, we will solve for x by combining like terms:

2x + 1 = 553

Now we will subtract 1 from both sides of the equation:

2x = 552

Finally, we will divide both sides by 2:

x = 276

So the smaller page number is 276.

Step-by-step explanation:

Answer:

Answer

Step-by-step explanation:

20s³ +50s²+32s+6

Answer:

There are few possible ways to find the complex zeros

You can find the complex zeros by using quadratic formula

[tex]x^2-6x+13=0[/tex]

[tex]=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\cdot \:13}}{2\cdot \:1}[/tex]

[tex]x_{1,\:2}=\frac{-\left(-6\right)\pm \:4i}{2\cdot \:1}[/tex]

[tex]x_1=\frac{-\left(-6\right)+4i}{2\cdot \:1},\:x_2=\frac{-\left(-6\right)-4i}{2\cdot \:1}[/tex]

[tex]x=3+2i,\:x=3-2i[/tex]

Answer:

The zeroes of the equation are -2 and -6.

Step-by-step explanation:

(x + 2)(x + 6) = 0

=> x = -2, -6

Hope it helps.

Answer: So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.

Step-by-step explanation:

To calculate the simple interest on an investment of $2500 at a 6% interest rate for 3 years and 5 months, you would use the formula:

Simple Interest = (Principal x Interest Rate x Time in Years)

In this case, the time in years would be 3.5 (3 years and 5 months)

Simple Interest = (2500 x 0.06 x 3.5) = $525

So, after 3 years and 5 months, the total amount of simple interest earned on an investment of $2500 at a 6% interest rate would be $525.

Translating the statement "Babies are illogical" into symbolic form willoll be C. P➡️~Q

Symbols and logical connectors are used in symbolic sentences to represent the sentence's logic.

A letter, such as p, can represent an entire statement in symbolic logic.

In symbolic form, the argument is p → q ~p ∴ ~q It is in the form of the fallacy of the inverse and it is a fallacy, or invalid

In this case, it should be noted that since p is that you are a baby and Q be you are logical. The symbolic form will be C.

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a) The margin of error for the 95% confidence interval is given as follows: $122.4.

b) The 95% confidence interval for the population mean amount spent on restaurants and carryout food is given as follows: ($1,750.6, $1,995.4).

c) The estimate of the total amount spent by Americans of age 50 and over on restaurants and carryout food is between $161,055,200,000 and $183,576,800,000.

d) As the distribution os skewed to the right, the median would be expected to be less than the mean.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

The margin of error is then defined as follows:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 80 - 1 = 79 df, is t = 1.9905.

The parameters for this problem are given as follows:

[tex]\overline{x} = 1873, s = 550, n = 80[/tex]

Hence the margin of error is of:

[tex]M = 1.9905 \times \frac{550}{\sqrt{80}} = 122.40[/tex]

Considering the sample mean and the margin of error, the bounds of the confidence interval are given as follows:

Considering the bounds of the confidence interval and the population of 92 million, the bounds of the estimate of the total amount are given as follows:

The relation between mean, median and skewness is given as follows:

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Answer:

Step-by-step explanation:

a)24

b)4

c)10

d)16

e)172

Answer:

Step-by-step explanation:

Solving by factoring is a strategy for solving a polynomial equation that is in quadratic form. Quadratic form means that the equation is of the form ax^2+bx+c=0, where a,b, and c are real numbers. When factoring, the goal is to express the equation as the product of two simpler equations. To do this, we must factor the quadratic equation into two linear equations, each with a single variable.

For example, consider the equation x^2+3x-4=0. To factor this equation, we can first rewrite it as (x+4)(x-1)=0. This is the same as x+4=0 and x-1=0. We can then solve each of these linear equations to find the solutions. In this case, the solutions are x=-4 and x=1.

Therefore, the strategy of solving by factoring is to rewrite a polynomial equation in quadratic form as the product of two simpler equations, and then solve each of these equations. The solutions to the original equation can then be found by solving each of the linear equations.

Answer:

$1,100

Step-by-step explanation:

The cost of the summer camp for the youngest child is around $500, when rounded to the nearest hundred.

The cost of the summer camp for the middle child is around $200.

The cost of the summer camp for the oldest is around $400.

500+200+400=1100

Answer: 222 gallons of gasoline to travel 444 miles.

Step-by-step explanation: To find how much gasoline the boat needs to travel 444 miles, we need to use the formula:

distance = rate x time

Where distance is the total distance to be traveled, rate is the distance per unit of fuel (370 miles/185 gallons) and time is the amount of fuel required to travel 444 miles.

So we can calculate the fuel required as:

Fuel = (distance) / (rate)

Fuel = (444 miles) / (370 miles/185 gallons) = 444/ (370/185) = 444/2 = 222 gallons.

So the boat needs 222 gallons of gasoline to travel 444 miles.

Triangle FYJ is congruent to triangle HYJ using the RHS congruency theorem.

FJ is congruent to segment HJ.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

We know right angle hypotenuse congruency, which states two right angle triangles are congruent if one of the legs and hypotenuse corresponding to the other right angle triangle is equal in measure.

Triangle FYJ is congruent to triangle HYJ as FY is congruent to HY and JH is congruent to JH.

So, Their hypotenuses are also equal in measure.

Hence, FJ is congruent to JH.

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Answer:

128

Step-by-step explanation:

1.2*4 =4.8

so 32*4 = 128