This is about transformation of objects.
Scale factor back to original size = 1/7
We are told that the rectangle was scaled by a factor of 7.What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;
7x and 7y.
Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Thus,the scale factor will be 1/7 back to the original size.Read more at; https://brainly.com/question/17292295
Explain what a polynomials is and identify the different parts of a polynomial.
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms explain how foil helps us to accomplish this and what category of polynomials foil applies to.
There are tow special case products where the product takes on special patterns explain these two cases and when they occur.
For each of the two special cases, illustrate your explanation with an appropriate exercise from the ( a+b)2=a2+2ab+b2 )(a-b)2=a2-2ab+b2 ) showing how the multiplication is performed using the special pattern formula then also showing the same result using foil.
A polynomial is an expression of more than one term. An expression is considered a polynomial when is has more than one term, otherwise, it would be called a monomial. These can be combined together through multiplication, addition and subtraction only. (Meaning no division or fractions)
Ex.
[tex]3 x^{2} + 3x - 3[/tex]
x is a variable (There can be more than 1 variable in a term. Ex. 3xy, 4xyz, 4ab)
*A variable may be represented by letters.
2 is an exponent
3 is a constant
Those are the parts of a polynomial.
Polynomials can be categorized depending on the number of terms and their degree.
A polynomial with two terms is called a binomial. If it has three terms it is called a trinomial. If the expression has more than 3 terms, they are generally called polynomials.
A polynomial can be categorized by degree as well. You can determine the degree of a polynomial by looking at the term that has the highest exponent.
Using the example above, you can categorize the polynomial as a 2nd degree trinomial because 2 is the highest exponent and it has three terms.
When you add and subtract polynomials you need to take note of the variables. You can only subtract and add like terms, which means that the variables and the exponents are the same.
Ex.
[tex]( 2x^{3} + 2 y^{2} + x + 1) + (4 x^{2} - y^{2} + y + 2)[/tex]
When you add these two polynomials, you can disregard the parentheses because according to the associative property of addition, no matter how you group the terms, the answer will be the same.
Like mentioned before you can only add and subtract like terms. It would be easier if you just group like terms together by rearranging the expression. Do not forget that the sign or operation comes along with them.
[tex]2 x^{3} + 2 y^{2} - y^{2} + 4 x^{2} + x + y + 2 + 1[/tex]
Now combine the like terms.
[tex]2 x^{3} + y^{2} + 4 x^{2} + x + y + 3[/tex]
Notice that we retained the terms [tex]2 x^{3} [/tex] , [tex]4 x^{2} [/tex], x and y, this is because they have no similar terms.
FOIL method is used when multiplying 2 BINOMIALS. Remember that a binomial is an expression with 2 terms.
FOIL means:
FIRST term: first terms of each binomial.
OUTSIDE term: The two outer terms when taking the equation as a whole.
INSIDE term: The two inner terms when taking the equation as a whole.
LAST term: Last term of each binomial (2nd term of each binomial)
To get the answer, you need to multiply them with their corresponding term.
Ex. (2x+3)(x-4)
F: 2x and x (2x)(x) = [tex] 2x^{2} [/tex]
O: 2x and -4 (2x)(-4) = -8x
I: 3 and x (3)(x) = 3x
L: 3 and -4 (3)(-4) = -12
Resulting expression:
[tex]2 x^{2} - 8x + 3x -12[/tex] -8x and 3x are similar or like terms, so you can combine them
[tex]2 x^{2} - 5x -12[/tex]
When doing multiplication with binomials, there are two special cases you can consider doing, which follow a pattern. The first is multiplying sum and difference.
The condition where you can apply the first special case is the first term needs to be the same and the second term are additive inverses.
(a+b)(a-b)
The resulting expression follows this pattern [tex] a^{2} - b^{2} [/tex]
Ex. (x+3)(x-3) = [tex] x^{2} - 3^{2} [/tex] or [tex] x^{2} -9[/tex]
You can use FOIL to check your answer:
F: (x)(x) = [tex] x^{2} [/tex]
O: (x)(-3) = [tex]-3x[/tex]
I: (3)(x) = [tex]3x[/tex]
L: (3)(-3) = [tex]-9[/tex]
Arrange the expression:
[tex] x^{2} - 3x + 3x - 9[/tex] Combining -3x+3x = 0
[tex] x^{2} -9[/tex]
The next special case is squaring a binomial and there are two scenarios that you can consider.
[tex] (a+b)^{2} [/tex] and [tex] (a-b)^{2} [/tex]
The resulting expression follows a certain pattern for each:
[tex] (a+b)^{2} [/tex] = [tex] a^{2} + 2ab + b^{2} [/tex]
[tex] (a-b)^{2} [/tex] = [tex] a^{2} - 2ab + b^{2} [/tex]
Let's use an example of each to demonstrate this and check with FOIL:
[tex] (a+b)^{2} [/tex]
[tex] (2x+4)^{2} [/tex]
a = 2x b = +4
Let's insert that into our pattern:
[tex] a^{2} + 2ab + b^{2} [/tex]
[tex] 2x^{2} + 2(2x)(4) + 4^{2} [/tex]
Simplify the expression:
[tex] 2x^{2} + 16x + 4^{2} [/tex]
[tex] 4x^{2} + 16x + 16 [/tex]
Let's check with FOIL
[tex] (2x+4)^{2} [/tex] = [tex] (2x+4)(2x+4) [/tex]
F: (2x)(2x) = [tex] 4x^{2} [/tex]
O: (2x)(4) = [tex]8x[/tex]
I: (4)(x) = [tex]8x[/tex]
L: (4)(4) = [tex]16[/tex]
Let's arrange the terms:a = 2x b = -4
Let's insert that into our pattern:
[tex] a^{2} - 2ab + b^{2} [/tex]
[tex] 2x^{2} - 2(2x)(-4) + (-4)^{2} [/tex]
Simplify the expression:
[tex] 2x^{2} - 16x + (-4)^{2} [/tex]
Let's check with FOIL
[tex] (2x+4)^{2} [/tex] = [tex] (2x-4)(2x-4) [/tex]
F: (2x)(2x) = [tex] 4x^{2} [/tex]
O: (2x)(-4) = [tex]-8x[/tex]
I: (-4)(x) = [tex]-8x[/tex]
L: (-4)(-4) = [tex]16[/tex]
Let's arrange the terms:What are the zeros of the polynomial y = (3x − 1)(x + 2)(2x + 1)?
Every five years in march, the population of a certain town is recorded. In 1995,the town had a population of 4,500 people. From 1995 to 200, the population increased by 15%. From 2000 to 2005,the population decrease d by 4%. What was the town's population in 2005?
Cora is taking three AP classes and two regular classes. Her AP classes count twice as much as her regular classes in her GPA. Each A is worth 4 points, Bs are worth 3 points, Cs are worth 2 points, and Ds are worth 1 point. What is Cora's GPA? Class Cora's grade AP English A AP Government A AP Algebra II A Spanish B Physics A
Cora's GPA, considering the weighted AP classes and grades achieved, calculates to be 3.875.
To calculate Cora's GPA with her AP and regular classes, we need to account for the weight of her AP classes.
Cora has five classes with three being AP and two regular.AP classes count twice as much as regular classes. Thus, AP classes will be counted as double credits.Calculate the points for each grade:AP English (A): 4 points, counted double = 4 × 2 = 8 pointsAP Government (A): 4 points, counted double = 4 × 2 = 8 pointsAP Algebra II (A): 4 points, counted double = 4 × 2 = 8 pointsSpanish (B): 3 pointsPhysics (A): 4 pointsTotal points = 8 + 8 + 8 + 3 + 4 = 31 pointsTotal credit count = 6 (for AP) + 2 (for regular) = 8 creditsCalculate GPA = Total points / Total credits = 31 / 8 = 3.875Therefore, Cora's GPA is 3.875.
A student needs to earn 80 points on the test in order to keep an A grade for the semester. Write an equation that represents the situation in terms of the number of correct answers
The equation that represents the situation is x = 80.
Explanation:To write an equation representing the situation, let's use the variable x to represent the number of correct answers on the test. Since each correct answer is worth 1 point, the total number of points earned is the same as the number of correct answers. Given that the student needs to earn 80 points to keep an A grade for the semester, the equation is:
x = 80
Therefore, if the student answers 80 questions correctly, they will maintain an A grade for the semester.
An error occurred in your bookkeeping department this month. The price of one of the smart phones that you sell is $489. Several customers were charged $565 for the phone instead. You know that the total sales for this month were $213,873 and that 401 phones were sold. How many phones were sold at the wrong price?
Divide (5.6 x 10^15) by (6.4 x 10^2). Express your answer in scientific notation.
Consider a population of bacteria that grows according to the initial value problem dP/dt=P/10, P(0)=300. Find the population size after 40 hours
What is the axis of symmetry of h(x)=5x^2+40x+64
Answer:
2
Step-by-step explanation:
give me brainliest
Write at least three different expressions that mean “slope”
Answer:
Step-by-step explanation:
Considering 'm' as the slope of a function y=f(x) we can have:
1. m=(y2-y1)/(x2-x1) which is the slope of a line based on two points from the line.
2. m=dy/dx which is the slope of the function y=f(x) in (x,y) by the derivative.
3. m=tan(Ф) which is the slope of a line when the angle (Ф) with respect x-axis is known.
A snowboarder traveled at a speed of 12 meters per second for 15 seconds. How far did the snowboarder travel?
18 meters
27 meters
180 meters
270 meters
The correct answer is C. 180 meters
Explanation:
The general formula to calculate distance is Distance = Speed x Time. This implies if you multiply the speed (rate of motion) by the time (seconds, minutes, etc) you can know the total distance traveled. In the case presented this means Distance = 12 meters per second (speed) x 15 seconds (time). Thus, the distance the snowboarder traveled was 180 meters as 12x 15 = 180. Also, the distance is expressed in meters because the unit used in the steed is meters per second.
is 1,200mm greater or less than 12m
Final answer:
1,200 millimeters (mm) is less than 12 meters (m). To compare, we convert 1,200 mm to 1.2 m and directly compare it with 12 m, clearly seeing that 1.2 m is less than 12 m.
Explanation:
To determine whether 1,200 millimeters (mm) is greater or less than 12 meters (m), we need to convert mm to meters. We know that 1 meter is equal to 1,000 millimeters. Therefore, we can convert 1,200 mm to meters:
1,200 mm ÷ 1,000 = 1.2 m
Now we can compare 1.2 m with 12 m directly. Since 1.2 is less than 12, we can conclude that 1,200 mm is less than 12 m.
To use an example for further clarification, imagine you are measuring the length of a room with a tape measure:
If the room is 1,200 mm (or 1.2 m) long, it is shorter than a room that is 12 m long.
The volume of a shampoo filled into a container is uniformly distributed between 374 and 380 milliliters. (a) what are the mean and standard deviation of the volume
The mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.
The standard deviation is calculated using the following formula:
[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]
Given the range (374 to 380 milliliters):
(a) Mean[tex](\(\mu\))[/tex]:
[tex]\[ \mu = \frac{{\text{min} + \text{max}}}{2} \][/tex]
[tex]\[ \mu = \frac{{374 + 380}}{2} \][/tex]
[tex]\[ \mu = 377 \text{ milliliters} \][/tex]
(b) Standard Deviation:
[tex]\[ \sigma = \frac{{\text{max} - \text{min}}}{{\sqrt{12}}} \][/tex]
[tex]\[ \sigma = \frac{{380 - 374}}{{\sqrt{12}}} \][/tex]
[tex]\[ \sigma \approx \frac{{6}}{{\sqrt{12}}} \][/tex]
[tex]\[ \sigma \approx \frac{{6}}{{3.464}} \][/tex]
[tex]\[ \sigma \approx 1.732 \text{ milliliters} \][/tex]
So, the mean volume of the shampoo is 377 milliliters, and the standard deviation is approximately 1.732 milliliters.
ASAP! hurry please! :)
the functions f(x) and g(x) are graphed
Answer:
AAAA
Step-by-step explanation:
I just took the test
Write a decimal that represents the value of $1 bill and 5 quarters.
What is the following product? Assume
The answer is B 10x56 Sq 6xy
Answer:
B
Step-by-step explanation:
edgen 2020
A train traveled 300 km in 5 hours and then increased in speed, traveling the final 100 km in 1.5 hours. What was the train's average speed in km/h?
66.7 km/h
60 km/h
61.5 km/h
54 km/h
Answer:
vm=( 57.1+66,6)/2≈ 61,5 km/h
Step-by-step explanation:
the lowest elevation in Long Beach California is 7 feet below sea level the elevation of Death Valley is about 40 times lower than the elevation of Long Beach what is the approximate elevation of Death Valley
[tex] - 7 - 40 [/tex]
The approximate elevation of Death Valley will be 280 feet.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The lowest elevation in Long Beach California is 7 feet below sea level the elevation of Death Valley is about 40 times lower than the elevation of Long Beach.
The approximate elevation of Death Valley will be
⇒ 7 x 40
⇒ 280 feet
The approximate elevation of Death Valley will be 280 feet.
More about the Algebra link is given below.
https://brainly.com/question/953809
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find the value of x
Answer with Step-by-step explanation:
since, DAC is a straight line
Hence, ∠BAD+∠BAC=180°
98°+∠BAC=180°
⇒ ∠BAC=180°-98°
= 82°
Now, we know that sum of angles of a triangle=180°
Hence, ∠BAC+∠ABC+∠BCA=180°
82°+32°+x=180°
x=180°-82°-32°
x= 66°
Hence, correct option is:
C. 66°
In this figure, ∠a and ∠b are 15 points here
Example: y = -2x and y = x + 3 2)
Does the point (2, 5) make either equation true? Explain.
How can you convert 5 feet 6 inches to inches
A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl. The rep uses a 1 for a girl and a 2 for a boy when running a simulation. Would the simulation be a fair representation of possible survey results? Why or why not?
A. Yes, because each of the two outcomes are equally likely.
B. No, because each of the two outcomes are not equally likely.
C. No, because the survey includes 300 results.
D. Yes, because the survey includes 300 results.
Answer:
A. Yes, because each of the two outcomes are equally likely.
Step-by-step explanation:
A sales representative for a baby food company wants to survey 300 random couples who are new parents to find out if their newborn child is a boy or a girl.
The representative uses a 1 for a girl and a 2 for a boy when running a simulation.
Yes, the simulation will be a fair representation of possible survey results.
A. Yes, because each of the two outcomes are equally likely.
Find the measure of the third angle of a triangle given that the first two angles are 44o and 72 o. Show your work.
Answer: The measure of the third angle of a triangle is 64°.
Step-by-step explanation:
Since we have given that
First angle = 44°
Second angle = 72°
Let the third angle be x.
As we know that the sum of all three angles of a triangle is supplementary.
[tex]44^\circ+72^\circ+x=180^\circ\\\\116^\circ+x=180^\circ\\\\x=180^\circ-116^\circ\\\\x=64^\circ[/tex]
Hence, the measure of the third angle of a triangle is 64°.
John has 51 cards. Paul has 32 cards. George has a number of cards greater than either Paul or John. How many cards might George have?
John has 51 cards.
Paul has 32 cards.
George has a number of cards greater than either Paul or John.
This means, George does have number of cards greater than both Paul and John.
Number of Cards with John is 51 and number of cards with Paul is 32 cards.
Therefore the number of cards that George may have is in between 33 and 51
If George has any number of cards greater than 32 and less than 52, then this number of cards is greater than cards with Paul but less than the cards with John.
Number of cards George has is > 32 but < 52
Hope this helps..!!
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Melanie is reading a book that is 300 pages long. If she has read 210 pages of the book, what percent of the book has she read?
Answer:
She has read 70 % of the book.
Step-by-step explanation:
Given : Melanie is reading a book that is 300 pages long. If she has read 210 pages of the book,
To find : what percent of the book has she read.
Solution : We have given
Total pages in book = 300 pages .
She read = 210 .
Percentage she read (%) = [tex]\frac{She\ read\ pages}{total\ pages}*100[/tex].
Percentage she read (%) = [tex]\frac{210}{300}*100[/tex].
Percentage she read (%) = [tex]\frac{210}{3}[/tex].
Percentage she read (%) = 70 % .
Therefore, She has read 70 % of the book.
10 points thanks in advanced
Mario has 3.875 liters of juice at the beginning of the day he drinks 2.79 liters during the day how much juice is left over st the end of the day
Answer:
The juice left at the end of the day is 1.085 liters.
Step-by-step explanation:
Juice at the beginning of the day: 3.875 liters
Juice drink by Mario during the day: 2.79 liters
Juice left at the end of the day = Juice at the beginning of the day - Juice drink by Mario during the day
= 3.875 - 2.79
= 1.085 liters
find the volume of a sq pyramid with height of x+8 and length of 3x and width of 3x