It is important to know that a Product is the result of a multiplication.
You have the following expression given in the exercise:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)[/tex]Notice that it is the multiplication of two Binomials and it has this form:
[tex](a+b)(a-b)[/tex]By definition:
[tex](a+b)(a-b)=a^2-b^2[/tex]This is called "Difference of two squares".
You can identify that, in this case:
[tex]\begin{gathered} a=3y \\ b=1 \end{gathered}[/tex]Therefore, you get:
[tex]\mleft(3y+1\mright)\mleft(3y-1\mright)=(3y)^2-(1)^2=9y^2-1[/tex]The answer is:
[tex]9y^2-1[/tex]Consider this prism. Enter the volume of the rectangular prism, in cubic centimeters. 3 3/4, 3 1/3, 2 1/2.
Solution
For this case we have the following dimensions:
x = 3 3/4 = 15/4
y= 3 1/3 = 10/3
z= 2 1/2 = 5/2
Then we can find the volume with the following formula:
[tex]V=x\cdot y\cdot z=\frac{15}{4}\cdot\frac{10}{3}\cdot\frac{5}{2}=\frac{125}{4}ft^3[/tex]Then we can convert to cm^3 like this:
[tex]\frac{125}{4}ft^3\cdot\frac{(30.48\operatorname{cm})^3}{1ft^3}=884901.46\operatorname{cm}^3[/tex]You went to the mall to buy a sweater that was 30% off and you had an additional 20% off coupon. The cashier took the 20% off first and then the 30% off of the reduced amount second. The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second. Would it matter which way this was done? Why or why not?
Explanation
let's check every case,
Step 1
A)The cashier took the 20% off first and then the 30% off of the reduced amount second.
let x represents the original price
to find the 20% we can use
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-20}{100}=x*(\frac{80}{100})=0.8x \\ new\text{ price =}0.8c \end{gathered}[/tex]then,the 30 % of the reduced amount, so
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.8x\rparen *\lparen}\frac{100-30}{100}=(0.8x)*(\frac{70}{100})=(0.8x)(0.7)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 2
B)The manager said "No, you are supposed to take the 30% off first and then the 20% off the reduced amount second
so
i) 30 of the first
[tex]\begin{gathered} new\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ new\text{ price= x*\lparen}\frac{100-30}{100})=x*(\frac{70}{100})=0.7x \\ new\text{ price =}0.7c \end{gathered}[/tex]then, 20 % off the reduced amount
[tex]\begin{gathered} final\text{ price = original price *\lparen}\frac{100-discount}{100}) \\ so \\ final\text{ price= \lparen0.7x\rparen *\lparen}\frac{100-20}{100}=(0.7x)*(\frac{80}{100})=(0.7x)(0.8)=0.56x \\ final\text{ price =0.56x} \end{gathered}[/tex]Step 3
so, we can conclude in both cases the final price will be the same, becuase we have a triple product
[tex]\begin{gathered} x*0.8*0.7=x*0.7*0.8 \\ 0.56x=0.56x \end{gathered}[/tex]so, the answer is
it does not matter which way the calculation is done, because the order does not affect the product
I hope this helps you
-7>-10 true or false
To answer this question we need to see it on an axis.
-7> -10 , it is true. -7 it's more near to 0.
16 ft.8 ftSurface Area =
The graph of y = x 2 has been translated 7 units to the left. The equation of the resulting parabola is _____.y = (x - 7) 2y = (x + 7) 2y = x 2 - 7y = x 2 + 7
The translation of a function to the left or to the right is a horizontal translation. Horizontal translation can be defined as the movement toward the left or right of the graph of a function by the given units. It should be noted that the shape of the function remains the same. The horizontal translation is also known as the movement/shifting of the graph along the x-axis. For any base function f(x), the horizontal translation by a value k can be given as
[tex]f(x)=f(x\pm k)[/tex]If the function is shifted to the right, the translation function would be
[tex]f(x)=f(x-k)[/tex]If the function is shifted to the left, the translation would be
[tex]f(x)=f(x+k)[/tex]If the graph of y = x² has been translated 7 units to the left. The equation of the resulting parabola would be
[tex]y=(x+7)^2[/tex]Hence the equation of the resulting parabola is (x+7)²
Part A: Colby's experiment follows the model:Part B: Jaquan's experiment follows the model:
Answer:
C
D
The population of bacteria after x days that are growing with a constant factor goes by:
[tex]P(x)=ab^{nx}[/tex]Where:
a = initial population
b = growth factor
n = number of periods in a day
a.) Colby's experiment:
a = 50
b = 2
Since they are doubling every 2 hours:
n = 24/2 = 12
Therefore, Colby's experiment follows:
[tex]y=50\cdot2^{12x}[/tex]b.) Jaquan's experinment:
a = 80
b = 2
Since they double every 3 hours:
n = 24/3 = 8
Therefore, Jaquan's experiment follows the model:
[tex]y=80\cdot2^{8x}[/tex]estimate the product by rounding to the nearest 10: 28×56×76
EXPLANATION
Given the operation:
28------> rounded to 30
56-------> rounded to 50
76 ------> rounded to 80
Now, we can mentally calculate that:
3x5= 15 so 30x50 = 1500 (two zeros)
15x8 = 120 so,
1500x80 = 120,000
The answer is 144,000.
1. 2х^2 * 3x^3y * 3x^3y=1. 2х^2 * 3x^3*y * 3x^3*y=
Given the expressions
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y= \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}= \end{gathered}[/tex]First: we group and multiply the numbers
[tex]\begin{gathered} (A).2x^2\cdot3x^3\cdot y\cdot3x^3\cdot y=(2\cdot3\cdot3)\cdot x^2\cdot x^3\cdot y\cdot x^3\cdot y=18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).2x^2\cdot3x^{3y}\cdot3x^{3y}=(2\cdot3\cdot3)x^2\cdot x^{3y}\cdot x^{3y}=18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Now we have the expressions
[tex]\begin{gathered} (A).18x^2\cdot x^3\cdot y\cdot x^3\cdot y \\ (B).18x^2\cdot x^{3y}\cdot x^{3y} \end{gathered}[/tex]Second: we multiply the expressionswith the same base adding its exponents
[tex]\begin{gathered} (A).18x^{2+3+3}\cdot y^{1+1}=18x^8y^2 \\ (B).18x^{2+3y+3y}=18x^{6y+2} \end{gathered}[/tex]The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If anastronaut weighs 215 pounds on the surface of the Earth, what will this astronaut weigh 2650 miles above the Earth? Assume that the radius of the Earth is 4000miles. Round your answer to one decimal place if necessary
Given:
F is inversely proportional to the square of the distance means that
[tex]F=\frac{k}{d^2}[/tex]So the value of "k" is:
[tex]\begin{gathered} 215=\frac{k}{4000^2} \\ k=215\times(4000)^2 \\ k=3440000000 \end{gathered}[/tex]Weigh in 2650 mile above
[tex]\begin{gathered} F=\frac{k}{d^2} \\ F=\frac{3440000000}{(2650)^2} \\ F=\frac{3440000000}{7022500} \\ F=489.85\text{ pound} \end{gathered}[/tex]Solve the following system using the elimination method. Enter your answer as an ordered pair in the form (x,y) If there is one unique solution. Enter all if there are infinitely many solutions and enter none if there are no solutions 6x - 5y = 41 2x + 6y = 6
Okay, here we have this:
Considering the provided system, we are going to solve it using the elimination method, so we obtain the following:
[tex]\begin{gathered} \begin{bmatrix}6x-5y=41 \\ 2x+6y=6\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ (-3)2x+6y=6(-3)\end{bmatrix} \\ \begin{bmatrix}6x-5y=41 \\ -6x-18y=-18\end{bmatrix} \end{gathered}[/tex]Now we will add the equations to eliminate the y term:
[tex]\begin{gathered} \begin{bmatrix}-23y=23\end{bmatrix} \\ \begin{bmatrix}y=\frac{23}{-23}\end{bmatrix} \\ \begin{bmatrix}y=-1\end{bmatrix} \end{gathered}[/tex]Finally, let's replace in the first equation to find the value of x:
[tex]\begin{gathered} \begin{bmatrix}6x-5(-1)=41\end{bmatrix} \\ \begin{bmatrix}6x+5=41\end{bmatrix} \\ \begin{bmatrix}6x=36\end{bmatrix} \\ \begin{bmatrix}x=\frac{36}{6}\end{bmatrix} \\ \begin{bmatrix}x=6\end{bmatrix} \end{gathered}[/tex]Finally we obtain that the unique solution for the system is the ordered pair: (6, -1).
your gonna need a calculator for this I don't have one help please
The correct answer is the option a) because in the table we can note that the values of the weight are strictly increasing, and the only option that meets this condition is the option a).
In the following table of values, what would be the value of “b” in ax2 + bx + c?
–2
–9
–1
–1
0
9
1
21
2
35
1
9
11
22
The value of b is 11.
From the question, we have
ax² + bx + c
using (0, 9)
substituting the value we get
9 = a(0)² + b(0) + c
c = 9
Therefore,
-1 = a(-1)² + b(-1) + c
-1 = a - b + 9
-1 - 9 = a - b
a - b = - 10
using (-2, -9)
-9 = a(-2)² + b(-2) + 9
-9 - 9 = 4a - 2b
-18 = 4a - 2b
2a - b = -9
combine the equation
a - b = - 10
2a - b = -9
solving the equations we get
a = 1
Then,
1 - b = -10
b = 1 + 10
b = 11
Hence, the value of b is 11.
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference. As the first integer to be subtracted from in a subtraction phrase, a minuend is the first number in the subtraction process.
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Express 4√90 in simplest radical form.
ANSWER
[tex]\text{12}\sqrt[]{10}[/tex]EXPLANATION
We want to find the simplest radical form of 4√90.
To do this, we have to reduce the number in the square root in factor form and then reduce it with the square root.
We have:
[tex]\begin{gathered} 4\sqrt[]{90} \\ \Rightarrow\text{ 4 }\cdot\text{ }\sqrt[]{\text{9 }\cdot\text{ 10}}\text{ = 4 }\cdot\text{ }\sqrt[]{3\cdot\text{ 3 }\cdot\text{ 10}} \\ \Rightarrow\text{ 4 }\cdot\text{ 3 }\cdot\text{ }\sqrt[]{10} \\ \Rightarrow\text{ 12}\sqrt[]{10} \end{gathered}[/tex]That is the simplest radical form.
Which of the following transformations are used when transforming the graph of the parent function f(x) = log7x to the graph of g(x) = -log7(3x)+4? Select all that apply.
In this problem, we have the transformations
option B (shift the graph of f(x) 4 units up
option C reflect the graph of f(x) over the y-axis
Subtract this question
[tex]{ \frac{5}{3}} [/tex]
Step-by-step explanation:
[tex]{ \purple{ \sf{3 \frac{2}{6} - 1 \frac{2}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{18 + 2}{6} - \frac{3 + 2}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} - \frac{5}{3}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} \times \frac{1}{1} - \frac{5}{3} \times \frac{2}{2}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20}{6} - \frac{10}{6}}}} [/tex]
[tex]{ = \purple{ \sf{ \frac{20 - 10}{6}}}} [/tex]
[tex]{ = \purple{ \sf{ { \frac{ \cancel{10}^{ \green{ \sf{5}}} }{ \cancel{ 6_{ \green{ \sf{3}}} }}}}}}[/tex]
[tex]{ = \purple{ \boxed{ \red{ \sf{ \frac{5}{3}}}}}} [/tex]
what is the only value of x not in the domain ?
The Solution:
Given:
Required:
Find the domain of the function. What is the value of x that is not in the domain of f(x).
Graphing the function, f(x), we get:
So, the domain of the function is:
[tex](-\infty,-1)\cup(-1,\infty)[/tex]To find the value of x that is not in the domain, we need to find the value of x for which the function is undefined. That is,
[tex]\begin{gathered} 6x+6=0 \\ 6x=-6 \\ \\ x=\frac{-6}{6}=-1 \end{gathered}[/tex]Thus, the value of x not in the domain is:
[tex]x=-1[/tex]
5) 5x + 7y + 3 is an example of a O monomial O binomial O trinomial O polynomial
Problem Statement
The question asks us for what the following expression is an example of
[tex]5x+7y+3[/tex]Solution
Monomial:
A monomial is an expression with only one term. For example:
[tex]x^2[/tex]Binomial:
A binomial is an expression with only two terms. For example:
[tex]2+3x[/tex]Trinomial:
A trinomial is an expression with 3 terms. For example:
[tex]5x+7y+3[/tex]Final Answer
Therefore, the answer is Trinomial
what us the alpha and betta of 3X square - 4x minutes and kisses ever
[tex] \frac{4x}{ {3 \times }^{2}} [/tex]
The values of α and β = 4/〖3x〗^2
A quadratic equation is a second-order polynomial equation in a single variable x
ax2+bx+c=0. with a ≠ 0
Given quadratic equation is 3x2 – 4x = 0
We have to alpha and beta from the given equation
We know that in the quadratic expression
α + β = -b/a. αβ = c/a.
from the equation expression
α + β = 4/〖3x〗^2
αβ = 0/3 ---- (1)
αβ = 0 ----- (2)
If we consider α = 0 from equation (2) then
α + β = 4/〖3x〗^2
β = 4/〖3x〗^2
If we consider β = 0 from equation (2) then
α + β = 4/〖3x〗^2
α = 4/〖3x〗^2
Therefore the values of α = β = 4/〖3x〗^2
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I really sure what to do for this question some help would be greatly appreciated
Given the Domain and the Range of the relation, you need to remember that the Domain is the set of all input values (x-values), and the Range is the set of all the output values (y-values).
Therefore, knowing the input values and the corresponding output values indicated in the Diagram, you can write the following ordered pairs:
[tex](1,9),(4,10),(10,3)[/tex]Notice that they have this form:
[tex](x,y)[/tex]Where "x" is the x-coordinate of the point, and "y" is the y-coordinate.
Therefore, you need to plot all the points on the Coordinate Plane in order to express the relation as a graph.
Hence, the answer is:
Solve using substitution. y = 7x + 3 y = 6x + 4(_ , _)
We have the following:
[tex]\begin{gathered} y=7x+3 \\ y=6x+4 \end{gathered}[/tex]solving using substitution:
[tex]\begin{gathered} 7x+3=6x+4 \\ 7x-6x=4-3 \\ x=1 \end{gathered}[/tex]for y:
[tex]y=7\cdot1+3=7+3=10[/tex]The answer is (1, 10)
what are the coordinates of the vertex for x^2+ 5x - 24 = 0
Solution:
We are required to find the coordinates of the vertex for x^2+ 5x - 24 = 0
[tex]The\text{ x-coordinate of the vertex is x=}\frac{-b}{2a}[/tex][tex]\begin{gathered} For\text{ x}^2+5x-24=0 \\ a=1 \\ b=5 \\ x=-\frac{5}{2(1)} \\ x=-\frac{5}{2} \\ x=-2.5 \end{gathered}[/tex]To get the y coordinate, substitute x = -5/2 into the equation
[tex]\begin{gathered} \begin{equation*} \text{x}^2+5x-24=0 \end{equation*} \\ =(\frac{-5}{2})^2+5(\frac{-5}{2})-24 \\ \\ =\frac{25}{4}-\frac{25}{2}-\frac{24}{1} \\ =\frac{25-50-96}{4} \\ \\ =\frac{-121}{4} \\ \\ =-30.25 \end{gathered}[/tex]Hence, the coordinate of the vertex is (-2.5, -30.25)
The table below shows the thickness of coins. Coin Thickness quarter i millimeters 12 millimeters dime nickel millimeters penny 13 millimeters Hailey stacks a dime on top of a penny. She estimates the thickness of the two coins to be less than 3 millimeters. Write a symbol (, or =) in the box to make the statement true. Then use the statement to tell whether Hailey's estimate is correct. 12 + 12 + 1 Is Hailey's estimate correct?
A dime has a thickness of 1 7/20 mm and a penny has 1 1/2 mm.
Stacking both coins, we will have :
[tex]1\frac{1}{2}+1\frac{7}{20}[/tex]and we have the inequality :
[tex]1\frac{1}{2}+1\frac{7}{20}\boxed{\text{ }}1\frac{1}{2}+1\frac{1}{2}[/tex]Note that 1 7/20 is less than 1 1/2, so the inequality symbol is "<"
[tex]1\frac{1}{2}+1\frac{7}{20}<1\frac{1}{2}+1\frac{1}{2}[/tex]since 1 1/2 + 1 1/2 is equal to 3mm
Therefore, the thickness of stacking coins is less than 3mm
Hailey's estimate is correct (Yes)
Priya rewrites the expression 8 − 24 as 8( − 3). Han rewrites 8 − 24 as2(4 − 12). Are Priya's and Han's expressions each equivalent to 8 − 24? Explain your reasoning.
The given expression is
[tex]8y-24[/tex]Priya rewrite the expression as
[tex]8(y-3)[/tex]Expanding priya's expression gives
[tex]\begin{gathered} 8(y-3)=8\times y-8\times3 \\ 8(y-3)=8y-24 \end{gathered}[/tex]Hence Priya's expression is equivalent to 8y - 24
Han's rewrite the expression as
[tex]2(4y-12)[/tex]Expanding Han's expression gives
[tex]\begin{gathered} 2(4y-12)=2\times4y-2\times12 \\ 2(4y-12)=8y-24 \end{gathered}[/tex]Hence, Han's expression is equivalent to 8y - 24
*Will mark brainiest* Rectangle ABCD is rotated 90° clockwise about the origin to produce Rectangle A'B'CD' What is the length, in units of line segment CD'?
When the given rectangle is rotated 90° around origin point, you obtain the same rectangle, but instead of a horizonatl rectangle as before, you get a vertical rectangle with height CD' and width A'D'.
The length of the segment CD' is 6 units
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on yourUse the number line to determine which statement is true.RSQP+ +24++61618202214128100The value at point P is greater than the value at point S.The value at point S is less than the value at point Q.The value at point S is greater than the value at point R.The value at point Q is less than the value at point P.
The values on the number line increases as we move towards the right. Looking at the number line,
Point P comes before point S. This means that the value of point P is lesser than that of point S. The first statement is wrong
Point S comes after point Q. This means that the value of point S is greater than that of point Q. The first statement is wrong
Point S comes after point R. This means that the value of point S is greater than that of point R. The first statement is true
Point Q comes after point P. This means that the value of point Q is greater than that of point P. The first statement is false
how do I calculate the area of a partial circle?
A part of a circle is called an arc and an arc is named according to its angle.
Calculate the product between 897 and 645
We need to calculate the product:
[tex]undefined[/tex]Answer:
578565
Step-by-step explanation:
A physical education teacher divides the class into teams of 5 to play floor hockey. There are atotal of 4 teams. How many students, s, are in the class? Solve the equation 8 + 5 = 4 to find thenumber of students.
we know that
the number of students (s) is equal to the number of teams, multiplied by the number of students in each team
so
s=4*5
s=20
answer is 20 students
Can you please solve this equation and please explain to me ^step-by-step^ (this is my homework)
In the equation
[tex]0.07(6t-4)=0.42(t-1)+0.14[/tex]to solve for t, we first expand both sides of the equation.
[tex]0.42t-0.28=0.42t-0.42+0.14[/tex]We subtract 0.42t from both sides to get
[tex]-0.28=0.42+0.14[/tex]The right side does not equal the left side of the equation; therefore, this equation has no solution and choice C is correct.
I need help checking to make sure my work is correct. Start with the basic function f(x) = 2x. If you have an initial value of 1, then you end up with the following iterations:f(1) = 2 x 1 = 2f^2 (1) = 2 x 2 x 1 = 4f^3 (1) = 2 x 2 x 2 x 1 = 8The question Part 1: If you continue the pattern, what do you expect would happen to the numbers as the number of iterations grows? Check your result by conducting at least 10 iterations. I put: f^4 (1) = 2 x 2 x 2 x 2 x 1 = 16f^5 (1) = 2 x 2 x 2 x 2 x 2 x 1 = 32f^6 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 1 = 64f^7 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 128f^8 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 256f^9 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 512f^10 (1) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 1 = 1024Part 2: Repeat the process with an initial value of -1. What happens as the number of iterations grows?
Given: The function below:
[tex]f(x)=2x[/tex]To Determine: The interation with initial value of 1
When the initial value is 1, it means that x = 1
If x =1, we can determine f(1) by the substituting for x in the function as shown below:
[tex]\begin{gathered} f(x)=2x \\ x=1 \\ f(1)=2(1)=2\times1=2 \end{gathered}[/tex][tex]f^2(1)=2^2\times1=2\times2\times1=4[/tex]Part 1:
It can be observed that as the number of iterations grow, the number increase in powers of 2
This can be modelled as
[tex]f^n=2^n\times1=2^n[/tex][tex]f^{10}=2^{10}\times1=1024[/tex]Part 2:
If we repeat the process with an initial value of -1. As the number of iterations grows, the number can be modelled as
[tex]\begin{gathered} f^{-n}=2^{-n}\times1 \\ f^{-1}=2^{-1}\times1=\frac{1}{2}\times1=\frac{1}{2} \\ \text{For initial value of -2, we would have} \\ f^{-2}=2^{-2}\times1=\frac{1}{2^2}\times1=\frac{1}{4} \end{gathered}[/tex]So, as the initial value decreases, it can be observed by the above calculations that the number would be decreasing by the the reciprocal of the power of 2.