Answer:
The value remains the same.
Step-by-step explanation:
using the expression: [tex](x + 1)^{2}[/tex],
where x = 2
substitute for x in the expression;
[tex](2 + 1)^{2}[/tex]
= [tex](3)^{2}[/tex]
=9
The value of the expression before expansion = 9
Lets expand the expression: [tex](x + 1)^{2}[/tex]
= (x + 1) (x + 1)
= [tex]x^{2}[/tex] + 2x + 1
substitute for x in the expression
= [tex]2^{2}[/tex] + 2(2) + 1
= 4 + 4 + 1 = 9
The value of the expansion after expansion = 9
The value remains the same before and after expansion.
The value of an expression, before and when it is expanded will be always same.
Let us consider that an expression,
[tex]f(x)=(x-1)^{2}[/tex]
Substitute x = 2 in above relation.
[tex]f(2)=(2-1)^{2}=1[/tex]
Now expand,
[tex]f(x)=(x-1)^{2}=x^{2} -2x+1\\\\f(2)=2^{2}-2*2+1\\\\f(2)=4-4+1\\\\f(2)=1[/tex]
Hence, the value of an expression, before and when it is expanded will be always same.
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Simplify.
-2i× (-3i)
-6
Answer:
(-2 i) * (-3 i) = -6
Step-by-step explanation:
This is a product between imaginary numbers, so have in mind how the imaginary unit multiplies by itself: [tex]i\,*\,i = i^2=-1[/tex]
So let's work on the product:
[tex]-2\,i\,*\,(-3\,i)= (-2)\,*\,(-3)\,*\,i\,*\,i =(6)\,* i^2\,=(6)\,*\,(-1)= -6[/tex]
1. In questions 18-1d, choose Yes or No
to tell if the number 1/2 will make each
equation true.
1a. 1/18 + 1/2 = 10/18 yes or no
1b. 1/3 + 1/2 =1/5 yes or no
1c. 5/8 - 1/2 = 1/8 yes or no. 1d. 3/4 - 1/2 = 1/4 yes or no
Answer:
Yes, No, Yes, Yes
Step-by-step explanation:
1a = Yes
1b= No
1c= Yes
1d =Yes
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What is the approximate area of the shaded sector in the circle shown below?
Answer:
I think it is B. 52.3
Answer:
13.1 in
Step-by-step explanation:
apex
Marisa has 24 quarters to play games at a carnival. She only wants to play Ring Toss and Knock Down the Clown. If each game costs 3 quarters, and she plays Ring Toss at least three times, how many different ways can Marisa play the two games?
A. 12 ways
B. 8 ways
C. 6 ways
D. 4 ways
Answer:
D.
Step-by-step explanation:
24 divided by 3 is 8 divided by 2 because of the two games is 4
The length of a rectangle garden is represented by 3x - 4 and the width is represented by 2x - 5. Which of the following represents the total area of the garden?
Answer:
area of rectangle garden=6x^2-23x+20
Step-by-step explanation:
given lengtarden=l=3x-4
width of rectangle garden=b=2x-5
area of rectangle garden=a=lb
=(3x-4)(2x-5)
=6x^2-15x-8x+20
=6x^2-23x+20
area of rectangle garden=6x^2-23x+20 answer
which of the following cannot be the probality of an event a)1/2 b) 10% c) 0.7. d) 3/2. which is the correct option with the solution
Answer:
D
Step-by-step explanation:
In probability,
a probability of 0 means that it is IMPOSSIBLE, sure that this event WILL NOT occur, ever. So, probability of anything less than 0 is not possible.
On the other hand, probability of 1 means that it is CERTAIN to happen. So, probabilty of anything greater than 1 can't happen.
So we can say:
0 <= Probability of an Event happening <= 1
Option A is 1/2, which is in the middle, so this is OKAY.
Option B is 10%, which is certainly close to 0 and between 0 and 1, so this is OKAY.
Option C is 0.7, which is close to 1 and greater than 0, so in between 0 and 1, certainly. So this is OKAY.
Option D is 3/2 which is 1.5, so this is GREATER THAN 1, so it can't ever be possible.
Option D is the correct choice.
simplify: (8^2/3)^4
Answer:
[tex](8^{\frac{2}{3} } )^{4} = 256[/tex]
Step-by-step explanation:
Given
[tex](8^{\frac{2}{3} } )^{4}[/tex]
Required
Simplify
To simplify this, we apply law of indices but first we start by solving the expression in bracket.
8 =2 * 2 * 2
8 = 2³
So, we substitute 2³ for 8
[tex](8^{\frac{2}{3} } )^{4}[/tex] becomes
[tex]((2^{3})^{\frac{2}{3} } )^{4}[/tex]
From law of indices
[tex]a^{n} = (a^{m})^{\frac{n}{m} }[/tex] ==> [tex](a^{m})^{\frac{n}{m} } = a^{n}[/tex]
So, [tex](2^{3})^{\frac{2}{3} } = 2^{2}[/tex]
At this point we have
[tex]((2^{3})^{\frac{2}{3} } )^{4}[/tex] = [tex](2^{2})^{4}[/tex]
Also, from law of indices
[tex](a^{m})^{n} = a^{m.n}[/tex]
So,
[tex]((2^{3})^{\frac{2}{3} } )^{4}[/tex] = [tex](2^{2})^{4}[/tex]
[tex](2^{2})^{4} = 2^{2*4}[/tex]
[tex](2^{2})^{4} = 2^{8}[/tex]
[tex](2^{2})^{4} = 256[/tex]
Hence,
[tex](8^{\frac{2}{3} } )^{4} = 256[/tex]
How do you find the whole number from the percentage increase?
(Give an example)
Can anyone find me all the answers to algebra 1 mathusee book thanks
Answer:
No.
Step-by-step explanation:
I need steps and help please
What is 5 1/3 minus 1 1/3 equal to?
HOPE IT HELPS YOU......
Lydia is at a coffee shop and knows
she can spend no more than $65
before tax. She sees this price list in
the coffee shop.
Item
Dark Roast Coffee
Pumpkin Spice Coffee
Breakfast Tea
Price per pound
$7.50
$10.50
$23.50
Part A
Write a number in each blank to complete an inequality Lydia can use to find how
many pounds of Pumpkin Spice coffee, p, she can buy along with 2 pounds of
Dark Roast coffee.
Answer:
[tex]10.50p+15\leq 65[/tex]
[tex]p\leq \frac{100}{21}[/tex]
Step-by-step explanation:
Let p represent pounds of Pumpkin Spice coffee.
We have been given that Lydia is at a coffee shop and knows she can spend no more than $65 before tax. She sees this price list in the coffee shop.
Item Price per pound
Dark Roast Coffee $7.50
Pumpkin Spice Coffee $10.50
Breakfast Tea $23.50
Lydia wants to buy 2 pounds of Dark Roast coffee, so the cost of 2 pounds of Dark Roast coffee would be [tex]\$7.50\times 2=\$15[/tex].
We are told that cost of each pound of Pumpkin Spice coffee is $10.50, so cost of 'p' pounds of Pumpkin Spice coffee would be [tex]10.50p[/tex].
Since Lydia can spend no more than $65 before tax, so the cost of 2 pounds of Dark Roast coffee and 'p' pounds of Pumpkin Spice coffee must be less than or equal to 65.
We can represent this information in an inequality as:
[tex]10.50p+15\leq 65[/tex]
Therefore, our required inequality would be [tex]10.50p+15\leq 65[/tex].
[tex]10.50p+15-15\leq 65-15[/tex]
[tex]10.50p\leq 50[/tex]
Divide both sides by 10.50:
[tex]\frac{10.50p}{10.50}\leq \frac{50}{10.50}[/tex]
[tex]p\leq \frac{50*2}{10.50*2}[/tex]
[tex]p\leq \frac{100}{21}[/tex]
[tex]p\leq 4.76190[/tex]
Therefore, Lydia can buy less than or equal to [tex]\frac{100}{21}[/tex] pounds of Pumpkin Spice coffee.
Answer:
4 pounds of pumpkin spice coffee
1. What is the total cost of a $95.00 item with a sales tax of 6%?
Answer: $100.70
Step-by-step explanation:
Answer:
100.70
Step-by-step explanation:
M(4,2)
N(-1,-2)
The figure shows two quadratic graphs M and N. N is a translation of M such that
the point (-1,-2) on M is translated to the point (4,2) on N. The equation
of N is y=-(x - 2)2 +6.
(a) Find the equation of M.
(2 marks)
Answer:
The equation of M is [tex]y=-(x+3)^2+6[/tex]
Step-by-step explanation:
we have that
The translation of M to N is
(-1,2) ----> (4,2)
The rule of the translation M to N is
(-1,2) ----> (x+a,y+b)
(-1,2) ----> (-1+a,2+b)
so
[tex]-1+a=4[/tex] ----> [tex]a=4+1=5[/tex]
[tex]2+b=2[/tex] ----> [tex]b=0[/tex]
The rule of the translation M to N is
(x,y) ----> (x+5,y)
The translation is 5 units right
I can say that the rule of the translation N to M is
(x,y) ----> (x-5,y)
we have the equation of N
[tex]y=-(x-2)^2+6[/tex]
Is a quadratic equation open downward
The vertex is (2,6)
Find the vertex of M
Applying the rule of the translation N to M to the vertex
(2,6) ----> (2-5,6)
(2,6) ----> (-3,6)
therefore
The equation of M is
[tex]y=-(x+3)^2+6[/tex]
fastas soon as possible............Find HCF
Answer:
[tex]y^4+1+\dfrac{1}{y^4}[/tex]
Step-by-step explanation:
Consider expression
[tex]y^7-\dfrac{1}{y^5}[/tex]
Rewrite it:
[tex]\dfrac{y^7\cdot y^5-1}{y^5}=\dfrac{y^{12}-1}{y^5}[/tex]
Consider the numerator:
[tex]y^{12}-1=(y^4)^3-1^3[/tex]
Use formula:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
So,
[tex](y^4)^3-1^3=(y^4-1)((y^4)^2+y^4\cdot 1+1^2)=(y^4-1)(y^8+y^4+1)[/tex]
Now,
[tex]\dfrac{y^7\cdot y^5-1}{y^5}=\dfrac{(y^4-1)(y^8+y^4+1)}{y^5}=\dfrac{y^4-1}{y}\cdot \left(y^4+1+\dfrac{1}{y^4}\right)[/tex]
Hence,
[tex]GCF(y^7-\frac{1}{y^5}, y^4+1+\frac{1}{y^4})=y^4+1+\dfrac{1}{y^4}[/tex]
Answer:
Step-by-step explanation:
Consider expression
Rewrite it:
Consider the numerator:
Use formula:
So,
Now,
Hence,
Answer:
Step-by-step explanation:
f(x) = 4x+8
g(x) = x+3,
Find f(x)*g(x)
Answer:
4x^2+20x+24
Step-by-step explanation:
(4x+8)(x+3)=4x^2+8x+12x+24=4x^2+20x+24
The value of f(x) * g(x) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3
We have two functions -
f(x) = 4x + 8
g(x) = x + 3
We have to determine f(x)*g(x).
What is function in mathematics ?A function in mathematics is an expression with a independent variable (x) in it. The variable is called independent because it is not dependent on any value to get its value. Function also has a dependent variable (y) whose value depend on x. Ex -
y = f(x) = ax + d
According to the question, we have -
f(x) = 4x + 8
g(x) = x + 3
Therefore -
f(x) * g(x) = (4x + 8)(x + 3) = 4x(x + 3) + 8(x + 3) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3
Hence, the value of f(x) * g(x) = 4[tex]x^{2}[/tex] + 20[tex]x[/tex] + 3
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what is the answer if you expand -7(k - 3)
y=f(x) = (1/2)
Find f(x) when x = 1
The value of function on x=1 is 0.5
Step-by-step explanation:
In order to find the value of a function on given input, the input is put at the place of variable in the function.
Given function is:
[tex]f(x) = (\frac{1}{2})^x[/tex]
We have to find the value of function on x = 1
Putting x = 1 in function
[tex]f(1) = (\frac{1}{2})^1\\= \frac{1}{2}\\= 0.5[/tex]
Hence,
The value of function on x=1 is 0.5
Keywords: Functions variables
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True or false:
The solution, root, x-intercept, and zero of a problem are the same.
The terms 'solution,' 'root,' 'x-intercept,' and 'zero' are related in mathematics, but they are not always the same.
Explanation:The statement in the question is false. Though the terms 'solution,' 'root,' 'x-intercept,' and 'zero' are related in mathematics, they are not always the same.
In quadratic equations, for example, the 'solution' refers to the values of x that make the equation equal to zero, while 'root' refers to the values of x that satisfy the equation. 'X-intercept' refers to the points on the graph where the equation intersects the x-axis, while 'zero' refers to the x-values for which the equation equals zero.
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3. Tim has 5/12 of a jar of blackberry jam and 3/8
of a jar of strawberry jam. Write 5/12 and 3/8
using a common denominator.
Answer:
The answers are 10/24 and 9/24.
Step-by-step explanation:
Given:
Tim has 5/12 of a jar of blackberry jam and 3/8 of a jar of strawberry jam.
Now, to write using a common denominator.
So, we get the multiples of denominator of the fractions to get common denominator:
12 - 12, 24, 36.
8 - 8, 16, 24.
Here we see that 24 is the common denominator.
Now, we multiply the numerator and denominator with the same number to get the common denominator of the fractions:
⇒ [tex]\frac{5}{12}=\frac{5\times 2}{12\times 2} =\frac{10}{24}[/tex]
⇒ [tex]\frac{3}{8}=\frac{3\times 3}{8\times 3} =\frac{9}{24}[/tex]
Therefore, the answers are 10/24 and 9/24.
Complete the statement to describe the expression abc + def.
The expression consists of
terms, and each term contains
factors.
Reng
Answer:
1) Two terms
2) Three factors
Step-by-step explanation:
We are given the following expression:
abc + def
We have to compete the given statement with the help of given expression.
The given expression consist of two terms, abc and def.Each term contain 3 factors:abc - 3 factors: a, b and c
def - 3 factors: d, e and f
The expression abc + def consists of two algebraic terms, each with three factors.
Explanation:The expression abc + def consists of two terms, and each term contains three factors. To elaborate, a term in algebra is a single part of an expression separated by plus or minus signs. The given expression has two distinct groupings separated by a plus sign: 'abc' and 'def'. Each of these groupings is considered a term. Moreover, within each term, there are three variables multiplied together, hence each term contains three factors. Understanding this fundamental concept of terms and factors is crucial for manipulating algebraic expressions, factoring, and solving equations more efficiently.
will make brainiest to the first two people to get it right
Name a pair of vertical angles
<2 and <5
<2 and <6
<5 and <6
Answer:
It's <2 and <5.
Triangle SQT is isosceles. The measure of angle STQ is 48°. Triangle S Q T is cut by perpendicular bisector T R. The lengths of line segments S R and R Q are congruent. Side lengths S T and T Q are congruent. Angles S T R and R T Q are congruent. What is the measure of Angle S T R? 24° 38° 48° 76°
Answer:
[tex]m\angle STR=24^o[/tex]
Step-by-step explanation:
we know that
[tex]m\angle STQ=m\angle STR+m\angle RTQ[/tex] ---> by addition angle postulate
we have
[tex]m\angle STQ=48^o[/tex] ----> given problem
[tex]m\angle STR=m\angle RTQ[/tex] ----> given problem
substitute in the expression above
[tex]48^o=2m\angle STR[/tex]
Divide by 2 both sides
[tex]m\angle STR=24^o[/tex]
Answer:
A.24
Step-by-step explanation:
Jennifer feeds 5 times as many fish as Tony. Tony feeds 56 fish. how many fish,f,does Jennifer feed?
Answer:
Jennifer feeds total fishes is 280
Step-by-step explanation:
Tony feeds total fishes is 56
Jennifer feeds 5 times as many fish as Tony feeds
Jennifer [tex]=[/tex] 5 × Tony
[tex]=[/tex] 5 × 56
[tex]=[/tex] 280
Jennifer feeds total fishes is 280
Final answer:
Jennifer feeds 280 fish.
Explanation:
To find out how many fish Jennifer feeds, we need to perform a simple multiplication. Since Jennifer feeds 5 times as many fish as Tony, and Tony feeds 56 fish, we can write the following equation to represent the situation:
f = 5 × 56
We then multiply 56 by 5:
f = 280
So, Jennifer feeds 280 fish.
what is the center of dilation
a
b
c
d
Answer:
AStep-by-step explanation:
Look at the picture.
Only from point A do the lines pass through the corresponding vertices of both triangles.
find the range of the function below if the domain is {-1,0,2}
f(x)=x^2 -2x +3
Answer:
{3, 6}
Step-by-step explanation:
f(x) is the same thing as y. f(x) or y are the values that are shown in the range.
The domain represents all possible values of x. Data must be in an (x, y) form, where any value of "y" would need a partner, "x".
Substitute all of the possible x-values into the formula to find all possible y-values (the range).
f(x) = x² - 2x + 3
f(-1) = (-1)² - 2(-1) + 3
f(-1) = 1 + 2 + 3
f(-1) = 6
f(x) = x² - 2x + 3
f(0) = (0)² - 2(0) + 3
f(0) = 0 - 0 + 3
f(0) = 3
f(x) = x² - 2x + 3
f(2) = (2)² - 2(2) + 3
f(2) = 4 - 4 + 3
f(2) = 3 Do not write repeated numbers
The possible y-values are 3 and 6.
Writ the range in set notation in the brackets {}. Order the numbers from least to greatest.
Range is {3, 6}.
The range of a function with a specified domain is equal to {3, 6}.
Range of the function:
The function is f(x) = x² - 2x + 3. Given the domain {-1, 0, 2}, we can find the corresponding range by evaluating the function at each point in the domain:
For x = -1: f(-1) = (-1)² - 2(-1) + 3 = 6.
For x = 0: f(0) = 0² - 2(0) + 3 = 3.
For x = 2: f(2) = 2² - 2(2) + 3 = 3.
The range of this function for the given domain is {3, 6}.
11. Higher Order Thinking Cora makes this
design with square and triangular tiles.
What is the area of the design? How did
you calculate your answer?
Step-by-step explanation:
With no photo of the design is imposible to calculate exactly the design area. However:
We know that the area of a square is:
[tex]A_{sq}=L^2[/tex] where L is the leght of the square's side
Also, the area a triangle is:
[tex]A_{tr}=\frac{h*b}{2}[/tex] where h is the height and b is the base (see the figure)
So, the total area, assuming that all square tiles are equal between them (the same for the triangular ones):
[tex]A_{total}=A_{sq}*n_{squaretiles}+A_{tr}*n_{triangtiles}[/tex]
Fulton is building a doghouse. He cuts 5 equal-sized pieces from a board that is 15 feet long. After cutting the pieces, he has 2
Which of these equations and expressions will, when solved or simplified, give the length of the 5 pieces of wood Fulton cut?
Answer:
X=15 divided by 2
Step-by-step explanation:
Where X equals 5.
Answer:
[tex]5x + 2\frac{1}{2} = 15[/tex] and [tex]\frac{15 - 2\frac{1}{2} }{5}[/tex]
Step-by-step explanation:
Assume the length of each piece of wood is x feet.
We can say that the length of uncut board = (number of pieces × length of each piece) + length of leftover board, or [tex]15 = 5x + 2\frac{1}{2}[/tex].
Apply the Symmetric Property of Equality:
[tex]5x + 2\frac{1}{2} = 15[/tex]
Subtract [tex]2\frac{1}{2}[/tex] from both sides of the equation:
[tex]5x = 15 - 2\frac{1}{2}[/tex]
Divide both sides by 5: (See image)
Cancel out the common terms from the numerator and denominator:
[tex]x = \frac{5}{2}[/tex]
[tex]= 2\frac{1}{2}[/tex]
multiply two and two thirds by two and two thirds
Answer:
Its 7 1/9! I hope this helped! Also what I used was mixed numbers calculator by calculator soup!
Step-by-step explanation:
What does it mean to be a storehouse of value?
O
A. It serves as a valid currency.
O
B. The item is divisible and each unit is worth the same
O
C. Any item that can be traded for another item.
O
D. Any item that maintains its worth over time.
Final answer:
Being a storehouse of value means the item retains its worth over time, allowing it to be saved, stored, and reliably used later as a medium of exchange, like money or other assets with lasting value.
Explanation:
To be a storehouse of value means that the item, such as money, can retain its worth over some time. Unlike goods that may deteriorate, go out of style, or otherwise lose value, a storehouse of value allows individuals to save and store their wealth, retrieving it later with confidence that it will still be valuable.
Money is a common store of value since you do not need to spend it right away and can trust that even with the potential erosion of value due to inflation, it will remain a valid medium for future transactions.
Goods such as houses, artworks, or financial assets are also considered stores of value, but money is distinguished by its liquidity—being readily exchangeable for other goods or services. Although not perfect due to inflation, money's role as a medium of exchange in financial markets and aggregate expenditure makes it a convenient choice for storing value, especially when compared to the barter system.
In conclusion, option D - Any item that maintains its worth over time, accurately describes a storehouse of value.