Answer:
8a^3.
Step-by-step explanation:
(a+b)^3=a^3+b^3+3a^2b+3ab^2
(a-b)^3=a^3-b^3-3a^2b+3ab^2
(a+b)^3+(a-b)^3=2a^3+6ab^2
According to the question
(a+b)^3+(a-b)^3+6a(a^2-b^2)
Put in the value
=2a^3+6ab^2 +6a^3–6ab^2
=8a^3
In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as, 8a³
What are algebraic identities?Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.
Given that,
A algebraic identity,
(a + b)³ + (a - b)³ + 6a(a² - b²)
It is known that,
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
So, now we can substitute expressions
(a + b)³ + (a - b)³ + 6a(a² - b²)
a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) + 6a(a² - b²)
a³ + b³ + 3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²
8a³
Hence, the simplest form is 8a³
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Please help ASAP!
Does this represent a nonlinear function, a linear function, or not a function?
Answer:
Not a function
Step-by-step explanation:
This is not a function because there are different outputs for the same input.
Answer:
NOT A FUNCTION
Step-by-step explanation:
a function cant have multiple y coordinates for the same X
∞¬
ω
What is the domain of this function. (Could someone explain it too? I wanna be able to do it myself as well)
[tex]answer \\ = - 2 , 2 ,3 , 4 \\ explanation \\ let \: r \: be \: a \: relation \: from \: a \: to \: b. \: then \: \\ the \: set \: of \: first \: components \: or \: the \\ set \: of \: elements \: of \: a \: are \: called \\ domain \: and \: the \: set \: of \: second \\ components \: or \: the \: set \: of \: elements \\ of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]
What is the vertex of the graph of the function f(x) = x2 + 8x - 2?
(-4, 18)
(0, -2)
O (-8,-2)
O (-4, -18)
Answer:
vertex = (- 4, - 18 )
Step-by-step explanation:
Given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 )
The the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 8x - 2 ← is in standard form
with a = 1 and b = 8 , thus
[tex]x_{vertex}[/tex] = - [tex]\frac{8}{2}[/tex] = - 4
Substitute x = - 4 into f(x) for corresponding y- coordinate
f(- 4) = (- 4)² + 8(- 4) - 2 = 16 - 32 - 2 = - 18
vertex = (- 4, - 18 )
The vertex of the parabola is (-4, -18).
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the vertex of the function f(x) = x² + 8x - 2, we first need to convert the function into vertex form, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Completing the square.
f(x) = x² + 8x - 2
f(x) = (x + 4)² - 18
Therefore,
The vertex of the parabola is (-4, -18).
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Which are linear pairs? Check all that apply.
A. ∠DAE and ∠EAD
B. ∠BAC and ∠CAD
C. ∠BAE and ∠EAD
D. ∠EAD and ∠DAC
E. ∠CAE and ∠BAD
Answer:
Options B, C and D
Step-by-step explanation:
Linear pair of angles means sum of the angles of the pair is 180° which are formed at a point of a line.
In other words, pair of supplementary angles is the linear pair.
From the figure attached,
Pair of the linear angles are,
1). ∠BAC and ∠CAD
2). ∠BAE and ∠EAD
3). ∠EAD and ∠DAC
Therefore, Options B, C and D are correct.
Answer:
B, C, and D
Step-by-step explanation:
Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. k = -1; f(x) = 4x^3 - 2x^2 + 2x + 4; Lower bound? yes/no?
Answer:
Yes, k is lower bound for the real zeros of the function.
Step-by-step explanation:
Lower Bound Theorem:
If you divide a polynomial function f(x) by (x - k), where k < 0, using synthetic division and this yields alternating signs, then k is a lower bound to the real roots of the equation f(x) = 0.
Given;
4x³ - 2x² + 2x + 4
k = -1
synthetic division;
-1 ] 4 -2 2 4
↓ -4 6 -8
---------------------------------------------
4 -6 8 -4
(the result has alternating signs, hence k is lower bound)
Thus, k is lower bound for the real zeros of the function.
Explain how to find the value of y that would make segment OP parallel to segment LN.
Answer:
[tex]y = 36[/tex]
Step-by-step explanation:
Given; the triangle above
Required
Find y
This question falls under the topic/subtopic similar triangles where we need to make comparison between similar sides'
But first, it should be noted that triangle MOP is similar to triangle MLN
This implies that
Side MP is similar to MN
Side MO is similar to ML
Mathematically; This can be represented as follows;
[tex]\frac{MP}{MN} = \frac{MO}{ML}[/tex]
Where MP =y; MN = y + 18; MO = 28; ML = 28 + 14
Substitute these values in the above expression
[tex]\frac{y}{y+18} = \frac{28}{28+14}[/tex]
[tex]\frac{y}{y+18} = \frac{28}{42}[/tex]
Multiply both sides by 42
[tex]42 * \frac{y}{y+18} = \frac{28}{42} * 42[/tex]
[tex]\frac{42y}{y+18} = \frac{28*42}{42}[/tex]
[tex]\frac{42y}{y+18} = 28[/tex]
Multiply both sides by y + 18
[tex](y+18)*\frac{42y}{y+18} = 28 * (y+18)[/tex]
[tex]42y = 28 * (y+18)[/tex]
Open Bracket
[tex]42y = 28 * y+28 * 18[/tex]
[tex]42y = 28y+504[/tex]
Subtract 28y from both sides
[tex]42y - 28y = 28y - 28y +504[/tex]
[tex]14y = 504[/tex]
Divide both sides by 14
[tex]\frac{14y}{14} = \frac{504}{14}[/tex]
[tex]y = \frac{504}{14}[/tex]
[tex]y = 36[/tex]
Answer:
y= 36
Step-by-step explanation:
also ily, no homo
Finn's pool leaked a total of 3.5 liters in 4 days. What rational number represents the average change in water volume each day?
Answer:
The rational number representing the average change in the volume of water each day is:
[tex]\frac{0.875 liters}{1 day}[/tex]
Step-by-step explanation:
Rational numbers are those that can be represented as the quotient of two integers. That is, rational numbers can be represented by a fraction [tex]\frac{a}{b}[/tex], where a is the numerator and b is the denominator that must be other than zero. To express the set of these numbers, mathematicians use a capital Q.
In this case we know that Finn's pool leaked a total 3.5 L in 4 days, so the rate can be written as:
[tex]\frac{3.5 liters}{4 days}[/tex]
Now you must make this division or quotient, where the denominator will be 1 because you must know the number of liters drained per day:
[tex]\frac{3.5 liters}{4 days}=\frac{0.875 liters}{1 day}[/tex]
So the rational number representing the average change in the volume of water each day is:
[tex]\frac{0.875 liters}{1 day}[/tex]
25.(01.05)
Given the point (5, 6) and the slope of 5, find y when x = 21. (1 point)
O 86
O 90
O 105
O 111
Step-by-step explanation:
This question gives us a point on a line and the slope of that line. So, the easiest way to answer this question is to use point-slope form, which is written as:
y-y₁ = m(x-x₁)
So, first of all, we are trying to find y (y, not y₁ which is the y-coordinate of the point we were given). We can go ahead and add y₁ to both sides to get:
y = m(x-x₁) + y₁
We can now simplify the equation to:
y = m·x - m·x₁ + y₁
Now we just input the given information.
m = 5 (slope)
x = 21
x₁ = 5
y₁ = 6
Now we have all the information we need and we can solve.
y = 5·21 - 5·5 + 6
y = 105 - 25 + 6
y = 86
So y, when x = 21, is equal to 86.
True or false all integers are rational
Answer:
The answer is True
Step-by-step explanation:
All rational numbers are integers
.............................
Answer:
[tex]\frac{18p-5}{30}[/tex]
Step-by-step explanation:
Answer:
18p-5 over 30.
Found in the LCM method
What is another name for ∠EBC?
Answer:
Number 4
Step-by-step explanation:
Angle CBE is the same thing as angle EBC. The only thing that matters when you're talking about ONE angle is the middle letter.
Answer:
It is number four: ∠CBE
A rectangular frame has a diagonal with a length of 20 inches and a longer side with a length of 15 inches
Which of the following is closest to the length of its shorter side?
(1) 9.7 inches
(3) 13.2 inches
(2) 11.9 inches
(4) 14.8 inches
Answer:
(3)13.2
Step-by-step explanation:
c²=a²+b²
20²=15²+b²
20²-15²=b²
400-225=b²
175=b²
b=√175
b=13.2inches
5^4=625 in log form pls.
Answer:4log5=4log5
Step-by-step explanation:
Take the log of both sides
log5^4 =log 625
By log log a^b=b loga
4log 5=log5^4
4log5 =4log 5
Expressions and equations can be written in logarithmic forms.
The logarithmic form of [tex]5^4 = 625[/tex] is [tex]\log_5(625) = 4[/tex]
The equation is given as:
[tex]5^4 = 625[/tex]
Take the logarithm of both sides of the equation
[tex]\log(5^4) = \log(625)[/tex]
Apply law of logarithm
[tex]4\log(5) = \log(625)[/tex]
Divide both sides of the equation by log(5)
[tex]4 = \frac{\log(625)}{\log(5)}[/tex]
Apply change of base law of logarithm
[tex]4 = \log_5(625)[/tex]
Rewrite the equation as follows:
[tex]\log_5(625) = 4[/tex]
Hence, the logarithmic form of [tex]5^4 = 625[/tex] is [tex]\log_5(625) = 4[/tex]
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Write each statement as an algebraic expression.The quotient of the number that is 1 greater than a number b and the number that is twice as large as b.
(b+1)/2b
quotient = divided by
we're dividing a number that is 1 more than b (b + 1), with a number twice as large as b (2b).
pls help for brainliest answer
Answer:
976 cm²
Step-by-step explanation:
25 x 10 x 2 = 500
14 x 10 = 140
14 x 24 = 336 ((14x24/2)x2)
500 + 140 + 336 = 976
Awnser needed thank you!
Answer:
Step-by-step explanation:
I think 33°
Answer:
its 34 i think
Step-by-step explanation:
Can someone help me please?
Answer:
Inverse Variation
Step-by-step explanation:
y = k/x
A box contains 4 black pens and 2 red pens. One pen is chosen at random, and then another pen is chosen at random without replacement. What is the probability a black pen was chosen, and then another black pen? *
Answer:
Probability is 2/5 or 40%.
Step-by-step explanation:
4/(4+2) = 4/6 = 2/3 first black pen is chosen.
3/5 - second pen is chosen without replacement.
2/3 *3/5= 2/5 - the probability a black pen was chosen, and then another black pen without replacement.
2/5*100 % = 40 %
A gift has the dimensions of 50 cm x 35 cm x 5 cm. You have wrapping paper with
dimensions of 75 cm x 60 cm. Do you have enough wrapping paper to wrap the gift? Why
or why not?
Answer:
Yes, there is enough wrapping paper
The area of the wrapping paper is greater than area of the gift
Step-by-step explanation:
What to do is to check the area of the wrapping paper and the gift if equal.
Looking at the dimensions of the gift, it is a cuboid
Area of a cuboid = 2(lb + lh + bh)
where l, b and h are 50, 35,5 respectively
= 2(250 + 175 + 1750)
= 4350 cm^2
The area of the wrapping paper is just the product of its side = 75 * 60 = 4500 cm^2
We can see clearly that the area of the wrapping paper is greater than area of the gift.
so we can conclude that it is enough to wrap the gift
x=12-1//3x
can anyone tell me the full answer
Answer:
x=9 is the answer......
help me agian (**) plzzzzzzzzzzzzzzzzzzzz
Answer:
130%
Step-by-step explanation:
1.3=
130/100=
130%
Hope this helps!
Answer:
130%
Step-by-step explanation:
To express a decimal as a percent, you need to multiply it by 100.
1.3×100=
130
1.3 as a percent is 130%
Please help! Correct answer only!
There is a raffle for a $380 prize. Out of 100 tickets, one ticket will win the prize, and the other tickets will win nothing. If you have a ticket, what is the expected payoff?
Answer:
$3.80
Step-by-step explanation:
380/100= an expected payoff of 3.8 dollars. Hope this helps!
The two-way frequency table below shows data on mindset and attendance at practice for students in Mateus's study.
Complete the following two-way table of row relative frequencies.
(If necessary, round your answers to the nearest hundredth.)
The two-way frequency table is completed using the rule of division which is shown below.
[tex]\begin{matrix} &\rm Growth \ mindset &\rm Fixed \ mindset &\rm Raw \ total\\\\\rm Attended \ every\ practice &0.7 &0.3 &1\\\\\rm Missed\ at\ least\ 1\ practice & 0.1343 &0.8657 &1\end{matrix}[/tex]
What is the two-way frequency?Two-way frequency tables demonstrate the potential relationship between two pairs of categorical data visually. The frequency (count) information appears in the four (or more) interior cells of the table, with the categories designated at the top and left sides.
The two-way frequency table is completed below.
[tex]\begin{matrix} &\rm Growth \ mindset &\rm Fixed \ mindset &\rm Raw \ total\\\\\rm Attended \ every\ practice &0.7 &0.3 &1\\\\\rm Missed\ at\ least\ 1\ practice & 0.1343 &0.8657 &1\end{matrix}[/tex]
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Answer:
Step-by-step explanation:
0.7 0.3
0.13 0.87
A store gives away gift bags during a sale. Of these gift bags, 50% are green, 20% are yellow, and 30% are blue. The average number of items in each green bag is 8. The average number of items in each yellow bag is 5. The average number of items in each blue bag is 8. What is the average number of items in all the gift bags? PLS, HELP WILL GIVE YOU 95 PTS!!!!!!!!
Answer:
7
Step-by-step explanation:
So I started with an equation (g for green variable, y for yellow variable, b for blue variable)
8g + 5y + 8b = ??
Because of the lack of variables, I'm not really sure how to tie in the 50%, 20%, and 30%. (It could be unnecessary information)
But going off the average number of items, you have 8 green, 5 yellow, and 8 blue. So you can add them together for 21. From here, you divide 21 by 3 to get your average, 7.
Answer:hmm
Step-by-step explanation:
What is the probability of pulling jack, queen, or king from a deck of cards?
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me....
3 x 1/4 what is the answer to the question?
Answer:3/4
Step-by-step explanation:
1x3=3
Answer:
I used an online calculator and I got 0.75
Step-by-step explanation:
Plz help...it’s a math question and I suck at math would mean a lot to me thx <3
Answer:
Read below
Step-by-step explanation:
11. YX = 4.5
RQ corresponds to ZY. If RQ is 4 and ZY is 3, then ΔQRP was dilated by 0.75 to form ΔYZX. (3/4 = 0.75). Using this knowledge, we can find the length of YX by multiplying 6 by 0.75. (YX corresponds to QP). 6 × 0.75 = 4.5.
12. 55°
All of a triangle's angles must add up to 180°. ∠Q is 88°. ∠Z is 37°. ∠Z is congruent to ∠R because corresponding angles in similar triangles are congruent. So, 88° + 37° = 125°. We need to get to 180°, so 180° - 125° = 55°.
13. 4.2
BC corresponds to DF. We need to find the scale factor, so divide 2.7 by 3.6. That equals 0.75. AC corresponds to EF. EF is 5.6, so multiply 5.6 by 0.75. That equals 4.2.
I hope this helps :))
Mark asked each student in a class to name their favourite colour. For this class, the number of students who said blue is three times the number of students who said green. Write down the ratio of the number of students who said blue to the number of students who said green.
Answer:
3:1
Step-by-step explanation:
Since there are 3 times more blue favorite kids, the ratio is
3:1
The ratio of the number of students who said blue to the number of students who said green is 3 : 1.
What is ratio?The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.
Given:
Mark asked each student in a class to name their favorite color.
For this class,
the number of students who said blue is three times the number of students who said green.
Let n be the number of students who said green.
Then, 3n, the number of students who said blue.
The ratio of the number of students who said blue to the number of students who said green.
= 3n/ n
= 3/1
= 3: 1.
Therefore, the ratio is 3 : 1.
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if f(x) is a linear function and the domain of f(x) is the set of all real number which statement cannot be true?
Options:
The graph of f(x) has zero x-intercepts. The graph of f(x) has exactly one x-intercept. The graph of f(x) has exactly two x-intercepts. The graph of f(x) has infinitely many x-intercepts.Answer:
(C)The graph of f(x) has exactly two x-intercepts.
Step-by-step explanation:
Given a linear function f(x)=ax+b where the domain of f(x) is the set of all real numbers, x.
(A)If f(x)=y, the graph of f(x) will have zero x-intercepts except at y=0 which is the equation of the x-axis.
(B)A linear function can only intersect the x-axis at exactly one point.
(D)When the linear function is f(x)=0, all points of x are x-intercepts of f(x). Therefore f(x) will have infinitely many x-intercepts at this point.
However:
A straight line cannot intersect the x-axis twice, therefore the graph of f(x) cannot have two x-intercepts.
The statement which cannot be true is Option C.
Answer:
C
Step-by-step explanation:
yes
Linda made 5 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 5 necklaces was $18.50. If the beads cost $1.50 for each necklace, how much did each pendant cost?
1.50 for beads x 5 necklaces = 7.50
Total.
18.50 -7.50 = 11.00
11.00 / 5 = $2.20 for was pendant
