The steps used by Taylor to solve the equation 3(x - 2) = 6(2x + 1) + 6 are shown below:

3(x - 2) = 6(2x + 1) + 6
x - 2 = 2(2x + 1) + 2
x - 2 = 4x + 2 + 2
x - 2 = 4x + 4
-3x - 2 = 4
-3x = 6
x = -2

Which properties did Taylor use to solve
the equation? Choose all that apply.

A. Distributive property

B. Commutative property

C. Inverse Operation Property

D. Associative property of multiplication

E. The sum of a number and its additive inverse is 0.

F. The product of a number and its multiplicative inverse is 1.

Answers

Answer 1

Both A and C are used within this problem. Distributing happens in the first and second step. Also, Inverse operations are used in nearly every step that is solving.

Related Questions

Who, in 1706, first gave the greek letter "pi" its current mathematical definition? *?

Answers

The notation with the Greek letter π comes from the initial words of Greek origin περιφέρεια 'periphery' and περίμετρον 'perimeter' of a circle, notation that was first used by William Oughtred (1574-1660) and whose use was proposed by the Welsh mathematician William Jones (1675-1749); although it was the mathematician Leonhard Euler, with his work Introduction to the infinitesimal calculation, of 1748, who popularized it.
It was previously known as Ludolph's constant (in honor of the mathematician Ludolph van Ceulen) or as a constant of Archimedes (not to be confused with Archimedes' number).

Jones poses the name and symbol of this number in 1706 and Euler begins to spread it in 1736.

Answer:
Welsh mathematician William Jones

Assume that the committee consists of 6 Republicans
and 8 Democrats. A subcommittee consisting
of 7 people is to be selected.
(1) How many such subcommittees are possible
if each subcommittee must contain exactly 3
Republicans and 4 Democrats?
(1) How many such subcommittees are possible
if each subcommittee must contain at least 1 and
no more than 3 Republicans?,

Answers

Both of these questions rely upon a function to choose a subset of members from a larger set. Let's assume you have M members in the larger set and you want to pick N of them. First, there's M! different ways to arrange the M members. And after arranging them, you can simply pick the 1st N members in line. So we have M! possibilities. But the order of the 1st N people doesn't really matter, and since there's N! different ways to arrange them, let's divide by N!, giving us M!/N!. But the order of the people we didn't pick (M-N) also doesn't matter, so we need to divide by (M-N)! as well. So we get M!/(N!(M-N)!) as the number of possible ways to pick N people out of M people. So let's define a function to represent this P(M,N) = M!/(N!(M-N)!) (1) How many such subcommittees are possible if each subcommittee must contain exactly 3 Republicans and 4 Democrats? We want 3 out of 6 Republicans and 4 out of 8 Democrats. So the number of possible subcommittees is: P(6,3)*P(8,4) = 20*70 = 1400 (2) How many such subcommittees are possible if each subcommittee must contain at least 1 and no more than 3 Republicans? Let's do this problem as the sum of 3 different types of subcommittees. They are 1 Republican and 6 Democrats, 2 Republicans and 5 Democrats, and 3 Republicans and 4 Democrats. So: P(6,1)*P(8,6) + P(6,2)*P(8,5) + P(6,3)*P(8,4) = 6*28 + 24*56 + 20*70 = 168 + 1344 + 1400 = 2912

Final answer:

The question requires the application of combination formulas to calculate the number of possible subcommittees with specific party member composition requirements.

Explanation:

The question deals with combinations in mathematics, specifically combinatorial calculation to determine the number of ways a subcommittee can be formed given certain restrictions on a party composition.

Part 1:

To find out how many subcommittees can be formed containing exactly 3 Republicans and 4 Democrats, we use the combination formula which is C(n, k) = n! / (k! * (n - k)!), where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial. There are 6 Republicans, so we can choose 3 of them in C(6, 3) ways and there are 8 Democrats from which we can choose 4 in C(8, 4) ways. The total number of such subcommittees is the product of these two combinations.

Part 2:

For the second part, we consider subcommittees with at least 1 and no more than 3 Republicans. This means we must calculate the sum of subcommittees for when there are exactly 1, 2, or 3 Republicans, combined with the appropriate number of Democrats to make a total of 7 members. We use the combination formula again for each scenario and add the results together.

Which of the two functions below has the largest maximum y-value?
f(x)=-x^4-2
g(x)=-3x^3+2
A. There is not enough information to determine
B. The extreme maximum y-value for both f(x) and g(x) is infinite
C. f(x)
D.g(x)

Answers

The answer is 'D'
APEX

Answer: D. g(x)

Step-by-step explanation: since,f(x)=-x^4-2

x^4>=0 for all x so,-x^4<=0 for all x

⇒ -x^4-2<=-2 for all x

⇒ f(x)<=-2 for all x so, maximum possible value of f(x)=-2

whereas g(x)= -3x^3+2 can take values from (-∞,∞)

so, g(x) has the maximum y value

helpppppppppppppppppppppppp

Answers

The reference angle is the angle made with the x-axis. For two points to have the same reference angle, they would need to have the same absolute value of their tangents = y/x.
For the first pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.
For the second pair of points: the first point has a tangent value of -sqrt(3), while the second has a tangent value of -1/sqrt(3), so these are not identical.
For the third pair of points: the first point has a tangent value of sqrt(3), while the second also has a tangent value of sqrt(3), so these have the same reference angle.
For the fourth pair of points: the first point has a tangent value of 1/sqrt(3), while the second has a tangent value of sqrt(3), so these are not identical.

So the only correct answer is the third choice.

99 points
What is the approximate volume of the cone?
Use 3.14 for π

1272 cm³

2120 cm³

4239 cm³

6359 cm³

Answers

So, when doing this kind of problem, the first thing that we would want to do is to multiply (9[tex]*[/tex]15), and then from there, we do, the sum of this, and then we would then multiply this by (3.14).But then after, we would then multiply this number.

And from doing and plugging in all of this, our answer would give us [tex](2120 \ cm^3)[/tex]

Your answer: (second option)

v=3.14(15)^2(3)
v=3.14(225)(3)
v=2119.5
v=2120
The answer is B

What’s the answer to this?

Answers

the answer is 6/(5x^10)

Root ((72x ^ 16) / (50x ^ 36))
The first thing we must do in this case is to rewrite the expression:
Root ((36x ^ 16) / (25x ^ 36))
(6/5) * Root ((x ^ 16) / (x ^ 36))
Then, for power properties we have:
(6/5) * Root ((x ^ (16-36))
(6/5) * Root ((x ^ (- 20))
(6/5) * Root (1 / (x ^ 20))
We rewrite the expression again:
(6/5) * ((1) ^ (1/2) / (x ^ 20) ^ (1/2))
(6/5) * (1 / (x ^ 10))
(6 / (5 * x ^ 10))
Answer:
(6 / (5 * x ^ 10))
option A

12 stamps increased by 125%

Answers

12 stamps increased by 125%; find the new amount.
The answer to this is 27.

12 x 2 = 24
12 ÷ 4 = 3
24 + 3 = 27

A man is in a tree house 7 ft above the ground. He is looking at the top of another tree that is 24 ft tall. The bases of the trees are 40 ft apart. What is the angle of elevation from the man's feet to the top of the tree? Round to the nearest degree.
A. 23
B. 31
C. 67
D. 59

Answers

Answer is A. Work is shown in picture. I tried my best to draw on my computer!

Final answer:

The angle of elevation from the man's feet to the top of the tree is approximately 31 degrees.

Explanation:

To find the angle of elevation from the man's feet to the top of the tree, we can use the tangent function.

The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (24 ft) and the adjacent side is the horizontal distance between the two trees (40 ft).

Therefore, tan(angle) = opposite/adjacent = 24/40 = 0.6.

Taking the inverse tangent, we get angle = arctan(0.6).

Rounding to the nearest degree, the angle is approximately 31 degrees.

Let p=x^2+6
Which equation is equivalent to (x^2+6)^2-21=4x^2+24 in terms of p?
Choose 1 answer:
A. p^2-4p-21=0

B. p^2+4p−45=0

C. p2−4p−45=0

D. p^2+4p−21=0

Answers

That's a bit of a nasty. Where ever you see (x^2 + 6) you put in p.
p^2 - 21 = 4(x^2 + 6)
p^2 - 21 = 4p
p^2 - 4p - 21 = 0

A <<<< answer.

Final answer:

The equation equivalent to (x^2+6)^2-21=4x^2+24 in terms of p is A. p² - 4p - 21 = 0.

Explanation:

To find which equation is equivalent to (x²+6)²-21=4x²+24 in terms of p, we follow a series of algebraic steps, substituting p with x²+6. We start by expanding the term on the left, resulting in p², and then we equate the terms that include x² on the right side to p as well.

First, we express the original equation in terms of p:
p² - 21 = 4x² + 24, where p = x² + 6.

Next, we substitute p in place of x² + 6:
p² - 21 = 4(p - 6) + 24

Now, we simplify the right side of the equation:
p² - 21 = 4p - 24 + 24

Which simplifies further to:
p² - 21 = 4p

Finally, we rearrange the equation to get all terms on one side:
p² - 4p -21 = 0

Therefore, the correct answer is A. p² - 4p - 21 = 0.

111 is what percent of 300

Answers

100%/x%=300/111(100/x)*x=(300/111)*x 100=2.7027027027*x 100/2.7027027027=x 37=x x=37%

Answer:

Step-by-step explanation:

bc its 37

which expression is equivalent to -3(2m-1)-n
6m-n-3
6m-n+3
-6m-n-3
-6m-n+3

Answers

-6m -n +3

by order of operations
-3(2m-1)-n=-6m+3-n=-6m-n+3

Let's simplify step-by-step.−3(2m−1)−n
Distribute:= (−3)(2m)+(−3)(−1)+−n=− 6m + 3 + −n
Answer: D= −6m − n +3

B). -3(2m-1)-n Final result : -6m - n + 3 Step by step solution : Step 1 :Equation at the end of step 1 : (0 - 3 • (2m - 1)) - n Step 2 : Step 3 :Pulling out like terms : 3.1 Pull out like factors :

-6m - n + 3 = -1 • (6m + n - 3)
Final result : - 6m - n + 3

If Ge=46 and dh=15 find gf

Answers

we have that
GE=46
DH=15
GF=?

we know that
the rhombus has two perpendicular diagonals
and
GE=GH+HE
GH=HE
DF=DH+HF
DH=HF
so
GE=46------------> GH=46/2------------> GH=23
DH=15-------------> HF=15

so
applying the Pythagorean theorem

GF²=GH²+HF²----------> 23²+15²----------> 754

GF=√754----------> GF=27.46 in

the answer is
GF=27.46 in

Answer:

GF=26.4

Step-by-step explanation:

21^2+16^2=C^2

441+256=c^2

697=c^2

GF=26.4

I hope this helps

The rate, r, at which people get sick during an epidemic of the flu can be approximated by r = 1600te^(−0.5t), where r is measured in people/day and t is measured in days since the start of the epidemic.

(a) When are people getting sick the fastest?

(b) How many people get sick altogether?,

Answers

When people are getting sick the fastest, the rate (r) is at its maximum. This will happen at half of the total time (t) because exponential has a negative term. The total number of people that get sick would be (r) divided by total time (t), and this will be greater than 1600.

10 POINTS + BRAINLIEST ANSWER!

At 12 P.M. on Sunday, there are 25,000 people in a football stadium that holds 65,000. Every minute after 12 P.M., the number of people in the stadium increases by 550. If m represents the time, in minutes, after 12 P.M., which of the inequalities below gives the set of minutes in which the football stadium is below capacity?

A. 550m < 25,000

B. 550m < 65,000

C. 550m + 25,000 < 65,000

D. 25,000 - 550m < 65,000

Answers

it is b. if it's wrong please let me know

C-550m + 25,000 < 65,000

a group of 31 friends gets together to play a sport. first people must be divided into teams. each team has to exactly 4 players, and no one can be on more than one team. how many can they make? (it is possible that not everyone can be on a team.)

Answers

We have the following values:
Total people: 31
People per team: 4
The number of teams will then be:
N = (31) / (4)
N = 7.75
Round to the previous whole number.
N = 7
There are 7 teams.
Answer:
they can make about 7 teams.

The center of a circle is located at (3,8) and the circle has a radius that is 5 units long What is the general form of the equation for the circle

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{8}{ k})\qquad \qquad radius=\stackrel{5}{ r} \\\\\\ (x-3)^2+(y-8)^2=5^2\implies (x-3)^2+(y-8)^2=25[/tex]

What are all solutions to the equation 2 cos Θ = 1 for 0 ≤ Θ ≤ 2pi? Round to the nearest hundredth.

θ ≈ 1.32, 4.97
θ ≈ 1.05, 5.24
θ ≈ 0.52, 2.62
θ ≈ 0.05, 2.89,

Answers

2 cos theta = 1 Cos theta = 1/2 Inverse of cos (1/2) = 60 and 300 in degrees. In radians we have 60 * pi/180 = 1.05 300 * pi/180 = 5.24

Answer:

1.a

2.d

3.c

4.a

5.b

Step-by-step explanation:

2.3,
12
5
,
5
2
, 2.2,
21
10
least to greatest

Answers

2,2.2,2.3,5,5,10,12,21

2, 2.2, 2.3, 5, 5, 10, 12, 21

Can any one help me with this! Please look at the picture below just the circled numbers!!

Answers

You are right to circle both 10 or 12. Neither can be solved without knowing something about the x values in 10 and the x value of the smaller base in 12.

The roots of the quadratic equation $z^2 + az + b = 0$ are $2 - 3i$ and $2 + 3i$. What is $a+b$?

Answers

The value of [tex]$a + b$[/tex] is 9.

To solve this problem

We can use the fact that the roots of the equation are given as[tex]$2 - 3i$ and $2 + 3i$.[/tex]

Quadratic equation roots occur in pairs of complex conjugates. Since[tex]$2 - 3i$[/tex] is the first root in this instance,[tex]$2 + 3i$[/tex] is the other root.

We now understand that the coefficient of the [tex]$z$[/tex] term is equal to the opposite of the sum of the roots of a quadratic equation. Stated otherwise, the total of the roots equals [tex]a[/tex] Thus, the two roots can be added together:

[tex]$(2 - 3i) + (2 + 3i) = 4$[/tex]

Therefore[tex], $-a = 4$, or $a = -4$.[/tex]

Next, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the coefficient of the [tex]$z^2$[/tex]term.

[tex]$(2 - 3i)(2 + 3i) = 4 - 6i + 6i - 9i^2 = 4 + 9 = 13$[/tex]

So, [tex]$b = 13$.[/tex]

Finally, we can find the sum[tex]$a + b$:[/tex]

[tex]$a + b = -4 + 13 = 9$[/tex]

Therefore, the value of [tex]$a + b$[/tex] is 9.

which of the following is an x-intercept of the function f(x)=x^2-25
A.-5
B.-20
C.-25
D.-15

Answers

The x-intercept of a function is when the y-value is 0.
Replace y with 0 in the equation. You get the following.

[tex]x^2-25=0[/tex]

Add both sides by 25

[tex]x^2=25[/tex]

Take the square root.

[tex]x= \pm \sqrt{25} [/tex]
[tex]= \pm 5[/tex]

This means that the x-intercepts are 5 and -5.

A is your answer.

The x-intercept of the function f(x) = x^ 2-25 is -5. The correct option is A.

What is the intercept function?

A rational function's intercept is the location on its graph where it crosses either the x- or y-axis. When the independent variable is 0, use the intercept function to find the value of the dependent variable (zero).

For instance, if your data points were collected at room temperature and above, you can use the intercept function to forecast a metal's electrical resistance at 0°C.

The x-intercept of a function is when the y-value is 0.

Replace y with 0 in the equation. You get the following.

[tex]x^2 - 25 = 0[/tex]

Add 25 to both sides

[tex]x^2 = 25[/tex]

Take the square root.

[tex]x = - \sqrt{25}[/tex]

[tex]x = -5[/tex]

Therefore, the correct option is A. -5.

To learn more about the intercept function, refer to the link:

https://brainly.com/question/11872755

#SPJ2

determine the relation of the following lines y = -2x +4 and y= -2x +1

Answers

They're parallel because they have the same slope.

Please show all sork

Answers

When attempting to describe sequences, it is often convenient to look at first differences. Here, they are 4, 6, 8, 10, each obviously 2 more than the next.

a) Second differences are 2.

b) The next three numbers will be
.. 30+12 = 42
.. 42+14 = 56
.. 56+16 = 72

c) There are a number of ways to write an equation for this. One of the simpler ones is to let a graphing calculator perform quadratic regression and tell you the equation.
.. a[n] = n(n +1)

d) 117 is not in the sequence. The sequence consists only of even numbers, of which 117 is not one.

e) 10100 is in the sequence. It is 100*101, hence the 100th term of the sequence.

PLEASE PLEASE HELP ME!!!!

Answers

Angle C is equal to 180 minus the other two angles.
180 - 35-52 = 93
Now we can solve for x.
3(x + 2) = 93
3x + 6 = 93
3x = 87
x = 29

A. x = 29
B. C = 93

Hope this helps =)

52+35 +3x+6 = 180
3x + 93=180
3x = 87
x = 29

<C = 3(29+2) = 3(31) = 93

PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER

Answers

I think the answer is B

Which expression best estimates -18 1/4 divided by 2 2/3?

18/3
-18/3
-18/(-3)
18/(-3)

Answers

just passed the test its letter b

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

[tex]-18\dfrac{1}{4}\div 2\dfrac{2}{3}[/tex]

We need to find the best estimation:

First we change the mixed fraction into improper fraction:

[tex]-18\dfrac{1}{4}\approx -18[/tex]

and

[tex]2\dfrac{2}{3}=\dfrac{8}{3}=2.6666....\approx 3[/tex]

So, it becomes,

[tex]-18\div3\\\\=\dfrac{-18}{3}[/tex]

Hence, Second option is correct.

What is the value of n?
Please explain I'm really lost :(

Answers

3n = 24
n = 8

answer
n = 8

4 x 6 = 3 x n
24 = 3n
n = 24 /3
n = 8

1 question. 11 points. thanks for the help

The equation p = 1.7t² + 18.75t + 175 approximates the average sale price p of a house (in thousands of dollars) for years t since 2010.

What is the best estimate for the price of the house in year 2020

Answers

533,000
I can't really explain it very well but I just took my test and I got it right

The equation [tex] p= 1.7t^{2}+18.75t+175 [/tex] approximates the average sale price p of a house (in thousands of dollars) for years t since 2010.

We have to calculate the best estimate for the price of the house in year 2020.

So, we have to calculate the best price of the house after 10 years.

So, putting the value t=10 in the given equation.

[tex] p= 1.7t^{2}+18.75t+175 [/tex]

[tex] p= (1.7 \times 100)+(18.75 \times 10)+175 [/tex]

p = 532.5= 533 (Rounded)

Since it approximates the average sale price p of a house (in thousands of dollars).

Therefore p=$533,000

Therefore, the best estimate for the price of the house in year 2020 is $533,000.

helpppppppppppppppppppppppppppppp

Answers

Answer:
4/9

Explanation:
For the left hand side:
log base 2 of (6x) - log base 2 of (√x) = log base 2 of (6x / √x)

Equating this to the right hand side we will get:
log base 2 of (6x / √x) = 2

Converting this into exponent form, we will get:
2^2 = 6x/√x
4 √x = 6x
4√x - 6x = 0
√x (3√x - 2) = 0
either √x = 0....> This value is rejected as the log base 2 of zero is undefined
or √x = 2/3 which means that x = 4/9

Hope this helps :)

Please help me with #1!!!!

Answers

Hi Alexis.

When finding the value of a function with a given number, always replace the variable (for x) and simplify. As we can see in your problem, f(x) is being replaced with "4", so substitute "x" with 4.
This leaves us with:
5(4) - 5. All we need to do now is simplify.
5(4) - 5
20 - 5
15.

From the work above, we can see that the function of f(4) has a value of 15.

I hope this helps!

The answer is 15 !!!!!!!!!!!

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