Determine whether each function is linear or quadratic. Identify the quadratic, linear, and constant terms. y=4 x(7-2 x)

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

The expression that represents the quotient of 3 and 3 less than a number is 3/(x - 3).

Let, x be a number

So the expression is, 3/(x - 3)

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.

The expression that represents the quotient of 3 and 3 less than a number is 3/(x - 3).

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The car's velocity after 15 seconds is 60.3 m/s.

The linear regression equation obtained by fitting the data using technology is:

The approximate velocity at time = 0 and x = 0 is as follows:

After 15 seconds, the velocity is:

Therefore, the car's velocity after 15 seconds is 60.3 m/s.

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n=4  is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12.

What is the probability in simple terms?

Number of socks = n .

Number of red socks = 3 .

Given

       3C2nC2=12

     ⇒nC2=3×2=6

    ⇒n=4

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Answer:

The answers are as follows:

Answer:

t = 0

Step-by-step explanation:

t + t = 0 , that is

2t = 0 ( isolate t by dividing both sides by 2 )

t = [tex]\frac{0}{2}[/tex] = 0

Answer:

t=0

Step-by-step explanation:

t+t is 0 and since were not given any numbers for t its automatically 0

47.4 is the mean of the data summarized in the given frequency distribution.

What is a frequency distribution?

speed        m f m*f

42-45       43.5 22 957

46-49    47.5 14 665

50-53    51.5 7 360.5

54-57    55.5 4 222

58-61    59.5 2 119

Total    49              2323.5

mean = 2323.5/49 = 47.4

The computed mean is not close to the actual mean because the difference between the means is more than 5%.

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Two different infinite geometric series that each have a sum of 8 are 32 + 32(3) +32(3)² + 32(3)³ + .................    and 24 + 24(2) + 24(2)²+ 24(3)³+ .............

An Infinite geometric series is the sum of the infinite terms and these terms have constant ratio between successive terms.

Let us take first term of the infinite series be a and r be the constant ratio between successive terms. Then formula for such  geometric series be a+ar+ar²+ar³+.............

And sum of such series is ,S =a/(1+r)

We have to find two infinite geometric series with sum S = 8

Let us take a=24 and r=2

Then sum, S = [tex]\frac{24}{2+1} =\frac{24}{3}=8[/tex]

Therefore such series will be:

24 + 24(2) + 24(2)²+ 24(3)³+ .............

Another possibility for sum 8 will be with a =32 and r=3

Then the sum, S = [tex]\frac{32}{3+1} =\frac{32}{4}=8[/tex]

Therefore another such infinite geometric series will be

32 + 32(3) +32(3)² + 32(3)³ + .................

Thus, two different infinite geometric series that each have a sum of 8 are 24 + 24(2) + 24(2)²+ 24(3)³+ ............. and

32 + 32(3) +32(3)² + 32(3)³ + .................

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Answer:

[tex]x = \frac{64}{3} [/tex]

Step-by-step explanation:

Based on the given conditions:

[tex] \frac{x}{32} = \frac{12}{12 + 6} ⟹ \frac{x}{32} = \frac{12}{18} [/tex]

Cross multiply the above

[tex]18x = 384 [/tex]

Divide both sides by 18 to find the value of x

[tex]x = \frac{384}{18} [/tex]

Therefore:

[tex]x = \frac{64}{3} [/tex]

The expression that gives the number of gallons of paint that Miki will need to buy to paint her room is F. (x + 6) / (x + 4)

Expression:

Expression are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

The area of Miki's room is x²+8 x+12 square feet. A gallon of paint will cover an area of x²+6 x+8 square feet.

Here we need to find the expression that gives the number of gallons of paint that Miki will need to buy to paint her room .

The number of gallons of paint required to paint the room is calculated by dividing the expression.

Then we get,

=> [tex]\frac{x^{2} +8 x+12}{x^2+6x+8}[/tex]

Factor the numerator and the denominator to simplify the fraction.

So, the factors of

=> x² + 8x + 12 = (x+6) (x+2)

and the factors of

=> x² + 6x + 8 = (x+4) (x+2)

When we apply the factors instead of the given expression,

Then we get,

=> [tex]\frac{(x+6)(x+2)}{(x+4)(x+2)}[/tex]

After the simplification we get,

=> (x +6) / (x + 4)

So, the option is F. (x+6) / (x+4) is the correct expression that gives the number of gallons of paint that Miki will need to buy to paint her room .

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Answer:

x = 44.25

Step-by-step explanation:

9 + 6.6x = 7x - 8.7

    -7x       -7x

---------------------------

9 - 0.4x = -8.7

-9             -9

-0.4x = -17.7

÷-0.4   ÷-0.4

-------------------

x = 44.25

The windows of house are 8 feet apart distance.

As we are provided with the the total width of house is 33 feet and 4 feet distance between the edge of the house and the end windows

So the space available for the windows is total width of the house minus the  distance between the edge of the house and the windows from both the sides = 33 - 2(4) = 33-8 = 25 feet

The length of the windows to be inserted is the product of number of windows  and their side = 3 × 3 = 9 feet

The total distance between the windows can be find out by reducing the distance covered by windows from the area available for windows = 25feet - 9 feet = 16 feet

There are three windows, so there will be only 2 gaps whose length is 16 feet / 2 = 8 feets

Hence, the windows of the house are 8 feet  apart

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Simplify each rational expression. State any restrictions on the variable.

[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\frac{(c-2)}{(c-5)}[/tex]

How the rational expression is simplified?

[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }\\\\= > \frac{(c-2)(c-6)}{(c-5)(c-6)} \\= > \frac{(c-2)}{(c-5)}[/tex]

What are the restrictions on the variable ?

If c= 5 , the denominator becomes,

[tex]c^{2} -11c+30[/tex]  =25-55+30=0

⇒   [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]

If c= 6 ,the denominator becomes,

[tex]c^{2} -11c+30[/tex] = 36- 66+30=0

⇒   [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]

So, the restrictions on the variable are:  c≠ 5,6

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Answer:

x=5/11 | x=6, A

Step-by-step explanation:

For the first question- 3(4-2x)=-x+1

Use algebra to solve

1. 3(4-2x)=-x+1 Distribute

2. 12-6x=-x+1 Seperate like terms

3. 12-1=6x-x Combine

4. 11=5x

5. x=5/11

For the second babysitting question, since we want to multiply the combined hours worked by 9 (the amount of money per hour, the equation should be A. Use algebra to find the hours.

1. 9(5+x)=99 Distribute

2. 45+9x=99

3. 9x=54

4. x=54/9

5. x=6

Emma initially had  £19 as the amount of money she initially had at the beginning

Emma gives  £8 to Hafid

Ben gives  £3 to Hafid

The total amount of money that Hafid can be calculated by adding Emma and Ben's money together.

= 3 + 8

= 11

They all have the same amount of money.

Emma initial amount can be calculated by adding 11 and the amount of money Emma gives to Hafid

= 11+8

= 19

Hence Emma initially had  £19

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Answer:

2 line is the answer to the questions

The greatest number of identical arrangements is 1 arrangements of 15 strawberries and 2 grapes.

It is required to find the solution.

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

Given:

In total, there are 15 strawberries and 30 grapes.

To find the greatest number of identical arrangements, first we need to find the greatest common factor of 15 and 30.

According to given question we have

GCF of (15,30) = 15

Therefore, the greatest number of identical arrangements is 1 arrangements of 15 strawberries and 2 grapes.

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Step-by-step explanation:

4.

[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{a - b}{a + b} [/tex]

[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{(a - b)(a - b)}{ {a}^{2} - {b}^{2} } [/tex]

[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{ {a}^{2} - 2ab + {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]

[tex] = \frac{5ab - ( {a}^{2} - 2ab + {b}^{2} ) }{ {a}^{2} - {b}^{2} } [/tex]

[tex] = \frac{5ab - {a}^{2} + 2ab - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]

[tex] = \frac{7ab - {a}^{2} - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]

[tex] \: [/tex]

5.

[tex] = \frac{5}{n + 5} + \frac{4n}{2n + 6} [/tex]

[tex] = \frac{5}{n + 5} + \frac{4n}{2(n + 3)} [/tex]

[tex] = \frac{5}{n + 5} + \frac{2n}{n + 3} [/tex]

[tex] = \frac{5(n + 3) + 2(n + 5)}{ {n}^{2} + 8n + 15 } [/tex]

[tex] = \frac{5n + 15 + 2n + 10}{ {n}^{2} + 8n + 15} [/tex]

[tex] = \frac{7n + 25}{ {n}^{2} + 8n + 15} [/tex]

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve these problems ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5ab}{ {a}^{2} - {b}^{2} } - \dfrac{a - b}{a + b} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5ab}{ (a + b)(a - b) } - \dfrac{a - b}{a + b} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5ab - (a - b)(a - b)}{ (a + b)(a - b) } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5ab - (a - b) {}^{2} }{ {a}^{2} - b {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5ab - (a {}^{2} - 2ab + {b}^{2} ) {}^{} }{ {a}^{2} - b {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5ab - a {}^{2} + 2ab - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{7ab - a {}^{2} - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5}{n + 5} + \dfrac{4n}{2n + 6} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{5(2n + 6) + 4n(n + 5)}{(2n + 6)(n + 5)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{10n +30 + 4n {}^{2} + 20n}{2n {}^{2} + 10n + 6n +30} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{4n {}^{2} + 30n + 30}{2n {}^{2} + 16n + 30} [/tex]

[ taking 2 common out ]

[tex]{ \qquad \sf  \dashrightarrow \: \dfrac{2n {}^{2} + 15n + 15}{n {}^{2} + 8n + 15}} [/tex]

The scaled distance using the given scale factor is; 1.613 units

We are given;

Distance between Earth and the sun = 150, 000, 000 km

Now, we are given that the scale model that represents Distance between Earth and the sun is 1:93,000,000.

This means that 1 unit represents 93000000 kilometers. Thus;

The scaled distance using the given scale factor is;

150,000,000/93,000,000 = 1.613 units

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The standard deviation of this distribution is 9.65 minutes.

Due to its description in terms of the second central moment, the standard deviation naturally arises in mathematical statistics.

Any distribution with finite first two moments can have its standard deviation defined, although the most common assumption is that the underlying distribution is normal.

In the above given question it is stated that:

mean(μ) of the distribution is 45 and let us consider the standard deviation to be σ

We convert this to standard normal as

[tex]P(X < x) = P(Z < \frac{( x - \mu)} {\sigma})[/tex]

We have , P(X > 55) = 0.15  (15%)

This can be simplified as:

P(X < 55) = 1 - 0.15

P(X < 55) = 0.85

[tex]P(Z < \frac{( x - \mu)} {\sigma}) = 0.85[/tex]

From Z table, z-score for the probability of 0.85 is found out to be  1.0364 ,

therefore :

[tex]\frac{( 55 - 45)}{ \sigma }= 1.0364\\\\ \sigma = ( 55 - 45) / 1.0364 \\\\\sigma = 9.65[/tex]

Hence the standard deviation is 9.65 minutes.

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If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped then the distance the object falls during 0.25 second time is 1 feet

Given,

The expression of distance in feet that an object falls = [tex]16t^{2}[/tex]

Where t is the time seconds

Then the time = 0.25 second

Substitute the values in the expression = [tex]16(0.25)^{2}[/tex]

=1 feet

Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped then the distance the object falls during 0.25 second time is 1 feet

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Based on the number given of  8.141141114, it is NOT a rational number.

A rational number refers to one that does not extend to infinity after the decimal. Some rational numbers will extend to infinity but they will have repeating numbers such as 0.3333333333.

The number  8.141141114, is not a rational number because it extends into infinity and the numbers after the decimal point are nonrepeating.

In conclusion, 8.141141114 is not a rational number.

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Answer:

perhaps it is 7.09809809876 or it might be 5.437437437, a recursive number.

Step-by-step explanation:

i might be

Answer:

-440

Step-by-step explanation:

Simplify

2(-4)^2+(-4)^3+24-18(-12)2

2(16)+(-64)+24-432

32-64+24-432

-440

The next three numbers of the sequence are -3, -5, -7,........

An arithmetic progression, or AP, is a series in which the next term is derived from the previous one. by modifying the previous word with a constant d known as the common difference. The arithmetic progression is if the first term of the series is a, a + d, a + 2d, a + 3d, ...

The given pattern forms an Arithmetic progression (A.P.)

The sequence is - 5 , 3, 1, -1, -3, -5, -7,........

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Answer: Yes only if is is so hot it will burn yout tung but you dont want cold coffe so

Step-by-step explanation:

Answer:

Step-by-step explanation:

I agree with the first answer but maybe people like cold brews, i know i do. also people on here be asking the craziest questions bro like i just answered "what are your thoughts about brainly being a dating app" i was like what ;-;

Step-by-step explanation:

Have you understand? please notify when you don't understand

Answer:

1/16

Step-by-step explanation:

Coin toss

probability 1/2×1/2×1/2×1/2 = 1/16