Given f(x) = 5x squared of 2 + 2 and g(x) = 8 - 3x, find the following.
12. Find g[f(-2)].
11. Find flg(x)).

Answer:

15, 21, 27

Step-by-step explanation:

[tex]a_n}[/tex] = [tex]a_{1}[/tex] + (n-1)d  

[tex]a_{n}[/tex] is the number in the sequence we are looking for

[tex]a_{1}[/tex]  This is the first term in the sequence that we do not know and we are looking for

n stands for the number of the term and d is the common difference.  We will put in all that we know and solve for the first term.

609 = [tex]a_{1}[/tex] + (100-1)6  

609 =[tex]a_{1}[/tex] + (99)6

609 = [tex]a_{1}[/tex] + 594  Subtract 594 from both sides of the equation

15 = [tex]a_{1}[/tex]

Now that we know that the first term is 15 we just add 6 to get the next term which is 21 and then add 6 again to get the last term 27.

Answer:

Hello,

Step-by-step explanation:

16)

Area of the square= 5²=25 (unit of square)

17)

Volume of the cube =3^3 =27 (unit of volume)

18)

side of the cube =5 (unit of lenght)

Volume of the cube = (5 (unit of lenght)) ^3

=125 * (unit of lenght)^3 =125 (unit of volume)

Answer:

D, [tex]w\geq 23[/tex]

Step-by-step explanation:

The length is 6 inches longer than it's width, therefore:

[tex]l=w+6[/tex]

The area of the rectangle is AT LEAST 667 square inches, so:

[tex]lw\geq 667[/tex]

Now, we have a system of two equations:

[tex]\left \{ {{l=w+6} \atop {lw\geq 667}} \right.[/tex]

We want to isolate the width, so substitute the first equation into the second to eliminate the length.

[tex](w+6)w\geq 667[/tex]

Simplify:

[tex]w^2+6w\geq 667[/tex]

Since we now have a polynomial equation that needs to be factored, set the value of one side to 0.

[tex]w^2+6w-667\geq 0[/tex]

Now factor the equation:

[tex](w-23)(w+29)\geq 0[/tex]

Taking each factor individually, we find the following:

[tex]w\geq 23\\w\geq -29[/tex]

Since a negative width doesn't make any sense, we can eliminate that solution, and we are left with the correct answer!

[tex]w\geq 23[/tex]

The image of D surely lies on the ray BA ,as ray BA is antiparallel to the ray BD.

Consider D’ to be the image of point D obtained ,when D is rotated 180 degrees anti-clockwise(or counter-clockwise),with B as center of rotation.

From the image above,it is clear that the rays BA and BD are antiparallel.

A ray is a segment of a line with a starting point and an infinite length in one direction.

Antiparallel rays are the rays which are parallel but oppositely directed.The angle between such rays is 180 degrees.

Hence,D’ must lie on the ray BA, as ray BA is antiparallel to BD(i.e the angle between the rays is also 180 degrees).

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90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.

What is a standard deviation?

Sample mean (T) = 13.11%

Sample standard deviation (s) = 2.6

Sample size (h) = 25

significance level = α = 1 -0.90 = 0.1

Degrees of freedom for t- distribution (df) = 24

Critical value = ta/2

df = [tex]t_{0.1}[/tex], df=24 = ±2.80

The margin of error (E) =[tex]t_\frac{a}{2} , df\frac{s}{\sqrt{h} }[/tex]

E=2.8X [tex]\frac{2.6}{\sqrt{25} }[/tex] =1.456

Limits of 90%. Confidence Interval is.

Lowest limit = X' - E = 13.11-1.456 = 11.65

Upper limit= X' + E = 13.11+1.456 = 14.566

90% confidence interval is 11.65 <µ< 114.566 as per standard deviation data.

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Answer: 3/4

Step-by-step explanation:

See attached work. Remember when dividing fractions, you must multiply by the reciprocal of the second fraction.

The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y).

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

For example 3x +5y

Given the phrase,

x over 4 = x/4

y over 3  = y/3

Combine x/4 + y/3

x over 3 minus y over 4 = x/3  - y/4

Therefore ;

(x/4 + y/3) ÷ (x/3  - y/4)

⇒ (3x + 4y)/12 ÷ (4x - 3y)/12

The second fraction will inverse in multiplication

⇒ (3x + 4y)/12 × 12/(4x - 3y)

⇒ (3x + 4y) / (4x - 3y).

Hence "The simplified form of a given phrase x over 4 plus y over 3 all over the quantity x over 3 minus y over 4 is (3x + 4y) / (4x - 3y)".

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Answer:

- 4/5 /decimal form -0.8

Step-by-step explanation:

Answer:

In one gram, there are 1000 milligrams.

To convert g to mg, multiply the gram value by 1000.

Answer:

36

Step-by-step explanation:

The constant is the number when complete simplified, which in this case would be only formed by squaring the 6, equaling 36.

Hope this helps! :)

Answer: +36

Step-by-step explanation:

(x - 6)² simplified: x^2 -12x + 36

The constant in this algebraic expression is 36 because it's value or number doesn't change in the expression (x^2 -12x + 36)

Answer:

15 games

Step-by-step explanation:

Since the team won 80% of the games and won 12, we can put these into an equation.

80% is also 0.8 so:

x * 0.8 = 12

To find x we can simply do 12 divided by 0.8 which equals =

15

Solution:

A. [tex](3-\sqrt{2}, 3+\sqrt{2})[/tex]

Hope this helps!

Answer:

Choice 3

Step-by-step explanation:

The graph fails the vertical line test.

Answer:x=−19

Step-by-step explanation: work in your head ppl

Answer: -3

Step-by-step explanation:

trust me

Answer:

Answer is in the picture attached

Answer: 51.96m

Step-by-step explanation:

We can solve this using cosine, remember SOHCAHTOA, so cos is adjacent over hypotenuse.

hyp = 60

adj = ?

[tex]cos = \frac{adj}{hyp}\\cos 30 = \frac{x}{60} \\\\cos30 *60=x\\x=51.96m[/tex]

3/7 of 6/1 means [tex]6(\frac{3}{7})=\frac{18}{7} =2\frac{4}{7}[/tex]

hope this helped

Answer:

6

Step-by-step explanation:

The square's side will be √144 = 12

The largest circle will have diameter of 12 so it's radius will be 12/2 = 6

The equation that best represents a the given situation is: 3n + 3 = 303., as found by number system.

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

Given: Sum of three consecutive integers is 303.

n = smallest integer.

According to question, the other two integers are: n + 1, and n + 2.Since the sum of the three consecutive integers is 303, addition operation on the values of number system

n + n + 1 + n + 2 = 303

3n + 3 = 303.

Hence, The equation that best represents a the given situation is:

3n + 3 = 303., as found by number system.

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Answer:

"Defined items" are defined in terms of "undefined terms".

Step-by-step explanation:

None.

In the possible diagram of the house, the lines formed by intersecting planes are; [tex] \overline{AG}[/tex], [tex]\overline{ AB}[/tex], [tex]\overline{AH}[/tex], [tex]\overline{GF}[/tex], [tex]\overline{ BH}[/tex], [tex]\overline{HF}[/tex], [tex]\overline{BC}[/tex], [tex]\overline{ HD}[/tex], and [tex]\overline{FE} [/tex]

The diagram found in a similar question has points A, G, B, H, and F on the roof.

The points on the walls of the house are; B, H, F, C, D, and E

A plane in Euclidean geometry is a surface that is flat, such that a line that connects two points on it lie completely on the plane.

A plane can be identified by three non collinear points that lay on it.

A line is a figure that does not have a curvature, width or depth, and it is infinitely long.

The planes on the roof are; ABH and AGHF

The planes on the walls of the house are; BCDH, and HDCF

The lines that are formed by the intersecting planes are therefore;

On the roof;

Between the roof and the walls of the house;

Between the two sides of the walls;

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After simplifying the expression √80y³, we get the answer as 4 y √5 y.

We are given that:

√80y³

We have to simplify it.

We will first make the factors of it.

Factors of 80:

80 = 2 × 2 × 2 × 2 × 5

Factors of y³:

y³ = y × y × y.

Now the expression can be re- written as:

√2 × 2 × 2 × 2 × 5 × y × y × y.

Simplifying it:

2 × 2 × y √5 y

4 y √5 y

Therefore, after simplifying the expression √80y³, we get the answer as 4 y √5 y.

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Answer:

i think its answer is A or D

Answer:

y =2/3 =4/3x

Step-by-step explanation:

The dimensions of the rectangle are:

To find the dimensions of the rectangle:

Let,

Extend the area equation as follows:

Rearrange:

Substitute known information for A:

To solve quickly, factor the left side (or use the quadratic formula):

The factorial solutions for w are -2 and 7/2.

Assuming this is a genuine rectangle, the width must be positive.

As a result, the length is:

That is,

Therefore, the dimensions of the rectangle are:

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The complete question is given below:
The area of a rectangle is 14 yd², and the length of the rectangle is 3 yd less than double the width. find the dimensions of the rectangle.

If the population of Nebraska was 1.8×[tex]10^{6}[/tex], then the state which had a smaller population is Rhode Island

Given,

The population of Nebraska = 1.8×[tex]10^{6}[/tex]

The population of Rhode Island = 1.1×[tex]10^{6}[/tex]

1.1×[tex]10^{6}[/tex] <  1.8×[tex]10^{6}[/tex]

So, Rhode island has population less than Nebraska

Hence, if the population of Nebraska was 1.8×[tex]10^{6}[/tex], then the state which had a smaller population is Rhode Island

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A positive association occurs when an increase in one variable is generally associated with the increase in the second variable and a negative association occurs when one variable tends to decrease as the other increases.

An association is any relationship between two factors that produces them subordinate, i.e. knowing the value of one variable gives us some data around the possible values of the moment variable.

The objective of this variable is to utilize clear measurements and visualisations to investigate affiliations among different kinds of factors.

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