f(x) = 3x + 2
g(x) = x^2 + 1
find gf(x) in the form ax^2 + bx + c

please add an explanation because i’ve seen it being solved i just do not understand some steps

like, where does 12x come from

Answer:

X=-12

Step-by-step explanation:

Subtract -5/2 on both sides:

X/3+5/2-5/2=-3/2-5/2

X/3=-8/2

X/3=-4

Multiply both sides by 3:

X/3*3=-4*3

X=-12

Answer:

x = -12

Step-by-step explanation:

To solve for x, we always want to isolate x {isolate = getting it by itself}

So, for the equation: X/3 + 5/2 = -3/2

we should first get x on its own side:

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

   [tex]-\frac{5}{2}[/tex]     [tex]-\frac{5}{2}[/tex]      {subtract 5/2 from both sides} {-3/2 - 5/2 = -8/2}

[tex]\frac{x}{3} = -4[/tex]

×3     ×3            {multiply both sides by 3 to find "1"x}

x = -12

check:

-12/3 + 5/2 = -3/2

-4 + 5/2  = -3/2

(5/2 = 2 [tex]\frac{1}{2}[/tex]  ;   2 [tex]\frac{1}{2}[/tex] - 4 = -1 [tex]\frac{1}{2}[/tex])

-1 [tex]\frac{1}{2}[/tex] = -3/2      {3/2 = 1 [tex]\frac{1}{2}[/tex]}

-1 [tex]\frac{1}{2}[/tex] = -1 [tex]\frac{1}{2}[/tex]

{TRUE}

so, x = -12

hope this helps!!

Answer:

70

Step-by-step explanation:

Valeria doesnt want any lollipops left over, but identical, so that means you have to add. You can divide the two colors otherwise you get a decimal, which you cant break a lollipop into, or an indefinite letter, a lollipop cant fit in that as well. The only sensible thing is to add them.

1) The normal room temperature is said to be about 20°C

2) 5 day is equivalent to 120 hr

3) 756 m³/s is equivalent 56000 L/s

4) It would take the snail 5 hours to crawl 75 m

An equation is an expression that shows the relationship between two or more numbers and variables.

1) The normal room temperature is said to be about 20°C

2) 1 day = 24 hr

5 day = 5 day * 24 hr per day = 120 hr

3) 1 m³ = 1000 L

756 m³/s = 56 m³/s * 1000 L/m³ = 56000 L/s

4) 1 m = 100 cm

75 m = 7500 cm

Time = 7500 / (25 cm/min) = 300 min = 5 hours

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Answer:

See below

Step-by-step explanation:

cos  2pi/3   =    -1/2

sin   2pi/3   =     sqrt (3)/2

cos   1 pi/6  =     sqrt(3)/2

sin   11 pi/6  =    - 1/2

so when you put in these values in  you will have :

(2*8) * (-1/2 + sqrt (3)/2 i )( sqrt(3)/2) + i (-1/2) )

= 16 ( - sqrt (3)4  + 1/4 i + 3/4 i - sqrt(3)/4  i^2 )        rememember i^2 =  - 1

= 16 ( 1/4  i  + 3/4  i )

= 16 i

1) Rotate triangle A 90° clockwise around O

C (5, 6) ⇒ D (1, 2)

2) Move triangle A' 6 spaces to the right

O (1, 6) ⇒ O' (7, 6)

D (1, 2) ⇒ D' (7, 2)

So Shape A ⇒ Shape B

The function that represents how much you would pay is:

p(x) = (x - $5)*0.9

Let's say that the cost of the repair is x.

First, we apply the coupon, so we discount $5 for the cost.

x - $5.

Then we apply another discount of the 10%, this is written as:

(x - $5)*(1 - 10%/100%)

(x - $5)*(1 - 0.1)

(x - $5)*0.9

Then the function that represents how much you would pay is:

p(x) = (x - $5)*0.9

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The forward differences for this data is 1, 1, 1, 1, 1, 1 (since 10 - 9 = 1, 11 - 10 = 1, etc). Since we only need one iteration of differences, a linear polynomial will fit the data exactly.

Jeremy's debt-to-credit ratio is 0.471.

debt-to-income ratio is the percentage of a consumer's monthly gross income that goes toward paying debts.

Here, Based on the given conditions,

formulate = Total debt / total credit limit

                 = 2355 / 5000

                = 471/1000

Cross out the common factor: 471/1000

Round 471/1000 to the required place:: 0.471

Thus, Jeremy's debt-to-credit ratio is 0.471.

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Answer:

1B + 26M - 26K

Answer That!! Hehehehe

By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.

In this question we must apply trigonometric rules to simplify a given number, in which case we can take advantage of this expression:

[tex]\sin \frac{\theta}{2} = \sqrt{\frac{1 - \cos \theta}{2} }[/tex]

If we know that [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex], then the rewritten expression is:

x = sin 85°

By using trigonometric rules and expressions we find that the expression [tex]x = \sqrt{\frac{1-\cos 170^{\circ}}{2} }[/tex] is equivalent to single trigonometric expression x = sin 85°.

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The linear equation will be 6x + y = 180 and 3x = y. Then the value of the variable x and y will be 20° and 60°.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

3x° + 3x° + y° = 180°  (Supplementary angle)

6x° + y° = 180° .....1

3x° = y° .....2   (Vertically opposite angle)

By solving equations 1 and 2, we have

x° = 20° and y° = 60°

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An equation is formed of two equal expressions. The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given graph is the graph of an exponential function, the general equation of an exponential function is given by the y=aeᵇˣ. To get the function f(x) and g(x), you need to substitute the points in the given function and produce the equation of each function.

The equation for f(x) from the given graph can be written as,

[tex]f(x)=e^{(\ln2)x}-2[/tex]

Now, similarly from the graph the function of g(x) can be written as,

[tex]g(x)=-3e^{(\ln2)x}+6[/tex]

Further, the equation of function g(x) in terms of f(x) can be written as,

g(x) = -3[f(x)]

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Step-by-step explanation: I got it right!

Answer: none

Step-by-step explanation:

Answer:

1/14

Step-by-step explanation:

Let A represent the event First person getting red velvet cake
Let B represent the event Second person getting red velvet cake

P(A) = Total number of Red Velvet Cakes ÷ Total Number of Cakes =

6/21 = 2/7

If the first person gets a red velvet cake, then there are 5 red velvet cakes and 20 total cakes

Therefore P(B|A) = Number of red velvet cakes left ÷ total number of cakes left = 5/20 = 1/4

P(A and B) == probability of both getting red velvet cake P(A∩B) = P(A).P(B|A) = 2/7 × 1/4 = 2/28 = 1/14

Given the data from the question, the expressions that are equal to 10⁵ are

To determine the expressions that are equal to 10⁵, we shall evaluate the options given from the question.

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(10⁴)¹ = 10⁴

Recall

Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ

Thus,

10³ ⋅ 10² = 10³⁺²

10³ ⋅ 10² = 10⁵

Recall

1 / Aᵐ = A⁻ᵐ

Thus,

1 / 10⁵ = 10⁻⁵

Recall

(Aᵐ)ⁿ = Aᵐⁿ

Thus,

(10³)² = 10⁶

Recall

Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10¹⁺¹⁺¹⁺¹⁺¹

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵

SUMMARY

(10⁴)¹ = 10⁴

10³ ⋅ 10² = 10⁵

1 / 10⁵ = 10⁻⁵

(10³)² = 10⁶

10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵

From the above illustrations, only 10³ ⋅ 10² and 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 are equal to 10⁵

Complete question

See attached photo

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the answer is 12

Step-by-step explanation:

The solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For the given inequality the solution can be found as,

         3|x-1| ≥ 12

         x-1 ≥ 4

         x ≥ 5

         3|x-1| ≥ 12

         - x + 1 ≥ 4

         -x ≥ 3

         x ≤ -3

Hence, the solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.

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The equivalent expression is: .[tex]3\frac{3}{8}[/tex]

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division)

Given:

(- 2 1/4)/(- 2/3)

=-9/4÷ (-2/3)

= -9/4 * (-3/2)

= 27/8

= [tex]3\frac{3}{8}[/tex]

Hence, the equivalent fraction is [tex]3\frac{3}{8}[/tex].

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Answer:

The answer is incorrect because the slope formula was used incorrectly in step 1 (parentheses weren't used during the substitution and/or the wrong values were substituted).

y=4x-6

Step-by-step explanation:

The equation we're looking for in slope intercept form looks like [tex]y=mx+b[/tex], where "m" is the slope, "b" is the y-coordinate of the y-intercept, and "x" and "y" are variables that have a certain mathematical relationship through this equation.

To find the equation itself, it usually is easier to find slope before finding the y-intercept.

There are many ways to represent slope (usually represented by the letter m), and while they all mean the same thing, they look different, some examples are shown below:

[tex]m=\frac{rise}{run} =\frac{\text{horizontal change}}{\text{vertical change}}=\frac{\Delta{y}}{\Delta{x}} =\frac{\text{change in }y}{\text{change in }x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this problem, since we are given ordered pairs, probably the most useful version will be the last one:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the values from the ordered pairs, it's important to remember that the ordered pairs are (x,y)... that the first coordinate is an x (and will go into the denominator, or bottom, of the fraction), and the second coordinate is a y (and will go into the numerator, or top of the fraction).

It actually doesn't matter which point we choose to be point 1, and which point we choose to be point 2.  For the least amount of confusion, I choose the first point they gave to be point 1, and the second point they gave to be point 2.

So, [tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex]

If I could give only one piece of advice, it would be "ANY time you substitute, use parentheses."  You can always simplify later, but for the initial substitution, keep them (this is why the "mistake" happened in this problem, and is the thing we need to fix).

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{(6)-(-2)}{(3)-(1)}[/tex]

Simplifying...

[tex]m=\frac{(6)+(2)}{(3)-(1)}[/tex]

[tex]m=\frac{8}{2}[/tex]

[tex]m=4[/tex]

Thus, the equation we want in slope intercept form, with the new information we know plugged in, looks like this:

[tex]y=(4)x+b\\y=4x+b[/tex]

"b" is still the y-coordinate of the y-intercept (which we don't know yet), and "x" and "y" are variables related through this mathematical equation.

With "m" solved for, we can solve for the "b" by using the relationship in the equation we have so far.

We know that every "x" and "y" ordered pair is an "x" related to the "y" by this specific equation.  Even though we don't know the specific value of "b", we know that the equation must be true for every ordered pair on the line.

While we don't know many associated "y" values and "x" values (for instance, we don't know what the "y" value is when the x is 10, and we don't know what the x value is the "y" is 26), we do know two associations for sure... from the two ordered pairs

[tex]\text{Point 1: } (1,-2)[/tex], and [tex]\text{Point 2: } (3,6)[/tex], so

 [tex]x=1 \text{ is related to } y=-2[/tex], and [tex]x=3 \text{ is related to } y=6[/tex]

... and they're related through this equation that we've almost found!

Now, in our equation, there is only room to associate one x and y value at a time, so we need to pick one known association, and substitute those values in.  Since this equation is supposed to relate the x to the y, it should be true for both points (so, we can try both, and it should work out the same.  If you don't want to try both, if you see one ordered pair that has numbers that look easier, use that one):

Substituting Point 1 to find b

[tex]y=4x+b[/tex]

[tex](-2)=4(1)+b[/tex]

simplifying the right side, 4*1 is 4...

[tex](-2)=4+b[/tex]

subtracting 4 from both sides of the equation, and simplifying the left hand side

[tex]-2-4=b\\-2+-4=b\\-6=b[/tex]

Substituting Point 2 to find b (not necessary, but a good double-check)

[tex]y=4x+b[/tex]

[tex](6)=4(3)+b[/tex]

simplifying the right side, 4*3 is 12...

[tex]6=12+b[/tex]

subtracting 4 from both sides of the equation, and simplifying the left hand side

[tex]6=12+b\\6-12=b\\6+-12=b\\-6=b[/tex]

So, as a verification, we get the same value of b (which we should have, because this equation is supposed to work for every pair of (x,y) that has this relationship, and those were the only two points that we knew that did).

Substituting the value we found for b:

[tex]y=4x+(-6)[/tex]

...and simplifying...

[tex]y=4x-6[/tex]

Answer:

It would be 2242.5

Step-by-step explanation:

1950X0.15=292.5

292.5+1950=2242.5

Answer:

11:18

Step-by-step explanation:

the lowest common multiple [meaning the nearest possible time these clocks will be ringing at the same time] of 42 and 56 is 168

(56 x 3 = 168 ; 42 x 4 = 168)

So, in 168 minutes, the clock will ring together again.

Now, we need to add 168 minutes to 08:30

(168 can be made up of 2 hours and 48 minutes [120 + 48 = 168])

08:30 + 2 hours = 10:30

10:30 + 48 minutes = 11:18

So, at 11:18, these clocks will ring together again

The correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given expression:-

2.3p – 10.1 = 6.5p – 4 – 0.01p

The same expression will be calculated as:-

Multiply the given expression by 100 we will get our answer.

E = 100 (s 2.3p – 10.1 = 6.5p – 4 – 0.01p )

E = 230p – 1010 = 650p – 400 – p

Therefore  the correct answer is option C which is 230p – 1010 = 650p – 400 – p this expression is same as of 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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Answer: 45

Step-by-step explanation: I used a graphing calculator and input all the equations and all the restraints, and I found that you can’t use the first equation since x has to be less than or equal to -3, and the question calls for x to be -2. So, in the second equation, there’s a point (-2, 16) and in the third equation there’s a point (1, -3). You know you have to use these two points since in the second equation, the restraint only lets you use numbers greater than -3 or less than 0, which cannot be one, and in the third equation, the restraint only lets you use numbers greater than 0, which can’t be -2. I hope that made some sense. So then, with substitution the equation would be 3(16)+(-3) which equals 45. 3(16)=48. 48-3+=45

The answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.

A rhombus is a two-dimensional shape having four parallel opposite pairs of straight, equal sides. This shape resembles a diamond and is what you'd find on a deck of cards to represent the diamond suit. Rhombuses can be encountered in a variety of common situations.

We have a rhombus shown in the picture.

The intersection point is P

From the definition of the rhombus: JK ≅ KM

According to the SAS congruency postulate, two triangles are congruent if a triangle has two sides and an included angle that are congruent to the two sides and an included angle of another triangle.

Thus, the answers are a rhombus, bisect a pair of opposite angles, and SAS congruency postulate respectively.

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Answer:

1 (2/3) or 1.66666667

Step-by-step explanation:

The slope of a line is found by using the equation :

y2 - y 1 / x2 - x1

So all we have to do is plug in our values given.

To find which belongs with which variable (such as x2 or y1), we do the following:

We know that the coordinates of a point are represented by (x, y). So we must assign a number to each points number.

(2, 8) will be x1 and y1.

(5, 13) will be x2 and y2

Plug in the values :

13 - 8 = 5

5 - 2 = 3

5 / 3 = 1 (2/3)

So, the slope of the line is 1.66666667 or 1 and (2/3)s

Answer:

D

Step-by-step explanation:

the zero is the value of x where the line crosses the x- axis, that is

zero is x = - 2

The linear velocity of the Ferris wheel in inches per second is 18.9 inches/second.

The speed of an object is the ratio of the total distance covered by the object and the total time taken by the object to complete that distance.

Here, the radius of the Ferris wheel is (r) = 30 feet.

The circumference of the wheel is

C= 2πr

C= 2 × π × 30 feet

C= 60π feet

Here, the Ferris wheel completes 7 revolutions.

Therefore, it covers the linear distance of

D= 7 × circumference of the wheel

D= 7 × 60π feet

D= 420π feet

Now, the Ferris wheel took 14 minutes to complete 420π feet.

Therefore, the speed of the wheel is

S= (420π/14) feet/minute

S= 30π feet/minute

S= (30π × 12)/60 inches/second

S= 6π inches/second

S= 18.9 inches/second

Therefore the linear velocity of the object will be 18.9 inches/second

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The data in the plot is Right skewed.

Therefore , Option A is the right answer

A right skewed distribution means most of the data lies to the right side of the graph's peak.

A dot plot is given and observing the data it can be seen that peak is towards the right side of the graph.

Thus the data in the plot is Right skewed.

Therefore , Option A is the right answer.

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