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The rule for g(x) = f(x-1)-3 is g(x) = (x-1)⁶-3(x-1)³ - 1

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable. Based on the information given, we can see that the variables that are illustrated in the question are f and g.

In order to write the rule for g(x) = f(x-1)-3 when f(x) = x⁶ - 3x³ + 2, replace x with x-1 in f(x) and subtract 3. That is:

g(x) =  f(x - 1) - 3

g(x) = (x-1)⁶ - 3(x - 1)³ + 2 - 3

g(x) = (x-1)⁶ - 3(x - 1)³- 1

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Answer:

12/7 is a improper fraction

Step-by-step explanation:

as a decimal it is 1.71428571429 and as a mixed number it is 1 5/7

Answer:

its gonna be 1 5/7

Step-by-step explanation:

7 goes into 12 1 time and there is 5 left over so thats gonna be 1 and 5/12 or

1 5/12

Answer: A

Step-by-step explanation:

I took the test

Answer:

m<1=50

m<2=130

m<3=50

m<4=130

m<5=40

m<6=40

m<7=90

m<8=140

Step-by-step explanation:

x = liters of solution at 20%

y = liters of solution at 70%

[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{acid only}}&\stackrel{\textit{liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{Sol'n at 20\%}&x&0.2&0.2x\\ \textit{Sol'n at 70\%}&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&50&0.4&20 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.2x+0.7y=20 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies x=50-y}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.2(50-y) + 0.7y=20} \\\\\\ 10-0.2y+0.7y=20\implies -0.2y+0.7y=10\implies 0.5y=10 \\\\\\ y=\cfrac{10}{0.5}\implies \boxed{y=20}[/tex]

Answer:

B 16/3

Step-by-step explanation:

on edg

The volume of the pyramid shown is 16√3 cm³.

Volume of a three dimensional shape is the space occupied by the shape.

Given a solid oblique pyramid.

It has an equilateral triangle as a base with an edge length of 4√3 cm and an area of 12√3 cm².

Volume of the pyramid = 1/3 × base area × height

Base area = 12√3 cm²

Height = 4√3 × tan (30°) = 4√3 × 1/√3 = 4

Volume = 1/3 × 12√3 × 4

             = 16√3 cm³

Hence the volume is 16√3 cm³.

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Answer:

Step-by-step explanation:

(-1, 1):  You can see that a vertical line through x = -1 is the center line (axis of symmetry) of this parabolic graph.  The vertex lies 1 unit above the x-axis:  y = 1.

The area of the floor in the scale drawing is 60 inches².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Actual rectangle:

Length = 24 feet

Width = 40 feet

Scale rectangle:

Length = 6 inches

Width = 40/4 = 10 inches

The area of the scaled rectangle.

= Length x Width

= 6 x 10

= 60 inches²

Thus,

The area of the scaled rectangle is 60 inches².

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Answer:

268°

Step-by-step explanation:

[tex] In\: \odot O, [/tex] AB is diameter.

So, [tex] \widehat{AB} \:\&\: \widehat {BA}[/tex] are semicircular arcs.

[tex] \therefore m\widehat {AB} =m\widehat {BA} = 180\degree [/tex]

[tex] \because \: m\widehat {BC} = m\widehat {BA} - m\widehat {CA} [/tex]

[tex] \therefore \: m\widehat {BC} = (180-92)\degree [/tex]

[tex] \therefore \: m\widehat {BC} =88\degree [/tex]

[tex] \because m\widehat {ABC} = m\widehat {AB}+m\widehat {BC} [/tex]

[tex] \therefore m\widehat {ABC} = 180\degree+88\degree [/tex]

[tex] \therefore m\widehat {ABC} = 268\degree [/tex]

Answer:

You need to combine like terms

Answer:

Given that ,

738 students wore red while 162 students wore green.

Therefore , total number of students ,

[tex]\dashrightarrow \: 738 + 162 \\ \dashrightarrow \: 900[/tex]

Now , 738 students out of 900 wore red.

So , percentage of students who wore red ,

[tex]\dashrightarrow \: \frac{738}{9\cancel{00}} \times \cancel{100} \\ \\ \dashrightarrow \: \cancel\frac{738}{9} \\ \\ \dashrightarrow \: 82\%[/tex]

hope helpful :-;

The answers are given as 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m

A curve is defined as a smoothly- flowing continuous line that has bent. It does not have any sharp turns. The way to identify the curve is that the line bends and changes its direction at least once. Curve of the graph is a pictorial representation of a particular function.

Given :  A object is thrown from the top of the building thus by observing the graph we derive the following information

1) Maximum height = 165 m

2) The object reaches maximum height at t=3 seconds

3) The time it took to reach the ground is 9 seconds

4) The building is 120 m tall

Hence, the answers are  1) 165 m 2)3 seconds 3) 9 seconds 4)120 m

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If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2

We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.

And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.

Given that  sinθ⋅cosθ = 1/2

2(sinθ⋅cosθ) = 1             .........(1)

We know that trigonometric identity,

sin(2θ) = 2 sinθ cosθ

so equation (1) becomes,

sin(2θ) = 1            

We know that sin(π/2) = 1

Comparing with equation sin(2θ) = 1 we get,

2θ = π/2

θ = π/4          

Using trigonometric table,

sin(π/4) = 1/√2

and cos(π/4) = 1/√2

The value of  sinθ+cosθ would be,

sin(π/4) + cos(π/4)

= (1/√2) + (1/√2)

= 2/√2

= √2

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The complete question is:

If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ

Answer:

y= ae^pi + C2e ^ -1/2 pi

Step-by-step explanation:

i couldnt type out symbols, hope this helps

Answer:

[tex]A_s=2.28yd^2[/tex]

Step-by-step explanation:

From the question we are told that:

Radius [tex]r=2yd[/tex]

Pie [tex]\pi=3.14[/tex]

Generally the equation for Area of the shaded part [tex](A_s)[/tex] is mathematically given by

[tex]A_s=Area\ of\ semi-circle(A_c)-Area\ of\ triangle(A_t)[/tex]

Generally the equation for Area of semi-circle is mathematically given by

 [tex]A_c=\frac{1}{2}\pi r^2[/tex]

 [tex]A_c=\frac{1}{2}*(3.14) (2)^2[/tex]

[tex]A_c=6.28yd^2[/tex]

Generally the equation for Area of triangle is mathematically given by

 [tex]A_t=\frac{1}{2} base*height[/tex]

 [tex]A_t=\frac{1}{2} (2+2)*2[/tex]

 [tex]A_t=4yd^2[/tex]

Therefore Area of the shaded part [tex](A_s)[/tex]

 [tex]A_s=A_c-A_t[/tex]

 [tex]A_s=6.28yd^2-4yd^2[/tex]

 [tex]A_s=2.28yd^2[/tex]

Answer: -40

Step-by-step explanation:

This answer is only correct if that last number is 52. So if the last number is something other than 52 then the answer is wrong,

Answer:

The answer is c- 1/2

Step-by-step explanation:

The situation involving coins that is modeled by the system of equations x + y = 24, 0.25x + 0.05y = 4.60 is given as follows:

You have a combination of 24 quarters and cents, and the total you have is of $4.60. How many coins of each type you have.

To obtain the meaning of each of the variables x and y, we look at the second equation, given as follows:

0.25x + 0.05y = 4.60.

This means that:

The result of this sum means that the total amount of money that you have is of $4.60.

The first equation is given as follows:

x + y = 24.

Which means that the total number of coins that you have is of 24.

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Answer:

(2 x 10) + (4 x 1) + (2 x 0.1) + (1 x 0.01)

Step-by-step explanation:

The expanded form of 24.21 = (20 + 4 + 0.2+ 0.01)

The expanded form of an equation requires writing out the place value term of each digit of the number given :

24.21 :

Tens digit = 2 × 10 = 20

Unit digit = 4 × 1 = 4

Tenth digit = 2 × 0.1 = 0.2

Hundredth digit = 1 × 0.01 = 0.01

Hence, the expanded form of the number is :

(20 + 4 + 0.2+ 0.01)

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The Answer is D

I REALLY hope this helps :D

It is the graph of f(x) translated 3 units down.

Answer:

D

Step-by-step explanation:

Because f(x) translated 3 down

The function which has greater slope is Function 2.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Function 1:

y = -2x + 10

and Function 2:

Slope = (5-10)/( 2-0) = -5/2

So, the Equation of line

(y - 10) = -5/2 (x -0)

y - 10 = -5/2x

y = -5/2x + 10

y= -2.5x +10

So, the slope of Function 1 is greater than slope of function 2.

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Answer: 8 miles

Step-by-step explanation:

1.25m+6=2m

--1.25m. -1.25m

6=.75

6/.75m=8 mile

s

Answer:

3 tan theta=root 3

tan theta=root 3/3

tan theta=0.57

Step-by-step explanation:

Answer:

72xy1

Step-by-step explanation:

becuz the multiple of 9,6 and 24 is 72 and the multiple of x is 1x which is just x and the multiple of y is 1y

Answer:

Step-by-step explanation:

Perimeter is the addition of all the sides.

So in this question, if you add up all the sides :

14x + 8x +7x +12

Simplify by adding all terms with x :

29x + 12  

(As you can not add a number constant to a variable )

answer:

5/3 m

Step-by-step explanation:

because 3/3=1 so teacher choose boys

The equivalent expressions of 10/9 + 2/9m − 4/9n are 2/9(5 + m - 2n) and -2/9(2n − m − 5)

From the question, we have the following parameters that can be used in our computation:

109+ 29m − 49n

Express the expression properly

So, we have the following representation

10/9 + 2/9m − 4/9n

Factor out 2/9

So, we have

2/9(5 + m - 2n)

Factor out -1 from the expression

So, we have the following representation

-2/9(2n − m − 5)

Hence, the equivalent expression is -2/9(2n − m − 5)

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uh     ..................

Answer:

80%

Step-by-step explanation:

divide the number of days that there was sun (4) by the total number fo days (5), then multiply by 100 to get to a percent.

if you have any questions, leave them in the comments and i will try to answer them, if this helped, please give brainliest.

Answer:

50

Step-by-step explanation:

According to a recent study of 35 students,Population-wide, there was a 2.8-hour standard deviation. 16.60 is the population mean's 95% confidence interval.

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