If f(x) = –3(1 – x – 4x2) give f-3.

Answer:

c. x > 2.

Step-by-step explanation:

4x + 1/2 (2x+4) > 12

4x + x + 2 > 12

5x > 10

x > 2.

The number of weeks when Salma and Henry would have the same amount of money is 20 weeks.

The form of the equations that represent the total amount of money saved is :

Total amount in the account = initial amount in the account + (amount added each week x number of weeks)

SS = $35 + ($8 x tt)

SS = $35 + $8tt

HH = $95 + ($5 x tt)

HH = $95 + $5tt

When they have the same amount in their account, the two equations woud be equal.

HH = SS

$95 + $5tt  =  $35 + $8tt

$95 - $35 = $8tt - $5tt

$60 = $3tt

tt = $60 / 3

tt = 20 weeks

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Bouman contributed to taking the first photograph of a black hole as she and her team created an algorithm that makes it possible to collect data and combine it into one image.

The article highlighted the importance of Katie Bouman in leading her team who created a computer software capable of using an algorithm that analyzes data and creates an image based on it. Its elaboration took about two years to complete but the results were very promising and promoted a great advance for science.

In conclusion, Bouman and the team were able to develop series of algorithms that converted telescopic data into the historic photo shared by the world's media.

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The Equation of line -

The slope intercept form of a line is given by -

y = mx + c

m is the slope of line

c is the y - intercept

Given is a line that passes through the point (3, 10) and in case [1] is parallel to line y = x - 1 and in case [2] is  perpendicular to y = x - 1.

Case 1 -  Line is parallel to the line y = x - 1

Assume that the equation of line is -

y = mx + c

Since, the line is parallel, both lines will have same slope and is given by -

m = 1

Since, the line passes through the point (3, 10) we can write -

10 = 1 x 3 + c

c = 7

We can write the equation of line parallel to line y = x - 1 as -

y = x + 7

Case 2-  Line is perpendicular to the line y = x - 1 -

Assume that the equation of line is -

y = mx + c

Since, the line is perpendicular, the product of slopes of both lines will be equal to 1. The slope (m) of the line will be -

m x 1 = -1

m = -1

Since, the line passes through the point (3, 10) we can write -

10 = -3 + c

c = 13

We can write the equation of line perpendicular to line y = x - 1 as -

y = - x + 13

Therefore, the equation of line -

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Answer:

2, 3

Step-by-step explanation:

[tex]g(x)=\frac{1}{2}(4x+6) \\ \\ =2x+3[/tex]

Answer: 8/23

Step-by-step explanation:

Make a two-way table

                             Did Assignment        Didn't do Assignment

Passed                            12                                        2

Did not pass                    3                                        6

Total                                 15                                       8                     = 23

2+6=8

8/23

The three more solutions to the given linear equation are (2,-9/2), (6,-3/2), and (5,-9/4).

Given equation:-

y = (3/4)x - 6

We have to create a table of values to obtain ordered pairs.

Also, we have to plot these ordered pairs to create a linear graph and based on the  graph we have created, we have to find three more solutions to the equation.

Let x = 0

y = 0 - 6 = -6

Ordered pair = (0,-6)

Let y = 0

0 = (3/4)x - 6

6 = (3/4)x

x = 8

Ordered pair = (8,0)

Let x = 4

y = 3 - 6 = -3

Ordered pair = (4,-3)

The graph of these three ordered pairs is attached below.

Based on the graph the other 3 ordered pairs that we can find are (2,-9/2), (6,-3/2), and (5,-9/4).

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Answer:

there's no ratio, or maybe u can help me out

Answer:

x=37

Step-by-step explanation:

3x + 3 + 2x - 8 = 180

solve for x and x = 37

hope this helped

have a good day sir ^^

Answer:

x=37

Step-by-step explanation:

180=5x+3-8

180=5x-5

+5      +5

185=5x

/5     /5

37=x

x=37

b = 4a is the answer.

Given,

a= 1/4 b

To find:

Make b the subject, the given equation

Solution:

Take 4 to the side of a

4a = 1b

Therefore,

b = 4a

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Answer:

Step-by-step explanation:

The rate of change (m) = 9

The starting number (b) = 100

The equation is: y = 9x + 100

(0, 100) is the ordered pair for the starting number.

See the image for the graph of y = 9x + 100.

To create the equation of a line, we need to determine the following:

Y-intercept/starting value = b

Slope of the line/rate of change = m

The ordered pair of the y-intercept or starting value is represented as (0, b), where b is the value of y on the y-axis where the line intercepts the y-axis and x = 0 at this point.

These values can be substituted into y = mx + b, which represents the equation of the line in slope-intercept form.

From the information given, we have:

Y-intercept/starting value (b) = 100

Slope of the line/rate of change (m) = 9

To write the equation of the line, substitute m = 9 and b = 100 into y = mx + b:

y = 9x + 100

The ordered pair for the starting number would be: (0, 100).

The image below shows the graph of y = 9x + 100.

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Answer:

Step-by-step explanation:

(a - b)² =

(a - b)(a - b) =

[(- 1)(b - a)] × [(- 1)(b - a)] =

(- 1)(- 1)(b - a)(b - a) =

(b - a)²

The line segment AD is 12 units.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The midpoint is halfway between the two end points:

Therefore, B is between A and C.

C is between B and D.

Hence,

AC = 8

BC = 5

BD = 9

AD = ?

Therefore,

AD = AB + BC + CD

AB = AC - BC

AB = 8 - 5

AB = 3 units

CD = BD - BC

CD = 9 - 5

CD = 4 units

Therefore,

AD = 3 + 5 + 4

AD = 12 units

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Answer:

See attachment.

Step-by-step explanation:

Given absolute value function:

[tex]f(x)=|x-4|-2[/tex]

The parent absolute value function is f(x) = |x|.

Graph of the parent absolute value function:

Translations

[tex]\textsf{For $a > 0$}:[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}.[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}.[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}.[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}.[/tex]

The graph of the given function is a transformation of the parent function by:

Therefore, the vertex of the given function is (4, -2).

Find two further points on the graph by inputting x-values either side of the x-value of the vertex into the given function:

[tex]\begin{aligned}\implies f(8)&=|8-4|-2\\&=|4|-2\\&=4-2\\&=2\end{aligned}[/tex]

[tex]\begin{aligned}\implies f(0)&=|0-4|-2\\&=|-4|-2\\&=4-2\\&=2\end{aligned}[/tex]

To draw the graph of the given function:

Answer:

16t+55t+6t=77. 55-6=49

If Lucy earns $15.75 per hour. Last week she worked 25 hours her gross pay is $393.75 . If Lance has a yearly salary of $52,300 and pays 21% in taxes her  taxed amount  is $10,983, net pay is  $41,317 and paycheck is $2,179.

1. Gross pay

Using this formula to determine the gross pay

Gross pay = Amount earn per hour × Number of hours worked

Let  plug in the formula

Gross pay =  $15.75 per hour × 25 hours

Gross pay = $393.75

2a. Taxed amount

Amount in Tax = Salary × Tax percentage

Amount in taxes = $52,300 × 21%

Amount in taxes = $10,983

2b. Net pay

Net pay = Gross  - Deduction

Net pay =  $52,300 - $10,983

Net pay = $41,317

2c. Paycheck

Paycheck = $52,300 / 24 months

Paycheck = $2,179 per paycheck

Therefore we can conclude that the her gross pay is $393.75

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The value of the x, when y = 10 by the direct proportional is found as x = -5.

As per the given question;

y is in the direct variation with x.

This can be written as; y ∝ x.

Or, y = kx

Where, k is proportionality constant.

put the values;  y = 6 when x = -3

6 = -3 k

k = -2

Now, the value of x when y = 10.

y = kx ; put the value of y and k

10 = (-2)x

x = -5

Thus, the value of x in direct variation with y = 10 is found as x = -5.

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If two  cars leaves from a place at the same time they travel in opposite directions and the speed of the first and second cars are 62 km per hour and 48 km per hours respectively , 5 hours will take before they are 550 km apart

The speed of the first car=62 km per hour

The speed of the second car=48 km per hour

Two cars leave from a place at the same time they travel in opposite directions

The relative speed of the car = Speed of the first car - (- Speed of the second car )

=62-(-48)

=110 km per hour

Time take = Distance between the two cars / Relative speed of the two care

=550/110

=5 hours

Hence, if two  cars leaves from a place at the same time they travel in opposite directions one at 62 km per hour the other at 48 km per hour, 5 hours will take before they are 550 km apart

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Using a linear function, it is found that:

a. The inequality for this situation is: 5 + 0.45x ≤ 12.

b. He can ride at most 15 miles without going over the limit.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which the coefficients are described as follows:

For the context of this problem, the slope and the intercept are defined as follows:

Hence the cost function, considering x miles, is given as follows:

C(x) = 0.45x + 5.

He wanted to spend $12 or less on a beach bike rental, hence the inequality that models this situation is given by:

C(x) ≤ 12.

5 + 0.45x ≤ 12.

The inequality is solved similarly to an equality, isolating the variable and finding the range of values, hence the solution is found as follows:

0.45x ≤ 7

x ≤ 7/0.45

x ≤ 15.6 miles.

The greatest whole number of miles is of 15 miles, as for 16 miles, the cost would be above $12.

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The function f(x)=[tex]\sqrt{3x-12} +2[/tex]. The Domain of the function is 4, we can also write {y|y∈R,y≥4}

Given that,

The function f(x)=[tex]\sqrt{3x-12} +2[/tex]

We have to find the range of the function.

Range is nothing but y but in the equation we have x so we find domain.

The domain is the set of inputs that a function will accept is known as the domain of the function in mathematics. It is occasionally indicated by dom(f), where f is function.

More specifically, f:X--->Y the domain of f is X given a function. It should be noted that in contemporary mathematical terminology, a function's domain is a component of its definition rather than a quality.

Take the function

f(x)=[tex]\sqrt{3x-12} +2[/tex]

Now,

3x-12≥0

3x≥12

x≥12/3

x≥4

Therefore, The Domain of the function is 4, we can also write {y|y∈R,y≥4}

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Answer:

2

Step-by-step explanation:

2

Answer:

4x^-x-1

Step-by-step explanation:

4x^-x/x^3-2

= 4x^-x/x

= 4x^-x-1

Answer:

  14

Step-by-step explanation:

You want to know how old Mark is if he is 6 years younger than twice his brother's age, and their combined age is 24.

Let m and b represent Mark's age and his brother's age, respectively.

The given relations are ...

Solving the second equation for b, we have ...

  b = 24 -m

Using that in the first equation gives ...

  m = 2(24 -m) -6

  m = 48 -2m -6

  3m = 42 . . . . . . . . . add 2m, combine like terms

  m = 14

Mark is 14 years old.

__

Check

Mark's brother is 24 -14 = 10. Twice that less 6 is 2×10 -6 = 14, which is Mark's age, as it should be.

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1. The biggest size of each brick that Hannah can be able to use is 32.

2. The value of x when there are now x cans stacked on a shelf that hold 36 cans when full is 22 cans.

From the information, Hannah needs to build two wall, one has a height of 1024 feet and the other of 672 feet and she has to use bricks of equal sizes for both wall. It should be noted that this implies that we've to calculate the highest common factor for 672 and 1024. This is 32.

2. The value of x will be:

= (36/2) + 4

= 18 + 4

= 22

Therefore, x is 22. This means that there are 22 cans.

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Answer: rectangle

Step-by-step explanation: brainliest please? i could really use it

Answer:

most likely 16 if its a long object or 8 if its a short one

Step-by-step explanation:

if u provided a graph it could help alot

The dilated picture of the point D dilation that is necessary is -6.

Given that,

To determine thee dilated image of point D (-2, 0), on the graph.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

The scale factor is defined as the ratio of modified change in length to the original length.

Here,Formerly point D is located at (-2, 0).

Now multiplying with the scale factor 3 the point goes

(-2 * 3, 0*3) => (-6, 0).

Thus, The required dilated image of the dilation of point D is -6.

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Answer:

r=-4

Step-by-step explanation:

use the slope formula

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

Then plug in x and y values and set that equal to m=1

1=[tex]\frac{-2-8}{r-6}[/tex]

multiply r-6 over

r-6=-10

r=-4

The set of possible values for "p" is ((4-√7)/9, (4+√7)/9).

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