3(4x-1) greater than or equal to 2(4-x)

The absolute value is defined as

[tex]|x|=\begin{cases}x&\text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]

So for example, if x = 3, then |x| = |3| = 3, since 3 is positive. On the other hand, if x = -5, then |x| = |-5| = -(-5) = 5, since -5 is negative. The absolute value is always positive.

For the inequality |7 + 8x| > 5, you consider the two cases where the argument to the absolute value (the expression you find inside the bars) is either positive or negative.

• If 7 + 8x ≥ 0, then |7 + 8x| = 7 + 8x, so that

[tex]|7+8x|>5\implies 7+8x>5 \implies 8x>-2 \implies x>-\dfrac14[/tex]

• Otherwise, if 7 + 8x < 0, then |7 + 8x| = -(7 + 8x), so that

[tex]|7+8x|>5\implies-(7+8x)>5\implies7+8x<-5\implies8x<-12\implies x<-\dfrac32[/tex]

The solution to the inequality is the union of these two intervals.

Answer:

d=2.5

Step-by-step explanation:

first find the coordinate of B(mid point of AC):A(3,7) C(6,11)

d=√(6-3)²+(11-7)²

d=√3²+4²

d=√9+16=√25=5

since B is the mid point : d/2=5/2=2.5

B(x1+x2/2 , y1+y2/2)   , x1=3 , x2=6, y1=7, y2=11

B(9/2,18/2)

B(9/2,9)

Find AB : the length or distance between 2 points:

d=√(x2-x1)²+(y2-y1)²

d=√(3-9/2)²+(7-9)²

d=√(-3/2)²+(-2)²

d=√1.5²+4

d=√6.25

d=2.5

Complete question is;

A student artist randomly selected two media from among: charcoal sketches, pencil drawings, and oil paintings, and then submitted all of her works in that media for a gallery showing. Identify the kind of sample that is described.

Answer:

Cluster sample

Step-by-step explanation:

Looking at the question, we can see that the media has already been grouped into 3 parts namely charcoal sketches, pencil drawings, and oil paintings. It has already been grouped into multiple groups for easy selection or identification.

Now this type of grouping is synonymous with cluster sampling because cluster sampling is a probability sampling technique in which the researchers divide the population into multiple groups known as clusters for research and this question clearly shows that the media has been grouped.

Answer:

90

Step-by-step explanation:

take one interior color and multiply by 5 for every interior color. then multiply by three for each trim. you get 15. multipy 15 by 6 for every exterior color and you get 90. there are 90 combinations.

Answer:

The inequality to describe the problem is 15 +c >25.

We must sell more than 5 cones to make a profit

Step-by-step explanation:

From this problem,  we can see that we need to sell a number of cones (c), that when added to the 15 cones that we have already sold, the result will be greater than 25.

To set up the inequality sign, we need to, first of all, know the inequality sign that we will be using. From the preceding statement, we can see that we need to sell greater than a certain number of cones.  

This should tell us that we will be needing the greater-than sign (>).

The next step is to know the format the equation should take:

We have sold 15 cones; We need to sell c more to make it greater than 25.

This will be 15 +c >25.

The inequality to describe the problem is 15 +c >25.

from this, we can see that c > 5 cones.

We must sell more than 5 cones to make a profit

Answer:

-40

Step-by-step explanation:

The team won 16 games and lost 8 games.

Subtraction is one of the four basic arithmetic operations that is used to find the difference.

A football team won 8 more games than they lost. They played 24 games in the season. How many games were won and how many were lost?

The team lost n games.

The team won 8 more games than it lost, so it won n + 8.

The total number of games the team played was n + n + 8, or 2n + 8.

The team played a total of 24 games, so

2n + 8 = 24

We now solve for n.

2n + 8 = 24

2n = 16

n = 8 (lost games)

n + 8 = 8 + 8 = 16 (won games)

Hence, The team won 16 games and lost 8 games.

Learn more about subtraction here;

https://brainly.com/question/11328248

#SPJ2

Answer:

[tex]y=8x-25[/tex]

Step-by-step explanation:

Given the coordinates:

(3,−1) and (4,7)

To find:

The equation of line passing through the given points.

Solution:

Let us have a look at the slope intercept form of a line:

[tex]y=mx+c[/tex]

c is the y intercept.

Where [tex]m[/tex] is the slope of the line passing through the points [tex](x_1,y_1),(x_2,y_2)[/tex]

Formula for slope is:

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

[tex]x_1 = 3\\y_1 = -1\\x_2 = 4\\y_2 = 7[/tex]

[tex]m=\dfrac{7-(-1)}{4-3}\\\Rightarrow m = 8[/tex]

So, equation of line becomes:

[tex]y=8x+c[/tex]

Let us put (4, 7) to find the value of c:

[tex]7=8\times 4 +c\\\Rightarrow c = -25[/tex]

So, the equation is:

[tex]y=8x-25[/tex]

The equation of the line passing through the points (3.-1), and (4,7) is [tex]y=8x-25[/tex].

Given information:

The given line passes through the points (3.-1), and (4,7).

It is required to write the equation of the line.

Use the two-point form of a line to write the equation of the line:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\y-(-1)=\dfrac{7-(-1)}{4-3}(x-3)\\y+1=8(x-3)\\y+1=8x-24\\y=8x-25[/tex]

From the above equation of the line, the slope is equal to 8.

Therefore, the equation of the line passing through the points (3.-1), and (4,7) is [tex]y=8x-25[/tex].

For more details, refer to the link:

https://brainly.com/question/19082942

Answer:

The answer is 153.86

Step-by-step explanation:

A= 3.14 x12.25>2

A= 38.465 x 4

A= 153.86

Answer:

`13.902

Step-by-step explanation:

Answer:

Inequality Form: x > − 122 /99

Interval Notation: ( − 122/ 99 , ∞ )

Step-by-step explanation:

x > - 9

x ∈ ( - 9 : + oo)

[tex]-\frac{1}{3}(5x+3)<14\\ \\-(5x+3)<42\\\\-5x-3<42\\\\-3-42<5x\\\\-45<5x\\\\5x>-45\\\\x>-9\\\\[/tex]

x∈ ( - 9 ; + oo)

Answer:

x > -9

Step-by-step explanation:

you want to multiply both sides of the inequality by 3/1 to make

-1/1 (5x+3) < 42/1

any expression divided by 1 remains the same

-1 (5x+3) < 42/1 ⇒ - (5x+3) < 42/1 ⇒ - (5x+3) < 42

Where there is a - in front of an expression in parentheses, change the sign of each term in the expression

-5x -3 <42

Then move the constant to the right-hand side and change its sign

-5 < 42 + 3

Add the numbers and you'll get

-5x < 45

Divide both sides of the inequality by -5 and flip the inequality sign and your answer would be

x > -9

Answer:

D. 1x8

Step-by-step explanation:

7/8 rounded is 1. And 8 and 1/10 rounder is 8, so therefore your answer is 1x8.

hope this helps! :)

Answer:

6

Step-by-step explanation:

Since the x coordinates are the same, we are only concerned about the y coordinates

Find the difference between -1 and 5

5 - -1

5+1

6

The distance is 6

Answer:

31.1

Step-by-step explanation:

Answer:

31.1

Step-by-step explanation:

124.4 / 4

= 0.1 * (1244/4)

= 0.1 * 311

= 31.1.

Answer:

The coordinates of point S are (4,-7).

Step-by-step explanation:

Given the locations of points S and T, the midpoint coordinates are set by midpoint formulas:

[tex]\bar x = \frac{x_{S}+x_{T}}{2}[/tex] and [tex]\bar y = \frac{y_{S}+y_{T}}{2}[/tex]

Where:

[tex]x_{S}[/tex], [tex]x_{T}[/tex] - x-Components of S and T.

[tex]y_{S}[/tex], [tex]y_{T}[/tex] - y-Components of S and T.

The coordinates of S are cleared:

[tex]x_{S} = 2\cdot \bar x -x_{T}[/tex]

[tex]y_{S} = 2\cdot \bar y - y_{T}[/tex]

If [tex]\bar x = 2[/tex], [tex]\bar y = -2[/tex], [tex]x_{T} = 0[/tex] and [tex]y_{T} = 3[/tex], the equations are now solved:

[tex]x_{S} = 2\cdot (2) -0[/tex]

[tex]x_{S} = 4[/tex]

[tex]y_{S} = 2\cdot (-2)-3[/tex]

[tex]y_{S} = -7[/tex]

The coordinates of point S are (4,-7).

Answer:

17.42

Step-by-step explanation:

Because the third place is less than 5 you have to round it to smaller number and that is 2.

If by any chance the third number was for example six you would have to round it to 3.

==========================================================

Explanation:

The word "combine" has three vowels o, i, and e.

One grouping of the three vowels together leads to oie, which we'll replace with Z for now.

So we have the "word" Zcmbn after taking out the vowels and replacing with Z temporarily. There are 5 letters in Zcmbn making 5! = 5*4*3*2*1 = 120 different permutations.

Within any permutation of Zcmbn, there are 3! = 3*2*1 = 6 ways to arrange the sequence oie

So overall there are 6*120 = 720 different ways to arrange the word "combine" such that all the vowels stick together.

Given:

Different functions in the ordered pairs.

To find:

The function which has an inverse that is also a  function.

Solution:

A relation is a function, if there exist unique output for each input.

The inverse of a function is a function, if there exist unique input for each output in the function.

It means, the inverse of a function is a function if each y value has unique x-value.

In {(-1, -2), (0, 4), (1, 3), (5, 14), (7,4)},

For y=4 we have x=0 and x=7, therefore, the inverse of this function is not a function.

In {(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} ,

For y=4 we have x=0 and x=5, therefore, the inverse of this function is not a function.

In {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} ,

For all y value we have unique x values, therefore, the inverse of this function is a function.

In {(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)},

For y=4 we have x=-1 and x=0, therefore, the inverse of this function is not a function.

Therefore, the correct option is C.

Answer:C

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Answer:

-2[tex]\sqrt{3x}[/tex] + 2[tex]\sqrt{15x}[/tex]

Step-by-step explanation:

Answer:

they are parallely far apart

The formula for the volume of a cone is [tex]V=\pi r^2\frac{h}{3}[/tex]

Plug in the values we know.

[tex]V=\pi (5)^2\frac{6}{3}[/tex]

[tex]V=\pi*25*2[/tex]

[tex]V=50\pi[/tex]

[tex]V=157[/tex]

^ If 3.14 was used for [tex]\pi[/tex]

Hope this helps.

頑張って!

Answer:

100 miles

Step-by-step explanation:

2 rides = 10$

3.5$=10 miles x 10=35$=100 miles

Answer:

8

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Functions can only have 1 range per domain (Only 1 Y output per X). Another method is by using the vertical line test, and in this case it fails because more than 2 points are on the same vertical line (x = 1 and x = 2)

Answer:

D

1/2 is 0.5

5/8 is 0.625

Which one is less than 0.625 and greater than 0.5?

0.6

Answer:

f(5) = 2

f'(5) = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

Tangent line to a function y = f(x) on a point (5, 2) passes through two points (5, 2) and (0, 1)

Let the equation of the line is,

y - y' = m(x - x')

Slope of a line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                                                                                   = [tex]\frac{2-1}{5-0}[/tex]

                                                                                   = [tex]\frac{1}{5}[/tex]

Therefore, equation of the line passing through (0, 1) and slope = [tex]\frac{1}{5}[/tex] will be,

y - 1 = [tex]\frac{1}{5}(x-0)[/tex]

y = [tex]\frac{x}{5}+1[/tex]

Function representing equation will be,

f(x) = [tex]\frac{x}{5}+1[/tex]

At x = 5,

f(5) = [tex]\frac{5}{5}+1[/tex]

     = 1 + 1

     = 2

f(5) = 2

f'(x) = [tex]\frac{d}{dx}(\frac{x}{5}+1)[/tex]

       = [tex]\frac{1}{5}[/tex]

Therefore, f'(5) = [tex]\frac{1}{5}[/tex] will be the answer.

Answer:

R(-2,0)

S(0,-4)

T(-4,-3)

Step-by-step explanation:

So first you gotta subtract 2 from each x value and 1 from each y value. After you do that, you get:

R(0,2)

S(-4,0)

T(-3,4)

then i put it all onto a graph, and rotated it 90* counterclockwise, from the origin, which puts it in quadrant 3, with the final coordinates above.