For the following exercises, solve each inequality and write the solution in interval notation.
31. | 3x − 4 | ≤ 8

Answer:

5/4 or 1.25

Step-by-step explanation:

y=mx+b is the form of all linear equations

m is the slope

here m = 5/4 so the slope is 5/4 or 1.25

Answer:

The answer is C. 270° < ∅ < 360°

Step-by-step explanation:

Given information:

sine < 0 and tans > 0.

Quadrant where sine < 0 is either III or IV.

Quadrant where tans > 0 is either I or III.

It is Quadrant III that has both sines < 0 and tans > 0.

Using the law of cosines on the given triangle, we see that; cosθ = 0.22

The law of cosines is expressed as;

c² = a² + b² - 2ab cos C

Now, in this case the angle is θ and employing this law of cosines gives us;

10.2² = 5.7² + 9.8² - 2(5.7 * 9.8)*cosθ

104.04 = 32.49 + 96.04 - 111.72 * cosθ

104.04 = 128.53 - 111.72 * cosθ

(128.53 - 104.04)/111.72 =  cosθ

cosθ = 0.22

Read more about Law of cosines at; https://brainly.com/question/4372174

#SPJ1

Answer:

Graph #1

Step-by-step explanation:

In this distance v time graph, a negative slope means moving toward Mr. Wilson, a positive slope means moving away from Mr. Wilson, and a flat section means staying at a particular location without moving.

A quantity with an initial value of 130 decays exponentially at a rate such that the quantity cuts in half every 9 weeks. 103.18 is the value of the quantity after 21 days.

A process known as exponential decay is when a quantity diminishes over time at a pace that reduces proportionately as the amount shrinks.

The term "exponential decay" refers to a population's or group's rate of decline when it is proportionate to the size of the population. The overall value falls in exponential decay, yet the percentage that departs stays constant over time.

Let, y = 130. aˣ

here, x = number of days

Given that,

A quantity with an initial value of 130 decays exponentially.

the quantity cuts in half every 9 weeks

the value of the quantity after 21 days = ?

So, 130 × [tex]a^{(7\times9) }[/tex] = 130 × (1/2)

or, a⁶³ = 1/2

or, a [tex](1/2)^{(1/63)}[/tex]

Thus, y = 130 × [tex](1/2)^{(x/63)}[/tex]

when x = 21

thus, y = 130 ×[tex](1/2)^{(21/63)}[/tex]

y = 130 × [tex](1/2)^{(1/3)}[/tex]

y ≈ 103.18

Hence, 103.18 is the value of the quantity after 21 days.

To know more about exponential decay refer to:

brainly.com/question/27822382

#SPJ1

Answer:

C

Step-by-step explanation:

join my stream for an explanation

(ChildofHermes)

please mark brainliest

im only streaming for 15 more hours

Answer:

Choice C

Step-by-step explanation:

2654^0 and 5^0

Which is greater?

There's a law of exponents for solving this type of question.

The law states that,

Same case here.

And,

Hence, they are same.

2654⁰ = 5⁰

Answer: the correct answer is choice A

Step-by-step explanation:

This is because the inequality symbols are pointed the correct way. The symbols are also showing the correct answers with the greater than or equal to sign is on the correct point value. You find the place for the equal to or greater/less than symbol by the open or closed circle point. An open circle means the number is not included in the answer while a closed circle is included in the answer.

Solving the quadratic function, the sales are of 9 million in the years of 2000 and 2012.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

The number of sales(in millions of dollars), in t years after 2000, is modeled by the following function:

[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]

The sales are of 9 million when S(t) = 9, hence:

[tex]S(t) = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]

[tex]9 = \frac{20t^2 + 800t + 300}{8t^2 + 10t + 100}[/tex]

[tex]72t^2 + 90t + 900 = 20t^2 + 800t + 300[/tex]

[tex]52t^2 - 710t + 600 = 0[/tex]

Which is a quadratic equation with coefficients a = 52, b = -710, c = 600, hence:

[tex]\Delta = (-710)^2 - 4(52)(600) = 379300[/tex]

[tex]x_1 = \frac{710 + \sqrt{379300}}{104} = 12.7[/tex]

[tex]x_2 = \frac{710 - \sqrt{379300}}{104} = 0.91[/tex]

t is measured in years after 2000, the sales are of 9 million in the years of 2000 and 2012.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

Answer:

In 1942 , the U.S. Mint produced 154,500,000 nickels. The scientific notation of 154,500,000 is obtained as [tex]$1.545 \times 10^{8}$[/tex].

Step-by-step explanation:

Step 1 of 2

Obtain the scientific notation.

Here the original number, 154,500,000 is greater than 1 so we will have a positive power of 10 .

Move the decimal point to get 1.545, a number between 1 and 10 . Then we get,

1.54500000

The count of the number of decimal places the point was moved is 8 .

Write as a product with a positive power of 10 .

[tex]$1.545 \times 10^{8}$[/tex]

Step 2 of 2

Check the answer.

Rewrite and simplify to check our answer.

[tex]$$\begin{gathered}1.545 \times 10^{8}=1.545 \times 100000000 \\=154500000\end{gathered}$$[/tex]

The value of x + y is 12

The equation is given as:

x^3 - y^3 = 218

Make x^3 the subject

x^3 = 218 + y^3

The next cubic expression greater than 218 is 343.

So, we assume

x^3 = 343

This gives

x = 7

Substitute x^3 = 343 in x^3 = 218 + y^3

343 = 218 + y^3

Evaluate the like terms

y^3 = 125

This gives

y = 5

So, we have:

x + y = 7 + 5

Evaluate

x + y = 12

Hence, the value of x + y is 12

Read more about equations at:

https://brainly.com/question/2972832

#SPJ1

Hello,

2x² - 9x - 35 = 0

a = 2 ; b = -9 ; c = -35

∆ = b² - 4ac = (-9)² - 4 × 2 × (-35) = 361 > 0

x1 = (-b - √∆)/2a = (9 - 19)/4 = -10/4 = -5/2

x2 = (-b + √∆)/2a = (9 + 19)/4 = 28/4 = 7

S = {-5/2 ; 7}

Answer:

So x = -5/2, 7.

Step-by-step explanation:

2x^2 - 9x - 35 = 0

Let's see if we can factor this.

We need 2 numbers whose product is  2* -35 ( that is -70) and whose sum is -9.

They are -14 and 5, so we write:

2x^2 - 14x + 5x - 35 = 0

Now we factor by grouping:

2x(x - 7) + 5(x - 7) = 0

(2x + 5)(x - 7) = 0

So x = -5/2, 7.

Answer:

The mean:

data: 3,6,9,10

You first add all of the numbers together.

3+6+9+10= 28

There 4 numbers in the data set, so you divide 4 by the sum of all of the numbers.

28/4= 7

So the mean is 7.

The median:

data: 3,6,9,10

first put all of the numbers in numerical order.

3,6,9,10

Then you find the middle number in the data set.

3,6,(the middle number here),9,10

to find the middle number, do the mean of 6 and 9

The mean of 6 and 9 is 7.5

So, 7.5 is the median

another example: 3,4,7,9,13

The middle number is 7

so 7 is the median

The mode:

data: 3,6,9,10

The mode is the number that is repeated the most

in this data, there is no mode.

but in this data: 4,4,6,9,11

4 is the mode because it was repeated the most

Answer:

angle 2 is equal to angle 1 ... vertically opposite angles equal

therefore angle 2 and angle 3 are supplementary...co-interior angles supplementary

therefore m is parallel to n

The missing step in solving the inequality is x > -9

From the question, we are to determine the missing step in solving the given inequality

1. The distributive property: 4x – 12 + 4 < 10 + 6x

2. Combine like terms: 4x – 8 < 10 + 6x

3. The addition property of inequality: 4x < 18 + 6x

4. The subtraction property of inequality: –2x < 18

5. The division property of inequality: ________

Applying the division property of inequality

-2x/-2 < 18/-2

x > -9

Hence, the missing step in solving the inequality is x > -9

Learn more on Solving inequalities here: https://brainly.com/question/246993

#SPJ1

The number of CDs the students at your high school bought in 2008 is 100

The graph of the question is added as an attachment

From the graph, we have the following highlights:

2008 is 4 years from 2004.

So, the prediction is;

Year 2008 = 200 - 4 * 25

Evaluate

Year 2008 = 100

Hence, the number of CDs the students at your high school bought in 2008 is 100

Read more about graphs at:

https://brainly.com/question/16473290

#SPJ1

The length of HJ is 3.5 cm

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Given:

AB = 3.5 cm, BC = 2.4 cm, and AC = 4.2 cm

As, ΔABC ≅ ΔHJK

So,

AB = HJ

BC = JK

AC = HK

Thus, HJ= AB = 3.5 cm

Learn more about this concept here:

https://brainly.com/question/4229988

#SPJ1

When you bisect something, you cut it into two equally sized pieces. (from Latin: "bi" = two, "sect" = cut)

Bisecting an interval creates two smaller intervals each with half the length of the original interval. Some examples:

• bisecting [0, 2] gives the intervals [0, 1] and [1, 2]

• bisecting [-1, 1] gives the intervals [-1, 0] and [0, 1]

• bisecting an arbitrary interval [tex][a,b][/tex] gives the intervals [tex]\left[a,\frac{a+b}2\right][/tex] and [tex]\left[\frac{a+b}2,b\right][/tex]

Answer:

See below.

Step-by-step explanation:

1) Simplify √20 to 2√5.

√5 × 2√5

2) Simplify.

2√5×5

3) Simplify 5 × 5 to 25.

2√25

4) Since 5 × 5 = 25,  the square root of 25 is 5.

2 × 5

5) Simplify.

10

When evaluated, this expression equals a positive whole number, therefore showing it is a integer.

The total money Dana spent in all is $24.75

Ratio are written as fractions of two integers. For instance a/b.

Amount spent for grandmother = $13.75

Amount spent on grand father = 4/5 * 13.75

Amount spent on grand father = $11

Take the sum

Total money spent = $13.75 + $11

Total money spent = $24.75

Hence the total money Dana spent in all is $24.75

Learn more on proportion here: https://brainly.com/question/19994681

#SPJ1

The answer choice which could be the length of side BC is; BC < 12.

It follows from the task content that the possible length of the side BC is to be determined.

Since, the sides given AB and BC both have length sum equal to 12. It follows from the triangle inequalities that the length of the third side must be less than the sum of lengths of the other two sides.

Read more on triangle inequalities;

https://brainly.com/question/309896

#SPJ1

The distance between car B's original point and the point where car A and car  B pass each other is 20 miles, given the speed of car A is twice the speed of car B, and they are 60 miles apart initially.

We assume the speed of car B to be x miles/hour.

Given car A going at twice the speed of car B, the speed of car A = 2x miles/hour.

When moving toward each other, the relative speed of the cars is the sum of their speeds.

Therefore, the relative speed = x + 2x miles/hour = 3x miles/hour.

The total distance between the cars is given as 60 miles.

Therefore, the time taken by car A and car B to reach the same point = 60/3x hours = 20/x hours.

Therefore, the distance from car B's original point and the point where car A and car B pass each other = Speed of car B*Time = x*(20/x) miles = 20 miles.

Therefore, the distance between car B's original point and the point where car A and car  B pass each other is 20 miles, given the speed of car A is twice the speed of car B, and they are 60 miles apart initially.

Learn more about speed, time, and distance at

https://brainly.com/question/4931057

#SPJ4

Answer: 1: 34 units    2: 24.5

Step-by-step explanation:

For figure 1, just split the area into squares and triangles and find the area of each. If you split figure 1 into 1 square and 3 triangles you get...

4x4= 16

(4x3)/2= 6

(4x4)/2= 8

(4x2)/2= 3

16+6+8+3 = 34

You do the same for figure 2, but use 4 triangles and 1 tiny square

1x1= 1

(4x3)/2= 6

(3x3)/2= 4.5

(4x4)/2= 8

(5x5)/2= 5

1+6+4.5+8+5= 24.5

You shouldn't need to worry about negative numbers because you are looking at the area

Answer:

1/0.7

Step-by-step explanation:

The expression x-y equals to 0.7 so we have to substitute 0.7 in the place of x-y....

----> 1/0.7

Dividing would make this equal to a long division answer (1.42857142857) so let's just leave it as a fraction!

I hope this helps! :)

Step-by-step explanation:

4^2

5^4

3^1×7^4

2^2 ×9^4

Two angles which are next to each other is referred to as adjacent angle in this case.

These are angles which have a common vertex and side and do not overlap with one another.

This angle lie next to each other when plotted hence the reason why they share a common vertex.

Read more about Adjacent angle here https://brainly.com/question/26768295

#SPJ1

Answer: 70.9 miles per hour

Step-by-step explanation:

The total distance traveled is 1188 miles (66313- 65125).

Since this was over 16.75, you'll want to divide 1188 by 16.75.

1188/16.75 = 70.9253731

And then round that off to 70.9

The location of the largest element in the matrix is a₂₁, which is 54. The location of the largest element in the matrix is a₂₁, which is 54.

Matrix is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.

The following details about the matrix can be written,

Learn more about the Matrix:

brainly.com/question/9967572

#SPJ1

The slope of the line represented by the given equation is 0.8

From the question, we are to determine the slope of the line represented by the given equation

The given equation is

[tex]y = \frac{4}{5} x-3[/tex]

The slope-intercept form of the equation of a line is given as

y = mx + c

Where m is the slope or gradient

and c is the y-intercept

By comparing with the given equation,

m = 4/5

m = 0.8

Hence, the slope of the line represented by the given equation is 0.8

Learn more on Slope of a line here: https://brainly.com/question/1884491

#SPJ1