use both addition and muiltpliction properties of inequality to solve the inequality graph the solutions on a number line 2(3y-5) less then -16​

Answer:

Step-by-step explanation:

According to the question we have the following

Initial number:

The slope:

The equation is:

The solution of the double inequality is -11 <= a <= 1 and the  three solutions in the solutions are -11, -10 and -9

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

1 <= (4 - a)/3 <= 5

Multiply through the inequality expression by 3

So, we have the following inequality expression

3 * 1 <= 3 * (4 - a)/3 <= 5 * 3

Evaluate the products in the above inequality expressions

So, we have

3 <= 4 - a <= 15

Subtract 4 from all sides of the inequality expression

So, we have

-1 <= - a <= 11

Multiply all sides of the inequality expression by 1

So, we have

1 >= a >= -11

Rewrite as

-11 <= a <= 1

The numbers in the above solution are -11, -10 and -9

Hence, the solution of the double inequality is -11 <= a <= 1 and the  three solutions in the solutions are -11, -10 and -9

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Answer:

We can split the solid into 6 rectangles

Rectangle1 with sides (2cm, 3cm)

Rectangle2 (square) with sides (3cm, 3cm)

Rectangle3 with sides (2cm, 3cm)

Rectangle4(square) with sides (3cm, 3cm)

Rectangle5 with sides (2cm, 3cm)

Rectangle6 with sides (2cm, 3cm)

Area of rectangle = Length x Breadth

\(area \ of \ rectangle1 = 6cm^2\\\\area \ of \ rectangle2 = 9cm^2\\\\area \ of \ rectangle3 = 6cm^2\\\\area \ of \ rectangle4 = 9cm^2\\\\area \ of \ rectangle5 = 6cm^2\\\\area \ of \ rectangle6 =6cm^2\\\)

The total surface area = 6 + 9 + 6 +9 + 6 +6 = 42 square centimeters

option D

The total surface area of all 6 rectangles is 42 square centimeters.

We can split the solid into 6 rectangles

Rectangle1 with sides (2cm, 3cm)

Rectangle2 (square) with sides (3cm, 3cm)

Rectangle3 with sides (2cm, 3cm)

Rectangle4(square) with sides (3cm, 3cm)

Rectangle5 with sides (2cm, 3cm)

Rectangle 6 with sides (2cm, 3cm)

Area of rectangle = Length x Breadth

Therefore the area of rectangle1=6cm^2

Area of the rectangle2=9cm^2

Area of the rectangle3=6cm ^2

Area of the rectangle4=9cm^2

Area of the rectangle5=6cm^2

Area of the rectangle4=6cm^2

The total surface area = 6 + 9 + 6 +9 + 6 +6 = 42 square centimeters

Therefore option D is correct.

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Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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Answer:

Step-by-step explanation:

Given

As per segment addition postulate

Substituting values

The vertical asymptotes for the function f(x) = (x^2)(x-6)(x+3)^-1 are x=6 and x=-3.

The vertical asymptotes for the function f(x) = (x^2)(x-6)(x+3)^-1 are x=6 and x=-3. This is because the denominator can be factored into two linear expressions: x-6 and x+3. When either of these expressions equals 0, the fraction becomes undefined and a vertical asymptote is created. To find the asymptotes, set each linear expression in the denominator equal to 0 and solve for x. For x-6, x=6; for x+3, x=-3. Therefore, the vertical asymptotes of the function are x=6 and x=-3. When x is close to either of these values, the fraction will become very large, making the graph approach the vertical asymptotes without ever touching them.

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Answer: y= 16.97 ×=7.27

Step-by-step explanation:

Click on file for workings

Answer: \(Domain = \{t: t\geq 0\}=[0,\infty)\) and \(Range = \{v: v\geq 550\}=[550,\infty)\).

Step-by-step explanation:

It is given that, the value of this account, v, is given by the function

\(v=550+16.5t\)

where, t is the number of years the money is in the bank.

We need to find the domain & range of this function.

Domain is the set of input values. Here, the domain is number of years which cannot be negative. So,

\(Domain = \{t: t\geq 0\}=[0,\infty)\)

Range is the set of output values. Here, the range is amount after simple interest which cannot be less than the principal value.

\(Range = \{v: v\geq 550\}=[550,\infty)\)

Answer:

Step-by-step explanation:

The y-intercept of g(x) is 3 * 2 = 6.

To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = 2f(2x + 3), this means we need to find the values of x that make f(2x + 3) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(2x + 3) = 0 for x.

Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(2x + 3) = 0, we get:

f(2(2) + 3) = 0

f(4 + 3) = 0

f(7) = 0

and

f(2(-4) + 3) = 0

f(-8 + 3) = 0

f(-5) = 0

Therefore, the x-intercepts of g(x) are at x = 7/2 and x = -5/2. These are the only intercepts of g(x) that we can determine for certain.

Answer:  x = -5.

To solve this equation, I first would like to warn you about the long answer I am about to post for you. I'll be putting in very detailed steps for you, showing you how to simplify and distribute numbers, etc. :)

Let us solve your equation step-by-step.

Step 1) Simplify both sides of the equation.

To simplify this, we will...

4 + (-2) (x) + (-2) (7) = (3) (x) + (3) (5)

4 + - 2x + - 14 = 3x + 15

(-2x) + (4 + - 14) = 3x + 15

Now, we combine Like Terms...

-2x + - 10 = 3x + 15

-2x - 10 = 3x + 15

Step 2) Subtract 3x from both sides.

- 2x - 10 - 3x = 3x + 15 - 3x

- 5x - 10 = 15

Step 3) Add 10 to both sides.

- 5x - 10 + 10 = 15 + 10

- 5x = 25

Step 4) Divide both sides by -5.

-5x/-5 = 25/-5

So, our final answer is x = -5.

Hope this helps!

The population function of the Western Lowland Gorillas can either represent population growth or population decay

The question is incomplete, as the resources to model the population of the Western Lowland Gorillas are not given.

However, the following is a general guide to solve the question.

An exponential function is represented as:

\(y = a(1 \pm r)^x\)

Where:

Given that the population of the Western Lowland Gorillas decreases, then the rate of the function would be 1 -r (i.e. an exponential decay)

Take for instance:

\(y = 2000 * 0.98^x\)

By comparison.

a = 2000 and 1 - r = 0.98

The above function can be used to model the population of the Western Lowland Gorillas

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Answer:

The bike will travel about 75 feet when the wheel makes 15 complete rotation

The wheel will make 8 rotations if Noha rides 40 feet

Step-by-step explanation:

The distance that a wheel can make in one rotation equal the circumference of the wheel

D = C × n, where

Let us use this fact to solve the question

∵ The circumference of the wheel  C = 5 feet

∵ The wheel makes 15 complete rotation

→ Substitute them in the rule above to find the distance

∵ D = 5 × 15

∴ D = 75 feet

The bike will travel about 75 feet when the wheel makes 15 complete rotation

∵ Noha rides for 40 feet

∴ D = 40

∵ C = 5 feet

→ Substitute them in the rule above to find the number of the rotation

∵ 40 = 5 × n

∴ 40 = 5n

→ Divide both sides by 5 to find n

∴ \(\frac{40}{5}=\frac{5n}{5}\)

∴ 8 = n

The wheel will make 8 rotations if Noha rides 40 feet

x = 5/4   or   x = 15/4

Step-by-step explanation:

The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.

In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:

f(x) = 1 / (b - a)

where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.

To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.

The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.

Therefore, the probability that the commuting time will be between 50 and 60 minutes is:

P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.

Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.

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Answer:

= 461 R 4

= 461 4/7

3231 divided by 7 equals

461 with a remainder of 4

Step-by-step explanation:

hope it helps

Answer:

It is 4.

Step-by-step explanation: I just did math in my head

Answer:

x = 4

Step-by-step explanation:

DB is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is

\(\frac{x}{6}\) = \(\frac{2}{3}\) ( cross- multiply )

3x = 12 ( divide both sides by 3 )

x = 4

The probability that one of the events Franco worked last year, selected at random, was a wedding is equals to the \( \frac{4}{17} \).

Franco is a professional DJ and he was very busy in work during Last year. Number of events where he worked = 26

Number of wedding where he worked

= 8

So, total events where he played his DJ

= 26 + 8 = 34

We have to determine probability that one of the events Franco worked last year, selected at random, was a wedding.

Now, one of event is Randomly selected from all of above events. Number of favourable outcomes for worked on wedding events = 8

So, probability of selected a wedding event \( = \frac{8}{34} \)

\( = \frac{4}{17} \). Hence the required probability value is \( \frac{4}{17} \).

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The correct sampling method described in the question is a stratified random sample among the simple random sample,  stratified random sample, cluster random sample and  Voluntary random sample

The sampling method described in the question is a stratified random sample.

In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.

In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.

Other sampling methods mentioned in the question are:

Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.

Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.

Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.

Therefore, the correct sampling method described in the question is a stratified random sample.

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Answer:

32pi - 64

Step-by-step explanation:

The two UNshaded areas are equal to each other. Each one is the

Area (square) - 1/4 Area(circle)

64 - 1/4 (64pi)

64 - 16pi

There are 2 of these unshaded pieces in this question.

Area (square) - 2 (64 - 16pi)

64 - 128 + 32pi

= -64 + 32pi

Area = 32pi - 64

Answer:

10yd x 14 yd x 3yd = 420yd ^3

Step-by-step explanation:

When calculating for the volume you multiply all three numbers. That’s why when you write your answer you cube it.

The measure in radians for the central angle of the circle is; 0.9 radians.

Since, the length of the arc is given as 7.2cm and it's radius is 8cm.

It follows that the angle measure of the central angle can be evaluated as follows;

7.2 = (A/6.28) × 2× 3.14 × 8

7.2 = 8A

A = 7.2/8

A = 0.9 radians.

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Answer:

$554.40

Step-by-step explanation:

Answer:

$110

Step-by-step explanation:

1/6 x 660

For a relative frequency table by rows 4-column table with 2 rows about the breakfast choices of boys and girls. The conclusion is of table is represented by option(b).

We have provided the following information about relative frequency table by rows, tables by row, 4 columns and 2 rows.

Now, we represent the above information into tabular form,

Eat cereal do not eat cereal Total

boys 68.3% 31.7% 100%

girls 69.1% 30.9% 100%

Now, we have to draw conclusion about the relative frequency of these results. From the table, the percentage of girls and boys who eat cereal is exceed from the not. Thus, we cannot say if a person eat cereal for breakfast, then he is a boy. Similarly we cannot know about gender of a person by eats cereal. The right conclusion is that if i am a girl in this group, i am more likely to eat cereal for breakfast than not. Hence, required option is option (b).

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Complete question:

relative frequency table by rows 4-column table with 2 rows. column 1 has entries boys, girls. column 2 is labeled eat cereal with entries 68.3 percent, 69.1 percent. column 3 is labeled do not eat cereal with entries 31.7 percent, 30.9 percent. column 4 is labeled total with entries 100 percent, 100 percent. What conclusion can you draw about the relative frequency of these results?

a) If you are a boy in this group, you are more likely not to eat cereal for breakfast than to eat cereal.

b) If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

c) If you eat cereal for breakfast, you are a boy.

d) Knowing if a person eats cereal will help determine gender.

Answer:

B. If you are a girl in this group, you are more likely to eat cereal for breakfast than not.

Step-by-step explanation:

Edge 2023

The company has a 20700 square foot area.

The surface of a shape's area is measured. To calculate the area of a rectangle or square, multiply its length and width. A is x times y in size. A 1,000 square foot house or apartment will typically have a square area that is 40 feet long by 25 feet wide.

Let's start by determining the store's width:

length = width + 65

180 = width + 65

width = 115 feet

Now, we can locate the store's location:

Area = length x width

Area = 180 feet x 115 feet

Area = 20700 square feet.

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Answer:

  (d)  x > 2

Step-by-step explanation:

You want the sensible domain of x if x is the length of a poster whose width is (x-2).

The width (x-2) needs to be positive, so we require ...

  x -2 > 0

  x > 2 . . . . . length must be greater than 2 inches for width to be positive

Answer:

3 and 7

Step-by-step explanation:

Answer:

(x,y) = (-6,-5)

Step-by-step explanation:

If you need the explanation let me know.

Answer:

x = -6

y = -5

Step-by-step explanation:

5x - 4y = -10

5x - 5y = -5

__________--

y = -5

5x - 4y = -10

5x - 4(-5) = -10

5x + 20 = -10

5x = -10 - 20

5x = -30

x = -30/5

x = -6

Answer:

y=mx+b

It's already in function notation. Unless you need to graph it or show it.