Which inequality models this problem?



The length of a rectangle is five times its width. If the perimeter is at most 96 centimeters, what is the greatest possible value for the width?



A.


2w + 2 • (5w) ≤ 96


B.


2w + 2 • (5w) ≥ 96


C.


2w + 2 • (5w) < 96


D.


2w + 2 • (5w) > 96

The student should understand how to use the concept of ratios to solve the problem. With a 56-foot length of rope and a ratio of 3:1, each unit is worth 14 feet. Thus, the longer piece, representing 3 units, is 42 feet.

The question is essentially asking for one to utilize the concept of ratios in problem solving. Given that a 56-foot rope is cut into two pieces in the ratio 3:1, the lengths of the two pieces would be divided in line with the said ratio. To obtain the lengths of the pieces in feet, you have to add the two parts of the ratio (3+1=4) and then divide the total length by this sum. In this case, 56/4 equals 14 feet. Therefore, one unit of the ratio is equivalent to 14 feet.

Following on, you multiply the first part of the ratio which is 3 by 14 to get the longer piece's length. Thus, the length of the longer piece is 42 feet.

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The behavior of the function f(x) as x becomes a very small negative number depends on the function's specific characteristics, such as decreasing values on a curve, a linear relationship, or asymptotic behavior.

When considering what happens to the function f(x) as x becomes a very small negative number, it depends on the behavior described by the function's equation. If the graph of the function shows a declining curve starting with a maximum at x = 0, as x becomes more negative, f(x) tends to decrease assuming that this behavior continues beyond the given graph. If the graph of f(x) shows a horizontal line between x = 0 and x = 20, this would typically indicate that for small negative values of x, the function would not be defined unless otherwise specified that the function's behavior extends with the same horizontal trend outside the given interval.

Situations such as the behavior of a spring force, described by a function like f(x) = -kx, might lead to a linear decrease as x becomes a small negative number, consistent with Hooke's Law. On the other hand, the presence of asymptotes would indicate that the function's value could grow without bounds as x approaches certain critical values, as seen in the case of a function like y = 1/x.

F(x) when x is a very small positive number then F(x) is a negative number with a small absolute value.

The correct option is (D).

The question shows a graph of a function[tex]\( f(x) \)[/tex]and asks what happens to[tex]\( f(x) \)[/tex] when [tex]\( x \)[/tex] is a very small negative number.

To answer this question, we do not need calculations but rather an interpretation of the graph. When [tex]\( x \)[/tex] is a very small negative number (approaching zero from the left), we need to look at the behavior of the graph as it approaches the y-axis from the left-hand side.

From the graph, it appears that as [tex]\( x \)[/tex] becomes a very small negative number (close to zero), [tex]\( f(x) \)[/tex] increases without bound. This suggests that[tex]\( f(x) \)[/tex]approaches positive infinity.

So, based on the graph, the answer would be:

[tex]\( f(x) \)[/tex] is a very large positive number.

This corresponds to option D on the multiple-choice answers provided.

Answer:

10 meters per second

Step-by-step explanation:

To find two positive real numbers whose product is a maximum, we need to use a mathematical technique called optimization. By solving the given equation and substituting the values back, we can find the two positive real numbers with a maximum product.

To find two positive real numbers whose product is a maximum, we need to use a mathematical technique called optimization. Let's define the two numbers as x and y.

Since the sum of the first number and three times the second number is 30, we can write the equation:

x + 3y = 30

To find the maximum product, we need to express the product of x and y in terms of a single variable. We can do this by substituting x = 30 - 3y into the product equation xy = (30 - 3y)y.

Now, we have a quadratic equation: y^2 - 10y + 15. Finding the maximum product corresponds to finding the vertex of this quadratic equation, which occurs when y = 5.

Substituting y = 5 back into the equation x + 3y = 30, we can solve for x: x + 3(5) = 30, x + 15 = 30, x = 15. Therefore, the two positive real numbers with a maximum product are x = 15 and y = 5.

The graph resembles a "V" shape with its vertex at the origin.

The function f(x) = |x| - 1 is a piecewise function that represents the absolute value of x minus 1.

The absolute value function  |x| returns the distance of x from the origin on the number line.

When x is positive or zero, |x| = x , and when x is negative, |x| = -x.

Thus, f(x) = |x| - 1behaves differently for positive and negative values of x .

For [tex]\( x \geq 0 \)[/tex], the function is f(x) = x - 1, and for x < 0, the function is f(x) = -x - 1.

The graph of  f(x)  consists of two straight lines intersecting at the point (0, -1), with a slope of 1 for [tex]\( x \geq 0 \)[/tex] and a slope of -1 for x < 0.

The graph resembles a "V" shape with its vertex at the origin.

Answer:

$6000

Step-by-step explanation:

Let recall

Given the formula I = P*r*t  or principal x rate x time

Where I=Interest earned

P=principal, the amount deposited or borrowed

R=the annual interest rate

T=Time frame

Therefore $1200 = Px0.04x5

P = 1200/(0.2)

P = 12000/2 = $6000

The amount of the initial investment id $6000

Solution:

Debt Ratio= (Total liabilities which includes debts, and other expenses) ÷ (Total amount of worth possessed)

A debt ratio of approximately 0.5 is considered to be reasonable.

Money Owed by you = $ 3450.00

[tex]0.5=\frac{3450}{\text{Credit limit}}\\\\ {\text{Credit limit}}= 3450 \times \frac{10}{5}\\\\ {\text{Credit limit}}= 6900[/tex]$

So, the Credit limit which gives Acceptable Debt of $ 3450.00 when debt ratio is approximately more or less than 0.5 is

Out of the following four options

Option (D) $ 7,000 is true, regarding Credit limit.

The position x where the object comes to rest (momentarily) is

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration (m / s²)v = final velocity (m / s)

u = initial velocity (m / s)

t = time taken (s)

d = distance (m)

Let us now tackle the problem!

This problem is about Kinematics.

Given:

vo = (-14.0i - 7.0j) m/s

a = (6.0i + 3.0j) m/s²

Unknown:

r = ? → v = 0 m/s

Solution:

To solve this problem, we need to use the following integral formula.

[tex]v = v_o + \int {a} \, dt[/tex]

[tex]v = (-14.0 \, \widehat{i} - 7.0 \, \widehat{j}) + \int {(6.0 \, \widehat{i} + 3.0\, \widehat{j})} \, dt[/tex]

[tex]v = (-14.0 + 6.0t) \, \widehat{i} + ( -7.0 + 3.0t ) \, \widehat{j}[/tex]

If the object comes to rest (momentarily) , then :

[tex]v_x = 0[/tex]

[tex](-14.0 + 6.0t) = 0[/tex]

[tex]6.0t = 14[/tex]

[tex]t = 14 \div 6.0[/tex]

[tex]\boxed {t = \frac {7}{3} ~ s}[/tex]

or

[tex]v_y = 0[/tex]

[tex]( -7.0 + 3.0t ) = 0[/tex]

[tex]3.0t = 7[/tex]

[tex]t = 7 \div 3.0[/tex]

[tex]\boxed {t = \frac {7}{3} ~ s}[/tex]

[tex]r = r_o + \int {v} \, dt[/tex]

[tex]r = 0 + \int { (-14.0 + 6.0t) \, \widehat{i} + ( -7.0 + 3.0t ) \, \widehat{j} } \, dt[/tex]

[tex]r = ( -14.0t + 3.0t^2 ) \, \widehat{i} + ( -7.0t + 1.5t^2 ) \, \widehat{j}[/tex]

At t = 7/3 s , then :

[tex]r = ( -14.0(\frac{7}{3}) + 3.0(\frac{7}{3})^2 ) \, \widehat{i} + ( -7.0(\frac{7}{3}) + 1.5(\frac{7}{3})^2 ) \, \widehat{j}[/tex]

[tex]r = [ (-16\frac{1}{3}) \, \widehat{i} + (-8\frac{1}{6}) \, \widehat{j} ] ~ m[/tex]

[tex]r \approx (-16.3 \, \widehat{i} - 8.2 \, \widehat{j} ) ~ m[/tex]

Grade: High School

Subject: Mathematics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Sperm , Whale , Travel

The required probability is 0.55 while selecting a group that has an average value of at least $26.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

John has six bills of paper money in the following denominations $1, $5, $10, $20, $50, and $100.

The total number of possible combinations = [tex]^6c_3[/tex] = 6!/313! = 20

Combinations for which the average value is at least $26:

(1.5.100), (1,10,100), (1.20,100). (1.50,100), (5,10,100), (5,20,100), (5,50,100), (10,20,100), (10,20,50), (10,50,100), (20,50,100)

Number of favorable combinations = 11

So, required probability = 11/20 = 0.55

Thus, the required probability is 0.55 while selecting a group that has an average value of at least $26.

Learn more about the probability here:

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Answer:

Step-by-step explanation: Taking into account that they are all like terms they can be combined, therefore there would only be one term. For example:

5x-3x+6x-x+2x=

Combine the like terms

2x+6x-x+2x=

It can be simplified further

8x-x+2x=

7x+2x=

9x

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

When the midpoints of adjacent sides of quadrilateral are connected by segments.

These segments form a parallelogram.

These segments  form parallelogram irrespective of kind of quadrilateral.

Since all sides of these segments are opposite to each other.

So, Option 'a' is correct.

Answer:

The correct option is C) Store B is reducing prices by 5% more than Store A.

Step-by-step explanation:

Consider the provided information.

Store B is advertising a sale that will reduce prices on all merchandise by one over five.

Convert one over five in percentage as shown below:

[tex]\frac{1}{5}=\frac{1}{5}\times{\frac{20}{20}}[/tex]

[tex]\frac{1}{5}=\frac{20}{100}[/tex]

[tex]\frac{1}{5}=20\%[/tex]

Thus, the store B reduce the prices by 20%.

Store A reduces the prices on all merchandise by 15%.

From the above calculation, it is clear that store B reduces more prices by 5%.

Therefore, the correct option is C) Store B is reducing prices by 5% more than Store A.

Answer:

True

Step-by-step explanation:

Two or more figures are congruent if all of their sides and angles are equal.

You can draw two not congruent triangles with equal congruent parts.

For example, you know that the sum of the inside angles of a triangle is 180º.

You could find two triangles with 90º 45º and 45º angles but with different-length sides.

Those would be congruent angles but not congruent triangles.