Carol is building a screen door. The height of the door is one foot more than twice its width. What is the width of the door if the height is seven feet?

Final answer:

The growth of Spanish colonies was hindered by the vast distance between the colonies and Spain, restrictive economic policies, environmental depletion, exploitation of resources, and conflict. The decline in indigenous populations and internal governmental strife also played significant roles.

Explanation:

Factors Hindering the Growth of Spanish Colonies

The growth of the Spanish colonies was hindered by several factors after the initial period of discovery and conquest. First, the distance and the expanse of the Atlantic Ocean created significant challenges for effective communication and administration between the colonies and Spain. Second, the rigid economic policies imposed by the Spanish Crown, which restricted colonial trade to raw materials to Spain and finished goods from Spain, limited economic diversification and local development.

Additionally, environmental depletion and exploitation of resources, alongside harsh treatment and violence against Indigenous populations, led to a decrease in the native labor force. As a substitute, the Spanish were compelled to import African slaves, which transitioned the labor system but did not solve the inherent problems of the colonial economy.

The desire for precious metals, such as silver and gold, and the competition for conversion to Catholicism often came at a substantial human cost, leading to significant loss of indigenous life due to disease and conflicts. Revolts and uprisings, such as the Pueblo Revolt, as well as internal government conflicts and higher tax burdens on the Criollos were also among the contributing factors that hindered the growth and stability of Spanish colonies.

Final answer:

To solve the inequality 22 >= 5(2y+3)-3y, we distribute the 5, combine like terms, then isolate and solve for y, showing that y must be less than or equal to 1.

Explanation:

To solve the inequality 22 >= 5(2y+3)-3y, follow these steps:

The final answer is that y must be less than or equal to 1.

Number 3. is wrong the correct answer is D.

The equation of the exponential graph is y = 100(0.5)^x

On the graph, we have the following points

(x,y) = (0,100) and (1,50)

An exponential equation is represented as:

y = ab^x

Where a = y, when x = 0.

This means that

a = 100

So, we have:

y = 100b^x

At the point (1,50), we have:

50 = 100b^1

Evaluate

50 = 100b

Divide both sides by 100

b = 0.5

Substitute b = 0.5 in y = 100b^x

y = 100(0.5)^x

Hence, the equation of the exponential graph is y = 100(0.5)^x

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Final answer:

Rivka and Sara can build their two rafts together in approximately 5.5 days, as they have a combined work rate of 11/30 rafts per day when they work together.

Explanation:

Rivka and Sara, working together to build their rafts, would combine their work rates to find out how many days it will take to build two rafts. Rivka can build a raft in 5 days, which means her work rate is 1 raft per 5 days or 1/5 raft per day. Sara can build a raft in 6 days, equating to a work rate of 1/6 raft per day.

When they work together, their combined work rate is 1/5 + 1/6 rafts per day. To combine these, we find a common denominator:

1/5 + 1/6 = (6 + 5) / 30 = 11/30 rafts per day

The question asks how long it takes to build two rafts. Therefore, we divide the total number of rafts by their combined work rate:

2 rafts / (11/30 rafts per day) = (2 * 30) / 11 days = 60/11 days ≈ 5.5 days

Hence, Rivka and Sara will take approximately 5.5 days, or 5.5 days rounded to one decimal, to build two rafts if they work together without stopping.

The rock climbers initial height above sea level is:

                                 50 meters.

The expression which is used to represent the elevation above sea level, in meters, of a rock climber after x minutes of climbing is given by:

                                     2x+50

Now, we are asked to find the rock climbers initial height above sea level i.e. we are asked to find the value of the expression when x=0.

Hence, when x=0 we  have:

2x+50=2×0+50

          = 50

Hence, the answer is: 50 meters.

It is found that in 2 hrs, the jet will travel 1,440 kilometers. And in 6 hrs, the jet will travel 4,320 kilometers.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

We can calculate this using the following steps:

60 kilometers in 5 minutes

x kilometers in 2 hours = 120 minutes

Therefore,

60 ( 120 )= 5  x

x = 60 ( 120 / 5)

x = 1440 kilometers

y kilometers in 6 hours = 360 minutes

60 (360) = 5 y

y = 60 ( 360 / 5)

y = 4320 kilometers

Hence, It is found that in 2 hrs, the jet will travel 1,440 kilometers. And in 6 hrs, the jet will travel 4,320 kilometers.

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|-4-7| is the expression represents the distance the two points, X and Y, on the number line

A number system is defined as a system of writing to express numbers.

Number line is a picture of a graduated straight line that serves as visual representation of the real numbers.

The x point is at minus four and y is at point three.

The distance will be always positive

As we count the units from -4 to 3 we get seven humps.

So the distance will be 7 units.

This we can get by taking |-4-3| which is |-7|=7 units.

Hence, |-4-7| is the expression represents the distance the two points, X and Y, on the number line

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In mathematics, it is common to combine two inequalities into a single compound inequality to indicate a range for a variable. Inequalities are also used in describing alternative hypotheses in statistics and conversions between measurement systems.

It is indeed sometimes possible to represent two separate inequalities as a single compound inequality in mathematics. This technique is often used to indicate that a value lies within a certain range. For instance, to show that a number x is greater than 1 but less than 3, we can write two inequalities: x > 1 and x < 3. These can be combined into a single compound inequality 1 < x < 3.

Inequalities are often used in various mathematical contexts, such as solving equations, graphing regions on a coordinate plane, or expressing ranges. Furthermore, in statistics, the alternative hypothesis is typically denoted using inequality symbols (≠, >, or <), showing a predicted difference or relationship.

To express equivalences between different measurement systems, a common approach is to use 1 as an exact value on one side of the equation, with the other side being inexact. Mathematically, you can rearrange equations for convenience into formats showing direct or indirect proportionalities, simplifying complex relationships into more manageable forms.

0.10d +0.25q = 7.00

 multiply everything by 100 to get rid of decimals

q = d+7 ( 7 more quarters than dimes)

10d +25(d+7) = 700

10d + 25d +175 = 700

35d +175 = 700

 subtract 175 from each side

35d =525

d = 525 / 35 = 15

15 dimes

 quarters = 15 +7 = 22

Answer:

Option d.

Step-by-step explanation:

Ryan works at the car wash and earns  = $5.30 per hour plus tips.

His earning from 32 hours of work = 32 × 5.30 = $169.60

He total earned = $403.00

Therefore, he earned from tips = $403 - $169.60

                                                  = $233.40

Ryan earned in tips $233.40.

The area of the triangle is 270 square centimeters.

To find the area of a triangle, we can use the formula A = (1/2)bh, where A represents the area, b represents the base length, and h represents the height. In this case, we are given the area of one triangle (150 square centimeters) when its height is 20 centimeters and its base length is 15 centimeters. Plugging these values into the formula, we get:

A = (1/2)(15)(20) = 150

Now, we can use this equation to find the area of another triangle with a height of 30 centimeters and a base length of 18 centimeters:

A = (1/2)(18)(30) = 270 square centimeters

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The graph of the function y = -2 - 3 is shifted down 3 units from the graph of the function y = -2x.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The equations of the functions are:

y  -2x

y = -2x - 3

The graph of the function y = -2x will be a straight line that is passing through origin (0, 0).

Applying transformation to the graph of the function y = -2x

y = -2x - 3

As we can see in the graph:

The graph y=-2x - 3 is shifted down 3 units from y = -2x

Thus, the graph of the function y = -2 - 3 is shifted down 3 units from the graph of the function y = -2x.

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The speed of the truck in feet per second will be 105.6 ft per second.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.

Another example could be kilo gram to gram.

1 mile = 5280 feet

And

1 hour = 60 minutes

1 hour = 60 × 60 seconds = 3600 seconds

Now

Given the speed of the truck is

⇒ 72 miles/hour

⇒ 72 × 1 mile/1 hour

⇒ 72 ×  5280 feet/3600 seconds

⇒  105.6 feets/second

Hence "The speed of the truck in feet per second will be 105.6 ft per second".

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