Enter the equation of the line meeting the given conditions. Please put the equation in standard form. Containing A(5, 3) and perpendicular to a line with slope of -2

The equation can be written as x+4=x^2 is \sqrt{x+4} =x, where x>0.

[tex]\sqrt{x+4} =x[/tex]

If we square both sides of the equation

We can rid of the exponent on the right side and add a square root to

x + 4.

[tex]\sqrt{x+4}=x[/tex]

Squaring on both sides we have,

The square root of a number is that factor of a number that when multiplied by itself gives the original number.

[tex](\sqrt{x+4}})^2=x^2[/tex]

x+4=x^2

Therefore, The equation can be rewritten as x + 4 = x^2.

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Final answer:

The correct option (C) identity property of multiplication. The equation 2*1=2 demonstrates the identity property of multiplication, indicating that any number multiplied by 1 yields the same number.

Explanation:

The mathematical property shown by the equation 2*1=2 is the identity property of multiplication. This property states that any number multiplied by 1 yields the number itself. Therefore, the correct answer is C.identity property of multiplication.

The identity property is essential because it confirms that 1 is the multiplicative identity in the set of real numbers.

Unlike the commutative property, which deals with the order of multiplication, or the associative property, which deals with the grouping of numbers, the identity property simply confirms that a number remains unchanged when multiplied by 1.

Scientific notations are the way through which a very small or a very large number can be written in shorthand. The area of Greenland in scientific notation is 8.4×10⁵ square miles.

Scientific notations are the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

The given area of Greenland is 840,000 square miles. Therefore, the area of Greenland in scientific notation can be written as,

Area of Greenland = 840,000 square miles

                               = 8.4 × 10⁵ square miles

Hence, the area of Greenland in scientific notation is 8.4×10⁵ square miles.

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The conjecture is true; by determining the pattern of increasing differences between consecutive numbers (increasing by 3), we can conclude that adding 12 to the last number, 13, gives us the next number in the sequence, which is 25.

The conjecture that the next number in the sequence -5, -2, 4, 13 is 25 can be tested by looking at the pattern of how the numbers are increasing. To do this, let's look at the differences between the numbers:

We see that the differences between the numbers are increasing by 3 each time (3, 6, 9). Therefore, if we continue this pattern, the next difference should be 9 + 3 = 12. If we add 12 to the last number in the sequence, 13, we get:

13 + 12 = 25

Therefore, the conjecture is true. The next number in the sequence is indeed 25.

34 gallon containers of paint can the painter buy.

Given that, A painter is buying gallon containers of paint. He has $375 to spend and each gallon container costs $11.

We need to find out how many gallon containers of paint can the painter buy.

The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit. It is a method that we use for most of the calculations in math.

Now, the number of gallon containers of paint can the painter buy=375/11

=34.09

Therefore, 34 gallon containers of paint can the painter buy.

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Answer:

Caroline expect to earn is $63 .

Step-by-step explanation:

As given

Caroline works in Shelley’s store.

She earns $36 for a 4-hour shift.

Thus

[tex]Caroline\ earns\ for\ one\ hour\ shift = \frac{Total\ hour\ of\ earning}{Number\ of\ hour}[/tex]

[tex]Caroline\ earns\ for\ one\ hour\ shift = \frac{36}{4}[/tex]

Caroline earns for one hour shift = $ 9

As given

If  Caroline works for 7 hours .

Thus

Caroline earns from work = Caroline earns for one hour shift × Number of hour .

                                          = 9 × 7

                                          = $ 63

Therefore the  Caroline expect to earn is $63 .

Answer:

50%

Step-by-step explanation:

The next table display all possible outcomes.

penny | dime

head   | head  

head   | tail

tail       | head

tail       | tail

If each single outcome is equally likely and there are 4 options , then all outcomes has a probability of 1/4 = 0.25 or 25%. The probability of getting one head and one tail is 50% because it's obtained by two outcomes.

The real interest rate that Sally pays the credit card company is 8% a year.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

Balance = $10,000

Interest rate = 17 percent

Now,

The real interest rate is the interest rate that has been adjusted to remove the effects of inflation. According to 1, it can be calculated as:

Real interest rate = nominal interest rate - inflation rate

In this case, the nominal interest rate is 17% and the inflation rate is 9%. Plugging these values into the formula, we get:

Real interest rate = 17% - 9%

Real interest rate = 8%

Therefore, by the given interest the answer will be 8% a year.

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The price to mail a package weighing 13 lbs can vary depending on the carrier and the type of service, but it typically ranges from about $20 to $100. Always check current rates on the carrier's website or at a local post office.

The cost to mail a package can vary considerably depending on various factors such as the carrier (USPS, UPS, FedEx, etc.), the package's size and shape, the destination, and the speed of delivery. However, assuming you're using USPS, their pricing often depends on the weight of the package. A package weighing 13 lbs currently could cost anywhere from around $20 to $100, based on various factors and the type of service you choose (like priority mail or ground shipping). It's always best to check the current rates on the carrier's website or at a local post office.

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Answer:

The answer is 2.

Step-by-step explanation:

In order to determine the value of the expression, we have to know about absolute value function.

The absolute value function is a function that only change the sign into positive and maintain the values. It is represented by " | x | " where x can be any number.

For example, if [tex]x=-2[/tex]

[tex]|x|=|(-2)|=2[/tex]

In this case, we have the next values:

[tex]a=5\\b=-3\\\\|a|-|b|\\|5|-|(-3)|\\5-3\\2[/tex]

Finally, the value of the expression is 2.

The insurance company is obligated to pay $99,000 for the claim of the stolen family heirloom ring.

Rowena's basic homeowners' insurance policy has a coverage limit of $150,000 with a $1,000 deductible. The deductible is the amount that Rowena must pay out of pocket before the insurance company pays for a claim.

When the family heirloom ring worth $100,000 is stolen, the insurance company will cover the value of the ring up to the policy limit minus the deductible.

Since the value of the ring is within the policy limit, the calculation for the amount the insurance company is obligated to pay is as follows:

Value of the ring = $100,000

Deductible = $1,000

Amount covered by insurance = Value of the ring - Deductible

Amount covered by insurance = $100,000 - $1,000

Amount covered by insurance = $99,000

Answer:

7.70

Step-by-step explanation:

The measure of the missing angle is 113.28°.

We can use the Law of Sines to determine the measure of the missing angle by assuming that it is opposite side c.

According to the Law of Sines, any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

So, Substituting the given values

16/sin(42°) = 10/sin(B) = c/sin(C)

Now, take first two ratios

sin(B) = 10*sin(42°)/16

sin (B) ≈ 0.4182

B ≈ sin⁻¹(0.4182)

B ≈ 24.72°

Using Angle Sum property

A + B + C = 180°

A + 42° + 24.72° = 180°

A ≈ 113.28°

Thus, the measure of the missing angle is 113.28°.

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The German invasion of Poland on September 1st 1939 caused Britain to declare war on Germany two days later, starting the war.

Final answer:

In mathematics, while a data set can have more than one mode if multiple values share the highest frequency, there is usually only one mean. The mode refers to the most common value, and the mean is the arithmetic average. Statistical tools often help calculate these measures of center.

Explanation:

Yes, there can be more than one mean or mode in a math problem. The mode is the most frequently occurring value in a data set, and a data set can have multiple modes if there are several values with the same highest frequency. When a data set has two modes, it is known as bimodal. In contrast, while there can be more than one solution to an equation (such as in quadratic equations), there is typically only one mean for a given data set. The mean is calculated by adding all the values together and dividing by the number of values. However, the mean can be influenced by skewed data or outliers more than the median or mode.

The measures of center like mean, median, and mode are critical in statistics for summarizing data. They provide different perspectives on the central tendency of the data. The mean is the arithmetic average, the median is the middle value when the data set is ordered, and the mode shows the most frequently occurring value(s). In analyzing data, statistical software or graphing calculators are often used to efficiently calculate these measures of center.

When considering the relationship between the shape of a distribution and the measures of center, typically, the mean is most affected by skewness and outliers. A skewed distribution will pull the mean toward the long tail while the median tends to resist the influence of outliers and skewed data. Mode, being the most frequent value, doesn't necessarily indicate skewness but can reveal frequency patterns within the data set.