JL is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain. ( I am falling behind on my online classes because this question is holding me back... I cannot compute anymore.... uuuurrghh)

Answer:

Option D) [tex]\displaystyle\frac{50}{8} < 6\frac{2}{5} < 6.45 < \frac{26}{4}[/tex]

Step-by-step explanation:

We are given the following information in the question:

We are given a set of numbers:

[tex]\displaystyle\frac{26}{4}, 6.45, 6\frac{2}{5}, \frac{50}{8}[/tex]

First, we write all the numbers in decimal form.

[tex]\displaystyle\frac{26}{4} = 6.5\\\\6\frac{2}{5} = \frac{32}{5} = 6.4\\\\\frac{50}{8} = 6.25[/tex]

Hence, the given numbers are:

6.5, 6,45, 6.4, 6.25

Arranging in order of least to greatest:

[tex]6.25 < 6.4 < 6.45 < 6.5[/tex]

Thus,

[tex]\displaystyle\frac{50}{8} < 6\frac{2}{5} < 6.45 < \frac{26}{4}[/tex]

Option D is the correct option.

Answer:

C - Opposite sides are congruent  

D - Corresponding parts of congruent triangles are congruent

Step-by-step explanation:

A parallelogram is a quadrilateral whose both pairs of opposite sides are parallel. In a parallelogram, the 2 sets of opposite sides are congruent. Also it has 2 sets of opposite angles congruent.

Therefore, the following are necessary when proving the opposite sides of a parallelogram are congruent.

C - Opposite sides are congruent  

D - Corresponding parts of congruent triangles are congruent

Answer: The functions all have the same slope

Step-by-step explanation:

just took the assessment and I got it right.

ANSWER

We need to rewrite [tex]x+2y=6[/tex], in slope intercept form.

[tex]\Rightarrow 2y=-x+6[/tex],

[tex]\Rightarrow y=-\frac{1}{2}x+3[/tex]

The given equation has a slope of [tex]-\frac{1}{2}[/tex].

ANSWER TO QUESTION 1

We now the write given options also in slope intercept form.

For the first one, we have

[tex]y=-\frac{1}{2}x+5[/tex]

This first equation also has a slope  of [tex]-\frac{1}{2}[/tex].

Hence [tex]y=-\frac{1}{2}x+5[/tex] is parallel to [tex]x+2y=6[/tex].

ANSWER TO QUESTION 2:

The second equation is;

[tex]-2x+y=-4[/tex].

We need to write this one too in slope intercept form.

[tex]y=2x-4[/tex]

This second equation has a slope of 2

Since [tex]2\times -\frac{1}{2}=-1[/tex], the line [tex]-2x+y=-4[/tex]

is perpendicular to [tex]x+2y=6[/tex].

ANSWER TO QUESTION 3

We rewrite the equation [tex]-x+2y=2[/tex] in slope intercept form.

[tex]\Rightarrow 2y=x+2[/tex]

[tex]\Rightarrow y=\frac{1}{2}x+1[/tex]

This equation also has a slope of [tex]\frac{1}{2}[\tex]

since the slope of [tex]-x+2y=2[/tex] is not equal to the slope of [tex]x+2y=6[/tex], and the product of these two slopes [tex]\frac{1}{2} \times - \frac{1}{2} \ne -1[/tex], the two lines are neither parallel nor perpendicular.

QUESTION 4

The given line has equation [tex]x+2y=-2[/tex]. We rewrite this equation in the slope intercept form.

[tex]\Rightarrow 2y=-x-2[/tex]

[tex]\Rightarrow y=-\frac{1}{2}x-1[/tex]

This line has a slope of [tex]-\frac{1}{2}[/tex].

Since this slope is the same as the slope of the given line,

[tex]y=-\frac{1}{2}x-1[/tex] is parallel to  [tex]x+2y=6[/tex].

See graph in attachment.

The correct option is [tex]\boxed{\text{\bf option C}}[/tex] i.e., the length is [tex]6\text{ cm}[/tex] and breadth is [tex]7\text{ cm}[/tex].

Further explanation:

The perimeter of arectangle is calculated as follows:

[tex]\boxed{\text{Perimeter}=2\cdot (l+b)}[/tex]

Here, [tex]l[/tex] is the length and [tex]b[/tex] is the breadth of the rectangle.

Given:

The length of the rectangle is [tex]5\text{ cm}[/tex] less than twice its breadth and the perimeter of the rectangle is [tex]26\text{ cm}[/tex].

Calculation:

Step 1:

First we write the dimensions in the form of variable [tex]x[/tex].

Consider [tex]x[/tex] as the breadth of the rectangle and [tex]y[/tex] as the length of the rectangle.

As per the question the length is [tex]5\text{ cm}[/tex] less than twice its breadth.

Therefore, the length can be expressed in the form of the equation as follows:

[tex]\boxed{y=2x-5}[/tex]  …… (1)

Step 2:

Now, we have to calculate the dimensions of the rectangle.

So, substitute [tex]l=2x-5[/tex] and [tex]b=x[/tex] in the formula of the perimeter of the rectangle to obtain the value of [tex]x[/tex].

[tex]\begin{aligned}\text{Perimeter}&=2\cdot (l+b)\\26&=2\cdot (2x-5+x)\\26&=2\cdot (3x-5)\\26&=6x-10\\6x&=26+10\\6x&=36\\x&=6\end{aligned}[/tex]  

Therefore, the breadth of the rectangle is [tex]6\text{ cm}[/tex].

Now, substitute [tex]x=5[/tex] in the equation (1) to obtain the value of the length.

[tex]\begin{aligned}l&=2x-5\\&=(2\cdot 6)-5\\&=12-5\\&=7\end{aligned}[/tex]

Therefore, the length of the rectangle is [tex]7\text{ cm}[/tex].

Thus, the correct option is [tex]\boxed{\text{\bf option C}}[/tex] i.e., the length is [tex]6\text{ cm}[/tex] and breadth is [tex]7\text{ cm}[/tex].

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Answer details:

Grade: Junior school

Subject: Mathematics

Topic: Area and Perimeter  

Keywords: Length, breadth, perimeter, area, side, dimensions, rectangle, shapes, figure, triangle, square, equation, variable, constant, twice, area, mensuration.

Answer:

Option A    

Step-by-step explanation:

Given : Equation [tex]y-1 = 2(x -2)[/tex]

To find : Which graph represents the given equation

Solution :

First thing we plot the graph of the equation.

We see that graph cuts at point (1.5,0) and (0,-3) to the coordinates.

From the given graph Option A graph cuts to these points.

Therefore, Option A is correct.

Refer the attached graph A.

Answer:

2x + 1 = 67

Let the smaller integer be x.

The next larger consecutive integer is 1 more than x, so it's x + 1.

x + x + 1 = 67

2x + 1 = 67

Answer:

To prepare for the unexpected, it is important to have a reserve fund set aside. Having a reserve fund is important, but it should not always be your first priority. If you have credit card or other debt, pay that off before you start to put your money in a reserve. Credit card debt has a high interest rate, while the money that you will save in your reserve probably won’t gain a lot of interest. Why not? When you choose a place to save your financial reserve, low risk is key. Remember that your financial reserve fund is for emergencies only. If you have an emergency and need to use it, do. Once you are back on your feet, replenish it. Also, once you have saved the amount you need, stop. Your extra savings will serve you better in an investment that yields higher interest.

Step-by-step explanation:

Words taken from the online site 1 on edge for "Why might a person need an emergency fund?"

The term “emergency fund” refers to helping those times when a person is in need of money. An emergency fund allows you to save on rarer credit interest.

What is emergency fund?

The term “emergency fund” refers to the person's use of money at the time of need. Emergency money is saving money. They improve our financial security and safety. The emergency money is a small amount of money. For example, home repairs, paying medical bills, trip planning.

An emergency fund is money kept in a bank account to cover unexpected expenses like medical bills or car or home repairs. An emergency fund can also assist you in the event of a lack of income due to a job loss or prolonged illness.

Hence, the significance of the emergency fund is aforementioned.

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If its rounded it would be 73 degrees

The conversion factor to convert cups to liters is 0.237. When converting from cups to liters, multiply the number of cups by 0.237.

According to the conversion table provided, the conversion factor to convert cups to liters is 0.237. That means for every 1 cup, it equals approximately 0.237 liters. To convert from cups to liters, you simply multiply the number of cups by this conversion factor, 0.237.

For example, to find out how many liters is 2 cups, you do the multiplication: 2 cups * 0.237 = 0.474 liters.

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The complete question is given below:

Given : A table showing conversions for common units of capacity.

                              Units of  capacity  

Customary System Units                             Metric System Units

        1 gallon                                                           3.79 liters

        1 quart                                                            0.95 liters

         1 pint                                                              0.473 liters

         1 cup                                                              0.237 liters

What is the conversion factor to convert cups to liters?

The conversion factor to convert cups to liters, according to the given table, is that 1 cup equals 0.237 liters. To convert any amount of cups to liters, multiply the number of cups by 0.237.

The table in your question provides the conversion factors for common units of capacity, including the conversion of cups to liters in both the Customary and Metric systems.

According to the table, 1 cup is equivalent to 0.237 liters. This means that to convert any given number of cups to liters, you multiply the number of cups by 0.237.

For example, to convert 5 cups into liters, you would perform the following calculation: 5 cups × 0.237 = 1.185 liters. This conversion factor is useful in everyday scenarios such as cooking or reading a recipe that uses different measurement systems.

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Final answer:

The future value of a rare postage stamp that cost $5000 and increases by 11% annually over 10 years is calculated using the compound interest formula V = P(1 + r)[tex]x^{n}[/tex], where P is the principal amount, r is the annual rate, and n is the number of years.

Explanation:

Calculating the Future Value of a Rare Postage Stamp

The value of a rare postage stamp, originally purchased for $5000, that has been increasing in value by 11% annually for 10 years can be calculated using the formula for compound interest: V = P(1 + r)[tex]x^{n}[/tex], where:

P = $5000,

n = 10 years.

Plugging these values into the formula, we get:

V = $5000(1 + 0.11) [tex]x^{10}[/tex]

Performing the calculations gives us the future value of the stamp after 10 years.

To make a profit of at least $600, the number of bookends that need to be sold is calculated by adding the desired profit to the initial cost, and then dividing this sum by the net revenue per bookend. The result is approximately 144 bookends.

The subject of this problem is Mathematics, specifically a topic within business math called 'breakeven analysis' or 'cost-volume-profit analysis'. It involves calculating the point at which revenue from selling a product equals the costs associated with producing and selling that product. In this case, you have spent $154 to make wooden bookends, and you plan on selling them online for $8.50 each. Additionally, there's a $3.25 fee per bookend for wrapping and shipping, which you charge to your customers. Your goal is to make a profit of at least $600.

To calculate the number of bookends that need to be sold, we first find the net revenue per bookend. This is the selling price minus the shipping cost, which comes out to $8.50 - $3.25 = $5.25 per bookend. The desired profit is added to the cost of making the bookends to find the total required revenue, which is $600 + $154 = $754.

Finally, total required revenue is divided by the net revenue per bookend to find the number of bookends that need to be sold: $754 ÷ $5.25 = approximately 144 bookends (rounded up to the nearest whole bookend since we can't sell a fraction of a bookend). So, in order for your profit to be at least $600, you must sell at least 144 bookends.

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Joey must work 26 weeks until he has enough to purchase the car.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

Joey wants to buy a used car,

The cost of the car is $2500.

The money he has saved is $1200

The money he makes by walking a dog is $50 per week.

Let w represent the number of weeks.

The equation for the condition can be written as:

The cost of the car is equated with the money he has and the money he earned in w weeks by dog walking.

2500 = 1200 + 50w

To determine the number of weeks he has to work to buy the car, the equation has to be solved for w,

50w = 2500 - 1200

50w = 1300

w = 1300 / 50

w = 26 weeks.

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Answer:

The discriminant of the given polynomial is 0.

Step-by-step explanation:

The discriminant of a quadratic polynomial [tex]p(x)=ax^2+bx+c[/tex] is

[tex]D=b^2-4ac[/tex]

The given expression is

[tex]9x^2-18x+9[/tex]

Here,

[tex]a=9,b=-18,c=9[/tex]

The discriminant of a given polynomial is

[tex]D=(-18)^2-4(9)(9)[/tex]

[tex]D=324-324[/tex]

[tex]D=0[/tex]

Therefore the discriminant of the given polynomial is 0.

Answer: 0.0625

Step-by-step explanation:

To calculate the total cost, multiply the price of each item by the number purchased then add those totals together. In this case, purchasing two hot dogs and one candy bar costs $5.00.

To find the total cost of purchasing two hot dogs and one candy bar, you would simply multiply the cost of each item by the number of that item you are buying, and then add all these costs together. So, if a hot dog is $2.00 and you want to buy two, this costs $2.00 * 2 = $4.00. A candy bar is $1.00 each, and if you want to buy one, this costs $1.00 * 1 = $1.00. So, the total cost would be the cost of the hot dogs plus the cost of the candy bar, which is $4.00 + $1.00 = $5.00. Therefore, the total cost of two hot dogs and one candy bar is $5.00.

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