The diagram shows the circle with equation x^2+y^2=20. Tangents touching the circle at points I and J pass through the point H (0,10). By letting the equation of a tangent be y=mx+10, find the two possible values of m.

The radical expression (6–√4)3 written in exponential form is 612.

Expression is a term used to describe the process of making clear or conveying one's thoughts, ideas, and feelings. It is a way of communicating with others and expressing oneself in a meaningful and effective manner. Expression can be done through verbal and non-verbal communication, including writing, art, music, dance, and other creative outlets. It can also be used to express emotions such as joy, sadness, fear, anger, and love. Expression is essential to healthy communication and can be a powerful tool for self-expression, personal growth, and development.

This is because raising a number to an exponent is the same as multiplying that number by itself the number of times specified by the exponent. In this case, the base number is 6, and the exponent is 12. When a number is multiplied by itself 12 times, it is referred to as an exponential expression. To convert the radical expression to an exponential expression, the radical needs to be converted to an exponent. The radical of 4 is 2, so the exponent is 12. This results in the answer 612.

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Answer:

The answer should be D.)

Answer:

4/3, -3

Step-by-step explanation:

slope is the number in front of the variable x, and y intercept is when x=0

Answer:

Let's start by finding out how many muffins were there in total before the ogre stole 20 of them. Let's call that number "x".

If 5/8 of them were left after the ogre stole 20, then 3/8 of them were taken.

So we can set up an equation:

x - 20 = 3/8x

To solve for x, we can start by multiplying both sides by 8 to get rid of the fraction:

8(x - 20) = 3x

8x - 160 = 3x

Now we can solve for x by subtracting 3x from both sides:

5x - 160 = 0

5x = 160

x = 32

So there were originally 32 muffins.

Now we can find out how many are left:

5/8 of 32 = 20

So there are 20 muffins left.

Step-by-step explanation:

There are 42 cubes needed to fill this prism.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Angie packed same-size cubes into a rectangular prism.

And, Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall.

Hence, Number of cubes to fill the prism is,

⇒ 3 × 2 × 7

⇒ 42

Thus, There are 42 cubes needed to fill this prism.

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Complete question is this,

Angie packed same-size cubes into a rectangular prism.

Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall. PLEASE HELP ME

What is the number of cubes needed to fill this prism?

Answer:

The solution to the equation 7x [6+10(1+1)] = 4 x 5 is x = 10/91.

Step-by-step explanation:

o solve the equation 7x [6+10(1+1)] = 4 x 5, we can use the order of operations, which tells us to first perform the operations inside the parentheses, then the multiplication and finally the multiplication by 7x.

So, we have:

7x [6+10(1+1)] = 4 x 5

7x [6+10(2)] = 20

7x [6+20] = 20

7x [26] = 20

182x = 20

To solve for x, we can divide both sides by 182:

182x/182 = 20/182

x = 20/182

Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, we get:

x = 10/91

Therefore, the solution to the equation 7x [6+10(1+1)] = 4 x 5 is x = 10/91.

By answering the above question, we may infer that Thus, the 159 feet that make up the perimeter of the area used for the new playground.

A limit is a closed path that encircles, separates, or encompasses a one-dimensional length, a two-dimensional shape. A circle's or an ellipse's perimeter refers to its outermost region. Many practical uses may be made of the perimeter calculation. The radius of an edge is used to calculate a shape's perimeter. Get the circle's radius by multiplying the lengths of the sides of irregular shapes. Every form's perimeter may be determined by multiplying its side lengths. The area around an object is called its perimeter. Your home's walled garden serves as a wonderful example of this. A thing's perimeter is the area surrounding it. A 200 foot barrier will be needed to contain a 50 by 50 foot yard.

Current playground size is 1,575 square feet, or 35 feet by 45 feet.

The difference between the old and new playgrounds is 1,575 square feet.

New playground length = 1,575 square feet / 42 feet 37.5 feet, where new playground width equals new playground area.

We can calculate the perimeter now that we know the new playground's width is around 37.5 feet:

The new playground's perimeter is equal to 2 (length + width).

The new playground's perimeter is 2 (42 feet plus 37.5 feet).

2 is the new playground's perimeter (79.5 feet)

The new playground's perimeter is 159 feet.

Thus, the 159 feet that make up the perimeter of the area used for the new playground.

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The similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given is right triangle PRQ, a perpendicular line is drawn to the side PQ from angle R

we need to tell the similar triangles,

From the figure we have,

Δ SRQ ~ Δ RPQ  ~ Δ SRP

And, according to the definition of similar triangle,

SP / RP = PR / RQ

PQ / RQ = RQ / SQ

Hence, the similar triangles are Δ SRQ ~ Δ RPQ  ~ Δ SRP

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Answer:

the answer is px and at ako

The length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).

Algebraic expressions are used to represent mathematical relationships and formulas, and can be used to solve equations and manipulate equations in order to isolate variables or solve for unknown quantities. They are used extensively in algebra, calculus, and other branches of mathematics.

We are given that the time for one swing is given by the formula:

t = 2√(L/32.2)

where L is the length of the rope swing in feet, and 32.2 is the acceleration due to gravity in feet per second squared.

We are also given that one swing takes 3.5 seconds, so we can write:

3.5 = 2√(L/32.2)

Squaring both sides, we get:

12.25 = 4(L/32.2)

Multiplying both sides by 32.2/4, we get:

L = 32.2 × 12.25/4

L ≈ 98.9 feet

Therefore, the length of the rope swing is approximately 98.9 feet (rounded to the nearest tenth of a foot).

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The correct statement regarding the inverse function is given as follows:

[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex], with a domain of x ≤ 3.

The function for this problem is defined as follows:

f(x) = 2(x - 3)² + 4.

The axis of symmetry of the function is of x = 3, hence the domain of the inverse function is given as follows:

x ≤ 3.

The inverse function is obtained exchanging x and y and then isolating y, hence:

x = 2(y - 3)² + 4

2(y - 3)² = x - 4.

[tex](y - 3)^2 = \frac{x - 4}{2}[/tex]

[tex]y - 3 = \sqrt{\frac{x - 4}{2}}[/tex]

[tex]f^{-1}(x) = 3 - \sqrt{\frac{x - 4}{2}}[/tex]

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Answer:

Step-by-step explanation:

200,000 square kilometers is a good estimate for the area of South Dakota because the actual area of South Dakota is approximately 199,729 square kilometers according to the United States Geological Survey (USGS).

This means that the estimate is only off by about 0.1% of the actual area. This level of accuracy is generally considered to be very good for an estimate, especially when dealing with large areas like states or countries.

Additionally, 200,000 square kilometers is a round number and easy to remember, making it a useful estimate in contexts where a precise value is not necessary. It also allows for quick comparisons with other areas or states that may be roughly similar in size.

Overall, 200,000 square kilometers is a good estimate for the area of South Dakota because it is reasonably close to the actual value, easy to remember, and useful for rough comparisons with other areas.

ALSO:

South Dakota is approximately 383 miles long (east to west) and 237 miles wide (north to south).

It has the approximate shape of a rectangle, its Area = (Base x Height)= (383 x 237)= 90,771.00 miles ^2 which are 235,095.81 Km^2. So by this geometric reasoning we can have a correct approximation of the area of ​​South Dakota.

Answer:

After the reverse stock split, Gene will own 120 shares of XYX Corporation.

To calculate the post-split market price per share, we can start by finding the total value of Gene's shares before the split:

Total value before split = 1,200 shares * $1.20 per share = $1,440

Since the reverse stock split is 1 for 10, the total number of shares outstanding will be reduced by a factor of 10, and the price per share will be increased by a factor of 10:

Total value after split = 120 shares * $12.00 per share = $1,440

Therefore, the post-split market price per share is $12.00.

Step-by-step explanation:

Answer:

Valid

Step-by-step explanation:

This argument is Valid because there could be many other reasons she needs dress altercations, however the most likely one is that she did not have her baby before next week.

Answer:

Step-by-step explanation:

The argument is valid.

We can analyze it using the following symbols:

Let A be the event that Bryony has her baby before next week.

Let B be the event that Bryony needs dress alterations before her sister's wedding next month.

Then the argument can be represented as follows:

If A, then not B.

B.

Therefore, not A.

This is a valid deductive argument form called modus tollens. The conclusion follows logically from the premises. Therefore, the argument is valid.

Answer:

The formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

Step-by-step explanation:

To obtain the formula for the function g(x) when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units, we can use the following transformations:

A vertical shift up by 1 unit is represented by adding 1 to the function: f(x) + 1

A horizontal shift to the left by 6 units is represented by replacing x with (x + 6): f(x + 6)

Therefore, the formula for the function g(x) is:

g(x) = f(x + 6) + 1

Substituting the expression for f(x), we get:

g(x) = √(x + 6) + 1

So, the formula for the function g(x) obtained when the graph of f(x) = √x is shifted up 1 unit and to the left 6 units is g(x) = √(x + 6) + 1.

Answer:

I do not have access to drawing tools. However, I can describe how to plot the function on a graph.

To plot the function h(x) = {-4, x < -3 and x+5, x > -3, you would start by drawing the x-y axes on a coordinate plane. Then, you would mark a point at x=-3 on the x-axis. At this point, the value of h(x) changes from -4 to x+5. So, you would draw a solid dot at (-3, 2) on the graph.

Next, you would draw a horizontal line at y=-4 to the left of x=-3, indicating that h(x) is always equal to -4 for x values less than -3.

Finally, you would draw a diagonal line starting from the dot at (-3, 2) and continuing to the right. This line represents the equation x+5 for x values greater than -3.

The resulting graph should have a horizontal line at y=-4 to the left of x=-3, a solid dot at (-3, 2), and a diagonal line extending to the right from the dot.

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Answer:

the answer for the problem is D.

The percent discount being offered is 20%.

What is percentage ?

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol %, which means "per cent" or "out of 100". Percentages are used to compare two quantities and express the relationship between them in terms of the fraction of one quantity that the other quantity represents.

To find the percent discount, we need to first calculate the amount of discount that is being offered. We can do this by subtracting the sale price from the original price:

Discount = Original Price - Sale Price

Discount = $79.95 - $63.96

Discount = $15.99

Next, we can calculate the percentage discount by dividing the discount by the original price and then multiplying by 100:

Percent Discount = (Discount / Original Price) x 100

Percent Discount = ($15.99 / $79.95) x 100

Percent Discount = 20%

Therefore, the percent discount being offered is 20%.

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Answer:

25.12cm

Step-by-step explanation:

The area of a circle is (π) x (radius)^2.

Here, you are given the diameter.

To find the radius, divide the diameter by 2, which results in 4.

(π) x (4)^2

Now square the 4, which results in 16

3.14 x 16 = 50.24

50.24 would be the area of the circle not cut in half, so divide 50.54 by 2 to get half.

50.24/2 = 25.12

Answer:

Step-by-step explanation:

The area of Circle is [tex]\pi r^{2}[/tex]

So, the area of half circle is [tex]\frac{\pi r^{2} }{2}[/tex]

Diameter is given = 8cm

so radius will be 4 cm

[tex]A = \frac{\pi 4^{2} }{2} \\A = \frac{\pi 16}{2} \\A = 8\pi[/tex]

A = 8 × 3.14

A = 25.12cm Square

The interval where both functions are decreasing is {-1, 2} and it is shown on the number line below.

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of g(x), we can logically deduce that the function g(x) decreases over the interval {-2, 2}. On the other hand (conversely), the function f(x) = -5|x + 1| + 10 decreases over the interval {-1, ∞}.

Therefore, the interval over which both functions decrease is denoted by the intersection of both functions;

Interval = {-1, 2}

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The interest rate of the saving account is 2.71%

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

Given, the interest rate of a savings account is represented by the formula such that:

r = [tex]\sqrt{\frac{V_2}{V_0} } - 1[/tex]

Where V₀ is the initial investment,

and V₂ is the balance of the account after 2 years.

In our case,

V₂ = 422

V₀ = 400

So the interest rate,

r = [tex]\sqrt{\frac{422}{400} } - 1[/tex]

r = 1.0271 - 1

r = 0.0271

therefore, the interest rate of the saving account is 2.71%

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Complete question:

The average annual interest rate r (in decimal form) of a savings account is V₂ represented by the formula r = [tex]\sqrt{\frac{V_2}{V_0} } - 1[/tex], where Vo is the initial investment, and V₂ is the balance of the account after 2 years. Find the average annual interest rate r of a savings account with an initial investment of $400 and a balance of $422 after 2 years.

Answer:

try 1/2

Step-by-step explanation:

The p-value for this sample is approximately 0.004655 which is smaller than the significance level of 0.005. This means that we reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the population proportions are not equal.

To test the hypothesis Hₐ : p₁ ≠ p₂ at a significance level of α = 0.005, we can use the two-sample z-test for proportions, where the test statistic is given by:

z = (p₁ - p₂) / sqrt{p(1-p)(1/n₁ + 1/n₂)}

where p = (x₁ + x₂) / (n₁ + n₂) is the pooled sample proportion, x₁ and x₂ are the number of successes in the two samples, n₁ and n₂ are the sample sizes for the two samples, and p₁ and p₂ are the sample proportions for the two samples.

Plugging in the given values, we have:

p₁ = 119/687 ≈ 0.1732

p₂ = 137/577 ≈ 0.2374

n₁ = 687

n₂ = 577

p = (119 + 137) / (687 + 577) ≈ 0.202

z = (0.1735 - 0.2376) / √{0.202 * (1 - 0.202) * (1/687 + 1/577)} ≈ -2.83

The test statistic for this sample is approximately -2.83

To find the p-value for this sample, we need to find the probability of observing a test statistic as extreme as -2.83, assuming that the null hypothesis is true. Since this is a two-tailed test, we need to find the area in the tails of the standard normal distribution that corresponds to a significance level of 0.005:

α/2 = 0.005/2 = 0.0025

Using a standard normal table or a calculator, we can find that the z-score corresponding to an area of 0.0025 in the left tail of the standard normal distribution is approximately -2.81. The z-score corresponding to an area of 0.0025 in the right tail is approximately 2.81.

The p-value for this sample is the sum of the areas in the tails beyond the test statistic:

p-value = P(Z ≤ -2.83) + P(Z ≥ 2.83)

P = 0.004655

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The value of x is 11.

A square is a two dimensional shape which consist of four sides and four angles, where each angle is 90 degrees.

Given is a square PQRS.

PR and QS are diagonals of the square.

Square has the property that the diagonals bisect the interior angles.

So, ∠Q will be bisected by diagonal QS.

So, ∠PQS = ∠SQR = (6x - 21)°

∠Q is the interior angle of a square, thus it is 90°.

∠Q = ∠PQS + ∠SQR

90 = 6x - 21 + 6x - 21

90 = 12x - 42

12x = 90 + 42

12x = 132

x = 11

Hence the value of x is 11.

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The measures of the angles are JKN = 27 degrees and JNK = 126

From the question, we have the following parameters that can be used in our computation:

The rectangle

On the rectangle, we have

JKN = NJK

Using the above as a guide, we have the following:

JKN = 27 degrees

The sum of angles in a triangle is 180

So, we have

JNK = 180 - 27 * 2

Evaluate

JNK = 126

Hence, teh angle is 126 degrees

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It is estimated that producing an additional 500 lb of paper once 10 tons have been produced would cost approximately $95,000.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To estimate the cost of producing an additional 500 lb of paper, we need to first convert 500 lb to tons.

1 lb = 0.0005 tons

So, 500 lb = 0.25 tons

Now, we can use the marginal cost formula:

MC = C'(t)

where MC is the marginal cost and C'(t) is the derivative of the cost function with respect to t.

We are given that C'(10) = 380, which means that the marginal cost of producing the 10th ton of paper is $380,000.

To estimate the cost of producing an additional 500 lb of paper once 10 tons have been produced, we need to find the marginal cost at t = 10.

Therefore, the estimated cost of producing an additional 500 lb of paper is:

MC(10) ≈ C'(10) ≈ $380,000 per ton

0.25 tons x $380,000 per ton = $95,000

Hence, it is estimated that producing an additional 500 lb of paper once 10 tons have been produced would cost approximately $95,000.

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The order of these numbers from least to greatest is 2.7 x 10³, 2.3 x 10¹¹, 6.5 x 10^12, 4.8 x 10^21

Index forms are simple described as the mathematical expressions or models used to represent numbers that are large or small in more appropriate ways.

They are also termed as scientific notations or standard forms.

Examples of index forms are;

2³ = 8

2 ² = 4

3 ³ = 27

From the information given, we have that;

2.7 x 10³

This is represented as; 2.7 × 10 × 10 × 10

Multiply the values

2700

2.3 x 10¹¹

This is represented as 2. 3 multiply by 10 in 11 times

6. 5× 10^12

This is represented by 6.5 multiplied by 10 in 12 places

4.8 × 10^21

This is represented by 4.8 multiplied by 10 in 21 places.

Hence, the exponent shows the greatest number

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After using the dimensions (length and width) of the pool to determine an expression that gives the perimeter of the rectangular pool is  P = 2 (5x- 4)

What is perimeter?

When defining a length in one dimension or a form in two dimensions, a perimeter is a closed path. The perimeter of a two-dimensional figure is the region that surrounds it. It provides the length of the shape, whether it is a circle, triangle, square, or rectangle. Area and perimeter are a 2D shape's two main properties.

The area of a given rectangular pool is

6x²−11x+3

⇒6x²− (9 + 2) x + 3

⇒ 6x²− 9x - 2x + 3

⇒ 3x(2x - 3) - 1 (2x - 3)

⇒ (3x - 1) (2x - 3)

An expression that gives the perimeter of the rectangular pool is,

P = 2 [ (3x - 1) + (2x - 3) ]

P = 2 [ 3x - 1 + 2x - 3 ]

P = 2 (5x - 4)

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The area of the rhombus is, A = (x² + 2x - 8) m².

A quadrilateral with all equal sides is a rhombus.

Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

A rhombus has 360° of interior angles total.

A rhombus's adjacent angles add up to 180°.

A rhombus's diagonals are perpendicular to one another and cut each other in half.

We also know That the area of a rhombus is, Half times the product of the two diagonals.

Given, A rhombus, with d₁ = (2x + 8) m and d₂ = (x - 2) m.

Therefore, The area of the rhombus is,

= (1/2)×(2x + 8)(x - 2) m².

= (1/2)(2x² - 4x + 8x - 16) m².

= (1/2)(2x² + 4x - 15) m².

= (x² + 2x - 8) m².

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