Find the lengths of the triangles altitude and base if its area is 384 squared feet

Factorization of the given polynomial is: (x - 15)(x - 15).

The length of a side is: x = 15

In the case of polynomials in mathematics, the factors of the polynomials are the polynomials which are multiplied to produce the original polynomial. For example, the factors of x² + 5x + 6 is (x + 2) (x + 3).

When we multiply both x + 2 and x  +3, then we will see that the original polynomial is generated.

We are given the polynomial as:

A = x² - 30x + 225

This can be broken down into:

A = x² - 15x - 15x + 225

A = x(x - 15) - 15(x - 15)

A = (x - 15)(x - 15)

Thus:

x = 15

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The total cost of the items if they were not sold as a combo is R137.

Let's assume that the individual prices of the two items are X and Y. Here we have to use the concept of algebraic equation. We have two unknowns (X and Y), and we use the information given about their combined cost and the savings made when sold as a combo to form an equation in terms of X and Y

When the items are sold individually, the total cost would be X + Y.

When the items are sold together as a combo, the cost is R100, and this saves R37 compared to the individual prices. This means:

X + Y - 37 = 100

Simplifying the above equation, we get:

X + Y = 137

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Answer:

A= 2w^2 + 11w +12

Step-by-step explanation:

(w + 4)(2w + 3) = l x b = A

2w^2 + 3w +8w +12 = A

A= 2w^2 + 11w +12

The value of CY is 4.4

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

Triangle ABC is similar to AXY

therefore,

represent CY is by x

9/9+4 = 10/(10+x)

= 9/13 = 10/10+x

= 13× 10 = 9( 10+x)

130 = 90 + 9x

9x = 130-90

9x = 40

x = 40/9

x = 4.44

therefore the value of CY is 4.44

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The expression (5/7)^-1  can be written without an exponent as 8/5.

Exponents have a number of important properties, such as the product rule (a^m × a^n = a^(m+n)) and the power rule ((a^m)^n = a^(m*n)). They are used in a wide range of mathematical contexts, including algebra, calculus, and geometry.

Given that (5/8)^-1, then we can deduced that the  negative exponent is the samething as putting it in the denominator, which can be exprtessed as;

=[1/ (5/8)]

=[1 ÷ (5/8)]

[1 * 8/5]

=8/5

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The area of the parallelogram above is 490 metres squared.

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

The area of a parallelogram can be calculated as follows:

area of a parallelogram = bh

where

Therefore,

b = 49 metres

h = 10 metres

Therefore,

area of a parallelogram = 10 × 49

area of a parallelogram = 490 metres squared

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The relationship between t, the number of tickets, and c, the total cost of tickets is: c = 55t

Relation between two variables, i.e, total cost and number of tickets:

The statistical relationship between two variables is called their correlation. The correlation can be positive, which means that the two variables move in the same direction, or negative, which means that when the value of one variable increases, the value of the other variable decreases.

Based n the Question:

Since there is no processing fee and the ticket price remains the same, we know that the fee will be proportional to the number of tickets purchased. The general form of the equation expressing the proportional relationship between the cost (c) and the number of tickets (t) is:

c = kt

where k is the constant of proportionality (the cost per ticket).

We can find k by using any of the data points given in the table. Using the first point, we have :

110 = k·2

Dividing the equation by 2:

110/2 = k = 55

Then using this value for k, the desired equation can be written:

c = 55t

Complete Question:

Total cost (in dollars) Number of concert tickets. the total costs in dollars are 110 275 440. the number in concert tickets are 2, 5, 8 Write an equation to describe the relationship between the total cost in dollars (c), and the number of tickets purchased (t),

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If on a monte carlo roulette wheel, there are 37 slots: 18 red, 18 black, and 1 green, the probability of getting 26 straight blacks is approximately 3.143 x 10^-16.

The probability of duplicating the exact sequence of 26 straight blacks that occurred on August 18, 1913, is extremely low. Each spin of the wheel is an independent event, so the probability of getting a black on any given spin is always 18/37, regardless of what happened on previous spins.

To calculate the probability of getting 26 straight blacks, we can use the formula for the probability of a sequence of independent events, which is the product of the probabilities of each event. Therefore, the probability of getting 26 straight blacks is (18/37)^26, which is an extremely small number, approximately 3.143 x 10^-16.

Therefore, the probability of duplicating the 26 straight blacks that occurred on August 18, 1913, is so low that it's effectively impossible. It's important to note that each spin of the wheel is independent, so even if the wheel had produced 25 straight blacks, the probability of the next spin being black would still be 18/37.

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Answer:

m = -1, c = 5

Step-by-step explanation:

Provided in the attachment.

The altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.

Altitude refers to the height of an object or location above a specific reference point, usually the Earth's sea level. In aviation, altitude is often used to describe the height of an aircraft above sea level, and is measured in feet or meters.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which are functions of an angle, and are used to relate the angles and sides of a right triangle.

In the given question,

To solve this problem, we need to use trigonometry and the fact that the plane descended at a 2° angle. Let's assume that the altitude of the plane at the George Washington Bridge is h feet.

Using trigonometry, we know that the tangent of the angle of descent is equal to the difference in altitude divided by the horizontal distance traveled. In this case, we have:

tan(2°) = (h - e) / 6

To solve for h, we need to isolate it on one side of the equation. Multiplying both sides by 6, we get:

6 tan(2°) = h - e

Adding e to both sides, we get:

h = 6 tan(2°) + e

We can use a calculator to find the tangent of 2°, which is approximately 0.03492. Substituting this value and the given distance of 6 miles into the equation, we get:

h = 6(0.03492) + e

h = 0.2095 + e

Therefore, the altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.

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The conditions does the function f(x) to meet in order to be able to use the integral test to verify convergence or divergence is

1) f(x) must be continuous, positive, and decreasing for all x greater than some fixed value N.

2) The series to be tested must have non-negative terms.

3) The integral of f(x) from N to infinity must converge or diverge.

To use the integral test to verify the convergence or divergence of an infinite series, the following conditions must be met for the function f(x)

1) f(x) must be continuous, positive, and decreasing for all x greater than some fixed value N.

2) The series to be tested must have non-negative terms.

3) The integral of f(x) from N to infinity must converge or diverge.

If these conditions are met, then the integral test can be used to determine whether the series converges or diverges. Specifically, if the integral of f(x) converges, then the series converges. On the other hand, if the integral of f(x) diverges, then the series also diverges.

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The numbers to correctly complete the table based on the function is 2, 3, 4, 5.

The function x-3 as any other function shows a pattern. In this case, it shows the way the value in column f(x) changes depending on the value of x. Here are some examples:

If the value of x is 34 =  34 - 3 = 31

If the value of x is 12 = 12 - 3 = 9

Based on this principle, the correct values to complete the table presented are 2, 3, 4, 5.

Note: This question is incomplete; below I attach the missing section.

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Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

The value of x is 7 !

__________________

hope it helps ⸙

The Polynomials that are listed in the question are the options labelled;

B, C, E

A polynomial is a mathematical expression that consists of variables, coefficients, and exponents.

The variables represent unknown values, while the coefficients are constants that multiply the variables or their exponents. The exponents indicate the power to which the variables are raised.

Polynomials can be added, subtracted, multiplied, and divided to create more complex expressions, and they are used in a wide range of mathematical applications, including algebra, calculus, and geometry.

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this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.

a) The equation that represents this situation is:

2x + 2y = 175

where x is the length of the short sides (in feet) and y is the length of the long sides (in feet).

b) The equation in terms of y is:

2(6) + 2y = 175

which simplifies to:

12 + 2y = 175

2y = 163

y = 81.5

However, this is incorrect because the length of the long sides cannot be expressed in terms of just y. We need additional information about the dimensions of the rectangle to determine the length of the long sides.

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One of the advantages of buying a franchise is that the purchaser has access to a proven business system is true.

Explanation:

A franchise is a company's business model and brand name that it allows to be used by third parties in exchange for a fee. The individual or entity who pays the fee is referred to as the franchisee. The purchaser of the franchise receives a licence to use the franchisor's trade name, business systems, operational procedures, goods, and other intellectual property, among other things. The franchisee is also required to follow certain operational protocols and sales/marketing strategies, as well as purchase products from the franchisor. For various reasons, a franchise is often viewed as a low-risk business opportunity for a potential business owner. Among the numerous advantages of buying a franchise, the ability to access a proven business system is one of the most important.

                         A proven business system is a set of guidelines, operational procedures, marketing and sales strategies, and other tools that have been shown to be effective for a particular franchise. By using a proven business system, the franchisee is less likely to fail and more likely to succeed. As a result, a franchisee's revenue stream will be more stable, allowing for long-term growth and success.

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Answer:

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

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

[tex]2x - 3y = - 3[/tex]

Step-by-step explanation:

[tex]m = \frac{ - 5 - 3}{ - 9 - 3} = \frac{ - 8}{ - 12} = \frac{2}{3} [/tex]

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

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

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

[tex]3y = 2x + 3[/tex]

[tex] - 2x + 3y = 3[/tex]

[tex]2x - 3y = - 3[/tex]

As per the given triangle, the scale factor is 24/5

To identify the scale factor, we can choose two corresponding sides of the triangles and set up a proportion. Let's choose the legs of the triangles. We know that the length of the left leg is 5, and the length of the right leg is 25/4. Therefore, we can write:

5/x = 25/4/12

Here, x represents the length of the corresponding leg of the right triangle. We can simplify this proportion by cross-multiplying:

5 x 12 = (25/4) x (x)

Multiplying both sides by 4/25, we get:

(4/25) x 5 x 12 = x

Simplifying, we get:

x = 24/5

Therefore, the scale factor is 24/5. This means that if we multiply the lengths of any side of the left triangle by 24/5, we will get the corresponding length of the right triangle.

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Complete Question:

The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a fraction in simplest form.

5 and 12, 25/4 and 15

Answer:

Send a proper picture, the fifth point is not visible.

The length of QR, considering the intersecting chords in the circle, is given as follows:

QR = 26.4.

A chord of a circle is a straight line segment that connects two points on the circle. Specifically, it is a line segment whose endpoints are on the circle. A chord is often denoted by drawing a line segment between the two endpoints, with the segment passing through the interior of the circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

The product to obtain the length QR is given as follows:

37QR = 25 x 39

Then the length QR is given as follows:

QR = 25 x 39/37

QR = 26.4.

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Answer:

Step-by-step

To make 100 to 250, you need to multiply 100 by 2.5 to make 250. In the similar way you need to multiply 80 by 2.5 which equals 200 which is the answer

The expression that could result in a final unit measure of dollars is given by (mnk²) dollars.

To write an expression that could result in a final unit measure of dollars, we need to consider the units given.

We have three units, i.e., m feet, n feet, and k dollars per square foot.

To convert these units to dollars, we need to multiply the given units with appropriate conversion factors.

The conversion factor for the given units is as follows:

Unit 1: 1 foot = k dollars (Conversion factor)

Unit 2: 1 foot = k dollars (Conversion factor)

Unit 3: 1 square foot = 1 x k dollars = k dollars (Conversion factor)

Now, let us write the expression that results in a final unit measure of dollars.

The expression should be written in HTML format.

Let us begin: Final Unit Measure = (Unit 1) x (Unit 2) x (Unit 3)

Final Unit Measure = (m feet) x (n feet) x (k dollars per square foot)

Final Unit Measure = m x k dollars x n x k dollars per square foot

Final Unit Measure = (m x k x n x k) dollars

Final Unit Measure = (mnk²) dollars.

Thus, the expression that could result in a final unit measure of dollars is given by (mnk²) dollars.

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As per the query, we have to find a number which is divided by 8 that answers 27, i.e., quotient is 27, and remainder is 4. The number is 220.

In this case, we used it to find the number that was divided by 8 and gave a quotient of 27 and a remainder of 4. As we know the rule:

Dividend = Divisor × Quotient + Remainder

x = 8 × 27 + 4 x = 216 + 4 x = 220.

Hence, the number is 220.

The formula I used is called the division algorithm. It’s a way to divide two numbers and get a quotient and remainder. We can use this formula to solve other division problems with remainders as well.

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Answer:

15 degrees,45 degrees, 120 degrees respectively

Step-by-step explanation: TO begin with total=1+3+8=12

1:3:8=12

1/12*180=15

3/12*180=45

8/12*180=120

The present value that must be invested to get $2500 after 6 years at a simple interest rate of 11.0% is $1509.64.

In this case, we know the final amount that we want to have after 6 years, which is $2500. We also know the interest rate, which is 11.0%. What we need to find is the principal amount, which is the present value that we must invest now to achieve the desired future value.

Using the formula for simple interest, we can rearrange it to solve for the principal:

Principal = Simple Interest / (Rate x Time)

We know that the simple interest is the difference between the final amount and the principal amount. Therefore, we can substitute the values into the formula:

$2500 - Principal = (Principal x 0.11 x 6)

Simplifying the equation, we get:

$2500 = Principal + (0.66 x Principal)

$2500 = 1.66 x Principal

Dividing both sides by 1.66, we get:

Principal = $1509.64

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Answer:

The volume of a rectangular prism is given by the formula V = l x w x h, where l is the length, w is the width, and h is the height.

The rectangular prism in question has the following dimensions:

Length (l) = 3 cm

Width (w) = 5 cm

Height (h) = 4 cm

Using the formula for volume, we get:

V = l x w x h

= 3 cm x 5 cm x 4 cm

= 60 cm³

Therefore, the volume of the rectangular prism is 60 cm³.

The answer is (d) 60 cm³.

I Hope This Helps!

In the bridge, when the south has 13 points and 3 clubs and bids 1 club, the north responding with 3 clubs means that the North has a strong hand with six or more clubs.

In the game of bridge, bidding is a method of indicating the strength of a player's hand, which is the number of tricks that they believe they can win if they become the declarer. Every player has to declare their abilities based on the bid of the previous player when it is their turn to bid.

The bidding starts with the dealer and proceeds in a clockwise direction. The players can either make a bid or pass. The following are the four basic bids in Bridge:

When South has 13 points and 3 clubs, he makes a 1 Club bid. This bid can be interpreted as follows:

South has a strong hand with five or more clubs and 13 to 21 high card points. When South bids 1 Club, he implies that he has a balanced hand, which means that he has four cards in each suit, or an unbalanced hand, which means that he has a long suit, a singleton, or a void in some other suit.

When North responds with 3 Clubs, it means that he has a strong hand with six or more clubs. North has understood that South has five or more clubs and therefore responds with the number of clubs that he has in his hand to show that he is strong enough to support South's suit. Thus, North is trying to force South to become the declarer in clubs.

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Answer:

Step-by-step explanation:

We can use the simple interest formula to solve this problem. The formula is:

I = P * r * t

Where:

I = Interest earned

P = Principal (initial amount of money)

r = Interest rate per year (as a decimal)

t = Time (in years)

From the problem statement, we know that:

I = $80.00

r = 0.04 (4% as a decimal)

t = 8 years

Substituting these values into the formula, we get:

$80.00 = P * 0.04 * 8

Simplifying:

$80.00 = 0.32P

Dividing both sides by 0.32, we get:

P = $250.00

Therefore, the principal is $250.00.

Answer:

6(2x - 1)(x + 2).

Step-by-step explanation:

12x²+18x-12

= 6(2x^2 + 3x - 2)

= 6 (2x - 1)(x + 2).

As per the concept of confidence interval, we can be 90% confident that the true proportion of red candies in all the bags is between 0.195 and 0.285.

To do this, we first need to determine the level of confidence we want for our interval.

Next, we use a formula to calculate the confidence interval. The formula for a confidence interval for a population proportion is:

p ± z x √(p(1-p)/n)

where p is the sample proportion (in this case, 120/500 = 0.24), z* is the z-score that corresponds to the desired level of confidence (for a 90% confidence interval, z* = 1.645), and n is the sample size (in this case, 500).

Substituting the values into the formula, we get:

0.24 ± 1.645 x √(0.24(1-0.24)/500)

Simplifying, we get:

0.24 ± 0.045

Therefore, the lower limit of the confidence interval is 0.195 (0.24 - 0.045), and the upper limit is 0.285 (0.24 + 0.045).

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