If the area is 384 square feet, then the length of the altitude is 36 feet, and the length of the base is 44 feet.
Let's start by using the formula for the area of a triangle in terms of its base and altitude:
[tex]Area = (1/2) * base * altitude[/tex]
We know that the area of the triangle is 384 square feet:
[tex]384 = (1/2) * base * altitude[/tex]
Next, we're given that the base is 8 feet longer than the altitude:
[tex]base = altitude + 8[/tex]
We can substitute this expression for the base into the area formula:
[tex]384 = (1/2) * (altitude + 8) * altitude[/tex]
Simplifying and multiplying out the right-hand side:
[tex]384 = (1/2) * (altitude^2 + 8altitude)\\768 = altitude^2 + 8altitude[/tex]
Now we have a quadratic equation in terms of the altitude. We can solve for the altitude by first rearranging the equation:
[tex]altitude^2 + 8altitude - 768 = 0[/tex]
Then, we can solve for the altitude using the quadratic formula:
[tex]altitude = (-8 ± sqrt(8^2 - 4(1)(-768))) / (2(1))\\altitude = (-8 ± sqrt(6400)) / 2\\altitude = (-8 ± 80) / 2[/tex]
We get two possible values for the altitude:
altitude = -44 or altitude = 36
Since the altitude of a triangle must be positive, we discard the negative solution and choose altitude = 36 feet.
We can then use the expression for the base in terms of the altitude to find the length of the base:
[tex]base = altitude + 8 = 36 + 8 = 44 feet[/tex]
Therefore, the length of the altitude is 36 feet and the length of the base is 44 feet.
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Correct question:
Find the lengths of the triangles altitude and base if its area is 384 squared feet. If its base is 8 feet longer than its altitude, find the length of the base and the altitude.
HELPPPPP!!!!!!!!!!!!!
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
Unit 1 is m feet, unit 2 is n feet unit 3 is k dollars per square feet, write an expression that could result in a final unit measure of dollars
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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The plane traveled 6 mores miles after passing the George Washington Bridge, descending at a 2° angle before landing in the Hudson River.
5a) At what altitude (in feet) did the airplane cross over the G.W. Bridge (e)?
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.
What is altitude?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.
What is trigonometry?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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A number divided by eight answers 27 remainders four whats the number
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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from his purchased bags, randy counted 120 red candies out of 500 total candies. using a 90% confidence interval for the population proportion, what are the lower and upper limits of the interval? answer choices are rounded to the thousandths place.
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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i need help on this question :(((
The Polynomials that are listed in the question are the options labelled;
B, C, E
What is a polynomial?
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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factor the polynomial to find the side length the polynomial is on the picture
Factorization of the given polynomial is: (x - 15)(x - 15).
The length of a side is: x = 15
How to factorize the polynomial?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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Write an equation to describe the relationship between t, the number of tickets, and c
, the total cost of tickets
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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Complete with he function table for each equation
The numbers to correctly complete the table based on the function is 2, 3, 4, 5.
What does the function of the table shows?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.
5 - 3 = 26 - 3 = 37 - 3 = 48 - 3 = 5Note: This question is incomplete; below I attach the missing section.
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Given the circle below with chords NO and PQ. Find the length of QR. Round to
the nearest tenth if necessary.
N
P
25
37
R
39
O
The length of QR, considering the intersecting chords in the circle, is given as follows:
QR = 26.4.
What is the chord of a circle?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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the perimeter of a rectangle is 175 feet. the short sides are each feet long, but the lengths of the long sides are . a) which equation represents this situation? correct b) write in terms of . incorrect
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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Factor the expression 12x²+18x-12
(URGENT)
Answer:
6(2x - 1)(x + 2).
Step-by-step explanation:
12x²+18x-12
= 6(2x^2 + 3x - 2)
= 6 (2x - 1)(x + 2).
Work out m and c for the line: y = 5 − x
Answer:
m = -1, c = 5
Step-by-step explanation:
Provided in the attachment.
Determine the total cost of the items if they were not sold to be as a combo if both are sold at R100 and when both sold at R100 you save R37
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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help
asap please need this
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
Translate the figure 5 units left and 5 units up. Plot all of the points of the translated figure. You may click a plotted point to delete it.
Answer:
Send a proper picture, the fifth point is not visible.
PLSSSS HELP IF YOU TURLY KNOW THISS
Given:-
[tex] \tt \: x - 5 = 2[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: x - 5 = 2[/tex][tex] \: [/tex]
[tex] \tt \: x = 2 + 5[/tex][tex] \: [/tex]
[tex] \boxed{ \tt{ \blue{ \: \: x = 7 \: \: }}}[/tex][tex] \: [/tex]
The value of x is 7 !
__________________
hope it helps ⸙
One of the advantages of buying a franchise is that the purchaser has access to a proven business system. T/F
True False
One of the advantages of buying a franchise is that the purchaser has access to a proven business system is true.
Explanation:
What is a franchise?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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A bank offers a CD that pays a simple interest rate of 11. 0%. How much must you put in this CD now in order to have $2500 for a home-entertainment center in 6 years. The present value that must be invested to get $2500 after 6 years at an interest rate of 11. 0% is $__?
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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Rewrite the following without an exponent.
(5/7)-1
The expression (5/7)^-1 can be written without an exponent as 8/5.
How can the exponent be written?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 figure is
The area of the parallelogram above is 490 metres squared.
How to find the area of a parallelogram?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
b = baseh = heightTherefore,
b = 49 metres
h = 10 metres
Therefore,
area of a parallelogram = 10 × 49
area of a parallelogram = 490 metres squared
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17) After 8 years at 4% simple interest per year, your savings account earns interest of $80.00. What is the principal
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.
The width of a rectangle is w + 4 and the length of the rectangle is 2w + 3. Which expression represents the area of the rectangle?
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
Find CY on the triangle Geometry
The value of CY is 4.4
What are similar triangles?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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Write an equation for line t. Show or explain how you determined your equation.
Enter your equation and your work or explanation in the box provided.
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]
7. What is the volume in centimeters of the rectangular prism bel
W
a. 12 cm³
b. 15 cm³
c. 20 cm³
d. 60 cm³
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!
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. 80
80
24
24
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
what conditions does the function f(x) have to meet in order to be able to use the integral test to verify convergence or divergence?
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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in bridge, south has 13 points and 3 clubs and bids 1 club. north responds with 3 clubs, what does that mean?
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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on a monte carlo roulette wheel, there are 37 slots: 18 red, 18 black, and 1 green. if you were to sit down and spin such a wheel 26 times, what would be the probability of duplicating the 26 straight blacks that occurred on august 18, 1913 at monte carlo?
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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