The star-spangled banner that flew over fort mchenry during the war of 1812 had a perimeter of 144 ft. Its length measured 12 ft more than its width. Use a system of equations to find the dimensions of this flag, which is displayed in the Smithsonian Institution's Museum of America History in washington, D. C

Answer:

D

Step-by-step explanation:

Answer:

x = 16

AB = 25

BC = 15

AC = 20

Step-by-step explanation:

I have marked the vertices to explain

There are three right triangles that can be seen in the picture

Δ ABC with legs BC and AC and hypotenuse AB

ΔACD with legs AD and CD and hypotenuse AC

ΔBCD with legs CD and BD and hypotenuse BC

We will using the Pythagorean formula in all three triangles:
hypotenuse² = sum of squares of legs

------------------------------------------------------------------------------------------

(1) Let's first find missing side BC

In right triangle ΔBCD ,
BC² = CD² + BD²

We have CD = 12, BD = 9
BC² = 12² + 9²
= 144 + 81

= 225

BC = √225 = 15

--------------------------------------------------------------------------------------------------
(2) Now let's focus on ΔABC

AB is the hypotenuse
AC and BC are the legs

AB² = AC² + BC²

or

AC² = AB² - BC²

Since AB = AD + BD = x + 9 and BC = 15

AC² = (x + 9)² - 15²

(x + 9)² = x² + 2 · 9 · x + 9² = x² + 18x + 81

15² = 225

AC² =  x² + 18x + 81 -225

AC² =  x² + 18x - 144                  (1)

-----------------------------------------------------------------------------------------------

(3) Now let's turn our attention to ΔACD with legs AD and CD  and hypotenuse AC

AC² = AD² + CD²

With AD = x and CD = 12,

AC² = x² + 12²

AC² = x² + 144                               (2)

------------------------------------------------------------------------------------------------

Equations (1) and (2) have the same left side, AC²
So the expressions on the right side must be equal

Therefore:

x² + 18x - 144     =  x² + 144

x² terms cancel out from left and right sides giving

18x - 144 =  144

Add 144 on both sides:
18x - 144 + 144 = 144 + 144

18x = 288

x = 288/18 = 16

Plugging this into equation (2) AC² = x² + 144 gives
AC² = 16² + 144

AC² = 256 + 144

AC² = 400

AC = √400

or

AC = 20

Since AB is the third unknown side and AB = x + 9 we get
AB = 16 + 9 = 25

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

The volume of a rectangular box is 109.86 cubic centimeters. The prism's breadth is 13.2 cm. The prism stands 4.1 cm tall.

The length of the rectangular prism is given as,

109.86 = L x 13.2 x 4.1

109.86 = 54.12L

L = 109.86 / 54.12

L = 2.03 cm

The length of the rectangular box will be 2.03 cm. Then the correct option is C.

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Answer:-15

Step-by-step explanation:

It is unlikely that the projected rebounds in 15 shots will actually happen.

Total shots fired equals 10.

To find that there were 15 shots total.

Consider S to be the likelihood that your team will rebound and miss a shot.

P(S) = Number of rebounds / Total Number of outcomes

P(S) = 7/15

P(S) = 0.46

Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.

Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.

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The complete question is-

During a basketball game, you record the number of rebounds from missed shots for each team.  How many rebounds should your team expect to have in 15 missed shots?

Picture for question is attached.

When the wet-bulb reading is 66°F, the relative humidity is 100%.

Based on the given information, the dry-bulb temperature and wet-bulb temperature are the same, which means the air is fully saturated with water vapor, and the relative humidity is 100%.

Relative humidity is the ratio of the amount of moisture in the air compared to the amount of moisture that the air can hold at a particular temperature. The wet-bulb temperature measures the lowest temperature that can be achieved by evaporating water into the air until it is fully saturated, while the dry-bulb temperature measures the actual temperature of the air.

When the wet-bulb and dry-bulb temperatures are the same, it means that the air is fully saturated and cannot hold any more moisture, resulting in a relative humidity of 100%.

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The minimum amount of money Camille could have is 0 dollars if she doesn't buy anything, and the maximum amount of money she could have is 166 dollars if she buys the maximum quantity of each item.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

We are given that;

The prices of different items at a garage sale: pants, shirts, shorts, and belts.  

Camille can buy up to 5 shirts.

Now,

If Camille buys 5 shirts, she would spend 5 * 6 = 30 dollars on shirts. Since she can buy up to 5 shirts, she may spend less than 30 dollars if she buys fewer shirts.

She can buy up to 10 pants, which would cost her 10 * 8 = 80 dollars.

She can buy up to 5 shorts, which would cost her 5 * 4 = 20 dollars.

She can buy up to 12 belts, which would cost her 12 * 3 = 36 dollars.

30 + 80 + 20 + 36 = 166 dollars

Therefore, by the  maxima and minima the answer will be 166 dollars if she buys the maximum quantity of each item.

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Answer:

  x = 1 or 5

Step-by-step explanation:

You want the value(s) of x that make 3x^2-x+1 and 2x^2+5x-4 have the same value.

Equating their values, we have ...

  3x² -x +1 = 2x² +5x -4

  x² -6x +5 = 0 . . . . . . . . . subtract (2x²+5x-4)

  (x -5)(x -1) = 0 . . . . . . . factor

  x = 1 or x = 5 . . . . . . values of x that make the factors zero

The two trinomials will have the same value for x=1 and for x=5.

__

Additional comment

The attached graph shows the points where the trinomials have the same value.

You need to buy 1 stamp that costs 12 cents, 3 stamps that cost 4 cents each, and 8 stamps that cost 1 cent each, to have a total of 40 stamps and spend exactly $1.

The reasoning is as follows:

If you were to buy only 1 cent stamps, you would need to purchase 100 of them to spend $1, which would exceed the required 40 stamps. On the other hand, if you were to buy only 12 cent stamps, you would only be able to purchase 8 stamps, which would fall short of the required 40 stamps. Therefore, a combination of all three types of stamps is necessary.

Starting with the most expensive stamp, one 12 cent stamp leaves you with 88 cents. Then, 3 stamps of 4 cents each will cost you 12 cents, leaving you with 76 cents. Finally, 8 stamps of 1 cent each will cost you 8 cents, which adds up to $1 and gives you a total of 40 stamps.

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Fοr the inequality the sοlutiοn set is x > -2.

In Algebra, an inequality is a mathematical statement that uses the inequality symbοl tο illustrate the relatiοnship between twο expressiοns. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the phrase οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa.

Tο sοlve the inequality, we can fοllοw these steps -

Subtract 3/2 frοm bοth sides -

-x/2 < 5/2 - 3/2

-x/2 < 2/2

-x/2 < 1

Multiply bοth sides by -2 (and flip the inequality since we're multiplying by a negative number) -

x > -2

The graph is drawn fοr the sοlutiοn.

The circle οn the left endpοint is nοt filled because the inequality is strict (i.e., nοt less than οr equal tο).

The arrοw οn the right endpοint is filled because the sοlutiοn set includes all values greater than -2.

Therefοre, the sοlutiοn set is all real numbers greater than -2, which can be represented οn a number line as a ray starting at -2 and mοving tοwards pοsitive infinity.

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The axis of symmetry of the parabola defined by the equation x=(1)/(36)y^(2)-(1)/(18)y+(37)/(36) is the vertical line x = (37)/(36). This is because the equation is in the form of y = ax^2 + bx + c, and the axis of symmetry is x = -b/2a. In this case, a = (1)/(36), b = -(1)/(18) and c = (37)/(36).

Therefore, the axis of symmetry is x = -(1)/(36) x -(1)/(18) = (37)/(36). This axis of symmetry divides the parabola into two symmetric halves and it is also the x-coordinate of the vertex of the parabola.

The vertex is the highest or lowest point of the parabola and it is the point of intersection between the axis of symmetry and the parabola. To find the y-coordinate of the vertex, we can substitute the x-coordinate of the vertex into the equation, which gives us y = (1)/(72) + (37)/(36) = (109)/(72). Therefore, the coordinate of the vertex is (37/36, 109/72).

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Therefore, the length of the other side of Ross's garden is approximately 13.7 feet.

A rectangle is a four-sided flat shape with four right angles (90-degree angles) between opposite sides. It is a type of quadrilateral, which means it has four sides. In a rectangle, the opposite sides are equal in length and parallel to each other, which makes it different from a square, where all sides are equal in length. The area of a rectangle can be found by multiplying the length by the width, and the perimeter can be found by adding up the lengths of all four sides.

Here,

Let the length of the other side of the garden be x feet.

Using the Pythagorean theorem, we have:

x² + 30² = 33²

Simplifying the equation:

x² = 33² - 30² = 1089 - 900

= 189

Taking the square root of both sides:

x = √189 ≈ 13.7 feet

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  All zeros of polynomial functions  -3/2 , 5i and -5i

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively. Some of the methods used to find the zeros of polynomial are grouping, factorization, and using algebraic expressions.

2x^3+3x^2+50x+75 equal to 0

2x^3+3x^2+50x+75 = 0

⇒ x^2 (2x + 3) + 25 (2x + 3) = 0

⇒ (2x + 3) (x^2 + 25 ) = =

If any individual factor on the left side of the equation is equal to  0, the entire expression will be equal to 0

2x + 3 = 0

x^2 + 25 = 0

so, x = -3/2  and x = 5i and -5i

The final solution is all the values that make  2x^3+3x^2+50x+75 = 0

x = -3/2 , 5i and -5i

Hence, all zeros of polynomial functions  -3/2 , 5i and -5i

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The values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.

To find two numbers a and b such that the system of linear equations is inconsistent, we need to make sure that the two equations have the same slope but different y-intercepts. This will result in the two equations being parallel to each other and never intersecting, making the system inconsistent.

The first equation is: ax - 3y = 2. We can rearrange this equation to solve for y and find the slope:

3y = ax - 2
y = (a/3)x - (2/3)

The slope of this equation is a/3.

The second equation is: -4x + 5y = b. We can rearrange this equation to solve for y and find the slope:

5y = 4x + b
y = (4/5)x + (b/5)

The slope of this equation is 4/5.

For the system to be inconsistent, the slopes need to be equal. So we can set a/3 = 4/5 and solve for a:

a/3 = 4/5
a = 12/5

Now we need to find a value for b that will result in a different y-intercept. We can do this by plugging in the value of a into one of the equations and choosing a different value for the y-intercept:

y = (12/5)(1/3)x - (2/3)
y = 4x - (2/3)

If we choose a different value for the y-intercept, such as -1, we can solve for b:

y = 4x - 1
5y = 20x - 5
b = 20x - 5y

So the values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.

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The answer of set U by listing its elements is {-3, -2, -1}

To rewrite the set U by listing its elements, we need to identify the integers that fall within the given range of -3<=z<=-1.

The appropriate set notation for listing the elements of a set is {element1, element2, element3, ...}.

So, the integers that fall within the given range are -3, -2, and -1.

Therefore, we can rewrite the set U as:

U = {-3, -2, -1}

This is the answer in the appropriate set notation, listing the elements of the set U.

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Answer: See the Picture.

Step-by-step explanation:

Please follow this account

Answer:

y = -  125/18

Step-by-step explanation:

okay so here what i got when i was doing the equation

5 ( y + 25) = - 13y

5 y + 125 = - 13y

then you subtract 125 from both sides

subtract the numbers

and my solution was y = - 125 / 18 trust me!

Hope that helped

The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

The given data set is,

14, 13, 13.5, 16, 14, 15.5, 14.5.

Hence, We get;

Order of data is,

⇒ 13, 13.5, 14, 14, 14.5, 15.5, 16.

Here, minimum is 13

Maximum is 16

Median is 14

Lower quartile range(Q1) is 13.5

Upper quartile range(Q3) is 15.5

Therefore, The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

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The polynomial g(x)=x^(3)+3x^(2)-x-3 is a cubic polynomial with 4 terms.

To prove its degree using successive differences, we first need to find the successive differences of the polynomial's y-values for consecutive x-values. We can do this by substituting x-values into the polynomial and finding the differences between the resulting y-values.

For x=0, g(x)=0^(3)+3(0^(2))-0-3=-3
For x=1, g(x)=1^(3)+3(1^(2))-1-3=0
For x=2, g(x)=2^(3)+3(2^(2))-2-3=11
For x=3, g(x)=3^(3)+3(3^(2))-3-3=30

The first successive difference is 0-(-3)=3
The second successive difference is 11-0=11
The third successive difference is 30-11=19

Since the successive differences are not constant, we need to find the successive differences of the successive differences.

The first successive difference of the successive differences is 11-3=8
The second successive difference of the successive differences is 19-11=8

Since the successive differences of the successive differences are constant, the degree of the polynomial is 3, which is one less than the number of times we had to find successive differences. This confirms that g(x)=x^(3)+3x^(2)-x-3 is a cubic polynomial.

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The value of x for the given equations are a. 10, b. -7, c = -8, d. 5.

Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics. One or more variables are identified as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root.

Given that,

2(x-3) = 14

2x - 6 = 14

2x = 20

x = 10

b. -5(x - 1) = 40

-5x + 5 = 40

-5x = 35

x = -7

c. 12(x + 10) = 24

12x + 120 = 24

12x = 24 - 120

x = -8

d. (x + 6) = 11

x = 11 - 6

x = 5

Hence, the value of x for the given equations are a. 10, b. -7, c = -8, d. 5.

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Maria has $22,000 invested in account A and $8,000 invested in account B.

Let's begin by setting up a system of equations to solve for the amount Maria has invested in each account. Let x be the amount invested in account A and y be the amount invested in account B. Since Maria has a total of $30,000 invested in both accounts, we can write the first equation as:

x + y = 30,000

Next, we can write an equation to represent the total annual interest earned from both accounts:

0.045x + 0.038y = 1,294

Now, we can use the substitution method to solve for x and y. We'll rearrange the first equation to solve for x:

x = 30,000 - y

Then, we'll substitute this value of x into the second equation:

0.045(30,000 - y) + 0.038y = 1,294

Simplifying the equation gives:

1,350 - 0.045y + 0.038y = 1,294

Combining like terms and isolating y gives:

0.007y = 56

y = 8,000

Now, we can substitute this value of y back into the first equation to solve for x:

x = 30,000 - 8,000

x = 22,000

So, Maria has $22,000 invested in account A and $8,000 invested in account B.

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The multiplication equation that can be used to determine the number of people who contributed to the cost of the season ticket package is: $745 = $186.25 x 4.

To write a multiplication equation that can be used to determine the number of people who contributed to the cost of the season ticket package, we can use the following equation:

Total Cost = Cost per Person x Number of People

In this case, the total cost is $745 and the cost per person is $186.25. We can plug these values into the equation to get:

$745 = $186.25 x Number of People

To solve for the number of people, we can divide both sides of the equation by $186.25:

Number of People = $745 / $186.25

Number of People = 4

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Therefore , the solution of the given problem of unitary method comes out to be Browns books are less expensive than Noble books at $5.50 each.

Take the lengths of this minute subsection and split the sum by two to complete a task using a unitary variable technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality. There are unanswered questions and changes (mathematics, algebra).

Here,

We must ascertain the price per book for each retailer in order to evaluate the costs of Browns and Noble books.

Two of Brown's books cost $11, so each volume costs $5.50 (11/2 = 5.50).

Five novels from Barnes & Noble cost $31, making each book $6.20 (31/5 = 6.20).

Browns books are less expensive than Noble books, which cost $6.20 per volume, at $5.50 each.

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1. 286

2. False

3. 84

1. The number of non-negative integer solutions of x1​+x2​+x3​+x4​=10 is 286.

2. The answer to the above question is not the same as the number of non-negative integer solutions of x1​+x2​+x3​≤10. The reason is that the first equation has 4 variables, while the second equation has only 3 variables.

Therefore, the number of solutions will be different.

3. The number of positive integer solutions of x1​+x2​+x3​+x4​=10 is 84.

1. To find the number of non-negative integer solutions of x1​+x2​+x3​+x4​=10, we can use the formula: C(n+k-1, k-1) = C(10+4-1, 4-1) = C(13, 3) = 286

Therefore, there are 286 non-negative integer solutions of x1​+x2​+x3​+x4​=10.

2. The answer to the above question is not the same as the number of non-negative integer solutions of x1​+x2​+x3​≤10 because the first equation has 4 variables, while the second equation has only 3 variables.

Therefore, the number of solutions will be different.

3. To find the number of positive integer solutions of x1​+x2​+x3​+x4​=10, we can use the formula: C(n-1, k-1) = C(10-1, 4-1) = C(9, 3) = 84

Therefore, there are 84 positive integer solutions of x1​+x2​+x3​+x4​=10.

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To find the altitude of the spherical segment, we need to use the formula for the total surface area of a spherical segment, which is given by:
A = 2πR(r + h), where R is the radius of the spherical surface, r is the radius of the base, and h is the height of the segment.

We are given that the total surface area of the spherical segment is 7 times greater than the surface area of the sphere inscribed in it, which means that:
7(4πR^2) = 2πR(r + h)
Simplifying this equation gives us:
14R = r + h

We are also given that the radius of the spherical surface is equal to R, which means that r = R. Substituting this into the equation gives us:
14R = R + h
Solving for h, we get:
h = 14R - R
h = 13R
Therefore, the altitude of the spherical segment is 13R.

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Assuming the lines, which appear to be diameters, are actual diameters. The value of x is 10.63.

Any straight line that connects two points on a circle's circumference and goes through the circle's center. The length of such a line in geometry. The greatest separation possible between any two points in a metric space (geometry).

Exterior angles are 128, 32, and 45

Interior angles are 11x+4 and 85

Exterior angles = interior angles

128 + 32 + 45 = 11x+4 + 85

205 = 11x + 88

11x = 205 - 88 = 117

x = 117/11

x = 10.63

Therefore, the value of x is 10.63.

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The graph of the function y=3x+1 is shown.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

We are given that;

The function is y=3x+1

Now,

When x = 0, y = 3(0) + 1 = 1, so one point on the function is (0, 1).

When x = 1, y = 3(1) + 1 = 4, so another point on the function is (1, 4).

When x = -1, y = 3(-1) + 1 = -2, so a third point on the function is (-1, -2).

Therefore, the graph will be given the attachment

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It will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.

We can use the following proportion to solve the problem:

1760 liters / 5 days = 3872 liters / x days

Where x is the number of days it will take to sell 3872 liters of fuel.

We can use the unitary method to solve this problem.

Let's start by finding out how much fuel is sold in one day. To do this, we need to divide the total amount of fuel sold (1760 liters) by the number of days it was sold for (5 days):

1760 liters ÷ 5 days = 352 liters per day

Now we can use this rate to find out how many days it will take to sell 3872 liters of fuel:

3872 liters ÷ 352 liters per day = 11 days (rounded to the nearest whole number)

Therefore, it will take 11 days to sell 3872 liters of fuel at the same rate as 1760 liters sold in 5 days.

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Answer:

x=55°, y=35°

Step-by-step explanation:

The angle between x and 35° is a right angle.

A right angle equals 90°.

Therefore. 90=x+35

x=55°

Now that x is known, we can find y.

The angle made between the x and y axis is 90°.

Therefore, 90=x+y

90=55+y

y=35°

Answer:

X=55° and Y=35° ................................