19. A ball is dropped from a height of 30 feet. At the same time, a ball is thrown straight into the air from a height of 5 feet with an initial velocity of 20 feet per second. The polynomials -16t2 + 30 and -16t2 + 20t + 5 represent the heights (in feet) of the balls after t seconds.

a. Write a polynomial that represents the distance between the heights of the balls after t seconds.

b. Interpret any coefficients and constants of the polynomial in part (a.)​

Answer:

The answer to your problem is, $0.60

Step-by-step explanation:

1 banana and 1 orange = 1.20.

We divide next:

1.20 / 2 = 0.60.

We know that because in the question it says one banana and one orange is 1.20. Next we divide because two items are sharing the same number.

1.20 / 2 = ? ( ? = 0.60 or 0.6 )

Thus the answer to our problem is, $0.60

Answer: Y=-3X+5

Step-by-step explanation:

Slope intercept form is Y=mx+b where m is slope and b is slope intercept to graph you can use desmos which is a free graphing calculator just punch in the equation exactly as I gave it. since m is slope it is -3 and b is y intercept so 5 so Y=-3x+5

Answer:

y = -3x + 5

Step-by-step explanation:

y = mx + b  The m is the slope and the b is the y intercept.  Substitute in the slope and the y-intercept

y = -3x + 5

First, graph the y-intercept.  That will be at the point (0, 5).  From that point, go down 3 units and then go one unit right.  You will be back on the line.  That is the slope.

Helping in the name of Jesus.

Answer: The probability of choosing a sophomore on the first draw is 125/512. Since the selection is random and without replacement, the probability of choosing another sophomore on the second draw is 124/511. Therefore, the probability of choosing two sophomores in a row is:

(125/512) x (124/511) = 0.0603 or approximately 0.06 (rounded to two decimal places).

Step-by-step explanation:

The value of f(3) using synthetic division is 72.

To find f(3) using synthetic division, we need to divide the polynomial f(v) by the factor (v - 3). This will give us the quotient and the remainder, which will help us find the value of f(3).

Write the coefficients of the polynomial in a row: 12 -40 4 17 21

Write the value of the factor we are dividing by to the left of the row: 3 | 12 -40 4 17 21

Bring down the first coefficient: 3 | 12 -40 4 17 21
          ------------------
             12

Multiply the first coefficient by the factor and write the result under the second coefficient: 3 | 12 -40 4 17 21
          ------------------
             12  36

Add the second coefficient and the result from step 4: 3 | 12 -40 4 17 21
          ------------------
             12  -4

Repeat steps 4 and 5 for the remaining coefficients: 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51

The last number in the bottom row is the remainder. This is the value of f(3): 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51  72

So, f(3) = 72.

Therefore, the value of f(3) using synthetic division is 72.

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The area that can be watered if the length of the pipe is 400, 700, or 1,100 inches long are:

Where L = 400, A [tex]\approx[/tex] 12.82

Where L = 700 A [tex]\approx[/tex] 44.43

Where L = 1,100 A [tex]\approx[/tex]  86.13

The length of the pipe is given by the function:

L =  111.25√A.

Where a = (L/111.25)²

Thus, for L = 400inches

A =  (400/111.24)²

(400/111.24)² = (400²)/(111.24)²

(400²)/(111.24)² = (160000)/(12369.5776)
Divide 160000 by 12369.5776 to get:

(160000)/(12369.5776) = 12.820128200735

Therefore, A = 12.820128200735,

A [tex]\approx[/tex] 12.82

Thus:

Where L = 700;
A = 44.434243
A [tex]\approx[/tex] 44.43

Where L = 1,100
A = 86.129479

A [tex]\approx[/tex] 86.13

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The equation which represents the total length of the siding is given by A , where A = 50 x 4 = 200 meters

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total length of the siding be represented as A

Now , the value of A is

Let the number of pieces be n = 48 pieces

Let the length of each piece be l = 3.7 meters

Now , total length of the siding A = number of pieces x length of each piece

On simplifying the equations , we get

The total length of siding A = 48 x 3.7 = 177.6 meters

Now , n ≈ 50 pieces

l ≈ 4 meters

So , total length of siding A = 50 x 4 = 200 meters

Hence , the equation is A = 50 x 4 = 200 meters

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The inequality (x + 2)/(x - 7)>0 can be solved algebraically by first subtracting 2 from both sides. This results in the inequality (x - 7) > 2. By dividing both sides by (x-7), the inequality can be simplified to 1>2/x-7. This simplifies further to -7>2/x, or x>-7/2. Therefore, the solution to the inequality is x>-7/2.

In plain terms, this means that a value of x must be greater than -7/2 in order for the inequality to be true. This implies that the value of x must be a number greater than -3.5, since -7/2 is the same as -3.5. Thus, if x is any number greater than -3.5, then the inequality (x + 2)/(x - 7) > 0 will be satisfied.

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Y= 3.2

When \( y \) varies directly as \( x \) and inversely as \( z \), the equation is given by:
\( y = \frac{kx}{z} \)

Where \( k \) is a constant.

Substituting the given values of \( x \), \( y \) and \( z \), we get:
\( 24 = \frac{k(120)}{16} \)

Solving for \( k \):
\( k = \frac{24*16}{120} = 4.8 \)

Substituting the values of \( k \), \( x \) and \( z \) into the equation, we get:
\( y = \frac{(4.8)*4}{15} \)

Therefore, the value of \( y \) when \( x=4 \) and \( z=15 \) is \( 3.2 \).

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The equation of line is y = -4x - 3 and the slope is m = -4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -2 , 5 )

Let the second point be Q ( -1 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 5 ) / ( -1 - ( -2 ) )

On simplifying , we get

Slope m = ( -4 ) / 1

Slope m = -4

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 5 = -4 ( x - ( -2 ) )

y - 5 = -4 ( x + 2 )

y - 5 = -4x - 8

Adding 5 on both sides , we get

y = -4x - 3

Hence , the equation of line is y = -4x - 3

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Answer:

Part A: To find the expression for the length of the rectangular space, we can use the formula for the area of a rectangle, which is length multiplied by width. We have the expression for the area as 8x² - 12x, and the expression for the width as 4x. So, we can write:

Area = Length × Width

8x² - 12x = Length × 4x

Simplifying the right side by multiplying, we get:

8x² - 12x = 4x × Length

2x² - 3x = Length

Therefore, the expression for the length of the rectangular space is 2x² - 3x.

Part B: To prove that the expression for the length from Part A is correct, we can multiply it by the expression for the width and simplify:

Length × Width = (2x² - 3x) × (4x)

= 8x³ - 12x²

= 4x(2x² - 3x)

= 4x(2x(x - 3))

This is in fact the same as the expression for the area of the rectangular space, 8x² - 12x, in standard form.

Answer:

Rational numbers are those that can be expressed as a ratio of two integers whereas irrational numbers are those which cannot be expressed as a ratio of two integers.

Rational numbers can be written in the form of a fraction whereas irrational numbers cannot be written in the form of fractions.

Rational numbers comprise of those perfect squares whereas irrational numbers comprise of surds.

The two values of x that are roots of the given equation are approximately 3.618 and 1.382.

What is quadratic equation ?

Quadratic equations are used to model a wide range of phenomena in many areas of science and engineering, including physics, biology, economics, and finance. They are also used extensively in mathematics for their elegant properties and applications in algebra, geometry, and calculus.

We start with the quadratic equation:

[tex]$x^2 - 5x + 5 = 0$[/tex]

To find the roots of this equation, we use the quadratic formula:

[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$[/tex]

where [tex]$a$, $b$,[/tex] and [tex]$c$[/tex] are the coefficients of the quadratic equation.

In this case, we have [tex]a = 1$, $b = -5$, and $c = 5$.[/tex] Substituting these values into the quadratic formula, we get:

[tex]$x = \frac{5 \pm \sqrt{(-5)^2 - 4(1)(5)}}{2(1)}$[/tex]

Simplifying the expression under the square root, we get:

[tex]$x = \frac{5 \pm \sqrt{5}}{2}$[/tex]

Therefore, the two roots of the equation are:

[tex]$x = \frac{5 + \sqrt{5}}{2} \approx 3.618$[/tex]

[tex]$x = \frac{5 - \sqrt{5}}{2} \approx 1.382$[/tex]

Hence, the solutions to the equation [tex]$x^2 - 5x + 5 = 0$[/tex] are approximately 3.618 and 1.382.

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The perimeter of kite FGHJ is 39. Rounded to 2 decimal places, the answer is 39.00.

What is the perimeter?

The perimeter is the total distance around the boundary of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape.

First, we need to find the length of the other two sides of the kite:

Since FH = 17 and FT = 10, we can find the length of TH by subtracting: TH = FH - FT = 17 - 10 = 7.

Similarly, since GJ = 10 and TJ = 5, we can find the length of GT by subtracting: GT = GJ - TJ = 10 - 5 = 5.

Now we can find the perimeter of the kite by adding up the lengths of all four sides:

Perimeter = FH + TH + GJ + GT

Perimeter = 17 + 7 + 10 + 5

Perimeter = 39

Therefore, the perimeter of kite FGHJ is 39. Rounded to 2 decimal places, the answer is 39.00.

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Complete question:

What is the 'perimeter of kite FGHJ? Round to 2 decimal places?

\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)

Adding/subtracting radical expressions and simplifying can be done as follows:

(a) \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}} \)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{112 x^{3} y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-3 \sqrt{28 x^{3} \cdot 4 y^{2}}\) = \( -2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\)

\(-2 y \sqrt{28 x^{3}}+3 x \sqrt{63 x y^{2}}-12 y \sqrt{7 x^{3}}\) = \( -14 y \sqrt{7 x^{3}}+3 x \sqrt{63 x y^{2}}\)

(b) \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{27 x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+2 \sqrt[3]{3^3 \cdot x^{5} y^{4}} \) = \( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \)

\( 7 \sqrt[3]{8 x^{2} y}+6 \sqrt[3]{x^{5} y^{4}} \) = \( 13 \sqrt[3]{x^{5} y^{4}} \)

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With speed = 10 m/s, the rope will hit ground after 3.36 seconds.

Speed is a measure of how fast an object is moving, usually measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). It is a scalar quantity, meaning it only has magnitude and no direction.

Mathematically, speed is defined as the distance an object travels per unit time. The formula for calculating speed is:

Speed = Distance / Time

where Distance is the distance traveled by the object, and Time is the time taken to cover that distance.

Now,

To find when the rope will hit the ground, we can use the kinematic equation:

y = vi * t + (1/2) * a * t²

where:

y = 50 m (the height of the cliff)

vi = 10 m/s (the initial velocity of the rope)

a = 9.8 m/s² (the acceleration due to gravity, acting downward)

t = time it takes for the rope to hit the ground

We can solve for t by setting y=50 and solving for t:

50 = 10t + (1/2) * 9.8 * t²

50 = t(10 + 4.9t)

t = 50/14.9=3.36 s

Therefore, the rope will hit the ground after 3.36 seconds.

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The value of x for the given pentagon will be 125 degrees.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:

• Triangle

• Quadrilateral

• Pentagon

• Hexagon

• Heptagon

• Octagon

• Nonagon

Given the values exterior angles of the pentagon such that, 70°, 60°, 65°, 40°, x°.

To calculate the value of x.

Since the Sum of all exterior angles of a pentagon is 360°,

Thus,

70 + 60 + 65 + 40 +x = 360

x + 235 = 360

x = 360 - 235

x = 125°

Therefore, the value of x for the given pentagon will be 125 degrees.

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The equation that represents the line of best fit for the scatterplot is given as follows:

B. y = -10x + 100.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the graph, we have that:

Hence option B is correct.

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The correct answer is b. 95%.

According to the Empirical rule, for a symmetric data set, 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations of the mean, and 99.7% falls within 3 standard deviations of the mean.

In this particular case, the mean response time is 26 minutes and the standard deviation is 3 minutes. Therefore, 1 standard deviation from the mean is 23 to 29 minutes, 2 standard deviations from the mean is 20 to 32 minutes, and 3 standard deviations from the mean is 17 to 35 minutes.

Since the question asks for the percentage of response times that fall between 20 to 32 minutes, we are looking for the percentage of data that falls within 2 standard deviations of the mean. Therefore, the correct answer is 95%.

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The probability of generating a value between -0.9900 and 2.9000 from a standard normal distribution is 0.4781. The probability of generating a value between -2.4200 and 2.4200 from a standard normal distribution is 0.9804. The probability of generating a value between -0.9900 and 20.1 from a standard normal distribution is 1.0000.

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1. Any normal distribution can be standardized by converting its values into z scores.The standard normal distribution is one of the forms of the normal distribution. It occurs when a normal random variable has a mean equal to zero and a standard deviation equal to one. In other words, a normal distribution with a mean 0 and standard deviation of 1 is called the standard normal distribution.

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The simplified form of the radical expressions are:
a) −12x2y6
b) 284x7t4y3

To simplify the following radical expressions, we need to factor the radicand and then use the properties of radicals to simplify.

For a) −72x4y122x8y2, we can factor the radicand as follows:

−72x4y12 = −(2*2*2*3*3)x4y12 = −(2*2*2*3*3)(x4)(y12)

Now we can use the properties of radicals to simplify:

√−(2*2*2*3*3)(x4)(y12) = √−(2*2)(2*2)(3*3)(x4)(y12) = −(2*2*3)(x2)(y6) = −12x2y6

For b) 7z21128x14t8y6, we can factor the radicand as follows:

1128x14t8y6 = (2*2*2*2*71)(x14)(t8)(y6)

Now we can use the properties of radicals to simplify:

√(2*2*2*2*71)(x14)(t8)(y6) = √(2*2)(2*2)(71)(x14)(t8)(y6) = (2*2*71)(x7)(t4)(y3) = 284x7t4y3

So the simplified form of the radical expressions are:

a) −12x2y6
b) 284x7t4y3

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The exponential function that models the percentage as a function of P is given as follows:

P(t) = 100(0.705)^t.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

The parameters for this problem are given as follows:

Hence the function that models the data in the table is defined as follows:

P(t) = 100(0.705)^t.

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Answer:

I'm sorry, but it is not clear what you are asking for. Can you please provide more information or a specific question?

Option d) The missing quantity A is $2520. The formula for future value is A=P(1+rt), where A is the future value, P is the principal amount, r is the interest rate, and t is the time period.

We are given the values of P, r, and t, and we need to find the value of A.

P = $1800
r = 8% = 0.08
t = 5 years

Plugging these values into the formula, we get:

A = P(1 + rt)
A = $1800(1 + 0.08*5)
A = $1800(1 + 0.4)
A = $1800(1.4)
A = $2520

Therefore, the future value of the investment is $2520. The correct answer is A = $2520.

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The answer of Caroline is 19.33 years old and Cameron is 53.67 years old

Let's start by assigning variables to represent Caroline's age and Cameron's age. We'll use C for Caroline's age and M for Cameron's age.

According to the problem, the sum of their ages today is 73, so we can write the equation:

C + M = 73

Five years ago, Cameron was 2 times older than Caroline. so we can write the equation:

M - 5 = 2(C - 5)

Now we can use the first equation to solve for one of the variables. Let's solve for C:

C = 73 - M

Next, we can substitute this value of C into the second equation:

M - 5 = 2(73 - M - 5)

Simplifying the equation gives us:

M - 5 = 146 - 2M - 10

3M = 161

M = 53.67

Now we can use this value of M to find C:

C = 73 - 53.67

C = 19.33

So Caroline is 19.33 years old and Cameron is 53.67 years old.

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The correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

The correct methods for "thinking out computation" (mental arithmetic) are a, b, and c.

a) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15. This method is correct because it breaks down the calculation into smaller, easier-to-manage parts.

b) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21. This method is also correct because it simplifies the calculation by subtracting 10 first, and then subtracting the remaining 7.

c) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997. This method is correct because it simplifies the calculation by multiplying 1000 by 3 first, and then subtracting 1 three to get the correct answer.

d) 150 ÷ 3 Think: what equals 150 x 3, that's 450. This method is incorrect because it is actually doing the opposite operation (multiplication instead of division) and therefore does not result in the correct answer. The correct method would be to think about how many times 3 can go into 150, which is 50.

In conclusion, the correct methods for mental arithmetic are those that break down the calculation into smaller, easier-to-manage parts and simplify the calculation to make it easier to solve.

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The correct methods for "thinking out computation" (mental arithmetic) are:
A) 7+8 Think: 7 plus 7 is 14, plus 1 more is 15
B) 38 - 17 Think: 38 minus 10 is 28, minus 7 more is 21
C) 999 x 3 Think: 1000 threes is 3000 minus 1 three is 2997
D) 150 ÷ 3 Think: what equals 150 x 3, that's 450

All four methods of "thinking out computation" provided in the question are correct and valid.

Method (a) is using the "doubles" method, which is a common mental arithmetic technique. By recognizing that 7+7 is 14, it is easy to add 1 more to get 15.

Method (b) is using the "subtracting by tens" method. By recognizing that 38 minus 10 is 28, it is easy to subtract 7 more to get 21.

Method (c) is using the distributive property of multiplication. By recognizing that 999 is very close to 1000, we can multiply 3 by 1000 and then subtract 3 to get 2997.

Method (d) is using the inverse operation of multiplication. By recognizing that 150 is a multiple of 3, we can think of 150 as 3 times some unknown number, and then determine that number by dividing 150 by 3. The answer is 50, which is the same as thinking of what equals 150 times 3 (450).

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The missing side of the triangle is 16 mm.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry.

As per the given diagram:

The sides and angles of the right-angled triangle is given:

To find v using the trigonometric ratio:

sinθ = (P/H) {P is perpendicular and H is hypotunese}

for θ = 30°

sin30° = (8/v)

1/2 = 8/v

v = 16 mm

Hence, the missing side of the triangle is 16 mm.

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Answer:

The answer is [tex](u + 3)(5u^{2} - 1)[/tex]

At least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.

What is standard deviations?

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Chebyshev's theorem states that for any distribution (not just the normal distribution), regardless of shape, at least 1 - 1/k^2 of the data values will be within k standard deviations of the mean, where k is any number greater than 1.

In this case, we want to know the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean. So we need to use Chebyshev's theorem with k = 2.

At least 1 - 1/2^2 = 1 - 1/4 = 0.75, or 75%, of the healthy adults have body temperatures within 2 standard deviations of the mean.

To find the minimum and maximum possible body temperatures that are within 2 standard deviations of the mean, we can use the formula:

Minimum = Mean - k * Standard deviation

Maximum = Mean + k * Standard deviation

Plugging in the values for this problem, we get:

Minimum = 98.33 - 2 * 0.67 = 96.99°F

Maximum = 98.33 + 2 * 0.67 = 99.67°F

Therefore, we can say that at least 75% of healthy adults have body temperatures within the range of 96.99°F to 99.67°F.

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The antenna's height is 12.1 meters, as stated throughout the announcement.

Building type refers to a grouping of buildings according to their purpose, location, and style that serves as the standard for evaluating and categorizing variants. Buildings must be categorized as either support, civic, commercial, industrial, or residential. Any kind of fella construction is a structural. It could be anything: a dam or a bridge, for instance. In contrast, a building is a closed construction with walls and a roof. Once more, the more precise phrase is "building," although "structure" is far more generic.

Based on the graph.

[tex]$$\begin{aligned}& \overline{O H}=\overline{C D}=1.51 \mathrm{~mm} . \\& \overline{O C}=24 \mathrm{~m} . \\& \angle O C A=20^{\circ} . \quad \angle O C B=41^{\circ} .\end{aligned}$$[/tex]

In RT [tex]$\triangle A O C_,$[/tex]

[tex]$$\begin{aligned}& \tan 20^{\circ}=\frac{A_0}{O C}=\frac{A_0}{24} \\& \text { So } A_0=\tan 20^{\circ} \times 24=8.74 \mathrm{~m}\end{aligned}$$[/tex]

In Rt ΔOBC.

[tex]$$\begin{aligned}\tan 41^{\circ} & =\frac{O B}{O C}=\frac{O B}{24} \\O B & =\tan 41^{\circ} \times 24=20.86 \mathrm{~m} .\end{aligned}$$[/tex]

[tex]A B=O B-O A=20.86-8.74=12.12 \mathrm{~m} \approx 12.1 \mathrm{~m} .[/tex]

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Answer:

12.1

Step-by-step explanation:

I got the question right

In response to the given query, the result we have is Hence, each expressions container contains 1/2 gallon of paint.

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

The remaining paint would be as follows if the art teacher had 8 gallons and the students had used 3/4 of it:

8 x 1 - 3/4 = 8 x 1/4 = 2 gallons.

The 4 bottles of the remaining 2 gallons of paint each contain the following amounts of paint:

1/2 gallon is equal to 2/4.

Hence, each container contains 1/2 gallon of paint.

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