"Fill in the blanks with perfect squares to
approximate the square root of 72.
sqrt[x] < sqrt90

The length of RS is 6.32 unit (B).

To find the length of RS, we can use the distance formula:

D = √[(x₂ - x₁)² + (y₂ - y₁)²]

where:

(x₁, y₁) = coordinate of point 1

(x₂, y₂) = coordinate of point 2

In this case, we have:

the coordinates of R: (-2, -4)

the coordinates of S: (-8, -6).

Plugging in these values into the distance formula, we get:

D = √[(-8 - (-2))² + (-6 - (-4))²]

D = √[(-6)² + (-2)²]

D = √[36 + 4]

D = √40

D = 6.32

Therefore, the length of RS is about 6.32 units.

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Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.

To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.

There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).

Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.

Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.

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The equation x = 10 tan (32°) could be used to find x in ∆ABC.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) , where:

\(sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse}\\ \\ tan(x)=\frac{sin(x)}{cos(x)} =\frac{opposite\ side}{adjacent\ side}\)

The question gives the value of the two sides and the value of an angle. From the trigonometric ratios presented before, you can write:

\(tan(32)=\frac{opposite\ side}{adjacent\ side}=\frac{x}{10} \\ \\ x=10\ tan (32\°)\)

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Answer:

29

Step-by-step explanation:

firat 4 78374748383838

9514 1404 393

Answer:

  d.  tan(16°) = x/6

Step-by-step explanation:

You can use logic to figure this out, even if you don't know much trigonometry.

Choices A and D are contradictory. One of them must be consistent with choice C. Choices C and D are also contradictory, so choices A and C must be in agreement and part of the set of statements that CAN be used.

Choice D is the statement that CANNOT be used to find x.

Answer:

step 2 to step 3

Step-by-step explanation:

step 2

2x - 7 = 3 ( add 7 to both sides )

2x = 10 ( error was made here in that they had - 4 )

Solution

The population of a city is modeled by the function

where y is the population of the city after t years starting in the year 2000

In what year will the population be 5000

Therefore in 32 years time the population will be 5000

Answer:

3 pounds! Do you remember me Im GamerSquash1w My other  account got deleted

Step-by-step explanation:

Answer:

m∠A = 166°

Step-by-step explanation:

∠B and ∠A are corresponding angles because the two lines are congruent. Therefore:

7x + 40 = 3x + 112

Subtract 3x from both sides:

4x + 40 = 112

Subtract 40 from both sides:

4x = 72

Divide both sides by 4:

x = 18

Plug this in for ∠A:

∠A = 7 (18) + 40

m∠A = 166°

Answer:

B

Step-by-step explanation:

-4y-3<9

-4y<12

y<-3

==> B

\(\text{Given that,}~ f(x) = 2x -1~ \text{and}~ g(x) = x^2- 3x -2 \\\\\text{Now,}\\\\~~~(f+g)(x)\\\\=f(x) + g(x)\\\\=2x-1 +x^2 -3x -2\\\\=x^2 -x -3\)

Answer:

(f + g)(x) = x² - x - 3

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x - 1 + x² - 3x - 2 ← collect like terms

= x² - x - 3 ← in standard form

On average, Brooke put approximately 1.6 cups of flour in each cake.

To find the average, we need to divide the total amount of flour used by the number of cakes.

Brooke used a total of 8 cups of flour to bake 5 cakes.

To find the average amount of flour per cake, we divide the total amount of flour by the number of cakes:

The average amount of flour per cake = Total amount of flour used / Number of cakes

Average amount of flour per cake = 8 cups / 5 cakes

Dividing 8 cups by 5 cakes, we get:

Average amount of flour per cake = 1.6 cups

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The given initial value problem's solution is y(t) = e^(-2t)(2cos(4t) + (1/8)sin(4t))

To solve the given initial value problem, we can use the method of solving second-order homogeneous linear differential equations with constant coefficients.

The characteristic equation corresponding to the given differential equation is:

r^2 + 4r + 20 = 0

To solve this quadratic equation, we can use the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 4, and c = 20. Substituting these values into the quadratic formula, we get:

r = (-4 ± √(4^2 - 4(1)(20))) / (2(1))

r = (-4 ± √(-64)) / 2

r = (-4 ± 8i) / 2

r = -2 ± 4i

The roots of the characteristic equation are complex conjugates: -2 + 4i and -2 - 4i.

The general solution of the differential equation can be written as:

y(t) = e^(-2t)(c1cos(4t) + c2sin(4t))

To find the particular solution that satisfies the initial conditions, we substitute the initial values into the general solution and solve for the constants c1 and c2.

Given y(0) = 2:

2 = e^(-2(0))(c1cos(4(0)) + c2sin(4(0)))

2 = c1

Given y'(0) = -1:

-1 = -2e^(-2(0))(c1sin(4(0)) + 4c2cos(4(0)))

-1 = -2(1)(0 + 4c2)

-1 = -8c2

c2 = 1/8

Therefore, the particular solution that satisfies the initial conditions is:

y(t) = e^(-2t)(2cos(4t) + (1/8)sin(4t))

This is the solution to the given initial value problem.

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Answer:

4.5

Step-by-step explanation:

Domain means that value of x and range means the value of f(x) so

\(f(x)=2x+1 \\f(1.75)=2(1.75)+1\\f(1.75)=4.5\)

so the range value is 4.5

Answer:

an = 1.2 + (n - 1) 1.5

Step-by-step explanation: opt A on edg

this formula, doesn't rely on a product, relies on a "sum", or is namely an arithmetic sequence, aₙ₋₁ -3 is another way of saying, the value of the previous term minus 3, so it relies on the ordinal value of a term, so is an recursive formula, well, let's get it when n = 4.

\(\begin{array}{ccll} order&term&value\\ \cline{1-3} 1&a_1&8\\ 2&a_2&a_{2-1}-3\\ &&a_1-3\\ &&8-3\\ &&5\\ 3&a_3&a_{3-1}-3\\ &&a_2-3\\ &&2\\ 4&a_4&a_{4-1}-3\\ &&a_3-3\\ &&2-3\\ &&-1 \end{array}\)

Answer: 4a + 16

Step-by-step explanation:

Total amount of drink in the jug is 1 1/10 litre.

To find the total amount of drink in the jug, we need to add the amount of water and the amount of lemon juice:

Amount of water = 3/5 litre

Amount of lemon juice = 1/2 litre

We need to find a common denominator to add these fractions. The smallest common multiple of 5 and 2 is 10. So we can rewrite the fractions with denominators of 10:

Amount of water = (3/5) x (2/2) = 6/10 litre

Amount of lemon juice = (1/2) x (5/5) = 5/10 litre

Now we can add the fractions:

Total amount of drink = 6/10 + 5/10 = 11/10 litre

Since the numerator is greater than the denominator, we have an improper fraction. We can convert it to a mixed number by dividing the numerator by the denominator:

11 ÷ 10 = 1 with a remainder of 1

So the total amount of drink in the jug is 1 1/10 litre.

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Answer:

$200

Step-by-step explanation:

30 * 5=150 +50=200

Answer:

its b

Step-by-step explanation:

Well the easy way to find this is to just solve the first one. the equation is

x-y>5 so you plug in the coordinate and you end up with 7-2>5 which is false. So any answer with option one is out and b is the only one that fits that description.

The equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is: (x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

To find the equation of the sphere passing through the point (4, 3, -1) with a center at (3, 8, 1), we can use the general equation of a sphere:

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

where (h, k, l) represents the center of the sphere and r represents the radius.

First, we need to find the radius. The distance between the center and the given point can be calculated using the distance formula:

√[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

Substituting the coordinates of the center (3, 8, 1) and the given point (4, 3, -1), we have:

√[(4 - 3)^2 + (3 - 8)^2 + (-1 - 1)^2]

Simplifying, we get:

√[1 + 25 + 4] = √30

Therefore, the radius of the sphere is √30.

Now we can substitute the center (3, 8, 1) and the radius √30 into the general equation:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30

So, the equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

This equation represents all the points on the sphere's surface.

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The best estimate of the side length of the frame of Alaine with mentioned area is 8.9 inches.

As per the known fact about squares, all its four sides are equal. Additionally, the product of two sides of square is its area. Using the formula based on it -

Area = side²

Keep the values in formula to find the side length of the frame of mentioned area

Side = ✓80

Taking square root on Right Hand Side of the equation

Side = 8.9 inches

Thus, as per the best estimate the side length of the frame is 8.9 inches.

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Option C is correct.  Less than 100  is closest to total deaths resulting from ladder misuse each year.

According to the Consumer Product Safety Commission (CPSC), on average, approximately 300 people die each year in the United States from falls involving ladders.

However, not all of these deaths are due to ladder misuse. In fact, the number of deaths resulting specifically from ladder misuse is likely to be lower. It is estimated that a significant portion of ladder-related fatalities are caused by factors such as overreaching, misusing the ladder, or failing to follow proper safety guidelines.

To reduce the number of deaths and injuries resulting from ladder misuse, it is important to follow safety guidelines and to choose the right ladder for the job, taking into consideration factors such as height, weight, and stability.

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The probability that a randomly selected quartz timepiece will have a replacement time less than 11.9 years is 0.0007 or 0.07%.

The given information is that a company XYZ knows that the replacement times for the quartz timepieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. We need to calculate the probability that a randomly selected quartz timepiece will have a replacement time of less than 11.9 years. Let us solve this problem using the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the given distribution into the standard normal distribution using the formula:
z = (x - μ)/σ
Where x is the replacement time, μ is the mean and σ is the standard deviation.

Putting the given values, we get:
z = (11.9 - 16)/1.4
z = -3.21
We need to find the probability that the replacement time is less than 11.9 years. This can be calculated as the area under the standard normal distribution curve to the left of z = -3.21.

Using the standard normal distribution table, we find that the area to the left of

z = -3.21 is 0.0007.
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Examples can be quotations, facts, narratives, statistics, details, analogies, opinions, and observations.

Rhetoric

Rhetoric is the art of persuasion, which along with grammar and logic , is one of the three ancient arts of discourse. Rhetoric aims to study the techniques writers or speakers utilize to inform, persuade, or motivate particular audiences in specific situations.

Rhetoric refers to the study and uses of written, spoken and visual language. It investigates how language is used to organize and maintain social groups, construct meanings and identities, coordinate behavior, mediate power, produce change, and create knowledge.

“rhetoric” is used almost exclusively as a negative term.

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Co-factors:Co-factors represent functions that result when some variables are fixed. The function can be divided into various co-factors based on the variables involved. In general, we can say that co-factors are the functions left when one or more variables are held constant.

Consider the following minimal sum-of-products (SOP) expression of a 5-variable function:f = a′bce + ab′c′e + cde′ + a′bc + bce′ + ac′d + a′b′c′d′e′. We need to derive six co-factors of the given function. They are: f_a, f_a', f_a'b', f_a'b, f_ab', and f_ab.1. f_a: We can take f(a=0) to find f_a = bce + b′c′e + cde′ + bc′d + b′c′d′e′2. f_a': We can take f(a=1) to find f_a' = bce + b′c′e + cde′ + bc + b′c′d′e′3. f_a'b': We can take f(a=b'=0) to find f_a'b' = ce + c′e′ + de′4. f_a'b: We can take f(a=0, b=1) to find f_a'b = ce + c′e′ + cde′ + c′d′e′5. f_ab': We can take f(a=1, b=0) to find f_ab' = ce + c′e′ + b′c′d′e′ + bc′d′e′6. f_ab: We can take f(a=b=1) to find f_ab = ce + c′e′ + b′c′d′e′ + bc′d′e′ROBDD:ROBDD stands for Reduced Ordered Binary Decision Diagram. It is a directed acyclic graph that represents a Boolean function. The nodes of the ROBDD correspond to the variables of the function, and the edges represent the assignments of 0 or 1 to the variables. The ROBDD is constructed in a top-down order with variables ordered in a given way. In this case, we are assuming top-to-bottom variable order a,b,c,d,e.

The ROBDD for the given function is shown below:The six nodes of the ROBDD correspond to the six co-factors that we derived in part (a). The fx​ labels are given to show which node corresponds to which co-factor.Changing variable order:If we change the variable order, we might get a smaller ROBDD. This is because the variable ordering affects the structure of the ROBDD. The optimal variable order depends on the function being represented. Without deriving another ROBDD, we can propose the first variable in a new order that is most likely to yield a smaller ROBDD.

We can consider the variable that has the highest degree in the function. In this case, variable c has the highest degree, so we can propose c as the first variable in a new order that is most likely to yield a smaller ROBDD. This is because fixing the value of a variable with a high degree tends to simplify the function. However, the optimal variable order can only be determined by constructing the ROBDD.

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The total area of the region bounded by the graph of y = x times the square root of \((1 - x^2)\) and the x-axis is 1/2.

Let the region bounded by the graph of y = x times the square root of\((1 - x^2)\) and the x-axis be the region R.

The total area of region R is given by A as;\(A = 2∫_0^1▒〖ydx〗\)

The boundary of the given region is given by y = x times the square root of\((1 - x^2)\) and the x-axis.

Thus, for any x in the interval [0, 1], the boundary of the region R can be represented as;\(∫_0^1▒〖x√(1-x^2)dx〗\)

Let \(u = 1 - x^2,\)

therefore, du/dx = -2x.

It implies that\(dx = -du/2x.\)

The integral becomes;\(∫_1^0▒〖(-du/2)√udu〗=-1/2 ∫_1^0▒√udu\)

=-1/2 2/3

= -1/3

Therefore the total area of the region bounded by the graph of y = x times the square root of \((1 - x^2)\)and the x-axis is 1/2. Hence, option B) 1/2 is the correct answer.

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