Your teacher has requested that two rows of strips be placed around the entire room what is the total length of strips that is required

Step-by-step explanation:

a) BD/AD=AB/AC=AD/CD; BD/AB=AB/BC=AD/AC; AD/AB=AC/BC=CD/AC;

b) if BC=2 and DC=10, then it is possbile to write:

BD/AD=AB/AC=AD/10; BD/AB=AB/2=AD/AC; AD/AB=AC/2=10/AC, then

AC/2=10/AC and AC²=20. According to the Pyphagorean's theorem AD²=AC²+CD² and AD=√120≈10.96

Answer: $41.62

Step-by-step explanation:

let the price of the jacket be X

then the price of belt will be X-8.61

according to question

X + X-8.61 = 91.85

2X - 8.61 = 91.85

2X = 91.85 + 8.61

2X = 100.46

X = $50.23

cost of jacket = $ 50.23

cost of belt = $ 41.62

Hope this helps!!!

Answer: $41.62

Step-by-step explanation:

*j = jacket*  *b = belt*
belt + jacket = 91.85 (the total cost of the belt and jacket)
belt = jacket - 8.61 (the price of the belt is $8.61 less than the jacket)

We can use substitution to solve for the value of b.
Substitute the second equation into the first equation:
(j - 8.61) + j = 91.85

Simplify by combining like terms:
2j - 8.61 = 91.85
Add 8.61 to both sides:
2j = 100.46
Divide both sides by 2:
jacket = 50.23

b = j - 8.61

b = 50.23 - 8.61

b = 41.62

Answer: 10,000 or 10^4

Step-by-step explanation: I will assume in the problem that the logarithm is of base-10. We can therefore rewrite the equation in words as 10^4=x. The general form of a logarithm is log base y of x=z. This can be rewritten as y^z=x. We are doing the same thing here. We know that 10^4 is 10,000 so that is our answer.

Hope this helps!

For practice here are some problems (assume all logarithms are our base 10): log x = 3, log x = 1.

The least distance by Pythagorean theorem is equal to √5. (Correct choice: B)

In this problem we find the representation of a point and a line on Cartesian plane. There is a least distance between the point and the line when the line segment between them is perpendicular to the line. The line segment AC fulfill these features. Given the location of points A and C, we can determine the distance by means of Pythagorean theorem:

d = √[(Δx)² + (Δy)²]

Where:

If we know that A(x, y) = (1, 3) and C(x, y) = (3, 2), then the least distance between the point and the line:

d = √[(3 - 1)² + (2 - 3)²]

d = √[2² + (- 1)²]

d = √5

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Steps  he could  use to solve the quadratic equation by completing the square is 5(x² + 4x) = –7

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants. It typically has two solutions, which can be found using the quadratic formula or factoring the equation.

Solution:

The three steps that Sergey could use to solve the quadratic equation by completing the square are:

1.Write the equation in the form ax² + bx + c = 0

2.Add and subtract (b/2)² to complete the square, resulting in an expression of the form a(x + p)^2 + q = 0

3.Solve for x by isolating (x + p)² and taking the square root, resulting in x = (-b ± sqrt(b² - 4ac)) / 2a

Therefore, the three options that correspond to these steps are:

5(x² + 4x + 4) = –7 + 20

x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot

5(x² + 4x) = –7

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One major weakness of the constitution was that it failed to provide for the elective principle. In other words, no member of the Legislative Council was elected by Africans through the ballot box.

Tact is a term that B.F. Skinner used to describe a verbal operant which is controlled by a nonverbal stimulus and is maintained by nonspecific social reinforcement. Less technically, a tact is a label. Chapter five of Skinner's Verbal Behavior discusses the tact in depth.

here, we have,

Tameka's company is introducing a new invoicing and billing system as tameka is presenting the new system to the accounting team, she is careful to explain why the changes are important by the time she is done, the accounting team has shown their acceptance of the new procedures. this is likely because Tameka has used tact.

Tact is the ability to avoid upsetting or offending people by being careful not to say or do things that would hurt their feelings. implies the skill in dealing with persons or difficult situations of one who has a quick and delicate sense of what is fitting and thus avoids giving offense.

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The last digit of the product is 5.

To find the last digit of the product of these numbers, we only need to focus on the last digit of each number, since the other digits do not affect the last digit of the product. We can observe that every odd number has a last digit of 1, 3, 5, 7, or 9. Therefore, we only need to consider the last digit of every fifth odd number in the given sequence.

The last digit of 2001 is 1.

The last digit of 2003 is 3.

The last digit of 2005 is 5.

The last digit of 2007 is 7.

The last digit of 2009 is 9.

The last digit of 2011 is 1.

The last digit of 2013 is 3.

The last digit of 2015 is 5.

The last digit of 2017 is 7.

The last digit of 2019 is 9.

To find the last digit of the product of these numbers, we need to multiply all of these last digits together. We can group the digits into pairs that multiply to 1, and there is one 5 remaining. Multiplying all of these digits together gives:

1 * 3 * 5 * 7 * 9 * 1 * 3 * 5 * 7 * 9 * 5 = 5

Therefore, the last digit of the product is 5.

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The possible values of b are 1/10, 1/2, 9/12, here we have to learn graph of a function. Diagram of question given below.

The graph of a function f in mathematics is the collection of ordered pairs where display style f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical situation when x and f(x) are real integers.

Subset, If every element of a set P is also an element of a set Q, then set Q is a superset of set P and set A is a subset of set Q. P and Q might be equal; if not, then P is a legitimate subset of Q.

Here, when [tex]b=0,\ f(x) = a*0^{x} = 0[/tex]

[tex]b=1,\ f(x)=a*1^{x} = a[/tex]

[tex]b > 1,\ f(x)=a*b^{x}[/tex]

[tex]a < b < 1,\ f(x) = a*b^{x}[/tex]

[tex]So, b\in(0,1)=b=\frac{1}{10} ,\frac{1}{2} ,\frac{9}{10}.[/tex]

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In a normal distribution curve, the mean is equal to center of the curve

In a normal distribution curve, the mean is equal to the center of the curve, also known as the peak, and is represented by the highest point on the curve.

The mean of a normal distribution is also the point around which the data points are symmetrically distributed, with an equal number of data points on both sides of the mean. This is why the mean is often referred to as the "average" of a normal distribution.

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No. 2: Kennedy error is that he mistakenly distributed the negative sign when multiplying -3 and +3. The correct answer is x² - 9.

No. 3: The product (x + 6)(x - 6) is equivalent to the expression x² - 6².

No. 4: The pattern for the squares of binomial are: (a + b)² = a² + 2ab + b²

and (a - b)² = a² - 2ab + b².

Sum and  difference pattern: (a + b)(a - b) =   a² - b²

No. 2

Kennedy made an error in multiplying (x - 3)(x + 3) because the correct result of this multiplication is x² - 9, not x² - 6x - 9.

This error occurred because Kennedy mistakenly distributed the negative sign when multiplying -3 and +3, resulting in an additional -6x term in the final answer.

The correct way to multiply (x - 3)(x + 3) is to use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:

(x - 3)(x + 3) = x² + 3x - 3x - 9 = x² - 9

No. 3

The product (x + 6)(x - 6) is equivalent to the expression x² - 36, which is called the difference of two squares because it represents the difference between two perfect squares: x² and 6².

Specifically, (x + 6)(x - 6) can be written as x² - 6², and using the identity (a + b)(a - b) = a² - b² we can simplify this to x² - 36.

No. 4

The pattern for the squares of binomial are:

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

The pattern for the product of a sum and a difference is:

(a + b)(a - b) =   a² - b²

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The interest rate is 0.04 or 4% when the time is equal to 2.5 years, principal amount is $3000 and interest is $300.

Simple interest is a type of interest that is calculated only on the initial principal amount of a loan or investment. It does not take into account any interest earned on the interest that has accumulated over time, as is the case with compound interest.

To find the value of r, the formula for simple interest is I = P * r * t

where:

I = Interest

P = Principal

r = Interest rate

t = Time

By substituting the given values in equation, we get:

$300 =  $3000 * r * 2.5

r = $300/($3000*2.5)

r = 0.04

Therefore, the interest rate is 0.04 or 4%.

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Answer: Let's use the variables c and a to represent the number of children and adults who used the pool, respectively.

We know that the total number of people who used the pool is 631, so we can write:

c + a = 631 (equation 1)

We also know that the total receipts for admission were $1013.00. The cost for children is $1.25 and the cost for adults is $2.00, so we can write:

1.25c + 2a = 1013 (equation 2)

Now we have two equations with two unknowns. We can solve for c and a by using elimination or substitution.

Let's use elimination. Multiply equation 1 by 1.25 to get:

1.25c + 1.25a = 788.75 (equation 3)

Subtract equation 3 from equation 2 to eliminate c:

0.75a = 224.25

a = 299

Now we can use equation 1 to solve for c:

c + 299 = 631

c = 332

Therefore, there were 332 children and 299 adults who used the pool that day.

Step-by-step explanation:

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

In which:

The radical form is given as follows:

[tex]\sqrt[m]{a^n}[/tex]

Meaning that the equivalence relation is given as follows:

[tex]\sqrt[m]{a^n} = a^{\frac{n}{m}}[/tex]

That is:

Hence the relation for the cube root of 21 is given as follows:

[tex]\sqrt[3]{21} = 21^{\frac{1}{3}}[/tex]

(applying the conversion of the fractional exponent to a radical expression).

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Answer:

Step-by-step explanation:

HI:

Area of rectangle: 8*8= 64

Area of triangle: 4*8=32/2= 16

64+16= 80

Answer: 80ft^2

The simplified form is  [tex]-(sina + 1)[/tex].

One of the most significant areas of mathematics, trigonometry has a wide range of applications. Trigonometry is a discipline of mathematics that primarily focuses on the analysis of how a right-angle triangle's sides and angles relate to one another.

Given the function:

[tex]\frac{cos^2a}{sina - 1}[/tex]

Simplifying by using conjugate multiplication:

[tex]\frac{cos^2a \times (sina + 1)}{sina - 1 \times (sina + 1)}[/tex]

[tex]= \frac{cos^2a \times (sina + 1)}{sin^2a - 1^2}[/tex]

using [tex]sin^2a + cos^2a = 1[/tex]

[tex]= \frac{cos^2a \times (sina + 1)}{-cos^2a}[/tex]

[tex]= -(sina + 1)[/tex]

Hence, the simplified form is  [tex]-(sina + 1)[/tex].

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Answer:

55

Step-by-step explanation:

The ? angle is 55 degrees since every triangle's angles add up to 180 degrees. We have 2 angles, one with 70 and another with 55, so we add them to get 125. Then we subtract 125 from the total angle of a triangle, 180-125, to get 55.

the answer is 55

they have the same degrees hope this helps

The required probability that the mean height of a sample of sixteen men falls between 66 and 68 inches is approximately 0.6827.

We know that the sample size n = 16, the population mean μ = 67 inches, and the population standard deviation σ = 4 inches.

The sampling distribution of the sample mean can be approximated by a normal distribution with mean μ and standard deviation σ/√n.

Thus, the distribution of the sample mean can be expressed as:

[tex]$\bar{X} \sim \mathcal{N}(\mu, \frac{\sigma}{\sqrt{n}})$$[/tex]

Substituting the given values, we have:

[tex]$\bar{X} \sim \mathcal{N}(67, \frac{4}{\sqrt{16}})$$[/tex]

[tex]$\bar{X} \sim \mathcal{N}(67, 1)$$[/tex]

To find the probability that the sample mean falls between 66 and 68 inches, we need to find the z-scores corresponding to these values and calculate the area under the normal curve between these z-scores.

The z-score corresponding to a sample mean of 66 inches is:

[tex]$z = \frac{66 - 67}{1} = -1$$[/tex]

The z-score corresponding to a sample mean of 68 inches is:

[tex]$z = \frac{68 - 67}{1} = 1$$[/tex]

Thus, we need to find the probability that the z-score falls between -1 and 1. Using a standard normal distribution table or calculator, we can find that this probability is approximately 0.6827.

Therefore, the probability that the mean height of a sample of sixteen men falls between 66 and 68 inches is approximately 0.6827.

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Answer:

2n^2

Step-by-step explanation:
The is a Quadratic sequence:

First difference is 6 10 14 18
Second difference is 4 4 4 4
Divide the second term by 2 which is 2n^2

Answer: Restaurant B

Step-by-step explanation:

First, Divide 14.52 by 11 as shown below to get the cost per burger for Restaurant A:

14.52/11 = 1.32

Next, divide 2.58 by 2 for the cost of the burger at Restaurant B:

2.58/2 = 1.28

Now we can see that Restaurant B's burgers are 4 cents cheaper than Restaurant A.

Good Luck!

Answer:

Fill in each blank with ONE word to create a sentence to explain slope in the context of this problem: The amount of [dependent variable] is [changing] at a rate of [slope] [units of dependent variable] per [unit of independent variable].

Step-by-step explanation:

Answer:

Question 3
Equation for Malik:
y = 350 + 7x

Equation for Saraiah:
y = 400 + 4x

Question 4
Both of them will have the same amount of money after
50/3 years
or
16 2/3 years
or
16 years 8 months

Step-by-step explanation:

#3

Amount in Malik's account after x years given 2% interest
y = 350(1 + 0.02x)
y = 350 + 7x

For Saraiah's account:
y = 400(1 + 0.01x)
y = 400 + 4x

#4

If both Malik and Saraiah have the same amount of money after x years, then the right side of both their equations must be equal

Therefore

[tex]350+7x = 400+4x\\\\\mathrm{Move}\:350\:\mathrm{to\:the\:right\:side \:by \:subtracting\: 350 \:from\:both\: sides}\\350+7x-350=400+4x-350\\\\\mathrm{Simplify}\\7x=4x+50\\\\[/tex]

[tex]\mathrm{Subtract\:}4x\mathrm{\:from\:both\:sides}\\\\7x-4x=4x+50-4x\\3x=50\\\\\mathrm{Divide\:both\:sides\:by\:}3\\\\\dfrac{3x}{3}=\dfrac{50}{3}\\\\x=\dfrac{50}{3}[/tex]

Therefore both of them will have the same amount of money after [tex]\dfrac{50}{3}[/tex] years which is [tex]{16\dfrac{2}{3}[/tex] years

2/3 year = 2/3 x 12 months = 8 months

So both of them will have the same amount of money after [tex]{16\dfrac{2}{3}[/tex] years or 16 years and 8 months

Therefore, the scale factor used in the drawing is 4000/3.

In mathematics, a factor refers to a number or algebraic expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because each of these numbers can be multiplied by another whole number to produce 12 (1 × 12, 2 × 6, 3 × 4). Factors play an important role in many areas of mathematics, including algebra, number theory, and geometry, and are used to simplify expressions, solve equations, and factorize polynomials.

Given by the question.

The scale factor is the ratio of the length of an object on the drawing to the actual length of the object.

Since 6 millimeters on the drawing represents 8 meters in reality, the scale factor can be expressed as:

Scale factor = Actual length / Length on drawing

Scale factor = 8 meters / (6 millimeters)

To simplify this fraction, we need to convert meters to millimeters by multiplying by 1000:

Scale factor = (8 meters * 1000) / 6 millimeters

Scale factor = 8000 / 6

The fraction cannot be simplified further, so the scale factor is:

Scale factor = 4000/3

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We can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

What is Line point postulate ?

The line-point postulate, also known as the incidence postulate, is a fundamental axiom in geometry that states that for any two points in a plane, there exists exactly one line that contains both points.

In other words, the line-point postulate asserts that a line can be uniquely determined by two distinct points that lie on it. This is one of the most basic and intuitive principles in geometry, and it is essential for building a foundation for more advanced concepts such as angles, triangles, circles, and more.

The Line-Point Postulate states that a line can be uniquely determined by any two distinct points on the line. In this diagram, we can see an example of this postulate in action.

For instance, we can say that line $q$ passes through points $J$ and $K$, so according to the Line-Point Postulate, this is enough information to uniquely determine the line $q$. Similarly,

Therefore, we can say that line $p$ passes through point $H$, which is also enough information to uniquely determine line $p$.

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Using arithmetic operation, the value for time spent on country driving is obtained as 25/44 hour.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Jorge's drive was 3/4 hour, and 2/11 hour of that time was spent on city driving.

To find the time spent on country driving, we can use arithmetic operation of subtraction.

Subtract the time spent on city driving from the total driving time -

Time spent on country driving = Total driving time - Time spent on city driving

= 3/4 hour - 2/11 hour

To subtract these fractions, we need a common denominator.

The smallest number that 4 and 11 both divide into is 44 -

3/4 = 33/44

2/11 = 8/44

So -

Time spent on country driving = 33/44 hour - 8/44 hour

= (33 - 8)/44 hour

= 25/44 hour

Therefore, Jorge spent 25/44 hour driving on country roads.

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Answer:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = $200.00

r = 0.09 (9% expressed as a decimal)

n = 1 (compounded annually)

t = 5 years

Plugging these values into the formula, we get:

A = $200.00(1 + 0.09/1)^(1*5)

A = $200.00(1.09)^5

A = $200.00(1.538624)

A = $307.72

Therefore, after 5 years, Megan will have $307.72 in her account.

Step-by-step explanation:

The expression "eight more than the sum of a number and 7 is 90" can be written as: 8 + (x + 7) = 90

From the question, we have the following parameters that can be used in our computation:

eight more than the sum of a number and 7 is 90

Express the numbers properly

So, we have

8 more than the sum of a number and 7 is 90

Express the operators properly

8 + (x + 7) = 90

hence, the expression is 8 + (x + 7) = 90

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The amount of dressing required to serve 11 guests who still want salad is therefore around 11 ounces. The answer, when adjusted to the closest whole ounce, is 11 ounces.

Round the figure up if 5, 6, 7, 8, or 9 follow the amount you are rounding. For instance, 40 when rounded to a nearest ten is 38. Round the figure down if it is followed by the digits 0, 1, 2, 3, or 4. 33 becomes 30 if it is adjusted to the nearest ten.

Many variables, such as the salad's serving size, the type of sauce, and personal preferences, will affect how much dressing is needed for 11 dinner guests. But as a general rule, a salad with dressing serving size is roughly 2-3 teaspoons (1 ounce = 2 tablespoons).

Assuming that each visitor will consume 2 tablespoons of dressings, the necessary quantity of dressing would be:

11 guests x 2 tablespoons/guest = 22 tablespoons

Tablespoons to ounces conversion:

22 tablespoons / 2 tablespoons/ounce = 11 ounces

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Neither of the given points is a solution to the system of linear inequalities.

What does solution to the system of linear inequalities mean ?

A system of linear inequalities is a set of two or more linear inequalities with the same variables. This system consists of two linear inequalities, each involving the variables x and y, and each inequality uses one of the inequality symbols.

The solution to a system of linear inequalities is the set of values for the variables that satisfy all the inequalities in the system simultaneously. This solution can be represented graphically as the region of the coordinate plane that satisfies all the inequalities in the system.

Check the given points whether they are solutions to the system of linear inequalities or not :

Substitute the x and y values of each point into both inequalities and check if they are true.

(a) (-4,1) :

y ≤ -3x - 2

1 ≤ -3(-4) - 2

1 ≤ 10

This is false, so (-4,1) is a not solution to the first inequality.

y > x - 2

1 > -4 - 2

1 > -6

This is true, so (-4,1) is a solution to the second inequality.

Since (-4,1) is a solution to only one of the inequalities and not both, it is not a solution to the system of linear inequalities.

(b) (2,2):

y ≤ -3x - 2

2 ≤ -3(2) - 2

2 ≤ -8

This is false, so (2,2) is not a solution to the first inequality.

y > x - 2

2 > 2 - 2

2 > 0

This is true, so (2,2) is a solution to the second inequality.

Since (2,2) is a solution to only one of the inequalities and not both, it is not a solution to the system of linear inequalities.

Therefore, neither of the given points is a solution to the system of linear inequalities.

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The longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure,

By considering base of the prism, we get

c²=6²+6²

c²=72

c=6√2 ft

Now, d²=c²+8²

d²=72+64

d²=136

d=√136

d= 11.7 ft

Hence, the longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.

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