PLEASE HELP ASAP 50 POINTS!!!!

The number of minutes to complete 1 lap is found as 5 minutes.

Multiplication is the reciprocal of division. If 3 groups of 4 add up to 12, then 12 divided into three categories of equal size results in 4 in each group.

The stated question:

10 minutes for 2 laps

Applying unitary method:

= 10/2

= 5

Thus, number of minutes to complete 1 lap is found as 5 minutes.

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The complete question -

10 minutes for 2 laps. Then, find number of minutes for 1 lap.

The area of the shaded region is 96ft²

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².

The area of a parallelogram is expressed as base × height

The area of parallelogram = 12× 12

= 144ft²

The area of the rectangle = l×w

= 8×6

= 48 ft²

The area of the shaded region = area of parallelogram - area of rectangle

area of the shaded region = 144-48

= 96ft².

Therefore the area of the shaded region is 96ft²

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This distribution of inequities ensures that the total amount of ticket sales revenue stays within the budget, that no more than 150 tickets are sold overall, and that no negative ticket sales occur.

Let x represent the quantity of single tickets sold and y represent the quantity of pair tickets sold. The entire revenue from ticket sales, R, is then calculated as follows:

R = 45x + 70y

The entire amount of ticket sales revenue is limited by the budget to $5000:

45x + 70y ≤ 5000

No more than 150 tickets may be sold in total.

x + y ≤ 150

X and Y must both be non-negative since we cannot sell negative tickets:

x ≥ 0\sy ≥ 0

As a result, the system of disparities that best captures this circumstance is:

5000 x + y 45x + 70y 150x 0y 0

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x1 = 1.3, x2 = 0.3, x3 = 0.7

The solution to the linear programming problem is: x1 = 1.3, x2 = 0.3, x3 = 0.7.

Using the Dual Simplex Algorithm (DSA), we can solve the problem by setting up the initial tableau:

x1 = −5x1 + x2 − 2x3

2x1 + x3 = 0

x1 − x2 ≥ 1

3x1 − x2 + x3 ≤ 3

Once the tableau is set up, we can use DSA to find the optimal solution.

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Answer:

To find the percentage of people in the world who speak Spanish, we can use the following formula:

percentage = (part/whole) x 100%

where "part" is the number of people who speak Spanish and "whole" is the total world population.

Substituting the given values, we get:

percentage = (527/7,530) x 100% ≈ 7.00%

Rounding to the nearest whole percent, we get that approximately 7% of people in the world speak Spanish.

The function h(x) can be expressed as f(g(x)) where g(x) = (x-7) and f(x) = x.

The function h(x) = (x-7)1 can be expressed in the form f(g(x)) where g(x) = (x-7) and f(x) is defined as f(x) = x1.

To find f(x), we need to isolate x on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 1, which is 1.

f(x) = x1 * 11 = x

Therefore, the function h(x) can be expressed as f(g(x)) where g(x) = (x-7) and f(x) = x.

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When the L shape attached is rotated about the origin (0, 0) by 90° counterclockwise it would look like option C.

A shows a rotation of 90°  clockwise about (0,0)

B shows a rotation of 180° about (0,0)

C shows a rotation of 90° anticlockwise about (0,0)

D shows a rotation of 90° anticlockwise, but the center of rotation is (1,1)

Recall that Rotation in math is a transformation that involves rotating a figure around a fixed point called the center of rotation by a certain angle in a clockwise or counterclockwise direction.

Thus, Option C above is the right answer.

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Evaluating the limit given by [tex]{ lim_{(x- > 9)} } (7x-63)/(x^2-2x-63)[/tex], we will obtain as a result [tex]7/16[/tex]

To evaluate the limit, we need to simplify the expression first. We can do this by factoring the numerator and denominator of the fraction:

[tex]lim_{(x->9)} (7x-63)/(x^2-2x-63) = lim_{(x->9)} (7(x-9))/((x-9)(x+7))[/tex]

Next, we can cancel out the [tex](x-9)[/tex] terms in the numerator and denominator:

[tex]lim_{(x->9)} (7)/(x+7)[/tex]

Now, we can plug in the value of x that the limit is approaching (9) into the expression:

[tex]lim_{(x->9)} (7)/(x+7) = (7)/(9+7) = (7)/(16)[/tex]

Therefore, the limit of the expression as x approaches 9 is 7/16.

Answer: [tex]{ lim_{(x->9)} } (7x-63)/(x^2-2x-63) = 7/16[/tex]

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Answer: If you want to live in a city with greater variability of temperature, you should look for cities with a continental climate. Continental climates are characterized by hot summers and cold winters, with large temperature fluctuations between day and night and between seasons.

Cities located in the interior of large landmasses, far from large bodies of water, are more likely to have a continental climate. Examples of cities with a continental climate include Moscow (Russia), Calgary (Canada), and Chicago (USA). These cities experience wide temperature swings throughout the year, with hot summers and cold winters.

On the other hand, cities located near large bodies of water tend to have a more moderate climate, with smaller temperature fluctuations. Examples of such cities include San Francisco (USA), Sydney (Australia), and London (UK). These cities experience mild summers and winters, with relatively constant temperatures throughout the year.

Step-by-step explanation:

when dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be -5.

The given polynomial equation is x^(4)-3x^(3)-7x^(2)-80 and we have to divide it by x-5 to find the remainder.

Set up the long division as follows:
```
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
```

Divide the first term of the dividend (x^(4)) by the first term of the divisor (x) to get the first term of the quotient (x^(3)):
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
```

Multiply the first term of the quotient (x^(3)) by the divisor (x-5) and write the result below the dividend:
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
    x^(4) - 5x^(3)
```

Subtract the result from the dividend to get the new dividend:
```
x^(3)
_______
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
    x^(4) - 5x^(3)
    --------------
         2x^(3) - 7x^(2)
```

Repeat the process with the new dividend until the degree of the remainder is less than the degree of the divisor:
```
x^(3) + 2x^(2) + 3x + 15
______________________
x-5 | x^(4) - 3x^(3) - 7x^(2) + 0x - 80
    x^(4) - 5x^(3)
    --------------
         2x^(3) - 7x^(2)
         2x^(3) - 10x^(2)
         ---------------
               3x^(2) + 0x
               3x^(2) - 15x
               ------------
                    15x - 80
                    15x - 75
                    --------
                         -5
```

The remainder is -5. Therefore, when dividing x^(4)-3x^(3)-7x^(2)-80 by x-5, the remainder will be -5.

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Answer:

To find YZ and DE in the sequence WXYZ FEDC, we need to understand how the sequence is constructed. The sequence is likely made up of two smaller sequences: WXYZ and FEDC.

To find YZ, we need to look at the WXYZ sequence. Since Y and Z are the last two digits of this sequence, we can conclude that Z is the last digit and Y is the second to last digit. Therefore, YZ = 30.

To find DE, we need to look at the FEDC sequence. Since D and E are the last two digits of this sequence, we can conclude that E is the last digit and D is the second to last digit. Therefore, DE = 96.

So, YZ = 30 and DE = 96

Step-by-step explanation:

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The answer is true, our inequality has a solution of x > 13. Our final answer is: 4(x^2 - x - 12) > (101 - 2x)^2

To create a radical inequality that has a solution of x > 13 and has at least 4 terms in it, we can start with the basic inequality x > 13 and add terms to both sides to create a more complex equation. For example:

√(x + 3) + 2 > √(x - 4) + 12

Now, we can rearrange the terms and square both sides to get rid of the radicals:

√(x + 3) - √(x - 4) > 10

(√(x + 3) - √(x - 4))^2 > 10^2

x + 3 - 2√(x + 3)(x - 4) + x - 4 > 100

2x - 2√(x + 3)(x - 4) > 101

Now, we can isolate the radical term and square both sides again:

-2√(x + 3)(x - 4) > 101 - 2x

4(x + 3)(x - 4) > (101 - 2x)^2

4(x^2 - x - 12) > 10201 - 404x + 4x^2

0 > 3x^2 - 403x + 10237

Since we want the solution to be x > 13, we can plug in 13 for x and see if the inequality is true:

0 > 3(13^2) - 403(13) + 10237

0 > 507 - 5239 + 10237

0 > 4505

Since this is true, our inequality has a solution of x > 13. Therefore, our final answer is:

4(x^2 - x - 12) > (101 - 2x)^2

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The simplified expression is (x+1)^2/(2x-1).

To simplify the expression ((x)/(x+1)+1)*(1+x)/(2x-1), we can begin by multiplying the numerator and denominator of the first fraction by x+1 to eliminate the fraction in the numerator:

((x)/(x+1)+1)*(1+x)/(2x-1)

= ((x)/(x+1)*(x+1)/(x+1) + (x+1)/(x+1)) * (1+x)/(2x-1)

= (x(x+1)/(x+1) + (x+1)/(x+1)) * (1+x)/(2x-1)

= (x + 1) * (1+x)/(2x-1)

= (x^2 + 2x + 1)/(2x-1)

Now, the expression is simplified to (x^2 + 2x + 1)/(2x-1).

We can further simplify this expression by factoring the numerator as (x+1)^2:

(x^2 + 2x + 1)/(2x-1) = (x+1)^2/(2x-1)

Note that I did not solve for any variables or values, as the original expression did not provide an equation or specific values to solve for. Instead, I simplified the expression to its most simplified form.

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Based on the provided information The result of rounding to four integer places is sin 58° ≈ 0.8480.

Making a number easier while maintaining a value that is near to what it was is known as rounding. Although less precise, the outcome is simpler to use. For instance, 73 is 70 when adjusted to the closest ten, since 70 is closer to 73 than 80 is.

Using a calculator, we can approximate sin 58° as follows:

sin 58° ≈ 0.8480

Rounding to four decimal places, we get:

sin 58° ≈ 0.8480

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The probability that none of the 3 detectors would work if there was smoke in the factory is 0.25³, or 0.015625 (1.56%).

Probability is a branch of mathematics that deals with the likelihood of certain outcomes or events occurring. Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. An event that is certain to occur has a probability of 1, while an event that is impossible to occur has a probability of 0. The probability of an event occurring can be calculated by dividing the number of successful outcomes by the total number of possible outcomes.

This probability indicates that the factory does have a safety problem, as there is a 1.56% chance that none of the smoke detectors would sound an alarm if there was smoke present. This presents a significant risk to the factory, as it could lead to an undetected fire that may cause damage to the facility or put employees in danger.

The company should look into ways to reduce the risk of the smoke detectors not working. One way to do this would be to increase the number of smoke detectors in the factory room, as the more detectors there are, the lower the probability that none of them will work. The company could also consider using more reliable smoke detectors that have a higher probability of working correctly when needed. Ultimately, the company should seek to reduce the risk of none of the detectors working by taking steps to increase the probability that at least one of them will sound an alarm in the event of smoke or a fire.

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Both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.

To determine if the functions f(x) and g(x) are inverses using composition, we need to find f(g(x)) and g(f(x)) and see if they both equal x.

First, let's find f(g(x)):
f(g(x)) = f((3)/(2)x+12)
= (2)/(3)((3)/(2)x+12)-8
= (2)/(3)(3)/(2)x + (2)/(3)(12) - 8
= x + 8 - 8
= x

Now, let's find g(f(x)):
g(f(x)) = g((2)/(3)x-8)
= (3)/(2)((2)/(3)x-8) + 12
= (3)/(2)(2)/(3)x - (3)/(2)(8) + 12
= x - 12 + 12
= x

Since both f(g(x)) and g(f(x)) equal x, we can determine that the functions f(x) and g(x) are inverses.

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Therefore , the solution of the given problem of triangle comes out to be  the shape is 55 square miles.

Because a triangular has two or more extra sections, it is a polygon. It's shape is a simple rectangle. A triangular shape can only be distinguished from a parallelogram by its sides A, B, and C. A singular plane rather than a cube is produced by Euclidean geometry when the edges are not perfectly collinear. A shape is referred to as triangular if it has three sides and three angles. An angle is the point where a quadrilateral's three sides meet. A triangle's sides add up to 180 degrees.

Here.

Two triangles with a base of 10 miles and heights of 7 miles and 4 miles can be formed from the composite design.

The following method can be used to determine a triangle's area:

A = (1/2)bh

where A represents area, B represents foundation, and H represents height.

We can calculate each triangle's area using the following formula:

=> Area of 1st triangle

=>  (1/2)(10)(7) = 35 square miles

=> Area of 2nd triangle

=>  (1/2)(10)(4) = 20 square miles

The two triangles' combined regions make up the composite shape's surface area.

55 square miles is the combined shape's area

=>  (35 + 20).

Consequently, the combined size of the two triangles in the shape is 55 square miles.

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a) The simplified expression is \frac{(x-4)}{2(x+2)}. b) The solution to the equation is x = -7.

a) To simplify the expression \frac{7}{x^2\ -\ 4}\div\frac{14}{x^2\ -6x\ +8}, we need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of \frac{14}{x^2\ -6x\ +8} is \frac{x^2\ -6x\ +8}{14}.

Now, we can multiply the two fractions: \frac{7}{x^2\ -\ 4} \times \frac{x^2\ -6x\ +8}{14} = \frac{7(x^2\ -6x\ +8)}{14(x^2\ -\ 4)}

Next, we can simplify the expression by canceling out any common factors. In this case, both the numerator and denominator have a factor of 7, so we can cancel them out:

\frac{7(x^2\ -6x\ +8)}{14(x^2\ -\ 4)} = \frac{x^2\ -6x\ +8}{2(x^2\ -\ 4)}

Finally, we can factor the numerator and denominator to see if there are any other common factors that can be canceled out:

\frac{x^2\ -6x\ +8}{2(x^2\ -\ 4)} = \frac{(x-4)(x-2)}{2(x+2)(x-2)}

Since both the numerator and denominator have a factor of (x-2), we can cancel them out:

\frac{(x-4)(x-2)}{2(x+2)(x-2)} = \frac{(x-4)}{2(x+2)}

So, the simplified expression is \frac{(x-4)}{2(x+2)}.

b) For the second part of the question, we need to solve the equation \frac{6}{x\ +1}\ =\ \frac{3}{x\ +\ 4}. To do this, we can cross-multiply and then simplify:

6(x+4) = 3(x+1)

6x + 24 = 3x + 3

3x = -21

x = -7

So, the solution to the equation is x = -7.

Note: The question is incomplete. The complete question probably is: a) Simplify the expression  \frac{7}{x^2\ -\ 4}\div\frac{14}{x^2\ -6x\ +8} . b) Solve the equation \frac{6}{x\ +1}\ =\ \frac{3}{x\ +\ 4}.

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The product of the two expressions can be set as the one in option 1.

The process of multiplying two given expressions with the aid of variables and constants is known as algebraic multiplication. The terms factors and multiplicands refer to the two expressions that make up an algebraic product, which is the combination of two expressions.

The two expressions can be set as follows:

4x³ + 0x² -3x + 4

                 2x - 5

As the x² term is not present we use the coefficient as 0.

Hence, the product of the two expressions can be set as the one in option 1.

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Therefore , the solution of the given problem of triangle comes out to be the HL Congruence Hypothesis cannot be used to demonstrate anything.

A triangular is a polygon because it has two or maybe more additional sections. It has a straightforward square form. Only the edges A, B, but also C distinguish a triangular from a parallelogram. When the sides are not exactly collinear, Euclidean geometry produces a singular plane instead of a cube. If a shape has three edges and three angles, it is said to be triangular.

Here,

According to the HL Congruence Theorem, a triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and corresponding limb of another right triangle.

We must assess whether the two right triangles have the following information in order to decide whether the HL Congruence Theorem can be used to prove that the triangles are congruent:

Both of them are right circles.

Each triangle has a limb that is congruent.

Each triangle's hypotenuses are similar to one another.

The HL Congruence Theorem allows us to infer that the triangles are congruent if all three requirements are satisfied.

The HL Congruence Hypothesis cannot be used to demonstrate anything if any one of the prerequisites is not satisfied.

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sin 2x = -4sqrt(3)/49, cos 2x = 47/49, and tan 2x = -8/15.

Answer:

Given the information sin x = 1/7, x in QII. The second quadrant (QII) lies between 90° and 180°.Therefore, we know the following about the values of the trigonometric functions:cos x is negative because it is in the second quadrant.tan x is negative because it is in the second quadrant.Therefore, cos x = -sqrt(48)/7 and tan x = -1/4.To find sin 2x, cos 2x, and tan 2x, we will use the following trigonometric identities: sin 2x = 2sin x cos x cos 2x = cos² x - sin² x tan 2x = 2tan x / (1 - tan² x)Substituting in the values for sin x and cos x, we get:sin 2x = 2(1/7)(-sqrt(48)/7) = -4sqrt(3)/49cos 2x = (-sqrt(48)/7)² - (1/7)² = 47/49tan 2x = 2(-1/4) / (1 - (-1/4)²) = -8/15Therefore, sin 2x = -4sqrt(3)/49, cos 2x = 47/49, and tan 2x = -8/15.

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The restrictions on the variable in the rational equation (1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) are x != 4 and x != -5.

The restrictions on the variable in the rational equation are x != 4 and x != -5. This is because the denominators of the rational expressions (x-4) and (x+5) cannot equal zero, as division by zero is undefined.

To find the restrictions, we can set each denominator equal to zero and solve for x:

x - 4 = 0 => x = 4

x + 5 = 0 => x = -5

So, the restrictions are x != 4 and x != -5.

In summary, the restrictions on the variable in the rational equation (1)/(x-4)-(2)/(x+5)=(2x-1)/(x^(2)+x-20) are x != 4 and x != -5.

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Answer: The median is the best measure of center for distributions that are skewed or have extreme values, since it is less affected by outliers than the mean. Therefore, the correct answers are:

- A bar graph that forms a gradual incline and a sharp decline of values.

- A bar graph that forms a sharp incline and a gradual decline of values.

Both of these graphs suggest that the data is skewed, and in these cases, the median is a better representation of the "typical" value than the mean.

The other two options do not provide enough information to determine whether the data is skewed or not, so we cannot say for certain whether the median is the best measure of center in those cases. The bar graph with values that hover around 10 y could have a symmetrical distribution with a mean and median that are the same, or it could have a skewed distribution where the median is a better measure of center. Similarly, the pyramid-shaped bar graph could have a symmetrical distribution, or it could be skewed in a way that the median is not a good measure of center.

Step-by-step explanation:

Khan and Jorman's scores will be the same in 4.545 weeks, and their score at that time will be 786.36 using the equal values.

With the equal values approach, two expressions are made equal, and the variable that makes them equal is then solved for. When solving systems of equations with two variables, this is often done in order to determine the values of the two variables that will simultaneously make the equations true.

Let us suppose the number of weeks = y.

Let us suppose the score = x.

Given that, Khan's current score is 750 and is rising 8 points per week.

Khan's score: y = 8x + 750

Jormans current score is 650 but is growing by 30 points each week:

Jorman's score: y = 30x + 650

Their scores will be equal at:

8x + 750 = 30x + 650

22x = 100

x = 4.545

Substitute the value of x in the equation to obtain y:

y = 8(4.545) + 750

y = 786.36

Hence, Khan and Jorman's scores will be the same in 4.545 weeks, and their score at that time will be 786.36.

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If cos tetha = -5/17 and tetha is in Q III, then sin tetha can be found using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.

Substituting the given value for cos tetha and solving for sin tetha gives:

sin^2 tetha + (-5/17)^2 = 1

sin^2 tetha = 1 - 25/289

sin^2 tetha = 264/289

sin tetha = √(264/289)

sin tetha = ±√264/17

Since tetha is in Q III, where sin is negative, the correct answer is:

sin tetha = -√264/17


If sin tetha = 1/4 and tan tetha = √3, then cos tetha can be found using the definition of tan tetha: tan tetha = sin tetha/cos tetha.

Substituting the given values for sin tetha and tan tetha and solving for cos tetha gives:

√3 = (1/4)/cos tetha

cos tetha = (1/4)/√3

cos tetha = √3/12


If sec tetha = -4 and tetha is in Q II, then cos tetha can be found using the definition of sec tetha: sec tetha = 1/cos tetha.

Substituting the given value for sec tetha and solving for cos tetha gives:

-4 = 1/cos tetha

cos tetha = -1/4

Once we have cos tetha, we can find sin tetha using the Pythagorean identity: sin^2 tetha + cos^2 tetha = 1.

Substituting the value for cos tetha and solving for sin tetha gives:

sin^2 tetha + (-1/4)^2 = 1

sin^2 tetha = 1 - 1/16

sin^2 tetha = 15/16

sin tetha = ±√(15/16)

Since tetha is in Q II, where sin is positive, the correct answer is:

sin tetha = √15/4

Once we have sin tetha and cos tetha, we can find the other trigonometric function values using their definitions:

tan tetha = sin tetha/cos tetha = (√15/4)/(-1/4) = -√15

cot tetha = 1/tan tetha = -1/√15 = -√15/15

csc tetha = 1/sin tetha = 4/√15 = 4√15/15

sec tetha = 1/cos tetha = -4 (given)

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The measurements are shown in the solution

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Given are right triangles, we need to find the value of x in each,

We will use Trigonometric ratios to find the same,

The sine is the ratio between the length of the opposite leg and the length of the hypotenuse.

The cosine is the ratio between the length of the adjacent leg and the length of the hypotenuse.

The tangent is the ratio between the length of the opposite leg divided by the length of the adjacent leg.

1) sin 21° = 11/x

x = 30.7

2) cos 34° = x/28

x = 23.21

3) tan 49° = 33/x

x = 28.68

4) T =  cos⁻¹ (11/23)

=  61.42°

5) T = sin⁻¹(21/44)

= 28.50°

6) T = tan⁻¹(8/12)

= 33.7°

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Answer:

#7
AB = 4.1

CB = 4.1

#10
AC = 21.21

CB = 15

#11
AC = 2.828
CB =2

#12
AB =  2.616
CB = 2.616

#13

AC = 6
CB = 3√2

#14

AC = 5.94

CB = 4.2

Step-by-step explanation:

The triangle is a right isosceles triangle with AB = AC

This means
AC² = AB² + CB²
= AB² + AB²
= 2AB²
AC =  AB√2

and

AC = CB√2                (since CB= AB)

#7
Given  AC = 5.8

We know AC = AB√2
[tex]AB= \dfrac{AC}{\sqrt{2}} = \dfrac{5.8}{\sqrt{2}} = 4.1[/tex]

CB = AB  is also  4.1

#10
Given AB = 15

AC = AB√2 =  15√2 =
CB= AB = 15

#11

Given CB = 2

AB = CB= 2

AC = CB√2 = 2√2 = 2.828

#12

Given AC = 3.7

We know AC = AB√2
AB= AC/√2 = 3.7 ÷ √2 = 2.616

CB = AB  is also  2.616

#13

Given AB = 3√2

AC = AB√2 = 3 x √2 x √2 = 3 x 2 =6   (√2 x √2 = 2)
CB = 3√2

#14

Given AB= 4.2

AC = 4.2 x √2 = 5.94

CB = AB = 4.2

Answer: 0.66 cents per pen

Step-by-step explanation:

$4.65 for a pack of 7 pens. You want to divide $4.65 by 7 and you get 0.66