Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.

Answer:

please open the following image for the answer

The solution for the given quadratic equation is  x = -11 or x = -1.

A quadratic equation is an equation of second order. Quad implies the square power, it is also called equation of degree 2.

The standard form of a quadratic equation is ax² + bx + c = 0.

Where a, b and c are constants.

here, given that,

The given quadratic equation is,

x² + 12x + 11 = 0.

The graph of the equation is, plotted below.

From the graph,

The solutions are x = -1 and x = -11

The second approach to find the solution for the given quadratic equation is factorization method,

x² + 12x + 11 = 0

x² + 11x + x + 11 = 0

x(x + 11) + 1(x + 11) = 0

(x + 11) (x + 1) = 0

x = -11 or x = -1

So, the required solution is x = -11 or x = -1.

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When the person has been dead for 2 minutes and comes back their experience of 2 minutes dead then we call that the person is suffering from Lazarus Syndrome .

What is Lazarus Syndrome ?

The Lazarus syndrome is referred as to your blood circulation returning spontaneously after your heart stops beating and it fails to restart despite providing  cardiopulmonary resuscitation (CPR).

In Simple words it can be called as returning to life after it appears that the person has  died.

So, if the person comes back to life after experience of 2 minutes of dead , then we say that the person has Lazarus Syndrome and got a heart attack .

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The possible number of the right triangle is 6. Hence option A is the correct option.

What is the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.

Given that △ABC is a right triangle.

The legs of the △ABC are a and b which are integers. The hypotenuse is b+1. Since b is an integer thus b+1 is an integer.

Pythagorean theorem:

The sum of the square of the legs of a right triangle is the square of the hypotenuse.

According to Pythagorean theorem,

a² + b² = (b+1)²

Applying the algebraic formula (a+b)² = a² + b² + 2ab

a² + b² = b² + 2b +1

Cancel out b² from both sides:

a² = 2b + 1

2b is always a positive number since 2 is multiplied with b. Thus 2b+1 is an odd number.

Since a² = 2b + 1, thus a² is an odd number.

The square of an odd number is an odd number. Thus a is an odd number.

Again given that,

b<100

2b < 200

2b + 1< 201

Putting 2b + 1 = a²:

a² < 201

Now putting a=1 in a² < 201:

1² < 201 (true)

Now putting a=3 in a² < 201:

3² < 201 (true)

Now putting a=5 in a² < 201:

5² < 201 (true)

Now putting a=7 in a² < 201:

7² < 201 (true)

Now putting a=9 in a² < 201:

9² < 201 (true)

Now putting a=11 in a² < 201:

11² < 201 (true)

Now putting a=13 in a² < 201:

13² < 201 (true)

Now putting a=15 in a² < 201:

15² < 201 (false)

If a = 1, 2b+1 = 1 which implies b = 0. The length of a side of a triangle is never zero. Therefore a ≠ 1.

Thus the possible values of a are 3,5,7,9,11,13.

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The mean, median, and mode of the heights of 20 people belonging to the same group were found to be 160.95 cm, 160 cm, and 160 cm respectively.

Mean:

Add all the heights together:

160 + 160 + 170 + 180 + 160 + 160 + 175 + 170 + 160 + 160 + 160 + 160 + 160 + 160 + 160 + 175 + 160 + 160 + 170 + 160 = 2605

Divide the sum by the number of data points (20):

2605 / 20 = 160.95

Median:

Arrange the data in numerical order:

160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 170, 170, 175, 175, 180

The median is the middle value, which is 160.

Mode:

The mode is the most common value, which is 160.

The mean, median, and mode of the heights of 20 people belonging to the same group were calculated by adding all the heights together and dividing the sum by the number of data points (20). The mean was found to be 160.95 cm. The data was then arranged in numerical order and the median was found to be the middle value, which was 160 cm. Lastly, the mode was determined to be the most common value, which was also 160 cm.

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With the help of equations we can say that the shark is 18 years old.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.  To determine the value

To determine the value A statement is not an equation if it has no "equal to" sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Hence, the shark is 18 years old.

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According to the  management at Oak Tree Golf Course received a few complaints about the condition of the greens. and with the Several players complained that the greens are emerged too fast. Rather than to  react towards  the comments of just a few, the Golf Association conducted in a survey of male and female golfers.

One of the biggest things  in holding  along with mid- and high-handicappers back is hitting more greens in regulation, mainly because  of it’s the key (usually) to stress-free two-putt pars and  to the occasional birdie. It’s also  one of the best way to eliminate certain trouble. If mid- or high-handicappers are missing around the  greens, that’s when problems can pile up into picture . But we all need  certain goals.  to Tina Tombs, a former LPGA pro and to  a GOLF Top 100 Teacher, said a high-handicapper should set an certain  goal at seven greens in regulation, while a lower handicap should be  strive for 10 per round.

If they aren’t carrying any of the 200 yards, then they should play 6,000 or less then that and they don’t do that in terms of the Preisinger says. Because when you wanted to  play too far back you can have four or five penalty shots off  around the tee.

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The probability that x + y <1/3 is 1/18, the probability that x + y < 3/2 is 0.875 and the algebraic expression for F(u) is: F(u) = 0, if u < 0; F(u) = 0.5u^2, if 0 <= u <= 1; F(u) = 1 - 0.5(2 - u)^2, if 1< u < 2; F(u) = 1, if u >= 2.

(a) The set of points (x,y) in the unit square S for which x+y < 1/3 is a triangle with vertices at (0,0), (1/3,0), and (0,1/3).

The area of this triangle is

0.5(1/3)^2 = 1/18

Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 1/9.

(b) The set of points (x,y) in the unit square S for which x+y < 3/2 is a polygon with vertices at (0, 0), (1, 0), (1, 0.5), (0.5, 1) and (0, 1) as S = [0,1]×[0,1] refer figure for clarity.

The area is

1*1 - 0.5*0.5²

= 1 - 0.125

= 0.875

Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 0.875

(c) To find an algebraic expression for F(u), we need to consider different cases for the value of u:

if u < 0, then the set of points (x,y) for which x+y <= u is empty, so F(u) = 0

if 0 <= u < 1, then the set of points (x,y) for which x+y <= u is a triangle with vertices at (0,0), (u,0), and (0,u). The area of this triangle is u^2, so

F(u) = 0.5u^2

if 1 <= u < 2, then the set of points (x,y) for which x+y <= u is a polygon with vertices at (0,0), (1,0) (1, u-1), (u-1, 1) and (0, 1). The area can be obtained by subtracting the area of triangle with vertices (1, u-1), (u-1, 1) and (1, 1), from area of square, that is 1 sq units.

F(u) = 1 - 0.5(2 - u)²

if u >= 1, then the set of points (x,y) for which x+y <= u is the entire unit square, so

F(u) = 1.

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Answer:

[tex]y < 1[/tex]

Step-by-step explanation:

[tex]8y - 5 < 3 \\ 8y < 8 \\ y < 1[/tex]

The fundamental theorem of algebra any polynomial was first proved by Carl Friedrich Gauss in 1799.

In 1799, Carl Friedrich Gauss was a German mathematician who proved that any polynomial equation with complex coefficients has at least one root in the complex plane. This is known today as the Fundamental Theorem of Algebra. Gauss started by examining a particular polynomial equation and then used his knowledge of the properties of polynomial functions to prove that any polynomial equation with complex coefficients must have at least one complex root. His proof used a combination of calculus and algebraic manipulations to establish that the coefficients of a polynomial equation must satisfy certain conditions in order for the equation to have a complex root. Once these conditions are satisfied, he showed that the equation must have at least one complex root.

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As per the concept of the normal distribution and the central limit theorem, the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.

The term normal distribution is defined as a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.

Here we have given that  agency will select a random sample of 500 voters from one region, Region A, of the city and here we also know that The proportion is of 0.47.

Then the mean and the standard deviation are 0.47 and 0.0223 respectively.

Here the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5 is calculated as,

=> Z = (0.5 - 0.47) / 0.0223

=> Z = 1.34

Then by using the Z table we have identified the value of P as 0.9099.

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A race car driver is 3.79 km away from where she started.

Assume that a race car driver turns southwest, at an angle of  45 degrees.

Also she turns East making another 45 degree angle.

So, we get a right triangle.

Let ABC be right triangle with A = 90°, B = 45° and C = 45°

For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)

Consider the sine of angle B

sin(B) = Opposite side of angle B / Hypotenuse

sin(45) = x / 2.75

x = 1.94

sin(C) = Opposite side of angle C / Hypotenuse

sin(45) = y/2.75

y = 1.94

So, the distance to north before paths crossed would be,

N = 4.69 - y

N = 3.31

And the distance after she passed her northern path.

E = 3.89 - x

E = 1.85

Let m be the distance from Starting Point to End Point.

Using Pythagoras theorem,

m² = N² + E²

m² = (3.31)² + (1.85)²

m = 3.79 km

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The researchers have increased the power of their analysis by increasing the sample size.

The number of subjects involved in a sample size is referred to as the sample size in market research.

Examine 15 randomly selected groups of subjects.

There are five main ways to increase the power of an experiment or study: increase the alpha level, decrease random error, conduct a one-tailed test, expand the sample size, or increase the effect size. Of these, only the first option, which increases the sample size, will increase power.

Thus, the researchers have increased the power of their analysis by increasing the sample size.

Complete question: As one step in the statistical analysis of the effectiveness of CHW intervention, researchers calculated the average percentage of postnatal care use found in 10 randomly selected groups of 50 mothers. How could the researchers have increased the power of their analysis?

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(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.

What is algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. It represents a value or a set of values, but it does not provide a specific numerical result until the variables are replaced with specific numbers.

(1) Let's say x is the number of fruit snacks Tyler ate.

Han ate 3/4 less than that, so the expression for the number of fruit snacks Han ate would be x - (3/4)x = x(1 - 3/4) = x/4.

(2) Let's say x is the number of miles Mai skated.

Clare skated 3/5 farther than that, so the expression for the distance Clare skated would be x + (3/5)x = x(1 + 3/5) = 8/5x.

(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.

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Answer:

C) [tex]x^{3} + 3x^{2} + 3x - 1[/tex]

Step-by-step explanation:

We have our equations. So, we will substitute them in our last equation, giving us:

[tex](x + 1) * (x^{2} + 2x - 1) + 2x[/tex]

Opening the parentheses gives us:

[tex]x^{3} + 2x^{2} - x + x^{2} + 2x - 1 + 2x[/tex]

Combining like terms:

[tex]x^{3} + 2x^{2} + x^{2} + 2x - x + 2x - 1[/tex]

Then, we combine:

[tex]x^{3} + 3x^{2} + 3x - 1[/tex]

So, your answer is C) [tex]x^{3} + 3x^{2} + 3x - 1[/tex].

Hope this helped!

Please give brainliest if possible!

The equation representing the polynomials are D = x³ + 3x² + 3x - 1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as D

Now , the value of D is

Substituting the values in the equation , we get

A = x + 1

B = x² + 2x - 1

C = 2x

The value of AB + C = D

And , AB = ( x + 1 ) ( x² + 2x - 1 )

On simplifying the equation , we get

AB = x ( x² + 2x - 1 ) +  ( x² + 2x - 1 )

AB = x³ + 2x² - x + x² + 2x - 1

AB = x³ + 3x² + x - 1

And , D = x³ + 3x² + x - 1 + 2x

D = x³ + 3x² + 3x - 1

Hence , the equation is D = x³ + 3x² + 3x - 1

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The length of the straw is equal to the length of the space diagonal of  rectangular box, that is 11.6 inches.

The length of the straw is equal to the space diagonal of the rectangular box. Space diagonals are three-dimensional diagonals.

If the length of the sides of the box is a, b, and c, then the space diagonal can be computed by applying the Pythagorean Theorem.

D = √(a² + b² + c²)

Substitute the following dimensions:

a = 10 inches

b = 3 inches

c = 5 inches

Then,

D = √(10² + 3² + 5²)

D = √(100 + 9 + 25)

D = √134 = 11.6 inches

Hence, the length of the straw is 11.6 inches.

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On solving the provided question, we can say that the fraction =5/12 = 0.4166666667  rounding off = 0

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here,

the fraction is

7/12 - 2/12

=5/12

= 0.4166666667

rounding off = 0

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Answer:

10.75 miles

Step-by-step explanation:

[tex]\frac{40}{100}[/tex]×x=4.3

40x=430

x=10.75

No, it is not possible to construct the triangle with the given sides measurement of 5.4 cm, 2.3 cm, 3.1 cm .

As given in the question,

In the given triangle,

Measurement of the sides of the triangle are  given by :

5.4 cm, 2.3 cm, 3.1 cm

To construct a triangle we need to follow the following property:

Sum of the measure of two sides of the triangle should be greater than the third side.

In the given measures:

( 2.3 + 3.1 ) cm = 5.4 cm which is equal to third side.

The property does not holds true.

Therefore, to construct a triangle with the given measure of the sides is not possible.

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Answer:

b = 4+15

b =19

Step-by-step explanation:

5x^2 + bx + 12 = 0

the sum of its roots = –b/a

m + n = - b/a

-4/5 + n = -b/5

-4 + 5n = -b

5n= -b + 4 -------------1

product of its roots = c/a

m*n = c/a

-4/5 * n = 12/5

-4 n = 12

n = -3 is the other root -------------2

Plug-in equation 2 in 1

5(-3) = -b + 4

-15 = -b + 4

b = 4+15

b =19

One of the solutions to the equation 5x^2+bx+12=0 is -4/5.the other solution is 2.4 + (-4/5) = 2.

The other solution to the equation 5x^2+bx+12=0 can be found by using the fact that the solutions of a quadratic equation of the form ax^2+bx+c=0 are given by the formula: x = (-b ± √(b^2-4ac)) / 2a.

In this case, a=5, b=b and c=12. We know that the product of the roots is equal to c/a and sum of roots is equal to -b/a. so the product of the roots is 12/5 = 2.4and the sum of the roots is -b/5 .

since we know that one of the solutions is -4/5, we can find the other solution by using the above formulas: -4/5 = 2.4 - other solution so the other solution is 2.4 + (-4/5) = 2.

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Answer:

i think its A=12BH+12BiH

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

The area of the sector is 113.14 square cm.

Step1:

Given, central angle, θ = 120°

Radius of circle, r = 21 cm

We have to find the area of a sector of the circle.

Area of sector = πr²θ/360°

= π(21)²(120°)/360°

= π(21)²(1/3)

= (22/7)(21)(21)(1/3)

= (22/7)(21)(7)

= (22)(21)

= 462 square cm.

Step2:

Therefore, the area of the sector is 462 square cm.

the area of a sector of circle of radius 12 cm and central angle 90°.

central angle, θ = 90°

Radius of circle, r = 12 cm

We have to find the area of a sector of the circle.

Area of sector = πr²θ/360°

= π(12)²(90°/360°)

= (22/7)(12)(12)(1/4)

= (11/7)(6)(12)

= 113.14 square cm

Therefore, the area of the sector is 113.14 square cm.

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Answer: If one of the roots of the equation 2x^2-bx-20=0 is -2.5, then by Vieta's Formulas, the other root is x = (20 + b)/4.

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

Given equation: 2x^2 - bx - 20 = 0

We are also given one of the solutions, which is -2.5.

We can start off by substituting -2.5 in place of x, in the given equation.

This is what it will look like:

2 * (2.5) ^2 - b (-2.5) - 20 = 0

After simplifying, the equation will now look like this:

12.5 + 2.5b - 20 = 0

Now, move all of the similar terms to one side of the equation:

2.5b = 20 - 12.5, which is basically 2.5b = 7.5

b = 7.5/2.5, which is b = 3

Now that we know what the value of "b" is, let's go back to the given equation (2x ^2 - bx - 20 = 0), and substitute "3" in place of "b".

It will look like this:

2x^2 - 3x - 20 = 0

We can now apply the Quadratic formula. The formula looks like this:

(-b ± √b^2 -4ac)

          2a

Substitute the values from the new equation into the formula:

3 ± √9 + 160

         4  

Simplify that:

3 ± 13

   4

You should now have two solutions:

x1 = 3 + 13,   which is x1 = 16/4 = 4            

         4

x2 = 3 - 13 , which is x2=-10/4, = -2.5

        4

Now, the root that was given to us at the start of the problem was -2.5, so the other solution is 4, which we just solved for.

I hope this helps!!

Therefore , the solution of the given problem of  surface area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

Its surface area serves as a proxy for how much overall space it occupies. The whole environment of a three-dimensional shape is taken into account when calculating its surface area. The overall size of something is its surface area. The volume of water in a cuboid can be determined by summing the face on each of the six rectangular sides. To determine the box's measurements, apply the following formula: For 2lh, 2lw, & 2hw, the surface is exactly the same (SA). The region is represented by the surface area of the muti form.

Here,

Given:

AB = D = 4 m (R = 2 m)

The size of the AB semicircle is:

=> Area = πr²/2

=>A = 2π

The dimensions of the little semicircle are a=5/6 + 2/3/2 m2 and a=5/6 + 3/2 m2.

The remainder area is therefore equal to A- a.

= 2π - (5π/6 + √3/2) m²

The unused space is equal to 2π - (5π/6 + √3/2) m²

Therefore , the solution of the given problem of area comes out to be  unused space is equal to 2π - (5π/6 + √3/2) m² .

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In the graph the letter "J" has a height of 17 units.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

According to the graph the distance from A to B is horizontal, so it need not be counted.

From B to C the distance is = 3 units

Again from C to O the distance is horizontal, so it need not be counted.

From O to D the distance is = 10 units

From D to E the distance is = 4 units

From E to F the distance is horizontal, so it need not be counted.

The distance from F to N need not be counted as it will be the repetition of the total height.

So, the total height is = 3 + 10 + 4 = 17 units

Therefore, the total height on the graph is 17 units.

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Answer: The perimeter of the shape is approximately 18.0 feet.

Step-by-step explanation:

The shape you described is a triangle, with one side of 8 feet and two sides of 5 feet. To find the perimeter of a triangle, we add up all the side lengths:

Perimeter = 8' + 5' + 5'

Perimeter = 8' + 10'

Perimeter = 18'

Rounding to the nearest tenth:

18 feet is the same as 18.0 feet rounded to the nearest tenth.

So, the perimeter of the shape is approximately 18.0 feet.

The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value). The range of a function is the set of all possible output values (y-values) that the function can produce.

When working with inequalities, the domain and range can be found by analyzing the inequality and the context of the problem.

To find the domain of an inequality function, we need to identify any restrictions or limitations on the input values (x-values) that would make the inequality invalid.

For example, if the inequality contains a denominator that cannot be equal to zero, we need to exclude those values of x from the domain.

To find the range of an inequality function, we need to identify the set of all possible output values (y-values) that would make the inequality true.

For example, if the inequality is in the form y > x, we know that all values of y that are greater than x will satisfy the inequality.

In summary, finding the domain and range of inequalities of a function involves identifying any restrictions or limitations on input values and the set of possible output values that would make the inequality true.

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