Assertion : If both zeros of the quadratic polynomial x k2 2 x 2 − + are equal in magnitude but opposite in sign then
value of k is ½.
Reason : Sum of zeros of a quadratic polynomial ax bx c 2 + + is a
-b

The average speed of Keddy based on time of travel and distance covered is 160 km/hr.

The time taken to reach the destination = 13:51 - 12:36

Performing subtraction

Time taken to reach the destination = 1:15 or 1 hour and 15 minutes

As we know, 1 hour has 60 minutes.

So, total time in hour = 1 + 15/60

Total time in hour = 1.25 hours

The speed, distance and time are related as -

Average speed = total distance travelled ÷ total time taken

Keep the values in formula -

Average speed = 200/1.25

Performing division

Average speed = 160 km/hr

Thus, the average speed of Keddy is 160 km/hr.

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The area of rectangle is  19.58 m.

The equation for calculating a rectangle's area. Rectangle's surface area. A = l × b. Once the length and breadth of a rectangle are known, its area may be computed. The area of the rectangle can be calculated as a square unit by multiplying the length and width.

The surface of a shape's area is measured. You must multiply the length and breadth of a rectangle or square in order to determine its area. A has an area of x times y.

length of the rectangle = 2 2/4 m

width of rectangle = 7 5/6 m

Area of rectangle = Length × Breadth

⇒ 10/4 × 47/6

⇒ 5/2 × 47/6

⇒ 19.58 m

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An equation of the line through the points (-6, 5) and (-3, -3) is y = -8x/3 - 11.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (-6, 5) and (-3, -3) by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 5 = (-3 - 5)/(-3 + 6)(x + 6)

y - 5 = -8/3(x + 6)

y - 5 = -8x/3 - 16

y = -8x/3 - 16 + 5

y = -8x/3 - 11

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The standard deviation is 6.

What a standard deviation means?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Standard deviation in statistics is a measure of dispersion of a set of data relative to the mean of the data set.

The square root of the variance of the data set gives the standard deviation of the data set.

In this case, the variance,

s²=36 ( as given, variance of the set of values is 36 )

The standard deviation,

s=√36 =6

Therefore, the standard deviation is 6.

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Answer:

The ratio of boys to girls in von's class is 2:3, which means for every 2 boys there are 3 girls.

The following can represent the number of boys and girls in her class:

If there are 12 students in the class, there would be 8 boys and 4 girls (2:3 ratio)

If there are 15 students in the class, there would be 10 boys and 5 girls (2:3 ratio)

If there are 18 students in the class, there would be 12 boys and 6 girls (2:3 ratio)

And so on.

It is important to note that as long as the ratio of boys to girls is 2:3, the numbers will represent the number of boys and girls in the class.

Step-by-step explanation:

"She" is the right pronoun to finish the phrase. The pronoun "she" is used to refer to the victorious candidate since she is considered to be female. The pronoun "they" is commonly used when referring to someone whose gender is unclear or undetermined.

A pronoun is a term that is used in a phrase in place of a noun. In order to avoid using the same nouns again and to refer to someone or something without using their name, pronouns are utilised. Pronouns can be classified into a variety of categories, such as personal pronouns (like I, me, you, him, her, it, we, us, and they), possessive pronouns (like my, mine, your, yours, his, her, hers, it, our, ours, and their, theirs), reflexive pronouns (like I, myself, you, him, her, it, ourselves, ourselves, and ourselves), and interrogative pronoun (such as who, whom, whose, which, what).

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The area of square A is 25 in² and each side measures 5 inches

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

For square B:

Area = side²

144 = side²

side = 12 in

For square C:

Area = side²

169 = side²

side = 13 in

To find the length of each square A side, we use Pythagoras theorem. Hence:

(Side C)² = (Side A)² + (side B)²

13² = (side A)² + 12²

169 = (side A)² + 144

(side A)² = 25

Side A = 5 in

Area of square A = (side A)² = 5² = 25 in²

The area of square A is 25 in²

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The ratio between of the two legs of a 30-60-90 triangle:

√3 : 2.

The correct option is D.

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Given:

A triangle is a 30-60-90 triangle.

So, the sides of a 30-60-90 triangle are always in the ratio of 1:√3: 2.

The side opposite is 60° is √3.

And The side opposite to 90° is 2.

So, the ratio,

= s/h

= √3 : 2.

Therefore, the ratio is √3 : 2.

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if A triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length then the other angle is 43 degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that a triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length

We have to find the measure of the third angle.

By angle sum property the sum of three angles is equal to 180 degrees.

43+94+x=180

137+x=180

Subtract 137 from both the sides

x=43 degrees.

Hence, if A triangle has a 43 degree angle and a 94 degree angle and a side of 6 centimeters in length then the other angle is 43 degrees.

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In the trigonometric functions angles are,

1) 53.13°

2) 48.19°

3) 36.87°

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given ,

1) sin x = [tex]\frac{4}{5}[/tex]

=> x= [tex]sin^{-1}\frac{4}{5}[/tex]

=> x = 53.13°

2) cos x = [tex]\frac{2}{3}[/tex]

=> x = [tex]cos^{-1}\frac{2}{3}[/tex]

=> x = 48.19°

3) tan x = [tex]\frac{3}{4}[/tex]

=> x = [tex]tan^{-1}\frac{3}{4}[/tex]

=> x = 36.87°

Hence the angles are,

1) 53.13°

2) 48.19°

3) 36.87°

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The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

The distance between Point P and Point Q on the number line is the absolute value of the difference between the coordinates of the two points.

In other words, if Point P has coordinate x and Point Q has coordinate y, then the distance between the two points is |x - y|. For example, if Point P has coordinate 3 and Point Q has coordinate 7, then the distance between the two points is |3 - 7| = |-4| = 4. This is because it is measuring the distance between two points in one dimension, that is on the number line.

The number line is a visual representation of the set of real numbers. It is a straight line with points that correspond to the numbers on the line. Each point on the number line corresponds to a unique real number, and the position of the point on the line indicates its value. The numbers on the left side of the number line are generally considered as negatives and the numbers on the right side as positives. The numbers on the line are evenly spaced, with the distance between any two consecutive numbers being the same, typically represented by 1 unit.

This question should be provided as:

The question is incomplete, thus the answer is general.

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The 29th term in the given arithmetic sequence is −170.

An arithmetic sequence can be defined in one of two ways. In an arithmetic sequence, "each term is obtained by adding a fixed number (positive or negative or zero) to its preceding term," or "each term is obtained where the differences between every two successive terms are the same." The arithmetic sequence that comes next is created by adding 4 to the term that comes before it.

Given that 89th term in an arithmetic sequence is -590

And 8th term is -23

-590 = a₁ + (89 - 1)d

-590 = a₁ + 88d

a₁ = -590 - 88d

and

-23 = a₁ + (8 - 1)d

-23 = a₁ + 7d

a₁ = -23 - 7d

Factor out a₁ in both equations

-590 - 88d =  -23 - 7d

-88d + 7d = 590 - 23

-81d = 567

d = -567.81

d = −7

As we have the d lets find fist term

a₁ = -23 - 7(-7)

a₁ = -23 + 49

a₁ = 26

Now, find  29th term

a₂₉ = 26 + (29 - 1)(−7)

a₂₉ = −170

Thus, the 29th term in the given arithmetic sequence is −170.

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The values of the constants for the given quadratic equation are a=2, b=3, and c=7.

The values of the constants for the given quadratic equation are a=2, b=3, and c=7.

The quadratic equation is defined as a polynomial with a degree of two or with a maximum power of a variable in a polynomial of 2, which will cut two intercepts on the graph at the x-axis.

Here is an equation to consider:

2x²+3x+7 = 0

Using the general equation as a comparison to the previous equation:

ax²+bx+c = 0

Thus, the constants' values will be as follows:

a=2, b=3 c=7

Therefore, for the following quadratic equation, the values of the constants are a=2, b=3, and c=7.

The values of the constants for the given quadratic equation are a=2, b=3, and c=7.

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The given equation  "x⁴- 52x² + 576 = 0" does not have any imaginary solution , the real solutions are  x = 4 or x = -4 or x = 6 or x = -6    .

The real solution in algebra is simply a solution of the equation which is a real number.

the equation is : x⁴ -52x² + 576 = 0 ;

we rewrite the equation as : ⇒  (x²)² - 52x² + 576 = 0;

let x² = u ;

the equation becomes ⇒u² - 52u + 576 = 0 ;

the equation in factor form is written as : ⇒ (u - 16)(u - 36) = 0  ;

this implies that ; ⇒ x² = 16   or   x² = 36  ;

that means that the real solutions are  ⇒ x = ±4  or x = ±6  .

The given question is incomplete , the complete question is

What are the real or imaginary solutions of the polynomial equation x⁴ -52x² + 576 = 0 ?

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(3, 4, 5), (5, 12, 13), (6, 8, 10), (9, 12, 15), and (15, 20, 25) are the five most common Pythagorean triples.

Any three positive integers that completely satisfy the Pythagorean theorem are considered Pythagorean triples. According to the theorem, the hypotenuse's square is equal to the sum of the squares of the other two legs of any right triangle. The Pythagorean triples are made up of the right triangle's three sides. In this article, we will learn how to make a few Pythagorean triples.

A set of three positive numbers known as Pythagorean triples conforms to the Pythagoras theorem's formula, which reads as follows: a2 + b2 = c2, where a, b, and c are positive integers. "c" denotes the "hypotenuse," or longest side, and "a" and "b" denote the remaining two legs of the right-angled triangle. (a,b,c) is how the Pythagorean triples are shown. Three, four, and five are the most well-known Pythagorean triples. We are able to demonstrate that the equations 3, 4, and 5 are correct. Find out how! 32 + 42 = 52 ⇒ 9 + 16 = 25. The Pythagorean triples 3, 4, and 5 are depicted in the right-angled triangle below.

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Answer:

x=99°

Step-by-step explanation:

total angle :

(n-2)×180°

=360°

x= 360°- 101° - 92°- 68°

x= 99°

Answer:

The value of X is 99 ( being the sum of all angle of quadrilateral is 360)

Feynman says Phlogiston Theory was not scientific is because it didn't utilized methods that were related to science.

The phlogiston theory, a debunked scientific hypothesis, suggested that combustible bodies contained a fire-like substance called phlogiston, which was released during combustion. Johann Joachim Becher first put forth the concept in 1667, and Georg Ernst Stahl later formalized it. Phlogiston theory sought to explain oxidation, the modern term for chemical processes like combustion and rusting.

According to the phlogiston theory, when something is burned, it dephlogisticates, releasing stored phlogiston that is then taken in by the air. The phlogiston is then absorbed by developing plants, which is why air does not spontaneously ignite and why plant matter burns so effectively.

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The  waiting time represents the 5th percentile is 160.852 days and the waiting time represents the third quartile is 220.22 days

The parameters that will help us to understand the solution are

Let X be the random variable representing the waiting time.

Here the mean = 203 days

Standard deviation (∑∝) = 25.7 days

For calculating the 5th percentile, we need to find the z- score having area 0.05.

By Z-score table we have Z= -1.64

Now, Using formula X=Z\standard deviation +mean

X = (-1.64)*(25.7)+203

 = 160.852 days

Waiting time representing 5th percentile = 160.852 days.

For calculating third quartile, we know that third quartile represents the area to the left of 75% = 0.75

we need to calculate the Z score when the area is 0.75. Using the table we get Z= 0.67

X = (0.67)*(25.7)+203

  = 220.22 (days)

Waiting time representing third quartile = 220.22 days

Conclusively, 160.852 days and 220.22 days represent the 5th and 3rd percentile and quartiles of the waiting time

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Correct question:

Assume the time spent (in days) waiting for a heart transplant for people ages 35-49 can be approximated by a normal distribution with mean of 203 days and a standard deviation of 25.7 days. what waiting time represents the 5th percentile? what waiting time represents the third quartile?

The sum of the interior angles for a Polygon of 5 angles is 540°

An angle is the opening formed by two half-straights (sides) with the same origin called vertex. For example, within a triangle there are three angles, which in total add up to 180°.

The sum of the interior angles of a Polygon is calculating by the formulation:

Sum of Interior Angles = (n-2) x 180°

Replacing the number of angles (n = 5) in the equation we get:

Sum of Interior Angles = (n-2) x 180°

Sum of Interior Angles = (5-2) x 180°

Sum of Interior Angles = 3 x 180°

Sum of Interior Angles = 540°

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Answer: True.

A diameter is a line that goes across the whole circle and passes by the center.

A chord is any line segment that connects two points on the circumference.

Since the diameter is a line from one opposite end of the circle to the other, it is connect two points on the circumference, thus it is a chord.

Step-by-step explanation:

Answer:

Adding or subtracting (depending on the missing sign) will eliminate the y term and make it easy to solve for x

Step-by-step explanation:

The first equation is missing a + or - sign

Regardless, it is easier to solve using elimination since the y coefficients are the same.

Adding or subtracting (depending on the missing sign) will eliminate the y term and make it easy to solve for x

If we use the method of completing the square to solve the quadratic equation x² + 5x - 1 = 0, we have to add (-25/4) to convert it to (x + 5/2)²  - 29/4 = 0

The standard form of a quadratic equation is:

ax² + bc + c = 0

In this case, the quadratic function is:

x² + 5x - 1 = 0

To solve it using the "complete the square" method, write the equation as:

(x + 5/2)² - 1 + .... = 0

The blank part in the above equation means we need to add a number to make the equality still holds.

Note that:

(x + 5/2)² = x² + 5x + 25/4

Hence,

(x + 5/2)²  - 1  =  x² + 5x + 25/4 - 1

Hence, we need to add (-25/4) to make the original equality holds:

(x + 5/2)² - 1 + (-25/4) = 0

(x + 5/2)²  - 29/4 = 0

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It means that the area of the gingerbread house Hillary will cover with icing is 0 cm^2.

To find the area of the gingerbread house that Hillary plans to cover with icing, we need to subtract the area of the window and the door from the total area of the front of the house.

The window measures 2 cm x 2.5 cm, so the area of the window is 2 cm x 2.5 cm = 5 cm^2

The door measures 2 cm x 3 cm, so the area of the door is 2 cm x 3 cm = 6 cm^2

The total area of the front of the house is the sum of the areas of the window and door, so we can find it by adding 5 cm^2 + 6 cm^2 = 11 cm^2

To find the area of the gingerbread house Hillary will cover with icing, we need to subtract the area of the window and the door from the total area of the front of the house:

Area of gingerbread house covered with icing = Total area of front of house - Area of window - Area of door

Area of gingerbread house covered with icing = 11 cm^2 - 5 cm^2 - 6 cm^2 = 0 cm^2

It means that the area of the gingerbread house Hillary will cover with icing is 0 cm^2. This means that the area of the window and door are equal to the total area of the front of the house and there's no space left to put icing on.

Thus, It means that the area of the gingerbread house Hillary will cover with icing is 0 cm^2.

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The window is 2 cm by 2.5 cm, so its surface is 2 cm by 2.5 cm, or 5 cm2.

The door is 2 cm by 3 cm in size, so its surface is 2 cm by 3 cm, or 6 cm2.

We can calculate the area of the front of the house by adding the areas of the window and entrance (5 cm2 + 6 cm2 = 11 cm2)

The area of the window and door must be subtracted from the overall front-of-the-house area in order to determine how much of the gingerbread house Hillary will ice:

Total frontage of the home divided by the size of the gingerbread house covered in frosting

Answer:

58°

Step-by-step explanation:

A right triangle is a type of triangle with exactly one angle equal to 90°. The other two angles sum up to 90°.

A triangle measures 180°. We plug in the given information from the question above…

90° + 32° = 122°

Applying the Triangle Sum Property…

180° - 122° = 58°

The solution of the given inequality is x < 0  or x > 6. [ And the Graph is given below]

It is quite similar to graphing linear equations to draw inequalities. Two further steps must be taken while concentrating on the inequality sign.

When you graph linear inequalities, you must perform two more steps i.e Choosing between a solid borderline and a dashed boundary line will be the first stage.

We can identify the boundary line with the inequality symbol.

We use a dotted boundary line if the inequality symbol is greater than or less than. This indicates that the answers are not part of the borderline.

We will use a solid line to denote that the solutions are included on the boundary line if the inequality symbol is greater than or equal to or less than or equal to.

Here we have

3 |x - 3| > 9    

Divide by 3 into both sides

=> [ 3|x - 3| ]/3 > 9/3

=> |x - 3| > 3  

As we know

=> |x - 3| > 3    

=>  (x - 3) < -3  or  (x - 3) > 3  

=>   x < 0         or    x > 6

Therefore,

The solution of the given inequality is x < 0  or x > 6. [ And the Graph is given below]

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Answer:

3

Step-by-step explanation:

The ratio of x to y is constant

And as you can see

X×6 = y

6×6= 36

8×6=48

10×6= 60

Therefore

X×6 =18

18÷6= 3

X=3

Theoretically, Usain Bolt can complete a kilometer in 96.9 seconds, and he also moves at an average speed of 1.032 * 10 m/s.

speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.

Given that, At the 2008 Summer Olympics, Usain Bolt won the 100 m sprint with a time of 9.69 sec.

Thus,

The average speed of the athlete = 100/9.69

The average speed of the athlete = 10.319 m/sec.

Also theoretically he can run 1 km in 96.9 seconds.

therefore, theoretically Usain bolt can run 1 km in 96.9 seconds, and also his average speed is  1.032 * 10 meters per second.

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Addition symbols are called plus signs. They are used to indicate a mathematical operation or expression that adds two numbers or values together. They are represented by a cross or a plus sign (+) and are usually placed between the two values being added.

The plus sign is often used in algebra and other mathematical equations to indicate that two numbers should be added together. It is also used in programming languages to indicate the addition of two values. Additionally, the plus sign is used to indicate the inclusion of something, such as a plus sign in front of a movie title to indicate that it is an extended edition.

The plus sign is an important part of mathematics and programming and is used in many different contexts. It is a versatile symbol that is used to indicate the addition of two values. Knowing how to use the plus sign correctly is an important part of understanding basic mathematics and programming.

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Answer:

see explanation

Step-by-step explanation:

• the diagonals bisect each other

that is the point F is the midpoint of both diagonals GJ and KH

Note that GJ ≠ KH

Then

GF ≅ FJ

KF ≅ FH

your error is in that you have mixed up the appropriate diagonals