Factorise the following expression

​please

The path may be Quadratic in nature.

The path of a firework is modeled by a quadratic function. The firework ascends from point of launch with decreasing speed (negative acceleration due to gravity) until it reaches its maximum height and then starts dropping back to the ground at increasing speeds due to positive acceleration exerted by the force of gravity.

The flight path of the parabola can thus be modeled by height as a function of elapsed time

h = f(t) where f(t) is a quadratic equation in t with the general form being

a · t² +b · t  + c

We can easily eliminate the linear model since that implies the firework will ascend at a constant speed forever

The exponential model indicates that at the moment of launch the speed of the firework is constant and then it suddenly accelerates. However, we know from observation that the firework has the highest speed at the moment of launch

Do not be confused by the shape of the graph - it seems to indicate the firework shoots down and up.

Note: The path may be going in a different direction, perhaps reflected or translated vertically or horizontally while maintaining the same shape.

Indeed the actual path of the firework is a reflection of the graph about the x-axis. so that it is a downward-facing parabola. The vertex of the parabola is the highest y-value which is the maximum height the firework would reach.

The height would be the y-axis and the time t the x-axis.

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Answer:

See below

Step-by-step explanation:

North, 50

West, 28

South, 71

Answer: i got North, 50

West, 28

South, 71

but have a good day

Step-by-step explanation:

Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.

Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.

This is represented as follows:

t = k(l/p)

Where, k is the proportionality constant.

Given that, it takes 10 hours to paint 400 feet of fence with six workers.

Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:

10 = k (400 / 6)

10 = k (66.66)

k = 10 / 66.66

k = 0.15

Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:

t = (0.15) (1000 / 10)

t = (0.15) (100)

t = 15

Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.

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Answer:

Step-by-step explanation:

Vertex:

(

−

5

3

,

−

10

)

Focus:

(

−

5

3

,

−

359

36

)

Axis of Symmetry:

x

=

−

5

3

Directrix:

y

=

−

361

36

x

y

−

3

6

−

5

3

−

10

−

1

−

6

0

15

Answer: 9x^2-48x+54?

It is favorable to play this game.

This question requires a mathematical calculation of expected value to determine if the game is favorable or not.

The expected value is calculated as the sum of the product of each outcome and its corresponding probability.

The probability of winning $x for each prime number (2, 3, 5, 7) is 1/4, and the probability of losing $x/2 for each composite number (4, 6, 8, 9, 10) is 1/5.

Expected value = (1/4)*2x + (1/4)*3x + (1/4)*5x + (1/4)*7x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2 - (1/5)*x - (1/5)*x/2

= (1/4)(2 + 3 + 5 + 7)x - (1/5)(x/2 + x + x/2 + x + x/2)

= (17/4)x - (5/2)x

= (17/4 - 5/2)x

= (3/4)x

Since the expected value is positive, it is favorable to play this game.

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It is true that Pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.

Pooled variance is a statistical method used to estimate the common variance of two small independent samples when the population variances are assumed to be equal.

The pooled variance is calculated by taking the weighted average of the variances of the two samples.

This method is often used in inferential statistics to make inferences about the means of the two populations from which the samples were drawn.

The pooled variance is used to estimate the variance of the difference between the means of the two populations, which is used to calculate the standard error and the t-statistic for testing the difference between the means. Therefore, The statement is true.

so, It is true that Pooled variance is used for an inference about two means for two small independent samples when we assume normal population with equal variance.

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Expression 1: 4t - (4t x 0.25) = 4t - (t) = 3t

Expression 2: 4 x (t - (t x 0.25)) = 4 x (t x 0.75) = 3t

where 't' is the cost of one T-shirt.

In expression 1, the original cost of the four T-shirts (4t) is multiplied by 25% (0.25) which is the given discount percent, and then subtracted from the original cost.

In expression 2, the original cost of one T-shirt (t) is multiplied by 25% (0.25) and subtracted from the original cost, and then the resulting cost (t x 0.75) is multiplied by four to represent the cost of four T-shirts.

Both expressions represent the cost of the four T-shirts after a 25% discount has been applied. they both yield the same result of 3t, which represents the final cost of the four T-shirts after the discount has been applied.

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Answer:

[tex]20x^{2} + 12x[/tex]

Step-by-step explanation:

We can expand this equation:

(4x * 5x) + (4x * 3)

= [tex]20x^{2} + 12x[/tex]

If simplified/factored further, we can take out the common variable, x, as well as 4, which is a common number shared between 20 and 12:

4x(5x + 3)

If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.

If the ratio of two quantities is constant, then the two quantities are either in direct proportion to one another or vary in direct proportion to one another.

The direct variation equation is represented by the symbols y=kx or k=y/x, where k is the proportionality constant or variation constant.

A) The relationship between the distance traveled and the number of traveled hours is straightforward.

B ) The only distinction between x and y representing the length of a table is in units.As a result, it also differs directly.

The amount of money saved in C increases as more $1-off coupons are used, and vice versa.

If the speed is increased in D, it will take less time to travel 60 miles.As a result, there is no direct variation.

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The value of x from the triangle is x = 56°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be represented as ABC

Let the second triangle be represented as ABD

Now , the measure of side ABD = x°

In the triangle ABC ,

∠ACB = 180° - 104° ( angles on a straight line = 180° )

So , the measure of ∠ACB = 76°

And , the measure of side ∠ACB = measure of side ∠ABC ( given )

So , the measure of side ∠ABC = 76°

And , for a triangle ∠A + ∠B + ∠C = 180°

Substituting the values in the equation , we get

The measure of ∠BAC = 180° - ( 76° + 76° )

The measure of ∠BAC = 28°

Now , the measure of ∠BAC + measure of ∠BAD = 90° ( given perpendicular line )

So , the measure of side ∠BAD = 90° - 28°

The measure of side ∠BAD = 62°

And , measure of side ∠BAD = measure of side ∠ABD ( given that they are similar )

So , the measure of side ∠ABD = 62°

And , for a triangle ∠A + ∠B + ∠D = 180°

Substituting the values in the equation , we get

The measure of side ABD = x° = 180° - ( 62° + 62° )

The measure of side ABD = x° = 180° - 124°

The measure of side ABD = x° = 56°

Hence , the measure of x is 56°

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Answer:

Let x be the breadth of the rectangular field.

The length of the field is 2x.

We know that the perimeter of the rectangular field is (2x + 2x) = 4x.

Meghna jogged 5 times around the field, so she covered a distance of 4x km.

We know that 4x = 3km.

So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.

Answer:

Let x be the breadth of the rectangular field.

The length of the field is 2x.

We know that the perimeter of the rectangular field is (2x + 2x) = 4x.

Meghna jogged 5 times around the field, so she covered a distance of 4x km.

We know that 4x = 3km.

So, x = 0.75km, and the length of the field is 2x = 2(0.75km) = 1.5km.

Answer:

Step-by-step explanation:

Given:   ∠A =75°, ∠B=60° and ∠C=x

To find: ∠C

Proof: In △ABC

∠A =75° (given)

∠B=60° (given)

∠A+∠B +∠C=180° (angle sum property of a triangle: states that the sum of interior angles of a triangle is 180°)

75°+60°+∠C=180°

∠C=180-75+60

∠C=180-135°

∠C=45°

Therefore is 45 degrees.

The system of equations have no solution, the correct option is A.

For a solution to be solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at single point(as we need common point, which is going to be intersection of course)(this can be one or many, or sometimes none)

Given;

-1/2x+1/2y=-1   (1)

x-y=2   (2)

Now, multiplying equation 1 by 2

-x+y=-2

y=-2+x

Substituting the value of y in equation 2

x+2-x=2

Therefore, the equation have no solution.

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Answer:

To determine which of the given lines is parallel to the line y = 2/3x + 5, we need to compare their slopes. The slope of a line is the coefficient of the x variable, in this case 2/3.

The lines that are parallel have the same slope.

A.y=2/3x-4 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.

B.y=2/3x-7 is parallel to the line y = 2/3x +5 because the slope of 2/3 is the same.

C.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.

D.y=-2/3x+5 is not parallel to the line y = 2/3x +5 because the slope of -2/3 is different from the slope 2/3.

So the answer is A and B are parallel to the line y = 2/3x +5

The length of diagonal BD from the parallelogram ABCD is 10.

E is the intersection of the diagonals BD and AC. The point of bisection is therefore designated E.

BE = DE (The diagonals of a parallelogram bisect each other) (The diagonals of a parallelogram bisect each other)

From the provided diagram:

BE = 5

DE = BE = 5

BD length equals BE plus DE

BD length equals (5 + 5) to 10.

ABCD is a parallelogram, what is the length of BD

Consequently, Diagonal BD is 10 in length.

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The probability that at least two of the balls have the same number is 27.40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes

No. of ways to succeed = 90P8

No. of possible outcomes = 90^8

No. of ways to succeed =

nPr = n! / (n-r)!

90P8 = 90! / (90-8)!

90P8 = 90! / (82)!

90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!

90P8 = 90*89*88*87*86*85*84*83

90P8 = 3.13x10^15

P(no 2 have same number) = 3.13x10^15 / 90^8

P(no 2 have same number) = 0.73

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(at least 2 have same number) = 1 - 0.73

P(at least 2 have same number) = 0.2740 = 27.40%

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It is right to receive a change of 19.50 if Juan gave php 100.00 to the fruit vendor

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating how many Juan spend we have:

Total cost = mango + pineapple

Total cost = 45.50 + 35.00

Total cost = 80.5

Calculating how much Juan should receive in change:

Change = Amount given - Total cost

Change = 100 - 80.5

Change = 19.5

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Correctly written question:

Juan bought a kilo of mango at 45.50 and pineapple at 35.00 is it right to receive a change of 19.50 if he gave php 100.00 to the fruit vendor?

The number of days that it will take for there to be fewer than 1,500 tables in the warehouse is given as follows:

More 24 days.

The initial number of tables is given as follows:

2,100 tables.

They ship 25 tables daily, hence the function for the number of tables after n days is given as follows:

T(n) = 2100 - 25n.

There will be fewer than 1,500 tables after n days, for which;

T(n) < 1500

Hence:

2100 - 25n.< 1500

25n > 600

n > 600/25

n > 24.

Hence the time is more than 24 days.

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Answer:

the answer is 0= -5/3x + c

Answer: non

as a wordf 2 b geven

Answer:

Hi, my name is Za'Riah! I will gladly help you with this problem. (see explanation)

Step-by-step explanation:

There really isn't much to explain or step out but here is the answer.

[tex]\frac{1}{2} - (\frac{1}{8}+ \frac{1}{8}) \\= \frac{1}{2} - \frac{1}{4} \\\\= \frac{1}{4}[/tex]

Send your request via email on the company mail, include your name, employee ID number, and the W2 you are asking for the particular year.

For more than a century, Walgreens has operated on the same set of values: Honesty, Trust, and Integrity with Our Customers, Our Shareholders, Our Suppliers, The Communities We Serve, and Among Ourselves.

Quality via dependable and consistent advice, goods, and services at all points of contact and through all channels.

kind, sensitive, and motivated to provide excellent service and a positive patient and customer experience in order to achieve healthy outcomes.

via service, knowledge, and the personal engagement of each member of the Walgreen team, a strong commitment to and presence in the community.

All products under the Walgreens brand come with a 100% satisfaction guarantee! Return the unused amount if you're not entirely happy, and we'll refund the entire purchase price.

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Answer: He dies.

Step-by-step explanation: A train is extremely powerful. It would kill on impact most of the time.

It can be written as

y = -6/7x - 6/7 * x1 + y1

What is the slop?

The slope, also known as the gradient, is a measure of the steepness of a line. It tells us how much the y-coordinate of a point on the line changes as the x-coordinate changes. The slope is often represented by the letter "m" in the equation of a line. The slope is defined as the ratio of the rise (the change in y-coordinate) to the run (the change in x-coordinate) between two points on a line.

An equation of a line in slope-intercept form is:

y = mx + b

where:

m = slope of the line

x = variable of the line

y = variable of the line

b = y-intercept

Given the y-intercept is -6 and the slope is -6/7, we can substitute these values into the equation above:

y = -6/7x + -6

This equation of the line is in slope-intercept form, and it can be used to find the y-coordinate of any point on the line given the x-coordinate, or to find the x-coordinate of any point on the line given the y-coordinate.

You can also write it in point-slope form.

The point slope form is

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line.

So it can be written as

y = -6/7x - 6/7 * x1 + y1

Where the x1 and y1 are arbitrary value which lies on the line.

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For the extra 30 feet of wire Jayden have to pay an amount of  $7.80  at a rate of $0.26 per feet.

In these type of problems, first we have to find out the unit price. First let's look at what data is available.

The length of wire Jayden bought = 70 feet

Amount Jayden paid for 70 feet = $ 18.20

Unit price or price of 1 feet of speaker wire =  Amount paid / length bought.

Unit price =  18.20/ 70 = 0.26.

So he have to pay 26 cents for each foot of wire.

Now let's calculate the amount for 30 feet of wire = Unit price × 30 = 0.26×30 = 7.80.

So Jayden have to pay $7.80 for the extra 30 feet of wire.

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Answer: A) 10√2

Step-by-step explanation:

You can find the value of x by using the Pythagorean Theorem.

a = 10

b = 10

c = x

a^2 + b^2 = c^2

(10)^2 + (10)^2 = c^2

100 + 100 = c^2

200 = c^2

Square root both sides.

c = √200

Simplify the square root. 100 x 2 is 200, and 100 is a perfect square.

√200 = √100√2

√100 can be simplified to 10. √2 can not be simplified.

The answer would be option A ) 10√2

The value of x in the given triangle is 10√2 units.

Pythagoras theorem states that in a right triangle the three sides are related by the formula, a²+b² = c², where c is the hypotenuse and a and b are the other two sides.

Given that, a triangle, we need to find the hypotenuse x,

Using the Pythagoras theorem,

10²+10² = x²

x² = 100 + 100

x² = 200

x = 10√2

Hence, the value of x in the given triangle is 10√2 units.

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If knitting club sold 40 scarves and hats at a winter festival and made $700 from sales and charged $18 for each scarf and $14 for each hat , then the system of equations which represents the constraints in this situation is  s + h = 40 and 18s + 14h = 700    .

let the number of hats sold be = "h"  ;

and let number of scarves sold be = "s" ;

the total number of scarves and hats sold are 40 ;

the situation is represented as : h + s = 40  ...equation(1) ;

the per unit cost for each scarf is = $18  ;

the per unit cost for each hat is = $14  ;

the amount for which the items are sold is = $700 ;

this situation is represented as  : 18s + 14h = 700 ...equation(2) .

From equation(1) and equation(2)  , we can conclude that ;

the system of equation to represent the situation is , s + h = 40 and 18s + 14h = 700  .

The given question is incomplete , the complete question is

The knitting club sold 40 scarves and hats at a winter festival and made $700 from the sales. They charged $18 for each scarf and $14 for each hat. If s represents the number of scarves sold and h represents the number of hats sold, write system of equations which represents the constraints in this situation ? ​

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Based on the investment amount, rate of interest and time, Rita earned more interest than Mita by $324.

Calculating simple interest in both the cases to find the earned interest. The formula for simple interest is as follows -

S.I. = PRT/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.

Interest earned by Rita -

S.I. = 6800 × 5 × 5/100

Performing multiplication and cancelling zero

S.I. = $1700

Interest earned by Mita -

S.I. = 8600 × 4 × 4/100

Performing multiplication and cancelling zero

S.I. = $1376

Difference in interest = Interest earned by Rita - Interest earned by Mita

Difference in interest = 1700 - 1376

Performing subtraction

Difference in interest = $324

The interest earned by Rita is more than the interest earned by Mita by $324.

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The cost of each cup of coffee, not including the tip, is $3.25.

One type of operation in mathematics is division. We divide the phrases or numbers into the same number of components during this operation.

Given:

Dax is buying coffee for 5 people in his office.

He also leaves a $2.00 tip for the Batista.

If his total, with tip, is $18.25,

then the total bill of the coffee,

= $18.25 - $2.00 (not including the tip)

= $16.25

The cost of one coffee is,

= $16.25 / 5

= $3.25.

Therefore, $3.25 is the cost of one coffee.

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Relative frequency distributions are generally more useful than frequency distributions when comparing identical-sized data sets.

Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

It is possible to display the frequency distribution of data in a table or graph. Frequency tables, histograms, and bar charts are a few popular ways to display frequency distributions.

Tables of frequencies: A frequency table is an easy way to show how frequently a certain value or feature occurs.

Assume, for instance, that we have gathered information on height from a sample of 50 kids.

Both histograms and bar charts use columns drawn on a graph to visually represent frequencies.

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Complete answer is:-

Fill in the blanks -

Relative frequency distributions are generally more useful than frequency distributions when comparing                  data sets