An aeroplane covers a distance of 1500km in a certain time at a certain speed.After increasing the speed by 100km/hr, it covers the same distance in a time which is half an hour less than the previous time. Find the previous speed of the aeroplane.
this is from quadratic equations CBSE grade 10
please answer ASAP

Answer:

A is the answer.

Step-by-step explanation:

In the first, we must know i^2 is (-1)

so we can get the answer is A.

A.(3x + 2i)(3x − 2i)

= (3x)^2 - (2i)^2

= 9x^2 + 4 (Answer)

B. (3x + 2)(3x − 2) = 9x^2 - 4

C. (3x + 2i)^2

= 9x^2 + 12ix - 4

D. (3x + 2)^2

= 9x^2 + 12x + 4

Answer:

(x + 7)(x - 4) = x2 - 4x + 7x - 28 = x2 + 3x - 28

Answer:

-3

Step-by-step explanation:

Based on his weekly salary and commission, we can calculate that Mr. Randall sold goods worth $1,800.

In the formula given, sales is represented as s. To find the total sales, you can solve the equation:

300 + 0.07s = 426

0.07s = 426 - 300

s = 126 / 0.07

= $1,800

In conclusion, Mr. Randall sold $1,800 worth of goods.

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The approximate value of the expression sec 4π / 13 is 1.76

Radian is a unit of measurement of angles equal to about 57.3° . equivalent to angle subtended at the center of a circle by a arc equal to length of radius

To Change Radian into degree, we multiple the angle with 180/π

The given Expression is

sec 4π / 13

Changing radian into Degree ,

=> 4π / 13 × 180 / π

=> 720 / 13

=> 55.38

Therefore , sec 55.38° is 1.7603

rounding off to two decimal places is 1.76

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By applying Pythagoras' theorem, the length of x is equal to 10 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:

x² = y² + z²

x² = 8² + 6²

x² = 64 + 36

x = √100

x = 10 units.

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Answer:

∠BDC=50°

Step-by-step explanation:

∠BDC=∠A[angles at the same segment)

∠A= 180-(65+65)=180-130= 50°

so, ∠BDC=50°

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The value of angle BDC would be,

⇒ ∠BDC = 50°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Since, We know that;

∠BDC = ∠A

By angles at the same segment.

Here, We have;

⇒ ∠A = 180-(65+65)

⇒ ∠A = 180-130

⇒ ∠A = 50°

Thus, The value of angle BDC would be,

⇒ ∠BDC = 50°

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The individuals in this data set are B) Rachael's Classmates

The first column of the table is what will give this away

==========================================================

This data set contains A) 4 Variables, 1 of which is quantitative

Why is this? Because the four variables are

Age is quantitative because it deals with a quantity or number. We can do things like find the average age and it makes sense to do so. The other variables are qualitative or categorical. Gender is nominal as you can't order the data. Birth month is ordinal though because we can order the months from January to December. The responses for "read horoscope" are nominal data because we cannot order "yes" versus "no".

Answer:

Step-by-step explanation:

The question is lacking appropriate diagram. Find the diagram to the question attached.

From the diagram, it can be seen that AD = AB+BC+CD

Given the following

AD = 23units

AB = 4units

CD = 12units

To get C=BC, we will substitute the given segments into the expression above as shown;

23 = 4+BC+12

23 = BC + 4 + 12

23 = BC+16

Subtract 16 from both sides

23-16 = BC+16-16

7 = BC

Hence the length of segment BC is 7units.

The intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric function is given below.

3 sec2x − 2 tan 2x − 4 = 0

Simplify the equation, then we have

3 sec2x − 2 tan 2x − 4 = 0

3 / cos 2x − 2 sin 2x / cos 2x = 4

3 − 2 sin 2x = 4 cos 2x

(3 − 2sin 2x)² = 16 cos² 2x

The graph of the functions is drawn below.

From the graph, the intersection of the graph is (0.65, 1.073). Then the solution of the equation the interval of [0, 2) will be 0.65.

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Answer:

cannot factor.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

9 is the correct answer

The area of the rectangle as a product of length and width is (6x² + 13x + 6) square units

An equation is an expression that shows the relationship between numbers and variables.

The area of a rectangle is the product of its length and its width. It is given by:

Area = length * width

From the diagram:

Area = 6(x²) + 13(x) + 6(1) = 6x² + 13x + 6 square unit

Also:

Length = x + x + x + 1 + 1 = 3x + 2

Length = 3x + 2 units

Width = x + x + 1 + 1 + 1 = 2x + 3

Width = 2x + 3 units

Area = length * width

Substituting:

Area = (3x + 2)(2x + 3)

Area = 6x² + 9x + 4x + 6 = 6x² + 13x + 6 square units

The area is (6x² + 13x + 6) square units

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-4>3

Step-by-step explanation:

Answer:

First line

Step-by-step explanation:

Isolating 2a is the first step, so adding 5 to each side. That leaves -2a > 8. Divide both sides by -2, and because it's a negative, you flip the sign. so you get a < -4

The three digit number is 727 while the one digit number is 4

Given data

The sum of a three-digit number and a one-digit number is 731.

The product of the numbers is 2,908

let three digit number be x, y, and z

let the one digit be w

The sum

xyz + w =731

xyz * w = 2,908

making xyz the subject of formula

xyz = 731 - w

plugging in xyz into xyz * w = 2,908

( 731 - w ) * w = 2908

731w - w^2 = 2908

w^2 - 731w + 2908 = 0

solving the quadratic equation gives

w = 727 or 4

since w is a one digit number then w = 4

plugging in w = 4 into xyz + w =731 we have

xyz + w =731

xyz + 4 =731

xyz =731 - 4

xyz  = 727

Hence the three digit number is 727 while the one digit number is 4

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When 3 is the input, the output is 10. When 10 is the input, the output is 15.

It should be noted that the input for the function is time, measured in hours. The output of the function is energy usage, measured in kilo watts.

From the information, the energy usage of a light bulb is a function. The input for the function is time measured in hours. The output of the function is energy usage, measured in Kilo watts. E (energy) is a function of t (time).

The graph of the function will show energy usage on the y axis and time on the x axis.

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The 3,572.1 m³ volume of the hexagon and the 19 m. length of the cars and 3-m connector, gives;

From a similar question, we have;

Side length of the hexagon = 8.1 m

Perpendicular distance from the center to a side of the hexagon = 7 m.

Therefore;

Cross sectional area of the hexagon, A is found as follows;

A = 6 × 0.5 × 7 × 8.1 = 170.1

Length of the tunnel, D = 3572.1 ÷ 170.1 = 21

D = 21 meters

Length of two cars and a connector, L = 8 + 8 + 3 = 19

The tunnel length, D = 21 m. is longer than the length of two cars and the connector, L = 19 m.

Therefore;

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The denominator has a single first-order term the closed-loop system has a single pole at:

s = -G(s) × (Kp + Kd × s) / Ki

The transfer function from the reference input θr to the Hapkit output θ for a closed-loop system with a unity gain negative feedback and a PID controller can be derived as follows:

Let's denote the transfer function of the plant (Hapkit) by G(s) the transfer function of the PID controller by C(s) and the transfer function of the feedback path by H(s).

The closed-loop transfer function T(s) is given by:

T(s) = θ(s) / θr(s)

= G(s) × C(s) / [1 + G(s) × C(s) × H(s)]

Since the feedback path has unity gain we have H(s) = 1.

Also, the transfer function of a PID controller with proportional gain Kp, integral gain Ki and derivative gain Kd is:

C(s) = Kp + Ki/s + Kd × s

Substituting these into the expression for T(s), we get:

T(s) = θ(s) / θr(s)

= G(s) × [Kp + Ki/s + Kds] / [1 + G(s) × [Kp + Ki/s + Kds]]

Multiplying both the numerator and denominator by s, and simplifying, we get:

T(s) = θ(s) / θr(s)

= G(s) × Kps / [s + G(s) × (Kp + Ki/s + Kds)]

This is the transfer function from the reference input θr to the Hapkit output θ for the closed-loop system.

The closed-loop system has as many poles as the order of the denominator of the transfer function T(s).

Since the denominator has a single first-order term the closed-loop system has a single pole at:

s = -G(s) × (Kp + Kd × s) / Ki

The pole may change as a function of the frequency s due to the frequency dependence of G(s).

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The expression a² - 2ab - 36b², can be factorize as: (a - 6b)^2.

The polynomial expression a² - 2ab - 36b² can be factored as shown below:

This is done by finding two numbers that multiply to -36 and add to -2ab. The numbers are -6b and 6b, and the expression can be written as:

(a - 6b)(a - 6b), which can be simplified to (a - 6b)^2.

Therefore, given the polynomial expression, a² - 2ab - 36b², when factorized, we would get (a - 6b)².

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The the function to estimate the average age of employee of a company is A(s)=0.285s + 59  , then the average age of employee in 2003 is 65.27 and in 2009 is 66.98

To estimate the average age of an employee in 2003, we need to find the value of A(s) when s = 22  ;

because the number of years between 2003 and 1981 is = 22 years ;

So , A(22) = 0.285×22 + 59 = 65.27  ;

The average age of an employee in 2003 is approximately 65.27.

To estimate the average age of an employee in 2009,

we need to find the value of A(s) when s = 28

because the number of years between 2009 and 1981 is = 28 years ;

So , A(28) = 0.285×28 + 59 = 66.98  ;

The Average age of employee in 2009 is approximately 71.48.

The given question is incomplete , the complete question is

The function​ A(s) given by ​A(s)=0.285s + 59  can be used to estimate the average age of employee of a company in the year 1981 to 2009. Let​ A(s) be the average age of an​ employee, and "s" be the number of year since​ 1981; that​ is, s=0 for 1981 and s=9 for 1990. What is the average age of the employee in 2003 and in​ 2009 ?

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The interest rate for the savings account is 5% after 4 years, $20,000 deposited in a savings account with simple interest earned $800 in interest.

We can use the formula for simple interest to solve the problem:

Simple interest = (Principal * Rate * Time) / 100

where Principal is the initial amount deposited, Rate is the interest rate, and Time is the time period for which the interest is calculated.

We know that the Principal is $20,000 and the time period is 4 years. We are also given that the interest earned is $800. So we can plug in these values and solve for the interest rate:

$800 = (20,000 * Rate * 4) / 100

Multiplying both sides by 100 and dividing by 20,000 * 4, we get:

Rate = $800 / (20,000 * 4 / 100) = 0.05 or 5%

Therefore, the interest rate for the savings account is 5%.

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For the steel plate which is to be cast,

The volume of molten metal required to avoid shrinking is about 1289mL.

The dimensions of a cubical riser, which can avoid shrinkage are 3.38cm.

The riser's adequacy cannot be proved.

This question is based on the basic principles of metallurgy.

A)

We calculate the volume of molten metal which is required to avoid shrinkage after accounting for the shrinkage which will occur.

So, the volume of metal required for final casting is:

Final Casting Volume (F.C.V) = Initial volume / (1 - Shrinkage)

The value of shrinkage is in decimals.

Here, the steel liquid shrinks by 3% during solidification.

Inital volume = 50*50*0.5

                     = 1250 cm³

So,

F.C.V = 1250/(1 - 0.03)

F.C.V = 1250/0.97

F.C.V = 1288.6 cm³

So, about 1289 mL of liquid steel is required to avoid shrinkage.

B)

If we need the riser to compensate for the shrinkage, we need it to provide enough metal while it solidifies.

So, Riser Volume = Shrinkage Volume

Shrinkage Volume (S.V) = (F.C.V)*(Shrinkage)

                               = 1288.6(0.03)

                               = 38.65 cm³

But since we need the dimensions,

Dimensions = ∛(S.V)                           (Cubical Riser)

                    = ∛(38.65)

                    = 3.38 cm

The dimension of the cubical riser is 3.38 cm.

C)

According to Cain's Rule, the volume of the riser is more than or equal to 1.5 times the volume of casting that it is intended to feed.

Without the casting volume, we cannot prove its adequacy.

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Based on the given information, ΔEFG is not necessarily congruent to ΔABD, even though EF is congruent to AB, FG is congruent to BD, and ∠E is congruent to ∠A. Additional information is needed to determine the congruence of the two triangles.

In order to determine congruence between triangles, we need to establish a sufficient set of congruence criteria. The given information tells us that two sides and a non-included angle of ΔABC are congruent to the corresponding parts of ΔABD. However, this information alone is not enough to guarantee the congruence of the two triangles.

To establish congruence, we would need additional information, such as the congruence of another angle or side. Without that additional information, it is not possible to conclude that ΔEFG is congruent to ΔABD solely based on the given information.

Therefore, while there are some similarities between ΔEFG and ΔABD, such as the congruent sides and angle, we cannot definitively state that the two triangles are congruent without further information or congruence criteria being provided.

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The given function shows imply that the graph g(x) is shifted two units right and three units up.

Option B is correct.

The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.

From the given information:

Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.

Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.

Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0.  We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.

Combining the two transformations, we have:

Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.

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The f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

To compute f′(a) algebraically for the given value of a, we use the following differentiation rule which is known as the Power Rule.

This states that:If f(x) = xn, where n is any real number, then f′(x) = nxⁿ⁻¹This is valid for any value of x.

Therefore, we can differentiate f(x) = −7x + 5 with respect to x using the power rule as follows:

f(x) = −7x + 5

⇒ f′(x) = d/dx (−7x + 5)

⇒ f′(x) = d/dx (−7x) + d/dx(5)

⇒ f′(x) = −7(d/dx(x)) + 0

⇒ f′(x) = −7⋅1 = −7

Hence, the derivative of f(x) with respect to x is -7.Now, we evaluate f′(a) when a = −6 as follows:f′(x) = −7 evaluated at x = −6⇒ f′(−6) = −7

Therefore, f′(a) when a = −6 is -7. This means that the slope of the tangent line of the graph of f(x) at x = -6 is -7.

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Answer:

2

Step-by-step explanation:

that's because there are two sandwiches and two drinks so one sandwich and drink is one lunch special

Ally will be able to cover 285 miles for the trip

Ally wants to rent the car for one day

The rents costs $35 and $0.35 per mile

Ally has $134.75 to spend for the trip

The number of miles Ally can drive for the trip can be calculated as follows

134.75 - 35

= 99.75

99.75/0.35

= 285

Hence Ally will be able to drive 285 miles for the trip  

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Answer:

1.76295

1.76( 1 dp)

Step-by-step explanation:

\($1. 61\)

\(1.61 \times 9.5 \\ 1.61 \times \frac{9.5}{100} \\ \frac{1.61}{1} \times \frac{9.5}{100} \\ \frac{ 15.295 }{100} \\ = 0.15295 \\ add \: 0.15295 \: to \: 1.61 \\ = 1.61 + 0.15295 \\ = 1.76295 \\ approx = 1.76\)

Answer:

y = 2x + 2

Step-by-step explanation:

The area of the figure is 23 square centimeters.

To find the area of the figure, we need to split it up into simpler shapes whose area we can easily calculate. The figure is a trapezoid, so we can split it up into a rectangle and two triangles.

The rectangle has a length of 5 cm and a width of 3 cm, so its area is:

A(rectangle) = length × width = 5 cm × 3 cm = 15 cm²

To find the area of each triangle, we first need to find the height of the trapezoid. The height is the perpendicular distance between the parallel sides, which is the distance between the bottom and top sides. The height of the trapezoid is:

height = 7 cm - 3 cm = 4 cm

Each triangle has a base of 2 cm (half of the top side of the trapezoid) and a height of 4 cm, so the area of each triangle is:

A(triangle) = (1/2) × base × height = (1/2) × 2 cm × 4 cm = 4 cm²

To find the total area, we add the areas of the rectangle and the two triangles:

A(total) = A(rectangle) + 2 × A(triangle)

        = 15 cm² + 2 × 4 cm²

        = 23 cm²

Therefore, the area of the figure is 23 square centimeters.

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