Solve by completing the square
x^2=11x-2

Answer:

.

Step-by-step explanation:

So from A to B. We can see that the coordinate point a is at negative 3 and at the point B is at negative 1. We can find the length of this line segment by taking a minus B on the number line or B.

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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It would take her 5 months

Answer: the answer to this is true

Answer:

A (First One)

Step-by-step explanation:

Side AC Is Congruent By Side DF

Side CB Is Congruent By Side FE

Side AB Is Congruent By Side DE

(There's no angles shown so it can't be the second option.)

The diagram has lines on the sides, if it we're SAS then the triangle would have an angle.

Answer:

ΔABC≅ΔDEF by SSS Postulate

Step-by-step explanation:

Hi there!

We are given 2 triangles

And we want to prove them congruent

You may notice that AC and FD have the same tick markings, AB and ED have the same tick markings, and CB and FE have the same tick markings

This means that those sides are congruent

In other words,

AC≅FD

AB≅DE

CB≅FE

If we have 3 pairs of congruent sides, that is enough for one concurrency postulate called side-side-side (SSS), which states that if 3 sides of a triangle are congruent to 3 sides in another triangle, then those triangles are congruent

So the triangles are congruent, but we need to put their vertices in the correct order

So if we make the name of the first triangle ABC, then we need to find the corresponding vertices in the second triangle

So let's find those vertices

D is corresponding to A, as they are both in between line segments that have 1 and 2 tick markings on them

E is corresponding to B, as they are both between line segments that have 2 and 3 tick markings on them

And finally, F is corresponding to C, as they are both between line segments that have 1 and 3 tick markings on them

So the name of the second triangle is DEF

ΔABC≅ΔDEF by SSS Posulate

Hope this helps!

Answer:

x = ±1

Step-by-step explanation:

=> 7x² = 13-6

=> 7x² = 7

Dividing both sides by 7

=> x² = 1

Taking sqrt on both sides

=> x = ±1

Answer:

\(x=\± 1\)

Step-by-step explanation:

\(7x^2+6=13\)

Subtract 6 on both sides of the equation.

\(7x^2+6-6=13-6\)

\(7x^2=7\)

Divide both sides with 7.

\(\frac{7x^2}{7}=\frac{7}{7}\)

\(x^2=1\)

Take square roots on both sides.

\(x=\± \sqrt{1}\)

The required, ratio of sides that is equivalent to tan V is SU/VS.

In the given figure,
Consider the triangles VSU and VUT. By applying the tangent function to both triangles, we can establish the following relationships:

The tangent of angle V is equal to the ratio of side SU to side VS, i.e., tanV = SU/VS.

Similarly, the tangent of angle V is also equal to the ratio of side UT to side VU, i.e., tanV = UT/VU.

By utilizing the tangent function in these two triangles, we can derive these equations.

Thus. the required, ratio of sides that is equivalent to tan V is SU/VS.

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The surface area of the solid of revolution generated when the given curve is revolved about the x-axis is 10700π.

The surface area of a solid of revolution is calculated by using the formula \(S = 2π∫a b f(x)dx\), where S is the surface area, a and b are the limits of integration, and f(x) is the equation of the curve. To find the surface area generated when the given curve y = 1 14e7x e−7x is revolved about the x-axis, we must first calculate the integral of the equation.

Integrating the equation yields \(S = 2π∫-5 5 [1 14e7x e−7x] dx\). This integral can be solved by using integration by parts. First, let \(u = 1 14e7x e−7\) and dv = dx. Then, du = (14e7x e−7x) dx and v = x. Substituting these into the integral we get \(S = 2π∫-5 5 [1 14e7x e−7x] dx = 2π[x1 14e7x e−7x - ∫x14e7x e−7x dx].\) The integral of x14e7x e−7x can be solved using integration by parts again. Let u = x and \(dv = 14e7x e−7x dx\). Then, du = dx and v = -1 14e−7x. Substituting these into the integral yields \(S = 2π[x1 14e7x e−7x - ∫x14e7x e−7x dx] = 2π[x1 14e7x e−7x + 1 14e−7x]\). Finally, plugging in the limits of integration yields Therefore, the surface area of the solid of revolution generated when the given curve is revolved about the x-axis is 10700π.

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Answer:

B

Step-by-step explanation:

Answer: inverse operation, subtraction

Step-by-step explanation: The key insight here is that we want to solve for x , and in doing so, we need to undo any operation being applied to it. Right now, only 5 is being added to it, so to solve for it, we need to do the inverse operation, subtraction

If you mean this: How to solve multiplication property of equality?

Multiplication Property of Equality

For all real numbers a, b, and c: If a = b, then a • c = b • c (or ab = ac).

I hope this is right :)

Answer:

715.5

Step-by-step explanation:

The formula is A=1/2 b*h

so, b*h = 53*27 = 1431

Divide by 2 and the answer is 715.5

Hope this helps :)

The most commonly cited disadvantage of using laboratory experiments to learn about human behavior is the lack of ecological validity.

Laboratory experiments involve studying human behavior in a controlled and artificial environment, often with specific tasks and conditions designed by researchers. While laboratory experiments offer advantages such as control over variables and the ability to establish cause-and-effect relationships, they also have limitations. One of the main disadvantages frequently mentioned is the lack of ecological validity. Ecological validity refers to the extent to which the findings from a study can be generalized to real-world settings and situations. Laboratory experiments often create an artificial setting that may not fully represent the complexities and nuances of everyday life.

Participants' behavior in a laboratory setting may differ from their behavior in natural settings due to factors such as the presence of observers, demand characteristics, and the controlled nature of the environment. As a result, the findings may not accurately reflect how individuals would behave in their natural environment, limiting the external validity and generalizability of the research findings. Researchers need to consider the trade-off between experimental control and ecological validity when designing studies and interpreting the results obtained from laboratory experiments.

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Step-by-step explanation:

Statements

Reasons

1. PQ || MN

1. Given

2. O is the midpoint of NP

2. Given

3. NO = OP

3. Definition of midpoint

4. ∠ZMO = ∠QOP

4. Alternate interior angles are congruent (corresponding angles of parallel lines)

5. ∠LNMO = ∠LPQO

5. Alternate interior angles are congruent (corresponding angles of parallel lines)

6. ΔMNO ≅ ΔPRO

6. Angle-side-angle (ASA) congruence theorem

7. AMNO ≅ AQPO

7. Corresponding parts of congruent triangles are congruent (CPCTC)

Farm Joe used \(7\frac{6}{15}\) kg of soil in this month.

The total weight of soil that Farm Joe ordered was:

3 bags x 4 2/5 kg/bag = 12 6/15 kg = 12 2/5 kg

The weight of the first bag used was 4 2/5 kg.

The weight of the second bag remaining is 2 3/4 kg.

The weight of the third bag remaining is 7/8 kg.

The total weight of soil used in this month can be found by subtracting the weight of the second and third bags remaining from the total weight of soil ordered:

12 2/5 kg - 2 3/4 kg - 7/8 kg

Converting all fractions to fifteenths:

12 8/15 kg - 5 1/15 kg - 1/15 kg = 7 6/15 kg

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By changing the given integral to polar coordinates and evaluating the integral over the region enclosed by the circle in the first quadrant, we find that the value of the integral is 0. This implies that the integral over the given region evaluates to zero, indicating a balance between positive and negative contributions within the integral.

To evaluate the integral, we can change to polar coordinates. In polar coordinates, the region enclosed by the circle x^2 + y^2 = r^2 in the first quadrant corresponds to the range of angles 0 to π/2 and the range of radii from 0 to r.

In polar coordinates, we have x = r cos θ and y = r sin θ. We also need to change the area element da to its polar form, which is r dr dθ.

The integral becomes:

∫∫ r ye^x da = ∫∫ r(r sin θ)e^(r cos θ) r dr dθ

We integrate with respect to r first, using the limits of 0 to r for r:

∫∫ r(r sin θ)e^(r cos θ) r dr dθ = ∫[0,π/2] ∫[0,r] r^2 sin θ e^(r cos θ) dr dθ

Next, we integrate with respect to θ, using the limits of 0 to π/2 for θ:

∫[0,π/2] ∫[0,r] r^2 sin θ e^(r cos θ) dr dθ = ∫[0,π/2] [-(r^2)e^(r cos θ)]|[0,r] dθ

Evaluating the limits of the inner integral:

-(r^2)e^(r cos θ)|[0,r] = -(r^2)e^(r cos r) + (r^2)e^(r cos 0)

                          = -(r^2)e^(r^2) + (r^2)

Now, we integrate with respect to θ:

∫[0,π/2] [-(r^2)e^(r cos θ)]|[0,r] dθ = [-r^2 e^(r^2) + r^2] |[0,π/2]

Evaluating the limits of the outer integral:

[-r^2 e^(r^2) + r^2] |[0,π/2] = [-(r^2)e^(r^2) + r^2] - [-(0^2)e^(0^2) + 0^2]

                                     = -(r^2)e^(r^2) + r^2

Since we are considering the region enclosed by the circle, the radius r is finite. As r approaches infinity, the value of -(r^2)e^(r^2) tends to negative infinity. Therefore, the value of the integral is 0.

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The zeros of the polynomial are: x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).We have found all three real zeros of the polynomial, which confirms that there are no complex zeros.

f(x) = 2x³ - 112x² + 27x - 41x + 15

To find the zeros and their multiplicities of this polynomial, we can begin by using Descartes' Rule of Signs. Let's consider the sign changes in the coefficients:

There are 2 sign changes in the coefficients (from 2x³ to -112x² and then to 27x, and finally to -41x and 15), which means there are either 2 or 0 positive real zeros.

There are no sign changes when we replace x with -x, which means there are either 0 or 2 negative real zeros.

Thus, there can be either 0, 2, or 4 real zeros, but we cannot determine their exact number or location with Descartes' Rule of Signs alone.

Next, we can use the Upper and Lower Bound Theorem to limit our search for rational zeros. According to this theorem, any rational zero of the polynomial must be of the form p/q, where p is a factor of the constant term (15 in this case) and q is a factor of the leading coefficient (2 in this case). Therefore, the possible rational zeros of the polynomial are:

±1/2, ±1, ±3/2, ±5, ±15/2, ±30

We can use synthetic division or long division to check these possible rational zeros and see which ones are actually zeros of the polynomial. Doing so, we find that the rational zeros of the polynomial are:

x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).

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P(A) = 1/600 = 0.0017

P(B) = 0.9 * 0.0017 + 0.1 * (1 - 0.0017) = 0.1014

A) P (has the virus | tested positive) = P (tested positive | has the virus) ×  

                                                          P (has the virus)/ P (tested positive)

                                                         = 0.9 × 0.0017/0.1014  

                                                         = 0.0151

B) P (does not have the virus | tested negative) = P (tested negative | does not have the virus) × P (does not have the virus)/ P (tested negative)

= (1 - 0.1) *× (1 - 0.0017)/ (1 - 0.1014)  

= 0.9999

Probability is the department of mathematics regarding numerical descriptions of ways likely an occasion is to occur, or how possibly it's far that a proposition is genuine. The possibility of an occasion varies between zero and 1, wherein, roughly speaking, 0 suggests the impossibility of the occasion and 1 shows certainty. The better the possibility of an event, the more likely it is that the event will arise.  

A simple instance is the tossing of an honest (unbiased) coin. since the coin is truthful, the 2 results ("heads" and "tails") are both equally likely; the possibility of "heads" equals the chance of "tails"; and considering the fact that no different results are feasible, the possibility of both "heads" or "tails" is 1/2 (that could additionally be written as 0.5 or 50%).

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Answer:

324, 900, 9

Step-by-step explanation:

When a shape has its size increased by a scale factor, the size of its lengths are multiplied by this scale factor, yet its area is actually multiplied by the scale factor squared. This is due to two lengths being multiplied to contribute to the area, not just one. If it was a volume, you would multiply by the scale factor cubed!

Onto the answer, just follow the advice above:

36 * 3^2 = 36 * 9 = 324 square inches,

36 * 5^2 = 36 * 25 = 900 square inches,

36 * 0.5^2 = 36 * 0.25 = 9 square inches.

Hope this helps :)

Two steps that will complete the list correctly are:

4. The original measurement should be multiplied by the conversion factors.

5. Verify that it makes sense.

A conversion factor can be used to switch from one set of units to another by multiplying or dividing a number. When a conversion is necessary, the appropriate conversion factor to an equivalent value must be applied.

Let's use an example of converting from inches to centimeters to address this query.

10 inches should be converted to cm.

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Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

\(\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx \)

Here 5 is a constant so it can come out . So that,

\(\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx \)

Now we can write √x as ,

\(\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx \)

Simplify ,

\(\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx \)

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

\(\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) \)

On simplifying we will get ,

\(\longrightarrow \underline{\underline{ I = 2 }}\)

Answer:

A)2

Step-by-step explanation:

we would like to integrate the following definite Integral:

\( \displaystyle \int_{0} ^{1} 5x \sqrt{x} dx\)

use constant integration rule which yields:

\( \displaystyle 5\int_{0} ^{1} x \sqrt{x} dx\)

notice that we can rewrite √x using Law of exponent therefore we obtain:

\( \displaystyle 5\int_{0} ^{1} x \cdot {x}^{1/2} dx\)

once again use law of exponent which yields:

\( \displaystyle 5\int_{0} ^{1} {x}^{ \frac{3}{2} } dx\)

use exponent integration rule which yields;

\( \displaystyle 5 \left( \frac{{x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1} \right) \bigg| _{0} ^{1} \)

simplify which yields:

\( \displaystyle 2 {x}^{2} \sqrt{x} \bigg| _{0} ^{1} \)

recall fundamental theorem:

\( \displaystyle 2 ( {1}^{2}) (\sqrt{1} ) - 2( {0}^{2} )( \sqrt{0)} \)

simplify:

\( \displaystyle 2 \)

hence

our answer is A

Answer:

80/295 = 27%

Step-by-step explanation:

Answer:

30 % of the costumers where serve tea

Answer:

56

Step-by-step explanation:

corresponding angle to 56 is also opposite to x which means it is also 56

Angle opposite to 56 be a

So

a and x are corresponding angles

so

Answer:

Step-by-step explanation:

Full volume is:

Volume of tea required:

The true statements for the given function f(x) are:

The value of g(1) is 3 and the y- intercept of g(x) is at the point (0, 1) .

The function g(x) = f( x - 3 )

g (1) = f (1 -3 )

       = f (-2 )

       = 3

g (-1) = f (-1 -3)

       = f (-4)

       = - 1

Substituting , x = 0 to find the y intercept of g(x)

g ( 0 ) = f ( 0 - 3)

          =f (-3)

          =1

The y intercept of g(x) is at the point (0, 1)

Thus, options 1 and 4 are the true statements for the given function.

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The solutions to the equation -30x² + 9x + 60 = 0 are x = 5/2 and x = -4/5.

To solve the equation, we can start by bringing all the terms to one side to have a quadratic equation equal to zero. Let's go step by step:

-5/3 x² + 3x + 11 = -9 + 25/3 x²

First, let's simplify the equation by multiplying each term by 3 to eliminate the fractions:

-5x² + 9x + 33 = -27 + 25x²

Next, let's combine like terms:

-5x² - 25x² + 9x + 33 = -27

-30x² + 9x + 33 = -27

Now, let's bring all the terms to one side to have a quadratic equation equal to zero:

-30x² + 9x + 33 + 27 = 0

-30x² + 9x + 60 = 0

Finally, we have the quadratic equation in standard form:

-30x² + 9x + 60 = 0

Dividing each term by 3, we get:

-10x² + 3x + 20 = 0

(-2x + 5)(5x + 4) = -10x² + 3x + 20

So, the factored form of the equation -30x² + 9x + 60 = 0 is:

(-2x + 5)(5x + 4) = 0

Now we can set each factor equal to zero and solve for x:

-2x + 5 = 0 --> x = 5/2

5x + 4 = 0 --> x = -4/5

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The calculated BMI for the given weight and height is approximately 28.478.

To calculate and output the BMI based on the user's weight and height inputs, you can use the following code in Python:

weight_pounds = float(input("Enter weight in pounds: "))

height_inches = float(input("Enter height in inches: "))

bmi = (weight_pounds * 703) / (height_inches ** 2)

print("BMI is", bmi)

When executed, the code prompts the user to enter their weight in pounds and height in inches. It then calculates the BMI using the provided equation and stores the result in the variable 'bmi'. Finally, it outputs the calculated BMI using the 'print' function.

Based on the example input provided (weight: 210 pounds, height: 72 inches), the output would be:

BMI is 28.478

This indicates that the calculated BMI for the given weight and height is approximately 28.478.

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Answer:

y=10

Step-by-step explanation:

Since this triangle has equal length sides, it is equilateral and also has equal measured angles. This means that each angle is 180/3=60 degrees.

To solve for y, we can do 5y+10=60. Simplifying, we get

5y=50

y=10.

Answer:

4

Step-by-step explanation:

So all the angles will have the same value. In a triangle all the angles will add up to 180, so each angle would have to be 60 degrees. So to know Y we need 6x+6=5y+10.  So subtract 10 from each side, then subtract 6x from each side to get 4=x

Differentiate y with respect to x for y = sin(cos x) and y = sin x cos x is that in the first function, we apply the chain rule, whereas in the second function, we apply the product rule.

When we differentiate a function, we find the rate at which the function changes at each point.

We can differentiate a function with respect to different variables.

In this case, we have to differentiate the given functions with respect to x.

Now, let's differentiate the two given functions one by one:

For the function y = sin(cos x)

The function y = sin(cos x) can be rewritten as:

y = sin u, where u = cos x

The derivative of the function y = sin(cos x) can be found by applying the chain rule.

The chain rule states that if y = f(u) and u = g(x), then the derivative of y with respect to x is given by:

dy/dx = dy/du * du/dx

Here, f(u) = sin u and g(x) = cos x.

So,

dy/dx = (cos u)(-sin x)

dy/dx = -cos x sin(cos x)

We know that u = cos x, so cos u = cos(cos x).

So,

dy/dx = -cos x sin(cos x)

For the function y = sin x cos x

We can use the product rule to differentiate the function y = sin x cos x.

The product rule states that if y = f(x)g(x), then the derivative of y with respect to x is given by:

dy/dx = f(x)g'(x) + f'(x)g(x)

Here, f(x) = sin x and g(x) = cos x.

So,dy/dx = sin x(-sin x) + cos x cos xdy/dx

= -sin2 x + cos2 x

We can use the trigonometric identity cos2 x + sin2 x = 1 to simplify ;

So,

dy/dx = -sin2 x + cos2 xdy/dx

= cos2 x - sin2 x

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