(d² + 14d + 5) + (d - 4)

The statement  that "If two adjacent angles form a right angle, then the angles are complementary", is true

The conditional is given as:

If two adjacent angles form a right angle, then the angles are complementary

As a general rule, complementary angles add up to 90 degrees i.e. right angle

This means that adjacent angles that add up to 90 degrees are complementary angles

Hence, the statement  that "If two adjacent angles form a right angle, then the angles are complementary", is true

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The expression for modelling the pattern is n² + 2

Charlie can observe 38 guppy fish in month 6.

Given,

Number of guppy fish in Charlie's fish tank for the first time = 3

Number of guppy fish after one month = 6

Number of guppy fish in the following month = 11

The increasing pattern of guppy fish in the tank:

First month = 6 - 3 = 3

Second month = 11 - 6 = 5

So, we get that the number of guppy fish is increasing by odd numbers.

That is, 3, 6, 11, ........

Now, we have to find an expression for this pattern.

First term is 3.

That is, first term² + 2 = 1² + 2 = 3

Let n be the number of term.

n = 3

So, third term be:

3² + 2 = 9 + 2 = 11

So the expression for modelling the pattern is n² + 2

Now, we have to find the number of guppy fish in month 6.

That is,

n = 6

So,

n² + 2

6² + 2 = 36 + 2 = 38

That is, Charlie can observe 38 guppy fish in month 6.

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a) [tex]x^{2}[/tex]+8kx +k=0,   b) k=1/16

Here we have equation is 2x -y = 1 , [tex]x^{2}[/tex]+4ky+5k=0

To show that [tex]x^{2}[/tex] +8kx +k =0, we have two equation 2x-y=1 and [tex]x^{2}[/tex] +4ky + 5k=0

So from the equation 2x - y = 1 we can find y

Therefore y = 2x-1

Now we will put the value of y in the equation [tex]x^{2}[/tex] + 4ky + 5k =0

a) We have [tex]x^{2}[/tex] + 4k(2x-1) +5k=0

              [tex]x^{2}[/tex] + 8kx -4k + 5k=0

             [tex]x^{2}[/tex] +8kx +k=0

b) Now we have to find the value of k, and as from the question it is given that [tex]x^{2}[/tex] + 8kx +k =0 have equal roots

Therefore we get [tex]b^{2}[/tex] + 4ac = 0 is the condition of the linear equation in two equal roots.

So from this we have b= 8k, a = -1, c= k

           [tex](8k)^{2}[/tex] - 4× 1×k =0

           64[tex]k^{2}[/tex] -4k =0

           4k(16k -1) =0

           16k-1=0

            k = 1/16

As k is a non-zero constant therefore we have not taken k=0. Therefore the value of k is 1/16.

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The complete question is:

Given the simultaneous equations 2x - y = 1 x² + 4ky + 5k = 0 where k is a non-zero constant a)show that x² + 8kx + k = 0. Given that x² + 8kx + k = 0 has equal roots., b) find the value of k.

Answer:

Step-by-step explanation:

z³/xy²

Answer:

She will pay her mom back and have 20 dollars over if she works one hour.

Step-by-step explanation:

Adding integers with a common sign.

When adding two integers with a common sign, we just add the absolute value of the numbers and the resulting answer is marked with the same sign given in the question.

This question has two possible answers.

Possibility 1:

Both the integers are of positive sign. As a result, the resulting integer after addition is positive.

Example:

Let c = 45 and d = 53.

The sum of c and d is then

sum = c + d = 45 + 53 = 98

Possibility 2:

Both the integers are of negative sign. As a result, the resulting integer after addition is negative.

Example:

Assume c = -23 and d = -61.

The sum of c and d is then

sum = c + d = (-23) + (-61) = -(23 + 61) = -84

Hence, we have added integers with a common sign.

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The equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex] is [tex]y=6[/tex]

As per the question statement, we are supposed to find the equation of a line that is also perpendicular to the line [tex]x = 11[/tex] and contains the point [tex](7,6)[/tex].

Before solving that, we need to know that the given line [tex]x = 11[/tex] is parallel to the y-axis as no point is passing through y axis hence the slope [tex]m_{1}[/tex] of the given line will be [tex]\frac{1}{0}[/tex].

The required line is perpendicular to the given line, so it will be parallel to the x-axis and hence it's slope would be slope [tex]m_{2}[/tex] = [tex]0[/tex]

We know the equation of the line passing through a some point [tex]x_{1}[/tex] and [tex]y_{1}[/tex] having slope m is given by:

[tex]y-y_{1} =m_{2} (x-x_{1})[/tex]

Here the required line is passing through (7,6), hence substituting the values of [tex]x_{1}, y_{1} ,m_{2}[/tex], we get

[tex]y-6=0(x-7)[/tex]

or [tex]y-6=0[/tex]

or [tex]y=6[/tex]

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Answer: The total weights of the two animals is  11. 92 × 10² Ibs

Step-by-step explanation:

According to the question, the standard equation for the circle is [tex]x^{2} +y^{2} =r^{2}[/tex] in which the points (x, y) are the circumference point and 'r' is the radius of the circle.

The given expression for the circle is shown below:

[tex]x^{2} +y^{2} -12x+6y-19=0[/tex]

Bring same variable terms to one side and again re-write the expression:

[tex]x^{2} -12x+y^{2} +6y-19=0[/tex]

Now, to do factors of the given expression add and subtract 36,9 on both the sides

[tex]x^{2} -12x+36+y^{2} +6y+9=19+36+9[/tex]

Factors can be re-written as:

[tex](x-6)^{2} +(y+3)^{2}=64[/tex]

Comparing the calculated equation for the circle with the standard equation, we circle

The center points as (6,-3) and radius as (r = 8).

Hence, the correct answer is Center(6,-3), r = 8.

What is circle?

The circle can be defined as a symmetrical shaped. It has more than one points and all are at the equidistant from the center.

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Answer:

B

Center (7, –5); r = 8

Step-by-step explanation:

The garden will stretch by 2/3 miles.

Given that Garden covers an area of 1/6 of a square mile and the garde is 1/4 mile wide.

As we know, the garden is a rectangle shape.

Here, we will use the formula of area of rectangle.

Area of rectangle is equal to the product of length and breadth.

Area =l×b

Here, the give area=1/6 miles² and b=1/4 mile.

Now, we will substitute the values in the formula, we get

1/6=l×(1/4)

Further, we will multiply both sides with 4, we get

4/6=4l/4

4/6=l

Now, we will simplify the left hand side, we get

2/3=l

Hence, the length of garden stretch when garden covers an area of 1/6 of a square mile and 1/4 mile wide is 2/3 mile.

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Answer:

Negative 2.5 greater-than negative 1.5

C

Step-by-step explanation:

-2.5 < -2

Using the Triangle Midsegment Theorem, the value of x in the figure is: 4.

The Triangle Midsegment Theorem states that:

The length of segment DE = 1/2(the length of segment BC)

Given the following;

DE = x + 1

BC = 4x - 6

Substitute

x + 1 = 1/2(4x - 6)

2(x + 1) = 4x - 6

2x + 2 = 4x - 6

2x + 2 - 4x = 4x - 6 - 4x

-2x + 2 = - 6

-2x + 2 - 2= - 6 - 2

-2x = -8

-2x/-2 = -8/-2

x = 4

Thus, using the Triangle Midsegment Theorem, the value of x in the figure is: 4.

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Answer:

Step-by-step explanation:

The answer to this my friend would be valid by the law of syllogism because our P is an angle bisector and our q is km. Our r is connecting to our p and says that they are congruent. Therefore if An angle bisector divides an angle into two congruent angles, then JKM and KML are congruent.

Hope this helps!

The Conclusion: ∠J K M ≅ ∠M K L is valid

Given data

An angle bisector divides an angle into two congruent angles. →KM is an angle bisector of ∠J K L .

Bisection is a term in mathematics that refers to dividing into two equal parts. This term is used more in the branch of mathematics called geometry.

Bisection can be done for an angle or line, for a line the given line is divided into two equal parts. Angle bisector divides the given angle into two equal parts to give two equal angles

When angle JKL is bisected by line KM. The line will lead to two angles which are:

These two angles are congruent and are represented by the formula below: ∠J K M ≅ ∠M K L

Hence we can say that the conclusion is valid

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The weight loss program is not statistically significant because the results are likely to occur by chance. (Option D)

Now,

Hence, the given program is not statistically significant because the results are likely to occur by chance. (Option D)

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(COMPLETE QUESTION:

Determine whether the results below appear to have statistical​ significance, and also determine whether the results have practical significance.

In a study of a weight loss​ program, 7 subjects lost an average of 43 lbs. It is found that there is about a 22​% chance of getting such results with a diet that has no effect.

Does the weight loss program have statistical​ significance?

A.No, the program is not statistically significant because the results are unlikely to occur by chance.

B.Yes, the program is statistically significant because the results are unlikely to occur by chance.

C.Yes, the program is statistically significant because the results are likely to occur by chance.

D.No, the program is not statistically significant because the results are likely to occur by chance.)

If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x

Given,

The initial fee of taxi cab = $2.85

The charges per mile = $2.70

Consider the number of miles as x

Then,

The equation of the fare = 2.85+2.70x

Hence, If the taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile, the the equation of the fare is 2.85+2.70x.

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The expression is 14 - 14.

Subtraction is a mathematical operation that is used to determine the difference between two or more numbers. The sign used to depict subtraction is -. Other mathematical operations are addition, multiplication and division.

In order to determine the expression for the amount of gas left, we need to subtract the gas bought from the gas used: 14 - 14

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According to the calculations made by Bob after downloading and calculating the correlation value as 0.5 from a given data set, he concludes that as the number of bedrooms in a particular home increase there is an increase in the selling price of the bed.

This increase in the selling price due to the increase in the number of bedrooms can be explained with the help of the Law of Demand which states that as the demand for a certain product increases its cost or the selling price also increases.

Thus, when Bob calculates the correlation factor, he finds that as the number of bedrooms increases there is also a hike in the selling price. As there should be a surplus to fulfill the demand for bedrooms.

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By applying the Tangent Secant Theorem to this circle, the value of x to the nearest tenth is equal to: A. 5.7.

The Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have:

(x + x + 3) × x = 9²

(x + 3)x = 81

2x² + 3x = 81

2x² + 3x - 81 = 0

Next, we would solve the quadratic equation by using the quadratic formula:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\x = \frac{-3\; \pm \;\sqrt{3^2 - 4(2)(-81)}}{2 \times 2}\\\\x = \frac{-3\; \pm \;\sqrt{9 + 648}}{4}\\\\x = \frac{-3\; \pm \;\sqrt{657}}{4}[/tex]

x = 5.7 or -7.2

Since the line segment cannot be negative, the value of x to the nearest tenth is equal to 5.7.

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Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

Answer:

The expression or number to which the logarithm is operated on is called the argument. From the mathematical expression (x=logbn) ( x = l o g b n ) , n is the argument of the logarithm. The argument of a log function is always positive and should not be equal to 1. Hope this answer helps you.

The time used for the return trip is t / 3

He drove to the nearest hospital with an average speed of v meters per seconds in t seconds.

Therefore,

average speed  = distance / time

average speed = v

time used = t

d = distance covered

Therefore,

v = d / t

d = vt

He drives home on the same path, but with an average speed of 3v meters/second. The time used for the return trip is as follows:

Recall he covered the same distance.

Therefore,

average speed = 3v

time used for the return trip = x

d = distance

Hence,

3v = vt / x

x = vt / 3v

x = t / 3

Therefore,  the time used for the return trip is t / 3

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Answer:

Mpq= (

[tex] \frac{4 \times \frac{1}{3} + - 2 \times \frac{1}{5} }{2} and \frac{3 \times \frac{1}{6} + 3 \times \frac{2}{3} }{2} [/tex]

[tex] \frac{16}{15} \: and \frac{41}{12} [/tex]

midpoint for PQ is (16/15; 41/12)

Answer:

5 x 4=20

Step-by-step explanation:

the x is a smaller number to tell you how many 5's there are which x=4 so the are 4 5's but you have to times(multiple) the two numbers.

5x4

=20

Answer: A

Step-by-step explanation:

A. 2.6x 10^-7

Answer:

a

Step-by-step explanation:

because you move the decimal 7 times to the right to put it into scientific notation

Two hikers are 22 miles apart and walking toward the each other, they meet in 4 hours. The rate of each hiker if one hiker walks 3.3 mph faster than the other are 2.2mph, 2.2mph, 3.3mph.

Distance divided by time is the dimension of speed. The SI measure of speed is the meter per second (m/s), although the most widely used unit in daily life is the kilometer per hour (km/h), or miles per hour in the US and the UK (mph). The knot is a popular choice for air and sea travel.

The instantaneous speed serves as the upper bound of the average speed as the duration of the time period gets closer to 0. The distance traveled by an object during a period of time divided by the length of the period gives the average speed of an object throughout that period. Velocity and speed are not the same thing.

Time divided by distance are the speed-related metrics. The kilometer per hour (km/h), or miles per hour in the US and UK, is the unit of speed that is most frequently used in daily life. The meter per second (m/s) is the metric unit of speed (mph). The knot is often used in air and sea transportation.

Since the hikers are moving at varying speeds, they collide in a location other than the center.

Let the distance travelled by Hiker A (slower) be x at speed s.

So, the distance travelled by Hiker B (faster) is (22 - x) at a speed (s + 1.1).

s = x / 4

s + 1.1 = 22 - x / 4

After resolving equations 1 and 2, we obtain:

x = 8.8m and s = 2.2mph

Therefore,

Speed of the Hiker A = 2.2 mph

Speed of the Hiker A = 2.2 mph

Speed of the Hiker B = 3.3 mph

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The amount each contestant will receive is as follows:

This year $52,000 college scholarship is being divided between the top two contestants .

Therefore,

Total amount to share to the top winners = 52000 dollars

The winner receives three times as much as the runner-up.

Therefore,

let

x = Amount received by the runner-up

Hence,

Amount the winner received = 3x

Therefore,

52,000 = 3x + x

52,000 = 4x

divide both sides by 4

4x / 4 = 52,000 / 4

x = 13000 dollars

Hence,

Amount the winner received =3(13000) = $39000

Amount received by the runner-up = $13,000

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Answer:

Use distance formula between these points to find length of one side of the square.....then multiply by 4 sides

sqrt( 5^2 + 12^2 ) =   13 units  side length

Step-by-step explanation:

And i think you can go from there if not please ask me to do the rest for you

The arithmetic and geometric average returns for a stock with annual returns of 9.4 percent, 8.2 percent, -7.3 percent, 4.1 percent, and 9.5 percent are 4.78% and 4.58% respectively.

The shares of ownership in a corporation or company that make up stock (also known as capital stock) in the financial world. A single share of stock represents a fractional ownership in the firm in relation to the entire number of shares (especially in American English, where the word "stocks" is also used to refer to shares). This typically entitles the shareholder (stockholder) to that portion of the company's earnings, proceeds from the sale of assets (after paying off all senior claims such as secured and unsecured debt), or voting rights, often allocating these in proportion to the amount of money each stockholder has invested.

Calculations:

Arithmetic returns=Total returns/Total time period

=(9.4+8.2-7.3+4.1+9.5)/5=4.78%

Geometric returns=[(1+rate1)(1+rate2)........(1+rate5)]^(1/5)

=[(1+0.094)(1+0.082)(1-0.073)(1+0.041)(1+0.095)]^(1/5)

=4.58%

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Answer:

LK = 7

Step-by-step explanation:

NK = NM + ML + LK ( substitute values )

23 = x - 6 + 9 + 2x - 19

23 = 3x - 16 ( add 16 to both sides )

39 = 3x ( divide both sides by 3 )

13 = x

Then

LK = 2x - 19 = 2(13) - 19 = 26 - 19 = 7