determine the interval(s) for which the function shown below is decreasing

Answer:

Step-by-step explanation:

Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)

where, (h,k) is the center and r is the radius.

therefore, from the question by rearranging the equation,

x² + y² + 4x − 6y + 12=0

viz, (x² +4x+4) + (y²-6y+9)-1=0  

(x+2)^2 + (y-3)^2=1

therefore from eqn1, (-2,3) is the center and radius is 1

[tex]{ \huge{ \boxed{ \red{ \sf{x = 7}}}}}[/tex]

Step-by-step explanation:-

[tex]{ \sf{126 = 2 \times 3 \times 3 \times k}}[/tex]

[tex]{ \sf{126 = 6 \times 3 \times k}}[/tex]

[tex]{ \sf{126 = 18 \times k}}[/tex]

[tex]{ \sf{126 = 18k}}[/tex]

Divide both the sides by 18 in order to find the value of k. Then,

[tex]{ \sf{ \frac{126}{18} = \frac{18}{18} k}}[/tex]

[tex]{ \boxed{ \boxed{ \purple{ \sf{x = 7}}}}}[/tex]

The required value of x is 3 in the given equilateral triangle.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.

The triangle given in the figure is an equilateral triangle.

We know that all sides are equal in the equilateral triangle.

As per the given figure,

side AB = side AC

6x - 3 = 3x + 6

6x - 3x = 6 + 3

Apply the arithmetic operation,

3x = 9

x = 9/3

x = 3

Therefore, the required value of x is 3 in the given equilateral triangle.

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Answer:

9.8 * 100 = 980

0.040 * 1000 = 40

61 / 10 = 6.1

8.909 * 100 = 890.9

Step-by-step explanation:

The size of angle QPR is 45° and the length of sides PQ and QR are both 27.20cm

An isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal angle,

since ∆PQR is a right angle isosceles triangle then, if angle Q is 90^°, QPR = PRQ=x( angles of an isosceles triangle).

Therefore 90+x+x= 180°

2x= 90

x= 45°

To find line PQ and QR, we use trigonometry ratio

cos 45°= adj/hyp

I/√2= QR/38.47

QR= 38.47/√2

= 27.20cm

QR= PQ= 27.20

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Lester's final score from the two Judges is 7.6

The scores of the judges are in percentage and this will be converted to decimal by dividing by 100

impact (worth 40%) = 0.4

composition (worth 30%) = 0.3

lighting (worth 20%) = 0.2

color balance (worth 10%) = 0.1

Average score from the Judges will be used to multiply the percentages

Impact: 8 and 9

= 8.5 * 0.4 = 3.4

Composition: 7 and 7

= 7 * 0.3 = 2.1

Lighting: 8 and 7

= 7.5 * 0.2 = 1.5

Color balance: 5 and 7

= 6 * 0.1 = 0.6

sum of the scores gives Lester's final score as 7.6

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Answer:

Raymond

Step-by-step explanation:

1 ) Eve and Patty swam fewer laps than Maureen so...

Eve and Patty < Maureen

2 ) Patty swam more laps than Eve...

Patty > Eve

3 ) Maureen swam fewer laps than Raymond...

Maureen < Raymond

4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...

Maureen and Raymond

5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.

Raymond

6 ) This mean that the one who swam the most laps is...

Raymond

Hope this helps! :)

The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.

The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.

Here,

a. The length of drain= 52 feet

the gradual decrease=0.125 ft

elevation at high end=126.30 feet

elevation at low end,

=126.3-(52*0.125)

=126.3-6.5

=119.8 feet

b. The elevation at one end=94.67 feet

The elevation at other end=84.12 feet

The difference in elevation,

=94.67-84.12

=10.55 feet

=10.55*12

=126.6 inches

The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.

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Answer: X

Step-by-step explanation:

you just start at 0 since that is the origin and go up 5

Answer: 10 rows of rose plants

Step-by-step explanation:

The number of rose plants in first, second third,..., and last row are respectively.

23,21,19,....,5.

number of rose plants: n

The sequence 23,21,19,....,5 is an A.P. with first term a(=23), common difference d(=−2) and n

=a+(n−1)d

⟹5=23+(n−1)×−2

⟹5=23−2n+2⟹20=2n⟹n=10

The equation of the line is y = x -3. The graph of the line is attached below.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

Given that the slope of the line is 1.

Assume that the equation of the line is y = mx +c, where m is the slope of the line and c is y-intercepts.

Putting m = 1 in y = mx +c:

y = 1 × x +c

y = x +c

Since the line passes through the point (-2, -5), thus the point satisfies  the given equation of line.

Putting x = -2 and y = -5 in y = x +c

-5 = -2 + c

c = -3

The equation of line is y = x - 3.

The points on the line are

(-2, -5), (0, -3), (3, 0).

Plot the points and join them:

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Considering the angle of elevations, the distance from point AA to point BB which is the height of the antenna is 5.34 meters

information given in the question

Mia stands at a horizontal distance of 15 meters from the building

The angle of elevation from her eyes to the roof ((point AA)) is 18

the angle of elevation from her eyes to the top of the antenna ((point BB)) is 53^

her eyes are 1.75 meters from the ground

The direction of movements describes a right angle triangle of

opposite = height of antenna + height of the building

adjacent = 15 meters

The  distance from point AA to point BB and the height of the antenna is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The  the height of the antenna is calculated using tan, TOA let the angle be x

tan x = Opposite / Adjacent

using 53 gives the height of the antenna + height of the building, while using 18 gives height of the building only

tan 53  = opposite / 15

opposite = 15 * tan 53 = 19.906 meters

opposite = 15 * tan 18 = 14.266 meters

Height of the antenna

= 19.606 - 14.266

= 5.34 meters

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Answer:

1.5 liters

Step-by-step explanation:

The length of the straw fitted in the box is 10.67 inches.

A cuboid is a solid three-dimensional object which has six faces that are rectangular with eight vertices, and twelve edges.

Given that, a straw is placed inside a rectangular box that is 5 inches by 5 inches by 8 inches, the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner,

Diagonal of a cuboid  = √ l² + w² + h²

Therefore, diagonal of the box = √ 5² + 5² + 8² = 10.67 in

Hence, The length of the straw fitted in the box is 10.67 inches.

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The value of c by using the mean value theorem is c = 6.25.

The mean value theorem in mathematics says that for any given planar arc between two endpoints, there exists at least one point where the tangent to the arc is parallel to the secant between its endpoints. It is one of the most significant findings in the real-world analysis.

Given that the function is f(x) = 5√x and the interval is (4,9).

Calculate the value of 'c' as below,

f(x) = 5√x

f(4) = 5√4 = 10

f(9) = 5√9 = 15

Calculate the value of f'(c) as below,

f'(c) = ( f(b) - f(a) ) / (b - a)

f'(c) = f(9) - f(4) / ( 9 - 4 )

f'(c) = (15 - 10 )  / ( 9 - 4)

f'(c) = 1

Again the value of f'(x) is,

f'(x) = 5/2/√x

f'(c) = 5 / 2 / (√c)

5 / 2 / (√c) = 1

√c = 5 / 2

c = 25 / 4

c = 6.25

Therefore, the value of c by using the mean value theorem is c = 6.25.

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The probability that exactly two of the four live in elderly care facilities is; 0.244

The binomial probability is defined as the probability of exactly x successes on n repeated trials, with p probability.

The general formula of binomial probability distribution is;

P(X = x) = nCx * p^(x) * (1 - p)^(n - x)

where;

Px = the probability of exactly x events occurring.

x = the number of expected successful outcomes.

p is probability of success

n is sample size

We are given;

p = 72% = 0.72

n = 4

Thus;

P(X = 2) = 4C2 * (0.72)^(2) * (1 - 0.72)^(4 - 2)

P(X = 2) = 0.244

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The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ , the correct option is (a) .

In the question ,

it is given that

the number is 5.96 × 10⁴ ,

we have to find that how many  times greater is 5.96 × 10⁴ then 2.98 × 10³ .

to find that the number is how many times greater ,

we divide 5.96 × 10⁴ by 2.98 × 10³ .

So , on dividing the numbers we get

= ( 5.96 × 10⁴ ) / ( 2.98 × 10³ )

= 5.96/2.98 × 10⁴⁻³

= 2 × 10¹

= 20 times

Therefore , The number 5.96 × 10⁴ is 20 times greater than 2.98 × 10³ .

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The equation Damian can use to found out how much money he still owes is -

y = - 43x + 774  

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

We have the following problem -

Damian bought a new game station for $774 using the stores zero interest finance plan. He will pay $43 a month for 18 months.

We can represent the equation he can use to found out how much money he still owes using a straight line as follows -

y = 774 - 43x

y = - 43x + 774              [x] is the number of month

Therefore, the equation Damian can use to found out how much money he still owes is -

y = - 43x + 774  

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Answer:

195312

Step-by-step explanation:

Using the formula for the sum of a geometric sequence,

[tex]\frac{2(1-(5)^8)}{1-5}=195312[/tex]

Step-by-step explanation:

=6a^3+7a^2-5a^3-9a^2-a

=a^3-2a^2-a this is the final answer.

The third term of F(n)=3n-4 is 5.

Two or more expressions with an Equal sign is called as Equation.

Given,

F(n)=3n-4

F of n equal to three times of n minus four.

We need to find the third term.

To find third term we need to plug 3 in place of n.

F(3)=3(3)-4

Three times three minus four

F(3)=9-4

Nine minus four gives 5

F(3)=5

Hence, the third term of F(n)=3n-4 is 5.

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The interest on the borrowed amount after 7 years is $486.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

Given that,

The amount borrowed is  P = $200.

Rate of interest is r = 18% per annum compounded quarterly.

Total time is t = 7 years

Then, the rate of interest for quarterly compounding is given by,

r  = 18 / 4%

  = 4.5%

And, total time period for compounding is,

n = 7 × 4

  = 28

The formula for compound interest is given as,

P[(1 + r / 100)ⁿ - 1]

Substitute the respective values to get,

200 × [(1 + 4.5 / 100)²⁸ - 1]

= 200 × 2.43

= 486

Hence, the interest due on the loan is given as $486.

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23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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An equilateral triangle in geometry is a triangle with three equal-length sides. An equilateral triangle has congruent sides, which means that each side is the same length. The triangle MDE is equilateral only because it is midpoint of ACB

If the square of the longest side is smaller than the sum of the squares of the two smaller sides, the triangle is said to have an acute angle according to Pythagoras's theorem. Given a triangle with sides "a," "b," and "c," with side "a" being the longest, the triangle is steeply angled if "a2" exceeds "b2" plus "c2."

By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you may determine whether the triangle is acute, right, or obtuse. The triangle is sharp because this total is higher.

Isosceles, equilateral, or scalene acute triangles are all possible. An acute triangle's longest side is located across from its biggest angle.

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Answer: The answer is A

Step-by-step explanation:

-5/8 is literally equal to -0.625 meaning this asnwer is equal not less

-0.5 is Greater than -0.625 because -0.6 is much larger

-8/5 is -1.6 which is Less than -0.625

Answer:

x= 68  z= 180  y=38

Step-by-step explanation:

She drinks 1/12 gallons of milk each day

From the question, we have the following parameters that can be used in our computation:

Size of milk = 1/2 gallons

Number of days = 6 days

These parameters can be represented as

(x, y) = (6, 1/2)

The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as

unit rate = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (6, 1/2)

Substitute the known values in the above equation

So, we have the following equation

Slope = (1/2 - 0)/(6 - 0)

Evaluate the quotient

Slope = 1/12

Hence, the number of gallons she drinks a day is 1/12

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In both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

What is  Obtuse triangle?

Triangle B = Obtuse triangle

Triangle C = Obtuse triangle

in both triangle one angle is larger than 90 degree . so these triangles are obtuse triangles.

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Number of camels are there at the safari park are 6 unit.

The animals at a safari park include camels, kangaroos and meerkats.

Let kangaroos are represented as K and Camels are represented as C and Meerkats are represented as M.

There are 12 more kangaroos than there are camels which means

K = C + 12.

There are 3 times as many meerkats as there are camels which means

M = 3C.

There are the same number of kangaroos as there are meerkats which means

K = M

If K = M

therefore,

3C = C + 12

2C = 12 ,

C = 6 unit.

So, K = 6 + 12 = 18

Or M = 18

Therefore  number of camels, kangaroos and meerkats at the safari park are 6 , 18 and 18 respectively.

Number of camels are there at the safari park are 6 unit.

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