Given the equation of the ellipse in general conic form, convert to standard form.
4x² + y² + 72x+10y + 285 = 0
.
O.
(x-6)²
16
(x+5)²
16
(x+9)²
16
(x+9)²
64
+ (y+8)²
64
+
+
+
(y-9)²
64
(y+5)²
64
(y+5)²
16
= 1
1
= 1
= 1

The initial population at time t = 0 is 1406.25.

The size of the bacterial population after 3 hours is 720,000.

The bacterial population would grow at an exponential rate. The equation that can be used to determine the bacterial population in 3 hours is

Bacterial population = initial population x ( 1 + 1)^t

Where

t = time = total number of minutes / 20 minutes

t = 120 / 20 = 6

Initial population:

90,000 / (2^6) = 1406.25

Population in 3 hours = 1406.25 ( 1 + 1)^9 = 720,000

t = (3 x 60) / 20

180 / 20 = 9

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The area of a football field, considering the proportions in this problem, is of:

0.279 hectares.

A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations to find the desired amounts in whichever context of the problem.

The composition of an year is given as follows:

Hence the number of seconds in an year is given as follows:

365 x 24 x 3600 = 31,536,000 seconds

The number of hectares cut in a year is:

8,800,000 hectares.

This amount in this time is equivalent to the area of a football field each second, hence this area is obtained as follows:

Area of a football field = 8,800,000/31,536,000 = 0.279 hectares.

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Money borrowed from x, y, z banks on loan are $5000, $5000, $9000 respectively.

What is loan?

A loan is the lending of money by one or more people, businesses, or other entities to other people, businesses, or other entities. The recipient incurs a debt and is often responsible for both the principal amount borrowed as well as interest payments until the debt is repaid.

Main Body:

The equations formed from the information given in question are:

x+y+z = 19000

16x+18y+15z = 305000 and,

2x-y = 5000

by solving these equation we get

x= $5000

y= $5000

z= $9000

Hence the answer to this question are $5000 for x, y bank and $9000 from z bank.

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Answer:

y = 1.25 * x

Step-by-step explanation:

y is the total cost. You get the total cost by multiplying the price with the amount of pounds of broccoli you buy

1870 yards is covered if all 11 players complete the drill.

Given:

Starting at the endzone, players sprint to the 10 yard line and back, the 25 yard line and back, and finally the 50 yard line and back.

one player yards covered = 10*2+25*2+50*2

= 20+50+100

= 70+100

= 170 yards.

11 players yards covered = 11*170

= 1870 yards.

Therefore 1870 yards is covered if all 11 players complete the drill.

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Answer:

Step-by-step explanation:

A day is 24 hours long, an hour is 60 minutes, and 24 multiplied by 60 is 1,440 minutes. To get the number of minutes in 30 days, we multiply 1,440 by 30 which is 43,200 minutes.

The Ratio of cholesterol to HDL cholesterol is 29/4

What does a math ratio mean?

Definitions: An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls

First, write the words that express the ratio. We want to know the ratio of  total cholesterol to his HDL cholesterol.

Write as a fraction.

Total cholesterol / HDL cholestrol

Substitute the values.

290/40

Simplify.

29/4

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Answer:

False

Step-by-step explanation:

1 + 2 (-4) = -7

1 - 8 = -7

-7 = -7

-4 (-4) = -1

16 = -1

16, 14, 12

80, 70, 60

Step-by-step explanation:

16×5 = 80

14×5 = 70

12×5 = 60

Answer:

16, 14, 12

80, 70, 60

Step-by-step explanation:

16×5 = 80

14×5 = 70

12×5 = 60

Hope it helps! :)

Answer is : 5a + 4b

The consecutive odd integers such that the sum of their squares is 34 are 3 and 5.

The square of the 3 is 9.

The square of the 5 is 25.

and both are the consecutive in the number line and their sum is 34 which satisfy the given statement.

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Answer:Smallest + Middle + Largest = 53

M= S + 2

L = 2S

Substitute M= S +2 and L = 2S into S + M + L =53

S + S + 2 + 2S = 53

4S + 2 = 53

4S/4 = 51/4

S = 12.75

M = 12.75 + 2

M = 14.75

L = 2 (12.75)

L = 25.5

Step-by-step explanation:

The option that accurately describes the benefit of comparison in the experiment is; The variability between each subject would be evenly distributed between the two groups, so any observed differences in the level of irritation between the two groups are more likely due to the new cream.

In a  research where there exists the possibilities of outcomes being partial, it means that the details being masked from the subject is referred to as single-blind.

In this research, we see that the subjects do not know about the cream that they are receiving whether it was either new or with no active ingredient. Therefore, it means the research will be more effective as there will be no latter psychological effects on the result

Due to the fact that the people were randomly assigned to one of the two groups, it means that there is some randomness to both groups that makes them the same. The group that doesn't get the cream will be identified as a control group.

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The Area of the fabric required is 3.6 square feet

The square's side length is 3 feet.

Due to the fact that Lin is creating a window covering for a window that is half circle-shaped on top of a square.

The window covering must therefore be a semicircle with a 3-feet diameter.

thus the semicircle's radius is equal to d/2 = 3/2 feet

Now, the Area of the semicircle,

[tex]A =\frac{1}{2} \pi r^{2} \\[/tex]

Putting the value of the radius in the equation, we have,

[tex]A =\frac{1}{2} \pi (\frac{3}{2} )^{2} \\\\A = \frac{1}{2} *\frac{22}{7} *\frac{3}{2} *\frac{3}{2} \\\\A = \frac{99}{28} = 3.53 = 3.6[/tex]

Hence, The Area of the fabric required = 3.6 square feet

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Answer:

Use the Intermediate Value Theorem to prove that every cubic function has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.

The required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct.

Given that,
To determine the equation that has the solution x = all real numbers.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Equation 1
5(3-x)+7x = 3x + 15 - x
15 - 5x + 7x = 3x +15 - x
2x = 2x
Since it implies the variable x solution as all real numbers,
While all other equation has a distinct unique solution,

Thus, the required equation that has a solution as x = all real numbers is 5(3-x)+7x = 3x + 15 - x. Option A is correct

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Answer:

30

Step-by-step explanation:

240/ 8 = 30.

alternatively, you can say 30 multiplied by 8 is 240. or you divide 240 by 30 and get 8.

Answer:

Yes correct so what is the question

240/8=30

Step-by-step explanation:

The ordered pair that are solution of the equation 3x-y= 1 is (−2, −7) , (−1, −4)

and  (3, 8)

What is ordered pair ?

An ordered pair is a set of two things in mathematics. The pair's objects must appear in a specific order for them to be considered distinct from one another, unless a = b. Ordered pairs are also referred to as 2-tuples, or sequences with a length of 2.

Checking the equation by putting the values of x and y in the given options

1. (-2,-7)

LHS

=3*(-2) - (-7)

= -6+7

=1

LHS = RHS

2. (-1,-4)

LHS

=3*(-1) - (-4)

= -3+4

=1

LHS = RHS

3. (0,1)

LHS

=3*(0) - (1)

= -1

=-1

LHS [tex]\neq[/tex] RHS

4. (3,8)

LHS

=3*(3) - (8)

= 9-8

=1

LHS = RHS

5. (4,2)

LHS

=3*(4) - (2)

= 12-2

=10

LHS [tex]\neq[/tex] RHS

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Answer:

I think so ;-;

Step-by-step explanation:

The line segment AD is congruent with DB because the corresponding parts of congruent triangles are congruent.

An Isosceles Triangle is defined as a triangle with two sides of equal length is an isosceles triangle.

Draw the DM as the perpendicular bisector of AB(Assumption)

Since DM is perpendicular to AB, m∠AMD = m∠BMD = 90°.

Since DM bisects AB, AM ≅ BM. With AD≅ DB (reflexive property), ∆ADM ≅ ∆BDM by SAS.

Finally, AD≅ DB because corresponding parts of congruent triangles are congruent.

Therefore, ∆ABD must be isosceles since two of the three sides are congruent.

Thus, line segment AD is congruent with DB.

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If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

In the question ,

it is given that

the when the object is dropped from height h then the velocity with which it hits the ground is given by the formula

v = √(19.6×h)

to find the height it was dropped , and it hits the ground with velocity 25.7 meter per second ,

we substitute v = 25.7 in the equation v = √(19.6×h) ,

we get ,

25.7 = √(19.6×h)

squaring both the sides , we get

19.6 × h = 25.7²

19.6 × h = 660.49

h = 660.49/19.6

h = 33.698

h ≈ 33.7

Therefore ,If an object hits the ground with a velocity of 25.7 meters per second, it was dropped from a height of 33.7 meter .

The given question is incomplete , the complete question is

Suppose that an object is dropped from a height of h meters and hits the ground with a velocity of v meters per second. Then v = √(19.6×h) . If an object hits the ground with a velocity of 25.7 meters per second, from what height was it dropped?

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There will be $9270.71 in the account in 5 years

What is future value ?

Future value refers to an asset's value at a future time. It calculates the nominal amount of money that a certain amount of money is "worth" at a specific point in the future under the assumption of a specific interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function.

Given

PMT = $150

r =  1.2%

t = 5years

Future value , FV = PMT [tex]\frac{(1+i)^{n}-1 }{i}[/tex]

i = 0.012 /12

n = 5 *12

FV = 150 [tex]\frac{(1 +\frac{0.012}{12})^{5*12} }{\frac{0.012}{12} }[/tex]

     = 9270.71

The amount in the account in 5 years is 9270.71

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Answer:

x = 1

Step-by-step explanation:

The equation x = -5 is a vertical line through point (-5, 0) on the x-axis.

For a line to be parallel to the line x = -5, it must be a vertical line.

Since the vertical line must include the point (1, 4), then the x-coordinate of every point on that line must be 1.

The equation is x = 1.

Answer:

65 good sir.

Step-by-step explanation:

Answer: 2560 eyeshadows

Step-by-step explanation:

512x5

Answer: 2560

Step-by-step explanation: First we can set up a proportion: [tex]\frac{5}{1} =\frac{x}{512}[/tex]

Then we can multiply 5 and 512, which gets us 2560. That's the answer, but for a different proportion, you would divide the last number, but in this case, since the last number's one, nothing changes.

hope this helps!

please give brainliest!

The perimeter and area of the shaded regions are 31.4 and 37.69 respectively.

a ) Big circle

Radius = r = 3

Perimeter of the big circle = 2 πr

                                       = 2 π* 3

                                      = 6 π

Area of the big circle =  π [tex]r^{2}[/tex]

                             =  π * 9

                            = 9 π

b) Small circle

Radius = r = 2

Perimeter of the small circle = 2 πr

                                       = 2 π* 2

                                      = 4 π

Area of the small circle =  π [tex]r^{2}[/tex]

                             =  π * 4

                            = 4 π

c)  Full circle

Radius = r = 5

Perimeter of full circle = 2 πr

                                       = 2 π* 5

                                      = 10 π

Area of full circle =  π [tex]r^{2}[/tex]

                             =  π * 25

                            = 25 π

d ) The shaded region

Perimeter of the shaded region of the circle =Perimeter of full circle

                                                                          =10π

                                                                          =31.4

Area of the  shaded region of the circle  = Area of full circle -(areas of big and small circles)

                                                                   = 25π - 13 π

                                                                   = 12 π

                                                                  = 37.69

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Answer:

722000

Step-by-step explanation:

the last 3 digits are below 500 so you round them down to 722000.

Answer: The second 2nd is the thousand

first 2 is near to thousand because it is ten thousand

third 2 is also near to thousand because it is hundreds

A test statistic is a figure obtained from a statistical analysis.It explains how far the observed data is from the null hypothesis, which states that there is no correlation between the variables or difference between the sample groups.

Obtaining p values using test statistic:

Given that ; we have a standardized test statistic and α - values ;

Let's define the decision region :

If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0

A.)

Left tail , Z = - 1.32 ; α = 0.10

We can use the Pvalue calculator from Z score :

Pvalue = 0.934

Pvalue > α ; Hence, we fail to reject the null, H0

B.)

Right-tailed test, z = 2.46, α = 0.01

Pvalue from Zscore calculator ;

Pvalue = 0.0069

Pvalue < α ; Hence, we reject the null, H0

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The average of Linda's six biology tests is 87.

Average:

Average is the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

Linda computed the average of her six biology test scores by mistakenly adding the totals of five scores and dividing by five, giving her an average score of 88. When Linda realized her error, she recalculated and included the sixth test score of 82.

Here we need to find the average of 6 six biology subjects.

In the given question, we know that,

Average of 5 biology subjects = 88

So, the total mark in those five subject is calculated as,

=> 88 x 5 = 440

So, the new total including the sixth subject is,

=> 440 + 82

=> 522

Therefore, the average of 6 subjects is calculated as,

=> 522/6

=> 87

So, the average of 6 subjects is 87.

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The average rate of change of the function g(x) = x² – 1 from x = 3 to x = 6 is 9.

What is the average rate of change of a function?

The average rate of change function describes the average rate at which one quantity changes in proportion to another's change.

We can write the Average Rate of Change of a function f from a to b as follows using function notation:

                                   [tex]r = \frac{g(b)-g(a)}{b-a}[/tex]

The given function is g(x) = x² – 1.

Then the rate of change of a function from x = 3 to x = 6.

so the value of a =  3 and b = 6, using the above formula, we get

                                           [tex]r = \frac{g(b)-g(a)}{b-a}\\r = \frac{g(6)-g(3)}{6-3}\\r = \frac{(36-1)-(9-1)}{6-3}\\\\r = \frac{35-8}{3}\\r = \frac{27}{3}\\\\r = 9[/tex]

Hence, The average rate of change of the function g(x) = x² – 1 from x = 3 to x = 6 is 9.

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