89. Philip solved the following problem incorrectly. Explain his mistake.
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The number of bacteria y in the culture after x hours will be y = 50(2)ˣ.

An exponential function faster and faster after every next value of the independent variable.

According to the given question the number of bacteria in a culture is increasing according to the law of exponential growth. after 3 hours, there are 400 bacteria, and after 6 hours, there are 3,200 bacteria.

We use the exponential growth equation y = arˣ where a is the initial value and r is common ratio and x represents time.

so 400=ar^3...(i)  and 3200= ar^6...(i)

Dividing equation (ii) by equation (i) and solve for r we get r³ so r =2

substitute r into first equation 400=a(2)³

8a = 400.

a = 50.

∴ The no. of bacteria at any given time x will be.        ( t is replaced by x)

y = 50(2)ˣ.

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The correct answer would be "A. $2,075 = $1,500 + (.0575*s)" total sales.

A sale is a deal in which two or more parties trade products or services for cash or other assets, usually between a buyer and a seller. It is an agreement between a buyer and seller on the price of a security and the delivery of the security to the buyer in exchange for the agreed-upon compensation constitutes a sale in the financial markets. The transaction is not regarded as a sale if the product or service in issue is given by one party to the other without receiving payment, but rather as a gift or donation.

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Answer:

101 1/2

3/2=1 1/2

100+1 1/2= 101 1/2

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

As a product, we can multiply the height and the base of the rectangle.

As a sum, we can find the area finding the sum of the areas of each pieces of the rectangle.

The missing pieces of that will fill into the circles is shown in the diagram attached below. Therefore, we would have the following:

21. Area as sum = 12x + 60

Area as Product = 12(x + 5)

22. Area as sum = 5x + 20

Area as Product = 5(x + 4)

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The 94 ft. by 50 ft dimensions of the court obtained from a similar question posted online, gives;

a. The ordered pair representing the location of the player in the bottom right corner is (47, -25)

b. The distance traveled by the ball obtained using Pythagorean theorem, is approximately 53.2 feet.

The possible dimensions of a rectangular court obtained from a similar question posted online are;

Length of the basketball court = 94ft.

Width of the basketball court = 50 ft.

From the question, we have;

Location of the court center = The origin of a coordinate plane

a. The ordered pair that represent the location of a player in the bottom right corner is found as follows;

Let (x, y) represent the coordinates of the bottom right corner of the court, we have;

Horizontal distance from the center of the court (the origin) to the right boundary of the court, x = (94 ft.)/2 = 47 ft.

Vertical distance from the center to bottom of the court, y = (50 ft.)/2 = 25 ft.

Following the convention of points to the right and above the origin being positive, while points below the origin are negative, we have;

The ordered pair (the coordinates of the player) that represents the location of the player in the bottom right corner is therefore;

b. The distance, d, that the ball travels is given by Pythagorean theorem as follows;

d = √((47 - 0)² + ((-25) - 0)²) = √(2834) ≈ 53.2

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Answer:

A Triangle

Step-by-step explanation:

Since the three points are not collinear, the vertices form a triangle.

the estimated solution for the equations 3 x + 5 y = 14 and 6 x - 4 y = 9 is (5/2, 4/3).

We have the equations:

3 x + 5 y = 14

6 x - 4 y = 9

The exact solution is the point (2.41, 1.36)

1.(5 / 2, 4 / 3)-----> (2.5, 1.33)--------> is the best approximation

2.(4 / 3, 5 / 2)------> (1.33, 2.5)

3.(7 / 3, 7 / 2)------> (2.33, 3.5)

4.(- 5 / 2,-7 / 5)----> (- 2.5, - 1.4)

The estimate solution is (5/2, 4/3).

Therefore, the estimated solution for the equations 3 x + 5 y = 14 and 6 x - 4 y = 9 is (5/2, 4/3).

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Answer:

1/4

Step-by-step explanation:

You jumped rope of 1/3 of 3/4 hour.

In math, "of" usually means times.

1/3 of 3/4 hour = 1/3 × 3/4 hour = (1 × 3)/(3 × 4) hour = 3/12 hour = 1/4 hour

Answer: 1/4

Answer:

 3:9 6:15 14:21 15:35 all of these should work

Step-by-step explanation:

using y=mx+c (equation of a line)

equation of one point form

y-y1=m(x-x1)

where y1=8,x1=6,m=1

y-8=1(x-6)

y-8=x-6

y=x-6+8

y=x+2

intercept form=2

or

y=mx+c where y=8,x=6,m=1

8=1(6)+c

8=6+c

8-6=c

2=c

or c=2

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Explanation:

Start at -4 on the x axis.

Draw a vertical line until reaching the curve.

Then draw a horizontal line until reaching the y axis.

You should arrive at y = -5. This tells us f(-4) = -5

The input x = -4 leads to the output y = -5

The point (-4, -5) is on the graph. This is the highest point, so it's the vertex of the V shape.

See the diagram below.

From the given statements, g(-13) = 20, that is option B, is true for g.

Here we are given that a function g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

Further, g(0) = -2 and g(-9) = 6

Let us evaluate each option one by one-

A. g(7) = -1

As we can see x can take values only from -20 to 5. And 7 is greater than 5. This means that the function us not defined at g(7) and hence, option A is not the correct option.

B. g(-13) = 20

Here, x=-13 is in our domain and y = 20 also lies within our range. Hence, this is the correct option.

C. g(0) = 2

We are already given that g(0) = -2. y can take only one unique value for every value of x and hence, g(0) cannot be equal to 2.

D. g(-4) = -11

As we can see y can take values only from -5 to 45. And -11 is smaller than 5. This means that the function us not defined at g(-4) and hence, option D is not the correct option.

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Your question was incomplete. Check for the full content below-

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

g(0) = 2

g(7) = -1

g(-4) = -11

g(-13) = 20

Answer:

5000 litres

Step-by-step explanation:

1 kilolitre is 1000 litres

Answer: The tank would hold 5000 Liters

If three lakes lost water during a drought, lake Jensen lost one-sixth of its water, lake Parlow lost 26% of its water, and lake Stockton lost thirty-three two-hundredths of its water, then the lake that lost the least amount of water is lake Stockton.

The lake that lost the least amount of water can be determined by converting the amounts lost by each of the lakes into percentage form.

As lake Jensen lost one-sixth of its water, it can be written in percentage form as,

Lake Jensen = 1/6 × 100 = 100/6 = 16.67 %

As given, Lake Parlow lost 26%

Lake Parlow = 26%

As Lake Stockton lost thirty-three two-hundredths, it can be written in percentage form as,

Lake Stockton = 33/200 × 100 = 0.165 ×  100 = 16.5 %

Thus, the least percentage of water lost is 16.5% by lake Stockton.

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It would take the assistant 20 hours to do the job alone.

From the information given, we have that;

Let the gardener be x

His assistant be y

So,

y = 1/ 5

x + y = 1/ 4

Substitute the value

x = 1/ 4 - 1/ 5

Find the LCM

x =  1 / 20

Take the reciprocal

x = 20 hours

Thus, it takes the assistant 20 hours to do the job alone.

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Answer:

sure y not

Step-by-step explanation:

basta alam ko y not hindi

It should be noted that the ratio of 91 to 7 will be 13:1.

It should be noted that when you want to calculate a ratio, you have to look at the common factor that the figures have.

In this case, the common factor that 91 and 7 has is 7

Therefore, the ratio will be:

= 91/7

= 13/1

In conclusion, the ratio is 13:1

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The number 1.092 × 10¹ is 15.6 times larger than  7 × 10⁻¹ .

A number is said to be in standard form if it can be written in a decimal number between 1.0 and 10.0 multiplied with power of 10.

For Example: 1.8x10² is a standard form .

In the given question

1.092×10¹   and    7×10⁻¹

both the numbers are in a standard form

For comparison we need to convert them in decimal form

1.092 × 10¹ = 1.092 x 10 = 10.92

7 × 10⁻¹ = 7/10 = 0.7

So , According to the question

Let 10.92 be x times larger than 0.7

which means

(0.7)*x=10.92

x=10.92/0.7

x=15.6

Therefore , 1.092 × 10¹ is 15.6 times larger than  7 × 10⁻¹ .

The given question is incomplete , the complete question is

How many times larger is (1.092 × 10¹) than (7 × 10⁻¹)?

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Answer:

7y2 + 8xy - 3

Step-by-step explanation:

7y2 + 6xy + 2xy -3  You distribute the - sign through the second binomial.  You are distributing or multiplying (-2xy -3) by -1  Combine like terms

7y2 + 8xy -3

Answer:

What is the difference of the two polynomials?

(7y2 + 6xy) – (–2xy + 3)

7y2 + 4xy – 3

7y2 + 8xy – 3 Correct

7y2 + 4xy + 3

7y2 + 8xy + 3

Step-by-step explanation:

Answer: 33

Step-by-step explanation:

(-3)+(6)^2

-3+36

33 (Answer)

Answer:

6/19

Step-by-step explanation:

19 = total pens (blue pens + green pens + red pens)

6 = total number of blue pens

By using the property of vertically opposite angles the value x= 4 and the angle z = 78°

Vertical opposite angles are angles made at the intersection of two lines, these are non adjacent angles that are opposite to each other.

Vertical opposite angles are equal to each other.

In the given figure (5x + 82)° and (11x + 58)° are vertically opposite angles.

(5x + 82)° = (11x + 58)°

5x + 82 = 11 x + 58

82- 58 = 11x - 5x

24 = 6x

x = 24 /6 = 4

Then (5x+82) = (5(4) +82)= 102

(5x + 82)° and z° both are angles on same line therefore their sum will be 180°

(5x+82) +z =180

102+z=180

z= 180-102 = 78

Therefore, the value x= 4 and the angle z = 78°.

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Answer:

-1 3/10 + (-3.8) = -5.1

Step-by-step explanation:

The largest integer is 0 (first option).

Integers are whole numbers. An integer is number that is not a fraction and not a decimal. Integers can either be positive, negative or zero. An example of an integer is 100, - 100 and 0.

An even number is a number that is divisible by 2 into two equal halves. An example is 2, 4, 6, 8. Consecutive even integers are whole even numbers that follow each other on the number line. An example is 2, 4, 6, 8.

If 0 is the largest number, the other three consecutive even integers would be : 0, -2, - 4, - 6. The sum of these numbers is -12.

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Answer:

Wait, can you explain the answer choices, I don't understand them.

Step-by-step explanation:

Answer:

x=17 3y=13+10-3

x=17y=20

Step-by-step explanation:

answer to the questions

Answer:

x = 3 y = 46

Step-by-step explanation:

8x+13 = 9x+10

-8x          -8x

13 = x+10

-10     -10

3 = x

180-37 = 143

3y+5 = 143

-5          -5

3y = 138

/3      /3

y = 46

Answer:

Yes

Step-by-step explanation:

If you use only perpendicular lines, all angles should be exactly 90 degrees

The length of the side of the frame will be 6.33  to the nearest inch.

All the sides of a square are congruent. Let a be the side length of the square. Then the area of the square is the square of the side length of the square.

Then the area of the square would be;

Area of the square = a² square units

We have been given that Rafael is constructing a square-shaped frame. And the frame has a 40 square inches surface area.

A = a²

40 = a²

a = √40

a = 6.33 inches

Hence, The length of the side of the frame to the nearest inches will be 6.33  to the nearest inch.

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