Math on the Spot There are tiger barbs in a aquarium and giant danios in a aquarium. Write a numerical expression to represent the greatest total number of fish that could be in both aquariums. Use the rule and the table to solve this problem. The rule for the number of fish in an aquarium is to allow of water for each of length.
Math on the Spot There are tiger barbs in a 30-gallon aquarium and giant danios in a 20-gallon aquarium. Write a numerical expression to represent the greatest total number of fish that could be in both aquariums. Use the rule and the table to solve this problem. The rule for the number of fish in an aquarium is to allow 1 gallon of water for each inch of length.
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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

9514 1404 393

Answer:

  2x +1 = 2x +3

Step-by-step explanation:

For there to be no solution, the coefficients of x must be the same, and the constants must be different. One possible choice of numbers is shown above.

Since no diagram attached there are two possible options.

Option 1

The quadrilateral is parallelogram.

In this case ∠A and ∠D sum up to 180°, therefore:

Option 2

The quadrilateral is isosceles trapezoid.

In this case ∠A is congruent with ∠D, therefore:

Answer:

115

Step-by-step explanation:

Answer:

Cost of Washer = $696

Cost of Dryer = $232

Step-by-step explanation:

Start by making and equation, put a variable for the missing prices, let's say the cost of the dryer is 'x' and since the cost of the washer is three times, it will be '3x'.

Put the equation together, so we can add the x variables together.

3x + x = 4x

The total cost will be what the '4x' is equal to.

4x = 928

Going back to algebra, we solve the equation by dividing both sides by 4.

x = 232

Remember x is the variable we gave to the dryer, so now we must find the cost of the washer. In order to do this, we will have to multiply it by 3.

3x

3(232) = 696.

To check the answer, we can add them together to make sure we get the total cost.

696 + 232 = 928

Answer: 2

Step-by-step explanation:

The constant of proportionality is the same as the slope of the line. Using the slope formula with the points (0, 0) and (2, 4), \(\frac{4-0}{2-0}=2\).

Answer:

we can say that You drive 43.79 km

Step-by-step explanation:

Distance covered for drive to school = 24.84 km

Distance covered for drive to friends = 18.95 km

We need to find how far do you drive.

It means we need to find the total distance covered

Total Distance Covered = Distance covered for drive to school + Distance covered for drive to friends

Putting values and finding total distance

Total Distance Covered = Distance covered for drive to school + Distance covered for drive to friends

Total Distance Covered = 24.84 + 18.95

Total Distance Covered = 43.79

So, the total distance covered by you during driving is: 43.79 km

Therefore we can say that You drive 43.79 km

Answer:

It's 9 3/8! :)

Step-by-step explanation:

Answer:

Median = 14

Step-by-step explanation:

2, 5, 14, 15, 21, 18, 15, 9, 2

First, order the numbers:

2, 2, 5, 9, 14, 15, 15, 18, 21

Then, cancel out the numbers, starting the first and last number, going outwards in. If there is 1 number left, it is your median. If there are 2 left, add the 2 numbers together and divide them by two:

2, 2, 5, 9, 14, 15, 15, 18, 21

2, 5, 9, 14, 15, 15, 18

5, 9, 14, 15, 15

9, 14, 15

14

The median is 14.

Please tell me if I was wrong! I hope this helps you!

Answer: The median is 14

Step-by-step explanation: The median is the number that is halfway into the data set. To find the median, the data should be arranged in order from least to greatest. For this example.  2,2,5,9,14,15,15,18,21. Find the number that is halfway. which is 14

Using translation concepts, it is found that his mistake was that he made the shifts on the wrong coordinates, and the new location is at (1,5).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Initially, researching the problem on the internet, it is found that the market is at position (3,8).

Then, it was shifted 2 units left and 3 units down, hence the new position is given by:

(3 - 2, 8 - 3) = (1,5).

His mistake was that he made the shifts on the wrong coordinates, and the new location is at (1,5).

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Answer:

-3 and 1

Step-by-step explanation:

(x+3)(x-1)=0

x+3=0

x-1=0

x=-3

x=1

Answer:

(C) The largest possible profit the company can make is 7 million dollars

Step-by-step explanation:

Proverbs 3:5-6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Trust in the Lord with all your heart

   and lean not on your own understanding;

in all your ways submit to him,

   and he will make your paths straight.

_________________________________________________________

Have a blessed day!!

:)

Answer:

What is your question??

The logarithmic equation is equivalent to this exponential equation is x = log (8/25) (option c).

In this case, we are asked to find the logarithmic equation that is equivalent to the given exponential equation:

2,400 = 7,500(10)⁻ˣ

To solve for x, we need to isolate it on one side of the equation. We can start by dividing both sides by 7,500:

2,400/7,500 = (10)⁻ˣ

The choice of base for the logarithm doesn't matter, as long as we use the same base for both sides. Let's use base 10:

log(2,400/7,500) = log(10⁻ˣ)

Using the properties of logarithms, we can simplify the right-hand side:

log(2,400/7,500) = -x*log(10)

We know that log(10) = 1, so we can simplify further:

log(2,400/7,500) = -x

x = log(8/25) = log(8) - log(25) = 0.9031 - 1.3979 = -0.4948

So the only answer choice that gives us the same equation as the original exponential equation is (C) x = log (8/25).

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Complete Question:

Which logarithmic equation is equivalent to this exponential equation?

2,400 = 7,500(10)^(-x)

A. x= -log (25/8)

B. x = log(-25/8)

C. x = log (8/25)

D. x = -log (8/25)

Answer:

A, B, E

Step-by-step explanation:

Notice that A, B, and E all maintain their common ratios, while C and D do not.

Answer:

\(\sf \dfrac{1}{16}\)

Step-by-step explanation:

    In exponent multiplication, if bases are same, add the powers.

             \(\sf \boxed{a^m*a^n=a^{m+n}}\)

             \(\sf \boxed{a^{-m}=\dfrac{1}{a^m}}\)

      \(\sf 4^6 * 4^{-8}=4^{6+(-8)}\\\\\)

                   \(\sf =4^{-2}\\\\ =\dfrac{1}{4^2}\\\\=\dfrac{1}{16}\)

The two unit rates that represent the given recipe are:

A unit rate is a rate in which the denominator is 1. In the given recipe, we can express two unit rates as follows:

Milk per egg:

The recipe uses 2 tablespoons of milk for every 3 eggs. To express this as a unit rate, we can divide both sides by 3 to get the amount of milk used per egg, hence, the unit is 2/3 tablespoons of milk per egg

Eggs per milk:

We can express the recipe in terms of eggs per tablespoon of milk. To do this, we can divide both sides by 2 to get the number of eggs per tablespoon of milk, hence, the unit is 3/2 eggs per tablespoon of milk

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Answer: 60 meters

The square root of 225 is 15.

15(4) = 60

==========================================

Explanation:

Points B, C and H are along the right wall as I've highlighted below. The fourth missing point of this wall is point G

The term "coplanar" means that all points are on the same plane. A plane is any flat surface that doesn't bend or curve.

The segment OB' has a length of 3 units

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

Scale factor = 4

Length of segment OB = 3/4

The above means that:

Length of segment OB' = Length of segment OB * Scale factor

Substitute the known values in the above equation

So, we have the following dilation equation

Length of segment OB' = 3/4 * 4

Evaluate

Length of segment OB' = 3

Hence, the length of OB' is 3 units

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The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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Answer:

1

Step-by-step explanation:

because all of the squares are shaded so it would be 1 whole

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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Simone can make two different rectangles with the following side lengths:

Rectangle 1: Length = 16 inches, Width = 1 inch

Rectangle 2: Length = 8 inches, Width = 2 inches

To find the side lengths of the two rectangles that Simone can make using 16 square inch tiles, we need to consider the factors of 16 and check which pairs of factors can form rectangles with the same area.

The factors of 16 are 1, 2, 4, 8, and 16. We can pair these factors to form different rectangles and calculate their areas:

Pairing: 1 and 16

Length: 16

Width: 1

Area: 16 square inches

Pairing: 2 and 8

Length: 8

Width: 2

Area: 16 square inches

Pairing: 4 and 4

Length: 4

Width: 4

Area: 16 square inches

Therefore, Simone can make two different rectangles with the following side lengths:

Rectangle 1: Length = 16 inches, Width = 1 inch

Rectangle 2: Length = 8 inches, Width = 2 inches

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Answer:

difference quotient

Step-by-step explanation:

Solution:

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.

Hence,

The final answer is OPTION A

Answer:   Two distinct lines are parallel if they are in the same plane and never intersect each other.

Step-by-step explanation:

answer is b

The value of 3f(x) + 2g(x) = -5x - 2

Given f(x) = -3x, g(x) = 2x-1 are the two functions

then by the algebra of two functions(adding two functions) we can find the value of 3f(x) + 2g(x)

Now find

3f(x) = 3(-3x) = -9x            -----------(i)

2g(x) = 2(2x-1)

        = 2(2x)-2(1)                        

2g(x) = 4x-2                     ----------(ii)

Now, add the above two equation (i) and (ii)

3f(x) + 2g(x) = -9x + 4x - 2  

                   = -5x-2  

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Answer:

The correct answer is "E"

Answer:

D. Dilation and reflection

Step-by-step explanation:

There are 4 main types of transformations, rotation, reflection, translation, and dilation. 3 of these transformations are defined as rigid, rigid means that the transformation preserves angles and distance between points. If these aspects are preserved than the image is congruent. The only non-rigid transformation listed is dilation, therefore D must be correct.  

Answer:

d

Step-by-step explanation:

Answer:

2  +   + 1 6

Step-by-step explanation:

Add the numbers:

6 + 5y - 4y + 10 + 3x -x    =  

1 6  +  5  −  4  +  3   −

Combine like terms:

16 + 5y - 4y +3x - x

16+ 1y + 3x -x

Multiply by 1

16 + 1y + 3x - x

16 + y + 3x - x

Combine like terms:

16 + y + 3x - x

16 + y + 2x

Rearrange terms:

16 + y + 2x

2x + y + 16

Answer:

16 + y + 2x

Step-by-step explanation:

\(6 + 5y - 4y + 10 + 3x - x\)

\(16 + 5y - 4y + 3x - x\)

\(5y - 4y = (5 - 4)y = 1y = y\)

\(16 + y + 3x - x\)

\( = 16 + y + 2x\)

Answer:

25l+20d=x and x ≤ 2000 needs to be part of the system.

Step-by-step explanation:

Given that:

Amount charged per lawn = $25

Number of lawns = l

Amount charged per driveway = $20

Number of driveways = d

Amount saved by Jamison = x

\(25l+20d=x\)

Amount given by parents = upto $2000

It means the parents will not give more money than $2000, therefore, we will use less than equal to inequality

x ≤ 2000

Hence,

25l+20d=x and x ≤ 2000 needs to be part of the system.