a 600 l tank is filled with pure water. a copper sulfate solution with a concentration of 20 g/l flows into the tank at a rate of 2 l/min. the thoroughly mixed solution is drained from the tank at a rate of 2 l/min. a. write a differential equation (initial value problem) for the mass of the copper sulfate. b. solve the differential equation.

The SAS states that two triangles that have two pairs of corresponding congruent sides and a pair of corresponding included congruent angles are congruent.

The RHS congruence criterion states that two right triangles that have a congruent pair of hypotenuses and a congruent pair of corresponding sides are congruent.

The SAS congruence criterion is a postulate that shows that if two triangles have two pairs of corresponding congruent sides and a pair of corresponding included congruent angles, then both triangles are equal or congruent to each other.

What is the RHS Congruence Criterion?

The RHS stands for "right angle-hypotenuse-side". This congruence criterion states if two right triangles have congruence hypotenuses and a pair of corresponding congruent sides, then the two right triangles congruent to each other.

In summary, SAS congruence criterion proves that two triangles with two pairs of corresponding congruent sides and a pair of corresponding included congruent angles are congruent, while the RHS congruence criterion proves that two right triangles are congruent if they have equal pair of hypotenuses and a congruent pair of corresponding sides.

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Answer:

Step 1: f(0) = -2

I also attached the graph in the explanation!

Step-by-step explanation:

f(x) = 0.5^x -3

f(0) = 0.5^0 - 3

f(0) = 1 - 3

f(0) = -2

I attached the graph below.

Answer:

Step-by-step explanation:

ormula for finding the asymptote of hyperbola is

y-k =+/- b/a( x-h).

Answer:

Based on the information provided, it can be conjectured that your cousin is 18 years old or older.

Step-by-step explanation:

Based on the information provided, it can be conjectured that your cousin is 18 years old or older.

It is 6x^3 - 15x^2 - 2x - 5

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Using the formula of combination and probability theorem , The answer is b) 75.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The formula for combination is:

[tex]C(n,r) = \frac {n!}{r!(n-r)!}[/tex]

selecting 1 blue ball from 5 blue balls = C(5,1)

=5

selecting 2 orange balls from 6 balls = C(6,2)

=15

Total ways of selection = 5*15=75

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The equation of f(x) from the graph if, G(x) = x², is F(x) = 2x² + 3, so option A is correct.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given:

G(x) = x²,

As you can see from the graph, the vertex of the parabola is (0, 3),

Write the equation of a parabola as shown below,

y = a(x - 0)² + 3

y = ax² + 3

Here a is the slope of the parabola,

slope = 4 / 2  (from the graph),

slope = 2

Thus, the equation will be,

y = 2x² + 3 or  F(x) = 2x² + 3

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Answer:

C

Step-by-step explanation:

I'm guessing you misspelled 410 as 419, but the equation is y=mx+b

Kim wants the money amount she puts in to pay off her $410 phone, or in other words, add up to $410.

The constant, or b, is 50. The m is 35, and the x is the months.

35m + 50 = 410

Answer: C. 35m + 50 = 410

Step-by-step explanation:

We know the cost is 410, so it will be = 410

We know that she pays 35 each month, which mean it is 35m

She put down 50 at the beginning, so it is + 50

So our equation is

35m + 50 = 410

Answer:

5. ∠HTS

6. DI

7. UF

8. ∠E

Step-by-step explanation:

5. We are given that ΔTSR ≅ ΔTSH, and according to CPCTC (corresponding parts of congruent triangles are congruent), ∠RTS corresponds with ∠HTS. Therefore, ∠RTS ≅ ∠HTS.

6. We are given that ΔECD ≅ ΔDJI, and according to  CPCTC (corresponding parts of congruent triangles are congruent), segment DE corresponds with segment DI. Therefore, DE ≅ DI.

7. We are given that ΔVUT ≅ ΔVUF, and according to  CPCTC (corresponding parts of congruent triangles are congruent), segment UT corresponds with UF. Therefore, UT ≅ UF.

8. We are given that ΔPQR ≅ ΔEFG, and according to  CPCTC (corresponding parts of congruent triangles are congruent), ∠P corresponds with ∠E. Therefore, ∠P ≅ ∠E.

Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next item in the sequence is obtained by adding the previous term by 8.

The difference between consecutive terms in an arithmetic sequence, sometimes referred to as an arithmetic progression, is consistently the same.

To find nth term we will use

[tex]a_{n}=a+(n-1)d[/tex]

where

a=first term

d=common difference

n=number of terms

In 8 16 24 and 32 since common difference d=8 between each successive term so this is a arithmetic sequence.

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Answer:

Step-by-step explanation:

A line on a graph is a series of points connected by a straight line. It is used to show continuous change or a relationship between two variables.

A line on a graph is a visual representation of a continuous change or a relationship between two variables. It is made up of a series of points connected by a straight line, making it easy to compare changes in data over a period of time. The points on the line represent the values for the two variables being graphed, with the horizontal axis (x-axis) representing one variable and the vertical axis (y-axis) representing the other. The points on the line can be joined with either a straight line or a curved line, depending on the type of data being graphed. For example, a straight line will be used to show a linear relationship between two variables, while a curved line might be used to show a non-linear relationship. By examining the line, it is possible to determine the rate of change or the correlation between the two variables being graphed.

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Multiplicity value is a measure of the number of times a given entity appears in a relationship.

It is expressed as either a single value (1:1, 1:N, or M:N) or as a range of values (e.g. 1..4). This value is used to define the type of relationship between two entities.Multiplicity value is a measure of the number of times a given entity appears in a relationship. It is expressed as either a single value, such as 1:1, 1:N, or M:N, or as a range of values, such as 1..4. These values are used to define the type of relationship between two entities. For example, a 1:1 relationship means that one entity is related to one other entity, such as one customer to one order. A 1:N relationship means that one entity is related to multiple other entities, such as one customer to multiple orders. An M:N relationship means that multiple entities are related to multiple other entities, such as multiple customers to multiple orders.

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Answer:

Step-by-step explanation:

The vector representing the path of the ship from port A to the refueling station has components <14, 23>, and the vector representing the path from the refueling station to port B has twice the magnitude as the vector from port A to the refueling station.

To find the characteristics of the vector representing the path of the ship from port A to port B, we can add the two vectors together.

The sum of two vectors <a, b> and <c, d> is given by <a+c, b+d>. Therefore, the vector representing the path of the ship from port A to port B is given by:

<14, 23> + 2*<14, 23> = <14+214, 23+223> = <42, 69>

The vector representing the path of the ship from port A to port B is <42, 69>. This vector has a magnitude of √(42^2 + 69^2) = √(1764 + 4761) = √(6525) = 81 and a direction given by the angle theta, where tan(theta) = 69/42.

I hope this helps! Let me know if you have any other questions.

Answer: D. components:LeftAngleBracket 28, 46 RightAngleBracket, magnitude: 53.85

Step-by-step explanation:

(Option D.) The Side-Side-Side (SSS) Theorem: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

The Side-Side-Side (SSS) Theorem is a valid theorem to show that two triangles are congruent. This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

In other words, if all three of the sides of one triangle are equal in length to all three of the sides of another triangle, then the two triangles are identical in size and shape. This theorem is a fundamental building block of geometry, and is often used to prove the congruence of two triangles in proofs or mathematical arguments.

Since the question is not complete, here's the full task:

Which theorem is not a valid theorem to show that two triangles are congruent?

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Numbers that undergo rigid transformations are congruent. Congruent can always require precise changes even if you could conceive of them as forms that "appear exactly the same."

A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.

∠X = ∠Q

And, also

XY = PQ

XZ = RQ

Therefore,

ΔXYZ ≅ ΔPQR

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Answer:

  F = 9/5C +32

Step-by-step explanation:

You want to rearrange C = 5/9(F-32) to make F the subject.

You can solve for F the same way you solve any similar 2-step equation:

  C = 5/9(F -32) . . . . . . given

  9/5C = F -32 . . . . . . . multiply by 9/5 (multiplication property of equality)

  9/5C +32 = F . . . . . . add 32 (addition property of equality)

The equation Josh can use to convert to °F is ...

  F = 9/5C +32

The process by which we can tell that if the inverse of the function is also a function is the Horizontal Line Test  .

The Inverse of the function is defined as a function, which can reverse into another function.

If the graph of the function does not pass the Horizontal Line Test, then the graphed function's inverse will not be a function; and  

If all horizontal lines cross at most one spot on the original graph, then the inverse of the function will be a function.

Therefore , the horizontal line test is used to check whether the inverse is a function or not .

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Answer:

24.6 cm^2

Step-by-step explanation:

3.28m = 328 cm

75mm = 0.075 cm

Area of rectangle: L x W

328 times 0.075 = 24.6 cm^2

Answer: 190 cm = 2.07787 yards, rounded to the nearest hundredth, 2.08 yards.

Step-by-step explanation:

divide 190 cm by 91.44 to get your answer.

The Elementary Matrix E is [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

We know that the Matrix

[tex]A = \left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right] , B = \left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]

[tex]EA = B[/tex]

⇒ [tex]E = B A^{-1}[/tex]

[tex]A^{-1} = \frac{1}{|A|} \times \left[\begin{array}{ccc}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\end{array}\right][/tex]

[tex]|A| = \left|\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right|[/tex]

[tex]= 2 \times4\times4-2\times5\times1 - 1\times(-2)\times4+1\times5\times3+3\times(-2)\times1 - 3\times4\times3\\= 32 -10+8+15-6-36 = 3[/tex]

[tex]A^{-1} = \frac{1}{3} \left[\begin{array}{ccc}11&-1&-7\\23&-1&-16\\-14&1&10\end{array}\right] \\A^{-1} = \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right][/tex]

[tex]\therefore E =\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right] \times \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right][/tex]

[tex]E = \left[\begin{array}{ccc}\frac{22+23-42}{3}&\frac{2+1-3}{3}&\frac{-14-16+30}{3}\\\frac{33+23-56}{3}&\frac{-3-1+4}{3}&\frac{-21-16+41}{3}\\\frac{-22+92-70}{3}&\frac{2-4+5}{3}&\frac{14-64+50}{3}\end{array}\right][/tex]

[tex]E = \left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]

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Answer:

$34.37.

Step-by-step explanation:

To calculate Daniel's local income tax withholding, we first need to determine his taxable income. To do this, we subtract the value of his exemptions from his yearly income: $41,300 - (4 x $900) = $37,500.

Next, we need to convert the local tax rate of 4 3/4% to a decimal by dividing it by 100: 4 3/4% = 0.0475.

Finally, we can calculate Daniel's local income tax withholding by multiplying his taxable income by the local tax rate: $37,500 x 0.0475 = $1,793.75.

To find the amount of local income tax that should be withheld from Daniel's weekly earnings, we simply divide his total local income tax by the number of weeks in a year: $1,793.75 / 52 = $34.37. Therefore, Daniel's local income tax withholding from his weekly earnings should be $34.37.

Simple 3-letter words or alphabets may be spelled verbally by kids as young as 3 years old

An alphabet is a standardized system of fundamental written graphemes that correspond to the phonemes of certain spoken languages. a group of letters or other symbols used to write one or more languages, especially if they are organized in a regular sequence. a set of symbols or signals used to represent letters.

Simple 3-letter words or alphabets may be spelled verbally by kids as young as 3 years old. Early exposure to the alphabet and the spelling tools it contains, like as songs and reading aloud to them, provides the foundation for their comprehension of how letters combine to form words.

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Answer:

no images are available here

The equation for the total square yards of cloth she needs for both pillows is 314+112=426.

The total number of square yards of fabric Lea needs for both pillows is the sum of the fabric needed for the first pillow and the fabric needed for the second pillow. This can be represented by the expression:

314 square yards + 112 square yards = 426 square yards

Therefore, the expression that represents the total number of square yards of fabric Lea needs for both pillows is:

314 + 112 = 426

This expression would simplify to 426 square yards. This expression uses the addition operator (+) to add the two quantities of fabric that Lea needs for each pillow. The result is the total number of square yards of fabric that she needs for both pillows.

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Answer:

$47.70

Step-by-step explanation:

To find what a number is in percent form, divide it by 100

9% ÷ 100 = 0.09

Multiply this by $530 to find the commission

530 × .09 = 47.7

$47.70

Answer:

0.2

Step-by-step explanation:

[tex]P(A \cap C)=P(A)P(C)=(0.5)(0.4)=0.2[/tex]

Using coordinates O(0,0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0) has the advantage of allowing the graph to be stretched or shrunk uniformly in both the x- and y-directions by a factor of 2. This can be useful if the scale of the graph needs to be adjusted, or if the graph needs to be compared to another graph with a different scale. It can also make the graph easier to read if the values of the variables being plotted are very large or very small.

By using coordinates that are multiples of the original coordinates, the shape of the graph is preserved, but the scale is changed. This can be useful if the purpose of the graph is to compare the relationships between different variables, rather than to provide an accurate representation of the actual values of the variables.

Answer:

Sienna

Step-by-step explanation:

Sienna achieved higher scores of 15-17 much more consistently than Willem, who often scored just 12 or 13.