Archimedes drained the water in his tub. The amount of water left in the tub (in liters) as a function of time (in minutes) is graphed. How much water was initially in the tub?

Hi there!

Remember, squared means multiplied by itself.

So, what number multiplied times itself gives us 100?

The answer is: 10.

10 times 10 (10 squared) equals 10.

Hope it helps.

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Hello!

We have two different scenarios that we have to solve in the question. We will be solving for both the x and y variable.

We were given the equation: -3y + 2x = -18

To solve for our variables, we will use the values given in our question.

Solve:

Lets solve for the value "y", where our x = 0

Plug in 0 to x and solve:

-3y + 2(0) = -18

-3y = -18

y = 6

Lets now solve for the value "x", where our y = 0

Plug in 0 to y and solve:

-3(0) + 2x = -18

2x = -18

x = -9

Therefore, our answers would be: y = 6, x = -9

Answer:

y = 6

x = -9

Answer:

Step-by-step explanation:original quantity = $30

New quantity = $39

increase amount = 39-30 = 9

Percent change:

30 x = 9

x = 9/30

x = 0.3

0.3x 100 = 30%

Since the quantity grows, it's a percent increase.

Answer: 0

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

0 divided by 1 is 0 similarly to other numbers.

For example 5/1 = 5

Although, 1/0 is undefined as it isn't legal.

Answer:

61

Step-by-step explanation

sped

Answer: b=−10x−10.54

Step-by-step explanation:

Let's solve for b.
30.4x+b=3.4(6x−3.1)

Step 1: Add -30.4x to both sides.

b+30.4x+−30.4x=20.4x−10.54+−30.4x

Answer: b=−10x−10.54

The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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The value of LM is 8 for the given line segment.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

Given the line segment KM with midpoint L

So,

KL = LM

(KM - LM) = LM

9x + 7 - 8x = 8x

x + 7 = 8x

7x = 7

x = 1

Now,

LM = 8(1) = 8 unit.

Hence "The value of LM is 8 for the given line segment".

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The key features of the parabola include the following:

A) opens down

C) directrix at y = 1/8

D) vertex at (-1/2, 0).

Mathematically, the standard equation of the directrix lines for any parabola is given by this mathematical expression:

y = a(x - h)² + k.

Where:

Based on the information provided about the parabola, we have:

4x^2 + 4x + 2y + 1 = 0

2(y + 1/2) = -4(x + 1/2)^2 + 1

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

By comparing to the standard form, we have:

Vertex, (h, k) = (-1/2, 0).

Additionally, the distance between the vertex and the directrix is given by:

y = |1/(4a)|

y = |1/(4 × -2)|

y = |-1/8|

y = 1/8.

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The HCF of 560 and 729 is 1.

To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.

Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.

Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.

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The value of the minimum sample size required to estimate the population proportion is 438.

Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Given:

The margin of error, ME = 0.04,

The value of p = 0.12,

The confidence level =  99%,

Calculate the minimum sample size as shown below,

ME = z √[p(1 - p) / n]

Calculate the value of z from the table attached below considering the confidence level, z = 2.576,

0.04 = 2.576 √[0.12(1 - 0.12) / n]

Squaring both sides,

0.0016 = 6.636 × 0.12 × 0.88 / n

n = 0.7 / 0.0016

n = 437.9 or 438

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The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

His change would be $1.27 because he paid $3.73 for the pen and marker.

Step-by-step explanation:

Explanation:

Refer to the diagram below. There are n = 9 sides

S = 180(n-2)

S = 180(9-2)

S = 180(7)

S = 1260

This nonagon (9 sided polygon) has its interior angles add up to 1260 degrees.

Answer: 4000

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

Given point ,

Substitute ,

Answer:

No

Step-by-step explanation:

Substitute the x- coordinate into the equation and if the value equals the y- coordinate then it makes the equation true.

y = - 7(5) = - 35 ≠ 4

Thus (5, 4 ) does not make the equation true

To draw a conclusion, a statistical analysis with a significance level (alpha) of 0.02 can be applied to compare the results.treated samples consistently show lower shrinkage temperatures compared to the control samples

In this study, the aim is to prove that electrical stimulation improves meat tenderness. Connective tissue (collagen) from beef steaks was examined, as lower collagen shrinkage temperature indicates higher tenderness.

The beef carcasses were split, with one side subjected to electrical current and the other side untreated as a control. Steak samples were cut from each side and tested for tenderness by determining the collagen shrinkage temperature.

I, it suggests that electrical stimulation does improve meat tenderness.

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Answer:

x = (v - u) / a

Step-by-step explanation:

v = u + ax.

subtract u from both sides:

v - u = ax.

divide both sides by a:

(v - u) / a = x.

so x = (v - u) / a.

this can also be written v/a - u/a

Answer:

3.33%

Step-by-step explanation:

Rate = 100xSI / PxT

P = 1000

SI = 100

T = 3

Rate = 100 x 100 / 1000 x 3 = 3.33%

Answer:

4.151

You're welcome.

Answer:

pls format

Step-by-step explanation:

Answer: D, 100

Step-by-step explanation:

Answer: 100 (D)

Step-by-step explanation:

cuz

Answer:

Negative numbers cannot have square roots.

Step-by-step explanation:

Anything multiplied by itself will always equal a positive number, not negative.

For this problem, we are told the price of a 4-foot long rectangle fabric. If we assume that a similar rectangle of fabric is 24 feet long, we need to calculate its cost.

The area for a rectangle is given below:

For two rectangles to be simillar, their dimensions must be related by a constant ratio. Therefore we have:

Which means that each side is increased by a ratio of 6 from the original rectangle. The second rectangle must be:

The area of the second rectangle is 36 times the one of the first. Therefore the price should be 36 times as well. We have:

The cost of the second one will be $594.

Answer:

  15

Step-by-step explanation:

The product of distances from P to the two intersection points along the same secant (tangent) is the same for each. For this purpose, the tangent can be considered to intersect the circle twice at the same point. That is ...

  PN·PM = PQ²

  x(2x +7) = (x +6)²

  2x² +7x = x² +12x +36

  x² -5x -36 = 0

  (x -9)(x +4) = 0 . . . . . . . true for x=9, x=-4

The relevant value of x is 9.

  PQ = x +6 = 9 +6

  PQ = 15

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer:

2 - √3

Step-by-step explanation:

Find other root. Use x as a substitute.

\(x = 2 + \sqrt{3}\\x - 2 = \sqrt{3}\\\left(x - 2\right)^2 = 3\\x^2 = 4 - 2 \times x \times 2 = 3\\x^2 - 4x + 1 = 0\)

Now, we must use the quadratic formula to find the rest of the solution.

\(x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}\\x = \frac{4\pm \sqrt{\left(-4\right)^2-4 \times 1 \times 1} }{2}\\\frac{4 \pm \sqrt{12} }{2} = 2 \pm 3\)

If one root of this polynomial [root] is 2 - √3, the other will be 2 + √3. Inversing that rule, the answer is 2 - √3.

The transformation of f(x) to g(x) is :

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

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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