the depth in inches of an object as it sinks in the river is found by the equation d=0.5t where t is measured in seconds which best describes the constant of proportionality

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Similar triangles are proportional, meaning one will be a factor larger or smaller than the other. This factor will be the same for all of the sides. So, we can say that one corresponding pair of sides is equal to another corresponding pair of sides.

BA / ED = AC / CD

42 / 6 = (64 - x) / (x)

6(64 - x) = 42(x)

384 - 6x = 42x

384 = 48x

x = 8

Hope this helps!

Answer:

the distance is 10

Step-by-step explanation:

since the slope is the same you know they're parallel, but just find the difference from the two y intercepts (the +3/-7) the difference is 10, so 10.

Answer:

40x+24y-56=

8(5x+2y-7)

Step-by-step explanation:

Hello there!

Answer:

16

Step-by-step explanation:

\( |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0\)

-12 < 0 so |-12| = -(-12) = 12

4 > 0 so |4| = 4

|-12| + |4| = 12 + 4 = 16

Answer:

16

Step-by-step explanation:

Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].

This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.

The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.

Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation

12+4=16

Thus, the answer is 16.

Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!

For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

If the slope of the triangles is equal then triangle A is similar to triangle B.

In the statement  when we simplify

(5/3)=(15/9),

(5/3)=(5/3),

Then the reason for this statement is "If the slope of triangles are equal"

And the definition of slope in general is m = y/x.

Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

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The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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There are countless possibilities for shapes that are similar but not congruent to shape 1, as long as they maintain the same proportions and shape.

There are many shapes that are similar but not congruent to shape 1. Similar shapes have the same shape, but their sizes may be different. In contrast, congruent shapes have the same shape and size.

One example of a similar shape to shape 1 is a rectangle that is twice as long and half as wide. Another example could be a square that is three times larger in area than shape 1.

A parallelogram that has the same base as shape 1 but is three times as tall is also similar but not congruent.

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Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

Answer:

5/9

Step-by-step explanation:

2/3 × 5/6

multiply them

2 × 5 = 10

_______

3 × 6 = 18

simplify

10/18 ÷ 2/2 = 5/9

answer: 5/9

Answer:

0 is greater than Negative two-thirds.

Negative 1 less-than negative one-third

Negative one-third greater-than negative two-thirds

Step-by-step explanation:

Two-thirds is equal to Negative two-thirds and Negative two-thirds greater-than one-third are incorrect.

Answer:

a c e

Step-by-step explanation:

Copying the data set into another program allows you to leverage the capabilities of that program for Statistical analysis.

The provided data set can be copied into another program, such as a spreadsheet or a statistical software program, to perform various data analysis tasks. Let's explore some common operations that can be performed using the data set.

1. Descriptive Statistics: By copying the data set into a spreadsheet or statistical software, you can calculate various descriptive statistics, such as the mean, median, mode, standard deviation, and range of the data. These statistics provide insights into the central tendency, variability, and distribution of the data.

A

1   4

2   8

3   9

4   5

5   2

6   7

7   7

8   5

9   8

2. Data Visualization: Once the data set is copied, you can create visualizations to better understand the data. This can include bar charts, histograms, line plots, or box plots, depending on the nature of the data and the insights you want to gain.

3. Data Manipulation: Copying the data set into a spreadsheet allows you to manipulate and transform the data as needed. You can perform operations like sorting, filtering, grouping, and calculating new variables based on existing ones. This enables you to extract meaningful information from the data set.

4. Statistical Analysis: If you are using statistical software, you can conduct advanced statistical analyses on the data set. This may involve regression analysis, hypothesis testing, analysis of variance (ANOVA), or clustering techniques, depending on the specific research question or objective.

5. Data Integration: If you have additional data sets or variables related to the given data set, copying it into a program allows you to merge or join different data sets, thereby enriching the analysis and providing a more comprehensive understanding of the data.

Overall, copying the data set into another program empowers you to perform a wide range of data analysis tasks, enabling you to explore, understand, and draw meaningful insights from the data.

In summary, copying the data set into another program allows you to leverage the capabilities of that program for statistical analysis, calculations, and visualizations, enabling you to gain deeper insights and draw meaningful conclusions from the data.

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Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

Did you mean \(log_{25}\) 125, so that your base is 25?  If so then all you do is ask  yourself "25 to what power is 125?" since \(25^{\frac{3}{2} }\) = 125, then the  \(log_{25}\) 125 = 3/2

Answer:

It has risen by $169

Step-by-step explanation:

299

130

----------

169

Answer:

1) zero

2) undefined

3) negative

4) positive

5) negative y= -30x+342

hope this helps;)

Answer:

None of them really,

A perfect square is a number that can be expressed as the product of two equal integers...which is not seen here.

Th closest perfect square that could be possible would be 64, but thats not an option, so go with none.

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Answer:

• Let f(x) be m

\(m = \frac{2x + 1}{x} \\ \\ mx = 2x + 1 \\ \\ mx - 2x = 1 \\ \\ x(m - 2) = 1 \\ \\ x = \frac{1}{m - 2} \)

Therefore:

\({ \boxed{ {f}^{ - 1} (x) = \frac{1}{x - 2} }} \\ \)

Answer:

The appropriate solution is "570". The further explanation is given below

Step-by-step explanation:

(1)

Choosing the right 1 member out of 5 seniors throughout the state.  

The remaining 2 candidates would be chosen from some of the other 13 committee members within a week of choosing 1 member from either the 5 in-state representatives.

So, throughout this case, the number among approaches p is supplied by:

⇒  \(p=5C_1\times 13C_2\)

       \(=5\times 78\)

       \(=390\)

(2)

Choosing the right one person of the legislature out of three non-senior members of the state  

In this scenario, as already mentioned, the second participant needs to be chosen from the 5 qualified out-of-state citizens. Currently that we would have chosen 2 members out of 14 members in all, the 3rd member should be chosen out of another leftover 12 people.  

Therefore, the amount of forms, throughout this case q, seems to be:

⇒  \(q=3C_1\times 5C_1\times 12C_1\)

       \(=3\times 5\times 12\)

       \(=180\)    

So that the total no. of ways will be:

⇒  \(p+q\)

⇒  \(390+180\)

⇒  \(570\)

Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

Answer:

A

Step-by-step explanation:

Range referes to the smallest and largest values, so the answer you have circles is correct.

Good Job!

Answer: A) Range

Step-by-step explanation:

The range is the difference between the biggest and smallest numbers (or, in this case, folders). If Jack wants to find a notebook that will fit a small and large folder, he will need to find the range.

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Using the concept of simple interest and compound interest, the first equation is \(S = 200(1.1)^t\), while the second is S = 250 + 20t

c. It will take over 7 years for the accounts to be equal.

The similarities between simple interest and compound interest is that both deals with saving of money over certain period of time with a fixed rate. While the difference between both is that in compound interest, the interest are compounded while in simple interest it is not. This implies that compound interest is an exponential function while simple interest is a linear function.

Simple interest = P(1 + rt)

Compound interest = P(1 + r/n)ⁿˣ

To solve this, we can write equations;

For the first scenario;

\(S = 200(1.1)^t\)

For the second scenario;

S = 250 + 20t

NB: The first case is a compound interest while the second is a simple interest.

c. To determine when the two accounts will be equal;

\(250 + 20t = 200(1.1)^t\)

Solving for t;

t = 7.01 ≈ 7 years

Therefore, it will take over 7 years for the accounts to be equal

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