10. If m and n are positive integers and
2x(5x+3y) = mx² + nxy, what is the value
of m-n?
(A) -4
(B) -1
(C) 1
(D) 4

(a) After 25 years 47.37g of the initial sample left in the sample. (b) 12.83 years takes  the initial sample to decay half of its original amount.

Given:

[tex]A(t) = 200 e^{-0.054t}[/tex]

Substituting 25 for t in the expression, we get:

A(25) = 200e⁰.⁰⁵⁴ × 25

         = 47.37 g

Thus, after 25 years, there will be 47.37g of the initial sample left in the sample.

(b.) 12.83 years takes the initial sample to decay half of its original amount.

We want to find t such that

[tex]A(t) = 200e^{0.054} \times t[/tex]

where, t = 100.

Solving for t, we get:

[tex]200e^{0.054} \times t = 100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.054 × t = ln(0.5)

Therefore,

[tex]t = \frac{\ln(0.5)}{0.054}[/tex]

  = 12.83 years.

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Answer:

17 and 18 because they are equal

Using the fact that the angles are supplementary, we can write and solve a linear equation to find that x = 5°.

Remember that two angles are supplementary if the addition of their measures is equal to 180°.

Here we know that angles J and K are supplementary, then we know that:

J + K = 180°

Here we also know that:

J = 120°

K = 12x

So we can write a linear equation of the form:

120° + 12x = 180°

12x = 180° - 120°

12x = 60°

x = 60°/12 = 5°

x = 5°

We conclude that the value of x is 5°.

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(a) The population of the state was 18.5 million in 2000. (b)The population of the state will reach 26.6 million in the year 2002

A population is a distinct collection of people, whether that group consists of a nation or a population that shares a specific trait.  A population is the group of people from which a statistical sample is taken in statistics. As a result, a population can be defined as any group of people who have something in common.

Since t = 0 ,

Then A = 18.5

(b) The population of the state will reach 26.6 million in the year 2002

2002, by using the formula is 18.5e^0.173*t

Given,

A= 26.6

Then,    

[tex]A = 18.5 x e^{(0.1708t)} 26.6[/tex]

  [tex]= 18.5 x e^{(0.1708t)} \frac{26.6}{18.5}[/tex]

  = [tex]e^{(0.1708t)} 1.437838[/tex]

   = [tex]e^{(0.1708t)} \ln (\frac{1.437838}{0.1708})[/tex]

t = 2.126116

t =2

Therefore, 2 is the round down to the nearest years. So 2002 is the approximate year the population reached 26.6 million.

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Answer:

20π cubic units

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cylinder}\\\\$V=\pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given:

Substitute the given values into the formula for the volume of a cylinder and solve for V:

[tex]\implies V=\pi \cdot 2^2 \cdot 5[/tex]

[tex]\implies V=\pi \cdot 4 \cdot 5[/tex]

[tex]\implies V=\pi \cdot 20[/tex]

[tex]\implies V=20\pi\;\; \sf cubic \;units[/tex]

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

sin x= 12/ 13

So, B = √13² - 12² = √169 - 144 = √25 = 5

cos x= 5/ 13

So, sin 2x= 2 sin x cos x =2 (12/13)(5/13) = 120/169

and, cos 2x= 1- 2 sin²x

                  = 1- 2( 144 / 169)

                  = -119/ 169

and, tan 2x = sin 2x/ cos 2x = 120/ 169 / (- 119/ 169)= 120/ 119

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I disagree with the student because y = x/9 represents a proportional relationship

Proportional relationships are relationships between two variables where their ratios are equivalent

A proportional relationship can we written as follows:-

y = mx

Where 'y' is dependent variable, 'x' is independent variable, and 'm' is the slope or we can say 'm' is constant of proportionality.

'm' can take any value whether negative or positive, decimal or whole number. 'm' is a real number.

The given problem is y = x/9 and student says we can only multiply constant, and not divide. We disagree with this comment because m= 1/9 is correct.

So y = 1/9 x makes sense.

Hence, y = x/9 represents a proportional relationship.

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By using various properties of triangles, we get the value of [tex]\angle[/tex]ABD is 47.5°.

What are the properties of a triangle?

A triangle's sides and angles serve as the foundation for all of its characteristics. Triangular closed polygons with three sides and three vertices are what the word "triangle" means. The three internal angles of a triangle add up to 180°.

Let us first name a few angles that we will be using throughout the solution.

Let, [tex]\angle[/tex]DEN=a

[tex]\angle[/tex]ENC=c

[tex]\angle[/tex]MEB=b

[tex]\angle[/tex]EMB=d

Now, since it is given that AD ≅ AE, let us assume that triangle ADE is an isosceles triangle, with AD=AE.

Hence we get

[tex]\angle[/tex]DAE+[tex]\angle[/tex]ADE+[tex]\angle[/tex]AED=180° (angle sum property)

35°+2[tex]\angle[/tex]ADE=180°

[tex]\angle[/tex]ADE=[tex]\angle[/tex]AED=72.5°

Next, we know that

[tex]\angle[/tex]AED+a+[tex]\angle[/tex]NEC=180° (linear pair property of angles on a straight line)

72.5°+a+30°=180°

a=77.5°

Since a=b (opposite angles)
we get, a=b=77.5°

Now in triangle ENC, if we take the sum of angles, we get

[tex]\angle[/tex]NEC+[tex]\angle[/tex]NCE+c=180° (angle sum property)

30°+25°+c=180°

c=125°

We also know that the sum of interior angles made by an intersecting line between 2 parallel lines (given shape is a trapezoid) is 180, hence we get

c+d=180°

d=55°

In triangle MBN, we have

d+b+[tex]\angle[/tex]MBD=180° (angle sum property)

55°+77.5°+[tex]\angle[/tex]MBD=180°

[tex]\angle[/tex]MBD=47.5°

Therefore, we get the value of [tex]\angle[/tex]ABD=47.5°

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Answer:

Cans of soup = 10

Frozen dinners = 5

Step-by-step explanation:

To determine the number of cans of soup and frozen dinners Caleb purchased, set up and solve a system of equations based on the given information.

Let x be the number of cans of soup Caleb purchased.

Let y be the number of frozen dinners Caleb purchased.

Each can of soup has 200 mg of sodium and each frozen dinner has 500 mg of sodium. The total amount of sodium in the purchased cans and frozen dinners is 4500 mg. Therefore:

[tex]200x + 500y = 4500[/tex]

Caleb purchased a total of 15 cans of soup and frozen dinners. Therefore:

[tex]x + y = 15[/tex]

To solve the system of equations, rearrange the second equation to isolate x:

[tex]\begin{aligned}x + y &= 15\\x + y -y&= 15-y\\x&=15-y\end{aligned}[/tex]

Substitute this into the first equation to eliminate the term in x, and solve for y:

[tex]\begin{aligned}200(15-y) + 500y &= 4500\\3000-200y + 500y &= 4500\\3000+300y &= 4500\\3000+300y-3000 &= 4500-3000\\300y&=1500\\300y \div 300&=1500 \div 300\\y&=5\end{aligned}[/tex]

Therefore, Caleb purchased 5 frozen dinners.

Substitute the found value of y into the rearranged second equation and solve for x:

[tex]\begin{aligned}x&=15-y\\x&=15-5\\x&=10\end{aligned}[/tex]

Therefore, Caleb purchased 10 cans of soup.

Answer:

Caleb purchased 10 cans of soup and 5 frozen dinners.

Step-by-step explanation:

Caleb purchased 10 cans of soup and 5 frozen dinners.

Let no. of can of soup be x and no. of frozen dinner be y.

To solve this, we can set up the following system of equations:

[tex]\tt x + y = 15[/tex]......[i]

[tex]\tt 200x + 500y = 4500[/tex]......[2]

Let's find the value by elimination method:

Multiplying equation one by 200.

we get,

[tex]\tt 200 x+ 200 y = 15*200[/tex]

[tex]\tt 200x +200 y =3000[/tex]

Subtracting equation 2 with equation 1.

[tex]\tt (200x+500y)-(200x +200 y) =4500-3000[/tex]

[tex]\tt \tt 300y = 1500[/tex]

[tex]\tt y =\dfrac{1500}{300}[/tex]

[tex]\tt y = 5[/tex]

Substitute the value of y into the first equation to find x.**

[tex]\tt x + 5 = 15[/tex]

[tex]\tt x = 15 - 5[/tex]

[tex]\tt x = 10[/tex]

Therefore, Caleb purchased 10 cans of soup and 5 frozen dinners.

Answer: 4. -1/6, 5. 2/5

Step-by-step explanation:

1. The formula for slope is rise/run. To find the slope, you subtract the y coordinates (it doesnt matter the order, and you divide it by the difference of the x coordinates.

2. The y coordinates for 3 are 10 and 6, and the x coordinates are 0 and 24.

10-6/0-24 is 4/-24 which is -1/6.

3. you do the same thing for #4. The y coordinates are 6 and 14, and the x coordinates are 0 and 20. 14-6/20-0=slope. 8/20 is the slope, and that is equal to 2/5.

4. the slope for 3 is -1/6 and the slope for 4 is 2/5.

Answer:

1/2

Step-by-step explanation:

Slope is rise (height)/run(length)

Slope is 1 meter/2 meters

The required amount at the end of the 7 years is given as $32,340

Given that,
An amount of $250 is contributed at the end of each month, and the balance earns interest at an APR of 6.2%.

Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.

here,
According to the question,
The total amount accrued after 7 years is given as,

[tex]y\:=\:250\cdot12\cdot 7\left[1\:+\:\frac{0.062}{12}\right]^{12\cdot 7}\\y = $32,340[/tex]

Thus, The required amount at the end of the 7 years is given as $32,340.

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The function [tex]y = (\frac{1}{2})^x[/tex] is a decreasing function.

The function [tex]y = (\frac{1}{2})^x[/tex] is shallower from left to right.

The value of the function [tex]y = (\frac{1}{2})^x[/tex] is unity at the y-intercept.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The given function is [tex]y = (\frac{1}{2})^x[/tex] which is an exponential function cause the exponent is the variable.

Now, At x = - 2 y = 4 ⇒ (- 2, 4),

x = - 1, y = 2 ⇒ (- 1, 2).

x = 0, y = 1 ⇒ (0, 1).

x = 1, y = 1/2 ⇒ (1, 1/2).

x = 2, y = 1/4 ⇒ (2, 1/4).

x = 3, y = 1/8 ⇒ (3, 1/8).

The function is a decreasing function as the value of x increases the value of the function is decreasing.

The function is shallower from left to right.

The value of the function is unity at y-intercept as anything raised to the zero power is 1.

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Required Answer -:

16cos³ x sin² x

2cos x - ( cos 3x + cos 5x )

= 2cos x - 2 cos 4x cos x

= 2cos x 2sin² 2x

= 4 cos x ( 2sin x cos x)²

= 16cos³ x sin² x

Thus,, the value of 2 cos x - cos 3x - cos 5x is = 16cos³ x sin² x

The value of the expression upon evaluation by using the distributive property as required is; 28.

It follows from the task content that the distributive property is to be used to determine the value of the expression given.

Since the given expression is; 8 • 3 ½.

It follows that the expression can be written as follows;

8 ( 3 + ½ )

Hence, by the distributive property, it follows that we have;

( 8 × 3 ) + ( 8 × ½ )

= 24 + 4

= 28.

On this note, the value of the expression is; 28.

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Answer:

$345 (PLEASE GIVE BRAINLYEST )

Step-by-step explanation:

1/3x=115

x=345

The simplification of the given expression on the basis of identity is given as  144 - 24y +  y².

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is (12 - y)².

It can be expanded on the basis of the algebraic identity (a - b)² = a² - 2ab + b² as follows,

(12 - y)²

= 12²- 2×12y + y²

= 144 - 24y +  y²

Hence, the given expression can be simplified as 144 - 24y +  y².

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Answer:

355 ÷ 8 = 44 with remainder 3

Step-by-step explanation:

                              44

                         -------------------------

                    8   | 355

                        -  32

                       --------

                              35

                           -  32

                           ------

                                3

Answer:

49

hope this helps!!

Answer:

1

Step-by-step explanation:

First, simplify the parentheses.

2 - 3 = -1

Then, put this simplified value into the original expression.

(2 - 3)^(-1)

= (-1)^(-1)

Finally, execute the exponent function.

(-1)^(-1) = 1/1 = 1

Answer:

1100

Step-by-step explanation:

First, we start off by finding 10% which is $100. We divide that by 10 to get $10 which is 10%. Now we need to multiply 10% (which is $10) by 10 which is   $100. That gives you this answer

The total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given data:

Charlie deposits, P =  $1000 into his investment account.

The account grows at a rate, r =  8% per year.

The time, t = 11 year

Calculate the simple interest as shown below,

[tex]SI = (P\times r\times t) / 100[/tex]

SI = (1000 × 8 × 11) / 100

SI = $880

Calculate the total amount by the formula given below,

Amount = A

[tex]A = P + SI[/tex]

A = 1000  + 880

A = $1880

Therefore, the total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.

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The resulting expression after the expressions are subtracted is 9x - 6y

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

(-x-3y)(−x−3y) is subtracted from (8x-9y)(8x−9y)

Rewrite these expressions properly

So, we have the following representations

(−x−3y) is subtracted from (8x-9y)

When the first equation is subtracted from the second, we have the following representation

8x - 9y - (-x - 3y)

Open the brackets

So, we have

8x - 9y + x + 3y

Evaluate the like terms

9x - 6y

Hence. the solution is 9x - 6y

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By using arithmetic progression, it can be calculated that

The common difference is 12

Third option is correct

A series of numbers is called an arithmetic progression if the difference between each term in the sequence is the same.

If there is always the same difference between any two consecutive terms in a series of integers, then progression is known as an arithmetic progression. Simply put, it means that the previous number in the series is added to determine the next number in the series. A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...

This is a problem on arithmetic progression

[tex]a _1 = 5[/tex]

[tex]a_n = a_{n-1} + 12[/tex]

[tex]a_2 = a_1 + 12[/tex]

[tex]a_2 = 5 + 12 = 17[/tex]

[tex]a_3 = a_2 + 12 = 17 + 12 = 29[/tex]

[tex]a_4 = a_3 + 12 = 29 + 12 = 41[/tex]

[tex]a_2 -a_1 = 17 - 5 = 12\\a_3 - a_2 = 29 - 17 =12\\a_4 - a_3 = 41 - 29 =12[/tex]

So the common difference is 12

Third option is correct

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By using arithmetic progression, it can be calculated that, the common difference is 12.

Third option is correct

If the common difference between each term in the sequence is the same, a group of numbers is referred to as an arithmetic progression.

A progression is referred to as an arithmetic progression if there is consistently the common difference between any two successive terms in a series of integers. To put it simply, it indicates that the series' next number is produced by adding the previous one.

An arithmetic progression or arithmetic sequence, also known as AP, is a set of numbers where the terms are always different from one another. The numbers 5, 7, 9, 11, 13, and 15 make up one mathematical progression with a common difference of 2.

We know that the arithmetic progression, this is based on the same

[tex]\begin{aligned}& a_1=5 \\& a_n=a_{n-1}+12 \\& a_2=a_1+12 \\& a_2=5+12=17 \\& a_3=a_2+12=17+12=29 \\& a_4=a_3+12=29+12=41 \\& a_2-a_1=17-5=12 \\& a_3-a_2=29-17=12 \\& a_4-a_3=41-29=12\end{aligned}[/tex]

So the common difference is 12

Third option is correct

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Step-by-step explanation:

your teacher could have explained this better by telling us that A(t) is the remaining amount of the original isotope.

(a)

we start with 200 g and let it do its thing for 25 years.

all we need to do is enter the number of years into the function formula (as this is a college question you are able to work with functions, right ?) and calculate :

A(25) = 200e^(-0.054 × 25) = 200e^-1.35 =

= 51.84805213... g ≈ 51.85 g

after 25 years, about 51.85 g of the sample will be left.

assuming you have a calculator (at least on your computer) that was really "difficult", don't you think ?

(b)

half of the original amount is 200/2 = 100 g.

so, we need to find the value for t so that A(t) = 100.

100 = 200e^(-0.054 × t)

100/200 = 1/2 = 0.5 = e^(-0.054 × t)

ln(0.5) = -0.054 × t

t = ln(0.5) / -0.054 = 12.8360589... years

I assume you need to round to the nearest hundredth here as well :

after about 12.84 years the sample will decay to half of the original amount.

Answer:

To solve this problem, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle. Since the angle formed by the ladder and the ground is 72 degrees, we can consider the horizontal distance between the base of the ladder and the wall to be the adjacent side of the right triangle, and the height of the ladder to be the opposite side.

We can set up the following equation to represent this relationship:

tan(72^{\circ}) = opposite/adjacent

Substituting the values given in the problem, we get:

tan(72^{\circ}) = 26 feet / adjacent

To find the value of the adjacent side, we can solve for "adjacent" in the equation above. We can do this by dividing both sides of the equation by 26 feet and then taking the inverse tangent (tan^(-1)) of both sides:

adjacent = 26 feet / tan(72^{\circ})

Using a calculator or a table of tangent values, we can find that the value of tan(72^{\circ}) is approximately 3.73. Substituting this value into the equation above, we get:

adjacent = 26 feet / 3.73

Solving this equation, we find that the horizontal distance between the base of the ladder and the wall is approximately 6.99 feet. Rounding this value to the nearest hundredth of a foot, we get an answer of approximately 6.99 feet.

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Answer: 8.03

Step-by-step explanation:

Answer:

[tex]y = \sqrt{34} \\\\x = \sqrt{106}[/tex]

Step-by-step explanation:

The inequality that shows how long the temperature in Austin will remain colder than that in San Antonio is 33.5 + 2.5t < 37.5 + 1.5t and the time is less than 4 hours

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

Austin

Initial temperature = 33.5 degrees Fahrenheit

Rate of increment = 2.5 degrees Fahrenheit

San Antonio

Initial temperature = 37.5 degrees Fahrenheit

Rate of increment = 1.5 degrees Fahrenheit

The above parameters mean that

Current temperature = Initial temperature + Rate of increment x Number of hours

So, we have

Austin: A(t) = 33.5 + 2.5t

San Antonio: B(t) = 37.5 + 1.5t

When Austin is colder than San Antonio, we have

A(t) < B(t)

Substitute the known values in the above equation, so, we have the following representation

33.5 + 2.5t < 37.5 + 1.5t

Evaluate the like terms

t < 4

Divide both sides by 1

t < 4

Hence, the interval is less than 4 hours

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The slope of the line given in the graph will be [m] is  - 0.78.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is the graph of a straight line.

The line passes through the coordinates as follows -

(- 1.8, 0)        [lying on x-axis]

(0, - 1.4)        [lying on y-axis]

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (- 1.4 - 0)/(0 + 1.8)

m = - 1.4/1.8

m = - 0.78

Slope of the line will be -0.78.

Therefore, the slope of the line given in the graph will be [m] = - 0.78.

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