What is the result of adding these two equations? \begin{aligned} 2x+3y &= -5 \\\\ 5x-y &= -12 \end{aligned} 2x+3y 5x−y ​ =−5 =−12 ​

answer= the lcm of 11,8a d 12 is 264

Answer:

-1.05

Step-by-step explanation:

The population of 2 guppy fishes that grows at a rate of 1700% per month indicates;

A population growth formula is a formula of the form; A = P·(1 + r)^t, where, A is the amount after a period of t months, (or days or years), at a growth rate of r.

Number of guppy fish bought = 2

Rate at which guppy populations grow = 1700% per month

The formula that models the population of guppies can be obtained as follows;

The population growth equation is an exponential formula that can be modeled using the following equation;

Where;

A = The number after the number of months

P = The initial population of the guppy fish = 2

r = The percentage growth rate = 1700%

t = The time of growth in months = 4

Therefore, after 4 months the population of guppy fish will be;

A = 2 × (1 + 17)^4 = 209952

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9514 1404 393

Answer:

  15 clean clothes

Step-by-step explanation:

The total of 3 clean and 4 dirty is 7 clothes, so 3 of 7 are clean.

  (3/7) × 35 clothes = 15 clean clothes

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

1/8 = 0.125

1/9 = 0.1

2/3 = 0.6

4/7 = 0. 571428

3/10 = 0.3

5/3 = 1.6

9/5 = 1.8

5/6 = 0.83

Answer:16x16

Step-by-step explanation:

Answer:

y=2x+9

Step-by-step explanation:

point slope form

y-y1=m(x-x1)

y-3=2(x+7)

m=2

y intercept: b=9

y=mx+b where m=2 b=9

y=2x+9

The length of AC is 12.5 and the length of AD is 3.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is the sum of its internal angles to 180 degrees

Given triangle ABC,

and D is a point on AB and E is a point on AC,

and forms a triangle ADE,

and  DE is parallel to AC,

taking ΔABC and ΔBDE

∠B = ∠B  (common angle)

because DE is parallel to AC, so corresponding angles are equal,

so ∠A = ∠D

and ∠C = ∠E

ΔABC ≈ ΔBDE (triangles are similar)

since both triangles are similar the ratio of their corresponding sides is equal,

AB/BD = AC/DE = BC/BE

given BD = 2, BE = 4, DE = 5 and EC = 6

BC = EC + BE = 4 + 6

BC = 10

AC/DE = BC/BE

AC = 5(10/4)

AC = 12.5

and AB/BD = BC/BE

AB = 2(10/4)

AB = 5

AD = AB - BD

AD = 5 - 2

AD = 3

Hence AC = 12.5 and AD = 3.

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The figure is in image.

Answer:

p = 1 or p = 7

So first number line is the answer we are looking for.

Step-by-step explanation:

|8-2p| = 6

To do that, we need to get rid of the brakes and rewrite equation in two forms:

8 - 2p = 6

or

8 - 2p = -6

For the first state:

8 - 2p = 6

- 2p = -2

2p = 2

p = 1

Now, the second state:

8 - 2p = -6

- 2p = -14

2p = 14

p= 7

The current record is 1 minute 40 seconds, which is equivalent to 60 seconds + 40 seconds = 100 seconds.

Frank Flea beat the record by 27 seconds, so the new record is:

100 seconds + 27 seconds = 127 seconds

Therefore, the new record is 2 minutes 7 seconds, or 127 seconds.

Answer:

In step 1 the y-intercept should be plotted at (0,-6)

Step-by-step explanation:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Since the formula is y = -3/4x -6

We just insert a 0 insted of the "x"

y = -3/4(0) -6

y=0-6

y=6

So the y-intercept sould be placed in (0,-6)

That's what he did wrong when graphing the equation.

Answer:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Step-by-step explanation:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Since the formula is y = -3/4x -6

We just insert a 0 insted of the "x"

y = -3/4(0) -6

y=0-6

y=6

So the y-intercept sould be placed in (0,-6)

That's what he did wrong when graphing the equation.

Answer: 64 boots in total

Step-by-step explanation:

Since a pair is 2, and there are 32 students that need a pair each, 32 x 2 = 64.

Answer:

(i) x ≤ 1

(ii) ℝ except 0, -1

(iii) x > -1

(iv) ℝ except π/2 + nπ, n ∈ ℤ

Step-by-step explanation:

(i) The number inside a square root must be positive or zero to give the expression a real value. Therefore, to solve for the domain of the function, we can set the value inside the square root greater or equal to 0, then solve for x:

\(1-x \ge 0\)

\(1 \ge x\)

\(\boxed{x \le 1}\)

(ii) The denominator of a fraction cannot be zero, or else the fraction is undefined. Therefore, we can solve for the values of x that are NOT in the domain of the function by setting the expression in the denominator to 0, then solving for x.

\(0 = x^2+x\)

\(0 = x(x + 1)\)

\(x = 0\)     OR     \(x = -1\)

So, the domain of the function is:

\(R \text{ except } 0, -1\)

(ℝ stands for "all real numbers")

(iii) We know that the value inside a logarithmic function must be positive, or else the expression is undefined. So, we can set the value inside the log greater than 0 and solve for x:

\(x+ 1 > 0\)

\(\boxed{x > -1}\)

(iv) The domain of the trigonometric function tangent is all real numbers, except multiples of π/2, when the denominator of the value it outputs is zero.

\(\boxed{R \text{ except } \frac{\pi}2 + n\pi} \ \text{where} \ \text{n} \in Z\)

(ℤ stands for "all integers")

Answer:

(i)  x ≤ 1

(ii)  All real numbers except x = 0 and x = -1.

(iii)  x > -1

(iv)  All real numbers except x = π/2 + πn, where n is an integer.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values).

\(\hrulefill\)

\(\textsf{(i)} \quad f(x)=\sqrt{1-x}\)

For a square root function, the expression inside the square root must be non-negative. Therefore, for function f(x), 1 - x ≥ 0.

Solve the inequality:

\(\begin{aligned}1 - x &\geq 0\\\\1 - x -1 &\geq 0-1\\\\-x &\geq -1\\\\\dfrac{-x}{-1} &\geq \dfrac{-1}{-1}\\\\x &\leq 1\end{aligned}\)

(Note that when we divide or multiply both sides of an inequality by a negative number, we must reverse the inequality sign).

Hence, the domain of f(x) is all real numbers less than or equal to -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x \leq 1\\\textsf{Interval notation:} \quad &(-\infty, 1]\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \leq 1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(ii)} \quad g(x) = \dfrac{1}{x^2 + x}\)

To find the domain of g(x), we need to identify any values of x that would make the denominator equal to zero, since division by zero is undefined.

Set the denominator to zero and solve for x:

\(\begin{aligned}x^2 + x &= 0\\x(x + 1) &= 0\\\\\implies x &= 0\\\implies x &= -1\end{aligned}\)

Therefore, the domain of g(x) is all real numbers except x = 0 and x = -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x < -1 \;\;\textsf{or}\;\; -1 < x < 0 \;\;\textsf{or}\;\; x > 0\\\textsf{Interval notation:} \quad &(-\infty, -1) \cup (-1, 0) \cup (0, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq 0,x \neq -1 \right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iii)}\quad h(x) = \log_7(x + 1)\)

For a logarithmic function, the argument (the expression inside the logarithm), must be greater than zero.

Therefore, for function h(x), x + 1 > 0.

Solve the inequality:

\(\begin{aligned}x + 1 & > 0\\x+1-1& > 0-1\\x & > -1\end{aligned}\)

Therefore, the domain of h(x) is all real numbers greater than -1.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &x > -1\\\textsf{Interval notation:} \quad &(-1, \infty)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x > -1\right\} \end{aligned}}\)

\(\hrulefill\)

\(\textsf{(iv)} \quad k(x) = \tan x\)

The tangent function can also be expressed as the ratio of the sine and cosine functions:

\(\tan x = \dfrac{\sin x}{\cos x}\)

Therefore, the tangent function is defined for all real numbers except the values where the cosine of the function is zero, since division by zero is undefined.

From inspection of the unit circle, cos(x) = 0 when x = π/2 and x = 3π/2.

The tangent function is periodic with a period of π. This means that the graph of the tangent function repeats itself at intervals of π units along the x-axis.

Therefore, if we combine the period and the undefined points, the domain of k(x) is all real numbers except x = π/2 + πn, where n is an integer.

\(\boxed{\begin{aligned} \textsf{Inequality notation:} \quad &\pi n\le \:x < \dfrac{\pi }{2}+\pi n\quad \textsf{or}\quad \dfrac{\pi }{2}+\pi n < x < \pi +\pi n\\\textsf{Interval notation:} \quad &\left[\pi n ,\dfrac{\pi }{2}+\pi n\right) \cup \left(\dfrac{\pi }{2}+\pi n,\pi +\pi n\right)\\\textsf{Set-builder notation:} \quad &\left\{x \in \mathbb{R}\left|\: x \neq \dfrac{\pi}{2}+\pi n\;\; (n \in\mathbb{Z}) \right\}\\\textsf{(where $n$ is an integer)}\end{aligned}}\)

Answer:C

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

Source: Dude trust me

Answer:

To find the square root of 27 over m to the fifth power, we can break it down into two separate parts: the square root of 27 and the square root of m to the fifth power.

First, we can simplify the square root of 27 to get √27 = √(9 x 3) = √9 x √3 = 3√3.

Next, we can simplify the square root of m to the fifth power to get (√m)^5 = m^(5/2).

Putting it all together, we get:

√(27/m^5) = √27/√m^5 = 3√3/m^(5/2)

Therefore, the square root of 27 over m to the fifth power is 3√3/m^(5/2).

Answer:

Thxs dude ;)

Step-by-step explanation:

Answer:

thank you, thank you

Answer:

Justin should have multiplied 3.8 and 7.9 first

Step-by-step explanation:

Multiply before adding

12.5 +3.8(x)x

12.5+3.8x7.9

Answer:Justin should have multiplied 3.8 and 7.9 first

Step-by-step explanation:

The value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

Let's simplify the expression step by step:

Recall the values of trigonometric functions for common angles:

cos(60°) = 1/2

sin(30°) = 1/2

tan(60°) = √(3)

cot(45°) = 1

sec(30°) = 2

Substitute the values into the expression:

\(2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30\)

= \(2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)\)

= 2(1/16 + 1/16) - (3 + 1) + 3*4

= 2(1/8) - 4 + 12

= 1/4 - 4 + 12

= -15/4 + 12

= -15/4 + 48/4

= 33/4

Therefore, the value of the expression \(2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.\)

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Answer:

8400

Step-by-step explanation:

Round it 5 and above go up 4 and below go down

Answer:

8,400

Step-by-step explanation:

it says round to the nearest hundred to find the answer look at the number behind the place value you want to round.

5 and up you round the number higher

4 and down you round it lower.

example:

35 rounded to the nearest ten is 40

34 rounded to the nearest ten is 30

If the least value of n is 4, then the inequality best shows all the possible values of n is, n ≥ 4. So Option B is correct

Inequalities are the comparison of mathematical expressions, whether one quantity is greater or smaller in comparison to another quantity.

We use these symbols to represent inequalities, '>' , '<', '≥', '≤'

Given that,

The least value of n is 4,

Inequality representation = ?

It is known that,

Least value  of n is 4

So, Minimum possible value of n is 4

Maximum value of n should be more than 4,

In order to satisfy the condition,

So,

n  > 4

By combining both the things,

It can be written as,

n ≥ 4

Hence, the best inequality representation is n ≥ 4

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Number of tenths are in the sum is 8

The decimal numeral system is the standard system for denoting integer and non-integer numbers.

Addition is the action or process of adding something to something else.

Given,

The numbers 0.65 and 0.24

Add them together

0.65 + 0.24 = 0.89

Here the number is a decimal number that is 0.89

If a number has a decimal point , then the first digit to the right of the decimal point indicates the number of tenths.

Therefore number 8 is in the tenth place

Hence, the number of tenths in the sum is 8

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The equation of the circle described in the problem is x² + (y - 8)² = 64.

What is the equation of a circle?

The general equation of any type of circle is represented by: x2 + y2 + 2gx + 2fy + c = 0, for all values of g, f, and c.

The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.

The standard form equation of a circle with center at (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

Substituting the given values into this equation, we get:

(x - 0)² + (y - 8)² = (8)²

Simplifying this equation gives:

x² + (y - 8)² = 64

Hence, This is the equation of the circle described in the problem.

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Answer:

Here's how I'd do it

Step-by-step explanation:

Answer:

The answer is the 3rd one, not equivalent. 8x+4y=4(2x+y)

Answer:

24 m²

Step-by-step explanation:

The area of a rhombus is the product of the two diagonals over 2

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer:

\((-\infty,1/4)\cup(1/4,\infty)\)

The answer is C.

Step-by-step explanation:

We are given the rational function:

\(\displaystyle f(x) = \frac{x-3}{4x-1}\)

In rational functions, the domain is always all real numbers except for the values when the denominator equals zero. In other words, we need to find the zeros of the denominator:

\(\displaystyle \begin{aligned}4x -1 & = 0 \\ \\ 4x & = 1 \\ \\ x & = \frac{1}{4} \end{aligned}\)

Therefore, the domain is all real number except for x = 1/4.

In interval notation, this is:

\((-\infty,1/4)\cup(1/4,\infty)\)

The left interval represents all the values to the left of 1/4.The right interval represents all the values to the right of 1/4. The union symbol is needed to combine the two. Note that we use parentheses instead of brackets because we do not include the 1/4 nor the infinities.  

In conclusion, our answer is C.

Answer:

The third one

Step-by-step explanation: