Solve each equation. Check for extraneous solutions. 3√2 x+6=18

Answer:

BC

Step-by-step explanation:

its easy d will keep going as shown the arrow so when its pass c it will be in between makinn it BC (i cant explain well but thats the answer)

x = 1 is not an extraneous solution.

✓(x² + 3) = x + 1

Taking square on both the sides of the equation, we get

(✓(x² + 3))² = (x + 1)²

x² + 3 = (x + 1)²

Using the identity (a+b)²= a² + b² + 2ab on the right hand side of the equation, we get

x² + 3 = x² + (1)² + 2(x)(1)

x² + 3 = x² + 1 + 2x

2x = 2

x = 1

Confirming the value is extraneous solution or not

Putting the root x = 1 in the original equation ✓(x² + 3) = x + 1, we get

✓(1² + 3) = 1 + 1

✓4 = 2

2 = 2

⇒ LHS = RHS

∴ x = 1 is not an extraneous solution.

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The linear equation in the slope-intercept form is:

y = (-1/3)*x + 4

Remember that if a line passes through two points (a, b) and (c, d), then the slope is given by:

slope = (d - b)/(c - a)

By looking at the graph, we can see that the points (0,4) and (3, 3), then the slope will be:

s = (3 - 4)/(3 - 0) = -1/3

And we can see that the y-intercept is y = 4 (because the line passes through the point (0,4))

Then the linear equation in the slope-intercept form is:

y = (-1/3)*x + 4

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Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

First calculate the 3-5 Triangle

Using Pythagorean Theorum,

[tex]\sqrt{5^{2}-3^{2} } =4[/tex]

That means that the other triangle side is 2.

Using Pythagorean Theorum again,

[tex]\sqrt{3^{2}+2^{2} } =\sqrt{13}[/tex]

The vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation of the function is given as

y = -2x^2

A quadratic function is represented as

y = a(x - h)^2 + k

Where the vertex is

vertex = (h, k)

This means that the equation y = -2x^2 can be rewritten as

y = -2(x - 0)^2 + 0

When the equations are compared, we have

vertex = (h, k) = (0, 0)

Hence, the vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)

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The probability of the new boy being paired up with a boy who does not love camping is 2/3 or 66.66%

Total no. of troop members = 15

No. of boys who love camping = 5

No. of boys who love fishing = 10

No. of boys who love archery = 3

No. of boys who love hiking = 12

The boy who enjoys carving = 1

Boys who do not like camping = 1 - 5/15 = 10/15 = 2/3*100 = 66.66%

So, the probability that the new boy will be paired up with a boy who does not love camping is 66.66% or 2/3.

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The lines represented by y = -5x + 10 and 5y = x + 15 are; Perpendicular

We are given the equation of two lines as;

Line 1; y = -5x + 10

Line 2; 5y = x + 15

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, for the equation in line 1, we know that;

slope = -5 while the y-intercept is 10

For line 2, the equation can be rewritten as;

y = ¹/₅x + 3

Slope = 1/5

y-intercept = 3

Now, we know that when two lines are perpendicular, it means that their slopes are negative reciprocals of each other.

Slopes of lines 1 and 2 are negative reciprocals of each other and thus they are perpendicular.

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Answer: yo wassup picture isn't straight cant see

Step-by-step explanation:

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. The expression be (x²+x)⁴ is expanded as x⁸ + 4x⁷ + 6x⁶ + 4x⁵ + x⁴.

The Binomial theorem tells us how to expand expressions of the form (a + b)ⁿ, for example, (x + y)⁷. The larger the power is, the harder it is to expand expressions like this directly.

The total number of terms in the expansion of (x+y)ⁿ are (n+1).

The sum of exponents of x and y is always n.

nC₀, nC₁, nC₂, … .., nCₙ are called binomial coefficients and also represented by C₀, C₁, C₂, ….., Cₙ

The binomial coefficients which are equidistant from the beginning and from the ending are equal.

i.e. nC₀ = nCₙ, nC₁ = nCₙ₋₁ , nC₂ = nCₙ₋₂ ,….. etc.

By using binomial expansion theorem, we get

x⁸ + 4x⁷ + 6x⁶ + 4x⁵ + x⁴

The expression be (x²+x)⁴ is expanded as x⁸ + 4x⁷ + 6x⁶ + 4x⁵ + x⁴.

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The single logarithm of log 3 + 4 log x is = log (3x^4).

What is a logarithmic function?

A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1

Write the given logarithmic expression in a single logarithm. log 3 + 4 log x

Given logarithmic expression is log 3 + 4 log x

Applying given properties of logarithmic function;

log a + log b = log (ab)

2 log a = log a²

Now, log 3 + 4 log x = log 3 + log x^4

= log (3x^4)

Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).

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The decay factor for the annual rate of change of - 55 % is 0.45.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = - 55 % = - 55 / 100 = - 0.55

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (- 0.55)

B = 1 - 0.55

B = 0.45

Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.45.

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$1.051271 is the exponential function to explain why continuous compounding does not give you much of an investment advantage.

With an example, what is compound interest?

Simple Interest: A = P(1+rt)

P: the principal, the amount invested

A: the new balance

t: the time

r: the rate, (in decimal form)

Ex 1 -  If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.

P = $1000, t = 2 years, r = 0.08.

A = 1000(1+0.08(2)) = 1000(1.16) = 1160

B) Suppose you invest $1 at 5% compounded yearly.

Suppose you invest $1 at 5% compounded continuously.

The 1st case gives you $1*(1.05)1 = $1.05

The 2nd case gives you $1*e0.05 = $1.05127

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well, let's keep in mind that a meter has 100 centimeters, thus 1.3 meters will be 1.3 * 100 cm, namely 130 cm.

[tex]\begin{array}{ccll} cm&year\\ \cline{1-2} 2 & 1\\ 130& x \end{array} \implies \cfrac{2}{130}~~=~~\cfrac{1}{x}\implies \cfrac{1}{65}=\cfrac{1}{x}\implies x=65[/tex]

The statement is True. Any two integers a, b will satisfy the condition which is: a + b > a - b

In the given question, we have been asked whether the statement a + b > a - b is True or not. For this, we know that the sum of any two Integer is always greater than the difference between them. This can be explained with the help of an example. Suppose a = 2, and b = 1.

Putting values of a, b in the condition, we get:

=> a + b > a - b  => 2 + 1 > 2 - 1

=>  3 > 1

Hence, the statement  a + b > a - b is True.

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Based on the fact that this is an equilateral triangle, the value of y can be found to be 5.

The figure given is an equilateral triangle which means that the lengths of all the sides are equal.

As DC is equal to 20, it means that all the other sides should be 20 as well.

This means that the value of y is:

20 = 15 + y

y = 20 - 15

y = 5

In conclusion, y is 5.

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Answer: [tex]x=\Large\boxed{\frac{2}{5} }[/tex]

Step-by-step explanation:

Given equation

[tex]-5x-(-6-4x)=-2(3x-4)[/tex]

Expand the parenthesis

[tex]-5x+6+4x=-2\times3x-2\times(-4)[/tex]

[tex]-5x+6+4x=-6x+8[/tex]

Combine like terms

[tex]-x+6=-6x+8[/tex]

Add 6x on both sides

[tex]-x+6+6x=-6x+8+6x[/tex]

[tex]5x+6=8[/tex]

Subtract 6 on both sides

[tex]5x+6-6=8-6[/tex]

[tex]5x=2[/tex]

Divide 5 on both sides

[tex]5x/5=2/5[/tex]

[tex]x=\Large\boxed{\frac{2}{5} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

44/15

Step-by-step explanation:

[tex]x-\frac{2}{5}+\frac{1}{2}x-3=1 \\ \\ \frac{3}{2}x-\frac{17}{5}=1 \\ \\ \frac{3}{2}x=\frac{22}{5} \\ \\ x=\frac{44}{15}[/tex]

The property which was used in step 1 to arrive at step 2 is: A. distributive property.

The distributive property states that when the sum of two (2) or more addends are multiplied by a number, the same output is produced as when each addend is multiplied respectively by the number, and the products are added together.

Mathematically, the distributive property of multiplication is given by this expression:

x(y + z) = xy + xz.

By applying the distributive property of multiplication to step 1, we have:

5(x - 7) = 55.

5x - 35 = 55

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Complete Question:

What property was used in step 1 to arrive at step 2?

Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.

distributive property

addition property of equality

subtraction property of equality

division property of equality

Answer:

A.) Distributive property.

Step-by-step explanation:

The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s

What is a slope-intercept function?

A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that  represents Macario's hourly wage y is shown thus:

y=9x+0.12s

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The rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).

Given that, a rotation and reflection composition is equivalent to other compositions.

Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape.

Rotation rule:

Rotation of a point through 180°, about the origin when a point A (x, y) is rotated about the origin O through 180° in the anticlockwise or clockwise direction, it takes a new position A' (-x, -y).

Reflection rule:

A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.

Therefore, the rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).

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The solution of the exponential equation 2e³x = 16 is x = 0.398.

Exponential equations are those in which the variables appear as exponents.

Now, for the stated equation 2 e³x=16;

Divide both side by 2

=> e³x = 8

=> x = 8/ e³

As, we are aware of the exponential function 'e' that is the value of e = 2.72...

Substitute the value of the exponent 'e' in the obtained expression.

=> x = 8/ (2.72)³

=> x = 8/20.132

=> x = 0.398

Therefore, the obtained value of x for the given exponential function is 0.398.

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answer :

so this is the answer of the value of x

The solution of the linear equation is x = 21.

Here we have the linear equation:

5x - 2x + 5 = 2x + 26

To solve this for x, move all the terms with x to the left side and all the others to the right side:

5x - 2x - 2x = 26 - 5

5x - 4x = 21

x = 21

The solution of the linear equation is x = 21.

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The given logarithmic representation i.e., (log x)² = log x² is true only for x = 1 and 100 and for rest it is not valid.

Given that, (log x)² = log x², let's proceed to simplify this in order to reach at the conclusion part.

(log x)² = log x²

(log x)² = 2log x

(log x)² - 2log x = 0

log x(log x - 2) = 0

⇒log x = 0 or log x - 2 = 0

Now, put log x = 0

⇒ x = 1

Now, put log x - 2 = 0

log x = 2

log x = 10²

x = 100

Hence, we got two values for x one is 1 and other is 100. Now, putting one by one in (log x)² = log x² in order to reach at the conclusion.

Put x = 1 in (log x)² = log x², we get

(log 1)² = log 1²

0 = 0²

0 = 0

⇒ true for x = 1

Now, put x = 100 in (log x)² = log x² , we get

(log 100)² = log 100²

2² = 2log 100

4 = 2 x 2

4 = 4

⇒ true for x = 100

So, (log x)² = log x² is true only when x = 1 and 100 for rest it is false.

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The value of the angle SRT using the given parameters is; ∡SRT = 90°

Collinear points are the points that lie on the same straight line or in a single line. Thus, the points T and W are collinear.

We are told that ∡TRV ≅ ∡VRW. That congruency statement can only be possible if both angles are 90°.

From the above, it means that we can say that;

∡TRV = ∡VRW = 90°

Now since the two lines intersect each other at point R, we can say that;

∡SRT = ∡VRW because they are both vertically opposite angles.

Thus;

∡SRT = 90°

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Answer: 90

Step-by-step explanation:RIGHT ON EDGE 2023

The location is 63° warmer in April than in December. The correct option is the third option  61 + |−2| = 63°, 61° is the farthest from 0°

From the question, we are to determine how much warmer the location is in April than in December

From the given information,

Average temperature in April = 61°

and

Average temperature in December = -2°

To determine how much warmer the location is, we will add the absolute values of the temperatures

That is,

61 + |-2|

= 61 + 2

= 63°

61° the temperature that is farthest from 0

Hence, the location is 63° warmer in April than in December. The correct option is the third option  61 + |−2| = 63°, 61° is the farthest from 0°

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