Solve each equation by factoring. Check your answers.
3 x²+8 x+4=0

KL = LM                         To find the measures of KL

8x-5 = 6x+3                

-6x      -6x                               8(4) - 5

___    ___                                32 - 5

2x - 5 = 3                                   27

   +5    +5

   __    __                        To find the measure of LM

2x = 8                                        6(4) + 3

---   ---                                         24 + 3

x = 4                                               27

The value of x for the given logarithmic equation 2㏒x = -4 is x = 0.01.

A logarithmic equation contains the log of a variable-containing representation. To begin dealing with exponential equations, check to see if both sides of a equation can be described as powers of a exact number.

The ㏒x function has the following properties:

Now, as per the given question;

The given equation is  2㏒x = -4.

Divide both side by 2.

㏒x = -2

Again, rewrite this function ㏒x = -2 in the exponential form by implementing  properties of ㏒.

Let x and a be the positive real numbers such that a ≠ 1, then,

㏒ₐx = y is equivalent to [tex]a^{y}[/tex] = x.

Then,

10⁻² = x

Now, solve the value of x.

x = 1/100

x = 0.01 in the decimal form.

Therefore, the obtained value of the logarithmic function 2㏒x = -4 is x = 0.01.

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The value of given logarithm log₂⁶(1/32) is -5/6

We have given a logarithm log₂⁶(1/32) .

Using base change property which is given by

 [tex]log_b^na^m=\frac{m}{n} log_ba[/tex]

The given logarithm becomes -

log₂⁶(1/32) = 1/6 log₂(1/32)

Using quotient property which is given by

logₐ m/n = logₐ m - logₐ n

The given logarithm becomes -

1/6 log₂(1/32) = 1/6 [ log₂1 - log₂32]

                      =  1/6 [ 0 - 5 ]

                      = -5/6

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Approximately 1 gallon of 4 buckets will be needed to paint 90ft²of fences.

Formula used: N = kA / p

Given information:

So,

Determine k.

This is something you must work out with the units when solving for k.

Then, we get:

Now, solve for 90 ft² as follows:

So,

After rounding off, the answer will be 4 buckets of 1-gallon.

Therefore, approximately 1 gallon of 4 buckets will be needed to paint 90ft²of fences.

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Answer: A. 18.32

B. 20

C. 31.16

Step-by-step explanation:

2.29 times 8=18.32 dollars spent on goodie bags

160 divided by 8=20 dollars per hour

160+18.32=178.32

1209.48-178.32= 31.16 more than what was spent in parts a and b.

Answer:

1

Step-by-step explanation:

because (5-3)=2  (2) means multiply the two 2's then divided by (2x2)  so, (2x2)/(2x2) would be 4/4 = 1

Answer:

[tex](-8)^7[/tex]

Step-by-step explanation:

You are multiplying (-8) 7 times. Therefore, it can be simplified down to [tex](-8)^7[/tex].

The situations are classified as follows:

A claim is classified as science if there are experiments, or statistical tests, that prove the claim. In the cats experiment, there is evidence, hence it is science.

A claim is classified as biased when no experiments are made, the observations are made with the "eye test". One example is watching a NFL game and saying that the team that gets the most passing yards generally wins, without making statistical tests to verify this.

For this problem, the ad for the tire is based on bias, as there were no experiments, just the eye test.

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Answer:

answer is 9

Step-by-step explanation:

a*a+b.

-2*-2+5.

4+5=9

Answer:

Part A

Plan 1

33

Plan 2

0.05x+16

0.05x+16=33

0.05x=17

17/0.05=340

341 calls would be enough.

Part B

AN easy way of doing this is by setting the equations equal to each other and then adding a variable to one side that would be the amount of calls made on plan B. Once you get rid of the initial price of 16 dollars, then you have 17 dollars to be set equal to plan B. You divide 17 by 0.05, which gives you 340, meaning that to make both plans equal to each other, you would have to make 340 calls. To make Plan 1 more economical, you would have to add 1 more call to set plan 2 0.05 cents more than Plan 2.

Step-by-step explanation:

1. The given equation is in the slope intercept form.

2. The standard form is x ₊ 2y = ₋6

3. The given equation is in the point slope form.

4. The standard form is 2x ₋ 3y = ₋3

Given,

the equation is y = ₋1/2x ₋ 3

the above equation is in the form of slope intercept form i.e,

y = mx ₊ c

to convert it into standard form i.e, ax ₊ by = c

therefore, 2y = ₋x ₋ 6

x ₊ 2y = ₋6

2. the equation is y ₋ 7 = 2/3 (x ₋ 9)

the above equation is in the form of point slope form.

i.e, y ₋ y₁ = m(x ₋ x₁)

therefore, to convert it into standard form i.e, ax ₊ by =c

y ₋ 7 = 2/3 (x ₋ 9)

3(y ₋ 7) = 2(x ₋ 9)

3y ₋ 21 = 2x ₋ 18

3y ₋ 2x = ₋18 ₊ 21

₋ 2x ₊ 3y = 3

2x ₋ 3y = ₋3

hence  we get the required results.

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Answer:

V= [tex]\sqrt[3]{36}[/tex]

Alternative Form

V≈3.301927

Evaluate

V

3

=36

Take the 3-th root on both sides of the equation

3

V

3

​

=

3

36

​

hope this helps now

Answer:

[tex]\mathrm{V=\sqrt[3]{36}}[/tex]

Step-by-step explanation:

Determine if 36 is a cube root

(a-b)•(a^2+ab+b^2) =

           a^3+a^2b+ab^2-ba^2-b^2a-b^3 =

           a^3+(a^2b-ba^2)+(ab^2-b^2a)-b^3 =

           a^3+0+0-b^3 =

           a^3-b^3

→ Using this checker, we can see that 36 is not a cube root because it cannot be factored as the difference between two perfect cubes.

Solve

v^3 - 36 = 0

v^3 = 36

v = ∛36

Answer:

Step-by-step explanation:

If you're solving for m:

3.18 + 2m = 12.7

-3.18            -3.18

Therefore making the new equation: 2m = 9.52

Divide- [tex]\frac{2m}{2\\} =\frac{9.52}{2}[/tex]

m = 4.76

Answer:$43.70

Step-by-step explanation:

120−54.67−13.49−8.14

=$43.70

Answer:

43.7

Step-by-step explanation:

120-54.67-13.49-8.14=43.7$

Express 64 as a product of its prime factors. The indices rule states

a^-n= 1/a^n. Apply the power rule (a^m)^-n= a^(-mn).

64 = 2x2x2x2x2x2 = 2^6

(1/2^6) = 2^-6

2^(-6x-1/6) = 2^(6x1/6) = 2^1

2^1 = 2

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An inverse function is one that reverses the action of another function.

The value of this function is y = 0.2.

Inverse operations are mathematical manipulations in which one operation reverses the action of the other, such as addition and subtraction, multiplication and division. In most cases, the inverse of a number is its reciprocal, i.e. [tex]x ^{- 1[/tex] = 1 / x. A number and its inverse (reciprocal) product equals one.

An inverse function is one that reverses the action of another function. A function g is the inverse of a function f if and only if y = f(x) and x = g. In other words, using f and then g is equivalent to doing nothing.

Let the given function be f(x) = 10x - 10

substitute the value of x = 0.2, then we get

f(0.2) = 10(0.2) - 10

simplifying the above equation be

f(0.2) = -8

y = 1/10(-8) +1

y = 0.2

Therefore, the value of y = 0.2.

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The order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is: A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

Generally, there are different types of transformation and these include the following:

A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

In this context, we can reasonably infer and logically deduce that the order of transformation which best describes how to sketch the graph of h(x) = ∛1 - x is to start by plotting the graph of the basic function y = ∛x, and then horizontally shift the graph of function y = ∛x to the left one​ unit, and then reflect the graph about the​ y-axis.

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Complete Question:

Which of the following order of transformations best describes how to sketch the graph of h(x) = ∛1 - x?

A. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ y-axis.

B. Starting with the graph of the basic function y = ∛x, vertically shift the graph up one​ unit, and then reflect the graph about the​ y-axis.

C. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the left one​ unit, and then reflect the graph about the​ x-axis.

D. Starting with the graph of the basic function y = ∛x, horizontally shift the graph to the right one​ unit, and then reflect the graph about the​ y-axis.

After solving the given inequality the answer is 3logx+log₁₀(x+2)>1.

So,

Given: 3log x + log(x+2) > 1

3log x + log(x+2) > 1 ⇒ 3logx+log₁₀(x+2)>1

Therefore, after solving the given inequality the answer is 3logx+log₁₀(x+2)>1.

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Answer:

-0.03

Step-by-step explanation:

[tex]3^{-3}=\frac{1}{3^3}\\=-\frac{1}{3^3}\\3^3=27\\=-\frac{1}{27}\\= -0.03[/tex]

Answer:

Stop please. You use brainly for answering and asking questions.

We need to know about translation, reflection and rotation to solve the problem. (1) We translate a triangle with respect to a horizontal and vertical direction. (2) We rotate a traingle about a given angle. (3) We refelct a triangle about a line of reflection which can be axis or vector.

(1) Translation of a triangle means changing it's position without changing the shape or size of the triangle. We translate a triangle with respect to a horizontal and vertical direction. We get the new triangle by adding the horizontal translation value to the x-coordinate and the vertical translation value to the y-coordinate.

(2) Rotation of a triangle is turning the triangle by an angle around a center point. When a triangle is rotated by 90° clockwise then (x,y) becomes (y,-x), when rotated by 90° anticlockwise (x,y) becomes (-y,x), when rotated by 180° clockwise or anticlockwise (x,y) becomes (-x,-y).

(3)Reflection of a triangle is finding a mirror like image of the triangle about  a line of reflection. The line of reflection may be either of the axes, a vector. To find the image we have to find the coordinates of the triangle that are of same distance from the line of reflection on the opposite side like they are from the original triangle.

Therefore we learnt about translation, reflection and rotation and saw that (1) Translation needs a horizontal and vertical direction for translating, (2) Rotation needs an angle of rotation and a center point and (3) Reflection needs a line of reflection.

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Answer:

see explanation

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 9, 31) and (x₂, y₂ ) = (15, - 41) ← 2 ordered pairs from the table

m = [tex]\frac{-41-31}{15-(-9)}[/tex] = [tex]\frac{-72}{15+9}[/tex] = [tex]\frac{-72}{24}[/tex] = - 3

the y- intercept is the value of g(x) when x = 0 , then from the table

y- intercept = 4

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then equation is

y = - 3x + 4

Answer:

−100x +10y+z

Step-by-step explanation:

I use the Expand Using Sum/Difference Formulas. When I plug in -100x + 10y +z it gives out the same thing.

The difference on the change of elevation is 440 feet.

From the information, it was stated that the hiking trail starting point is 180 ft below sea level and that the ending point is 260 above sea level.

Therefore, the difference in the change will be:

= Ending level - Starting level

= 260 - (-180)

= 260 + 180

= 440 feet

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The statement "As the value of x increases, the value of f(x) moves toward a constant." is true. Option  A

A relation between a collection of inputs and one output for each of those inputs is the definition of a function.

The given function is;

F(x)=(1/5)^x-2

The statement that is true of this function is as follows;

As the value of x increases, the value of f(x) moves toward a constant.

Therefore, the assertion that is true about this function is that when the value of x rises, the value of f(x) advances toward a constant. This is because of the way that the function works.

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CQ

Select the correct answer. Which statement is true of this function?

f(x)=(1/5)^x-2

A.

As the value of x increases, the value of f(x) moves toward a constant.

B.

The domain of the function is (-2, ∞).

C.

The function has a y-intercept at (0,-2).

D.

The function is increasing.

The area of the given rectangle is 6ft².

So, length 2 feet less than 3 times its width:

Then function: L = 3w - 2

Now, the area of the rectangle: l × w

Therefore, the area of the given rectangle is 6ft².

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Based on the logical fallacy given by saying that they can either go to the amusement park or the library, the category is False dilemma.

A False dilemma is a logical fallacy where the speaker makes it seem as though there are no other options to be considered. The possibility of there being other options is therefore ignored.

In the above thought, the speaker says that they can either go to the amusement part or to the library. They then pick the library because the amusement park is too expensive.

This is a logical fallacy because there were other places they could have gone to that were not even considered.

In conclusion, the statement above that presents only two choices of places to go which were the library or the amusement park is an example of a false dilemma.

Rest of the question:

Identify the logical fallacy in the given statement.

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The nth term of the sequence is 2n + 1

The formula known as the nth term allows us to locate any term in a series. The letter n stands for number. By changing the term number's value, we can create a series that uses the nth term (n).

The sequence 3,5,7,9.....

n =1

3 = 1 + 2

3 = 1 + (2×1)

n = 2

5 = 1 + 4

5 = 1 + (2×2)

n = 3

7 = 1 + 6

5 = 1 + (2×3)

n = 4

9 = 1 + 8

9 = 1 + (2×4)

9 = 1 + 8

Therefore, the expression for the Nth is 1+ 2n or 2n + 1

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Answer: 299^2 ft

Step-by-step explanation: Literally all you have to do is Base X Hight and you get the answer. The base is basically just the length.

Hope this helps!

well, let's start like the crab, from the back, what would the amount be after 10 years, with a 10.5% annual rate, compounding annually of course.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=750\left(1+\frac{0.105}{1}\right)^{1\cdot 10} \implies A=750(1.105)^{10}\implies \boxed{A \approx 2035.56}[/tex]

when will it double?  well, hmmm 750 doubled will be 1500, so

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 10.5\%\to \frac{10.5}{100}\dotfill &0.105\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases}[/tex]

[tex]1500=750\left(1+\frac{0.105}{1}\right)^{1\cdot t} \implies \cfrac{1500}{750}=(1.105)^t\implies 2=1.105^t \\\\\\ \log(2)=\log(1.105^t)\implies \log(2)=t\log(1.105) \\\\\\ \cfrac{\log(2)}{\log(1.105)}=t\implies 6.94\approx t\qquad \textit{about 6 years and 344 days}[/tex]