Factor the expression. 25-40 x+16 x²

[tex]23^8\cdot 23^n=(23^5)^3\implies \underset{same~base}{\stackrel{same~exponent}{23^{8+n}=23^{(5)(3)}}}\implies 8+n=(5)(3) \\\\\\ 8+n=15\implies n=7[/tex]

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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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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2 log(x) = -1 => x = 0.3162, by properties of logarithm.

Now,

2 log(x) = -1

=> log (x) = [tex]\frac{-1}{2}[/tex]

Since, generally the base of log is 10, raising them to 10.

=> [tex]10^{log_{10}(x)}=10^{\frac{-1}{2}}[/tex]

=> x = 0.3162 ( as [tex]a^{log_a(x)} = x[/tex])

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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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In mathematics, an inverse function is one that "reverses" another function. The inverse of y = 2x + 8 is f⁻¹(x) = x/2 − 4.

The inverse function of a function f in mathematics exists a function that reverses the operation of f. If the inverse of f exists, it is shown by the f⁻¹. The inverse of f exists if and only if f exists bijective.

An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f ⁻¹.

Let the function be y = 2x + 8

Interchange the variables.

x = 2y + 8

Solving for y

y = x/2 − 4

Replace y with f⁻¹(x), we get

f⁻¹(x) = x/2−4

Verify if f⁻¹(x) = x/2−4 is the inverse of f(x) = 2x+8.

The inverse of y = 2x+8 is f⁻¹(x) = x/2−4.

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Answer:

D

Step-by-step explanation:

٦٦٦٣ع٣٧ his face and I will ask my mom if I am ejjejdjjdhfjfjjfjdjjejriirjtndnjwjwuirjrnt778888766555673829

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.

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:

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

The area of the running track to the nearest tenth of a yard is 1456 yards

The length of the field is 100 yards with a width of 40 yards.

Notice that the two semicircles on both ends form a circle with diameter 40 yards. Since it's diameter is 40, then it's radius is 20. We can get the length of the rectangle by subtracting two 20 from 100 or subtracting it's diameter to the entire length 100:

= 100-20-20

=100-40

=60

Since we formed a rectangle with two semicircles on both ends, we have the length of the rectangle 60 yards and the width 40 yards.

We first get the circumference of the circle.

C=πd

=(3.14)(40)=125.6

Then we get the measure of the two lengths of the rectangle which is 60

60+60=120

We multiply 145.6 by 10 and we get 1456

Therefore, the area of the running track to the nearest tenth of a yard is 1456 yards.

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Answer:

3570 square yards.

Step-by-step explanation:

A=  ℓh-ℓh+πr square-πr square

A=60 * 100 - 40 * 100 + π(30) square - π(20) square

A= 6000-4000+900π-400π

A=2000+500π

A=2000+500*3.14

A=3570 square yards.

The total Cost of a bench is 1.008x.

According to the statement,

We have to find that the cost of the bench.

So, For this purpose, we know that the

The cost function may be accustomed find the typical cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

The owner of the outdoor furniture center decides to use the 120% markup. at the tip of the season, he wants to sell all the benches that are available. he sells the benches for 20% off.

Then

Since we've provided that

Let the price price be 'x'.Mark up % = 120%

So, price value would be 120x/100

Then

Discount % = 20%

Amount of discount is given by

20* 1.2x/1000.

24x

So, it becomes,

Amount after discount is given by

1.2x - 0.24x = 0.96x

Amount of sales tax would be

100+5/100*0.96x

105/100*0.96x

1.008x.

So, The total Cost of a bench is 1.008x.

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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 equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings is y = 75 + 15x

The equation to describe the linear relationship:

The amount Jaycee has in her vacation savings = Amount Jaycee has saved + Additional amount jaycee saved per week(Number of weeks Jaycee saved)

y = 75 + 15(x)

y = 75 + 15x

For instance, if jaycee has saved for 5 weeks, the

amount Jaycee has in her vacation savings is

y = 75 + 15x

y = 75 + 15(5)

= 75 + 75

y = $150

Therefore, the equation to describe the linear relationship between x, the number of weeks from now, and y, the amount Jaycee has in her vacation savings is y = 75 + 15x

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Answer:

Step-by-step explanation:

1. 170, 13 7/8, 13.5, 64/5

2. Plant D = 5.2 in Plant B =5.3 in Plant C = 5.5in Plant A =5.92

3. Chelsea, Finn, Erin, Mitchell

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:

Step-by-step explanation:

Let two consecutive odd integers be x and x+2

Given, their sum is 20.

x+x+2=20

2x=20−2

2x = 18

x=9

Therefore, other number is

x+2=9

9+2=11.

Thus, the numbers are 9,11.

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

check

9 + 9 + 2 = 20

20 = 20

the answer is good

The value of the greater integer is 7.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

The sum of an integer and 2 times the next consecutive integer is 20.

let, the number = x

so, the next consecutive integer = x+1

ATQ, x+2(x+1)=20

    ⇒3x+2=20

    ⇒3x=18

    ⇒x=6

i.e. the greater integer = x+1 = 7

Hence, the value of the greater integer is 7.

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The circle below has a sector 120° shaded. 120° 22. Then area of sector is 200.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Area of sector=theta/360*πr^2

Given π = 7,

theta=120 degrees

d=22, so r=11.

Area of sector=210/360*7*7^2

=0.583*7*7*7

=200.08

Therefore area of sector is 200.

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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!

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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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:

[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 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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Answer:

answer is 9

Step-by-step explanation:

a*a+b.

-2*-2+5.

4+5=9

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 98000}}{\left( \cfrac{7}{100} \right)98000}\implies 6860[/tex]

Answer: 9.1 - 12.9 = -3.8

Step-by-step explanation:

9.1

12.9

———-

-3.8

the smaller number is getting subtracted by the bigger number which makes it a negative unless u made a error and placed the numbers in wrong order. The order of numbers won’t matter if it’s multiplication or addition. But if it’s division or subtraction it will change the final answer

The rate r with the given distance is 65 miles/hour.

Given that, the formula d=2r can be used to find the distance d travelled after 2 hours at rate r.

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, the distance may refer to a physical length or an estimation based on other criteria.

Now, the given formula is d=2r.

So, the formula for r is r=d/2

Distance = 130 miles

Then, the rate r = 130/2 = 65 miles/hour

Therefore, the rate r with the given distance is 65 miles/hour.

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Answer:

No

Step-by-step explanation:

Its not a function because there wouldn't be a reasonable answer if you try solving the equation.

Answer:

yes, it is a function

Step-by-step explanation:

y = -x + 4 is a line. In order to be a function every input can have only one output. Any x you put into that equation will spit out only one y. It passes the vertical line test (ALL lines except a vertical line pass the vertical line test.) So it is a function.

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

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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