Which statement is true about f(x) +2=1/6|x-3|?

The value of the expression 4(2x - 1) when x = 6 is 44. Option A

Algebraic expressions are defined as expressions that are made up of coefficients, terms, variables, factors and constants.

They are also identified with arithmetic operations, such as;

From the information given, we have that;

4(2x - 1)

expand the bracket, we get;

8x - 4

Substitute the value of x as , we have;

8(6) - 4

Multiply

48 -4

Subtract the values

44

Hence, the value is 44

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On solving the provided question we can say that the expressions are    

a)  1000

b  10

c) 100000.001

d) 99000

In mathematics, it is pοssible to multiply, divide, add, or remove. The construction of an expression is as follows: Expressiοn, number, and mathematical operatοr Numbers, variables, and functions are the building blocks of a mathematical expressiοn (such as addition, subtraction, multiplicatiοn or division etc.)

Expressiοns and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic οperation between them is called an expression or an algebraic expressiοn. For instance, the expressiοn 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expressiοn, all of which are separated by the arithmetic sign +.

The expressiοns are

a)10¹⁵/10¹² = 10³ = 1000

b)10¹/10⁰ = 10/1 = 10

c)10⁵ + 10⁻³ = [tex]\dfrac{10^8 +1}{100}[/tex]= 100000.001

d)10⁵ - 10³ = 100000 - 1000 = 99000

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On solving the provided question we can say that the equation is p + 1.25p = 1225 => 2.25p = 1225 => p = 544.44

A formula is a formula that connects two statements and uses the equal sign (=) to indicate equality. A formula that proves the equality of two formulas is called an equation in algebra. For example, in the expression 3x + 5 = 14, the equal sign separates the variables 3x + 5 and 14. The relationship between the two sentences on either side of the letter is represented by a mathematical formula. In many cases, only one variable can also act as a symbol. For example, 2x – 4 = 2. 

the equation is

p + 1.25p = 1225

2.25p = 1225

p = 544.44

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The 8.4% compounded quarterly is the better investment because it gives a good return.

(i)

S = P

S = P(1.0854) (1.0854)

AP(1) = 1.0846 - 1

AP(1)= 0.08546 or 8.546%

(ii)

r = 0.084/4

AP(2) = (1 + 0.084/4)⁴ -1

AP(2) = 1.08688 - 1

AP(2) = 8.668%

The 8.4% quarterly investment is therefore preferable.

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The value of x for the given circle will be going to be 50°.

A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.

In our daily life, we always see circle objects for example our bike wheel.

Area of circle = πr² and the perimeter of circle = 2πr

where r is the radius of the circle.

Angles of Intersecting Chords Theorem

When two chords cross inside of a circle, the resulting angle's measure is equal to the product of the lengths of the arcs it intercepts and its vertical angle, divided by two.

So, angle x = (190° + 40°)/2  = 115°

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The percent of two inches to the length of a ruler is 16.7 percent.

The length of a standard ruler is 12 inches. Therefore, the percent of two inches to the length of a ruler can be calculated as follows:

percent length = 2 / 12 × 100

Hence,

percent length = 200 / 12

percent length = 16.6666666667

percent length = 16. 7 %

Therefore, the percent length of 2 inches to the length of a ruler(12 inches) is 16.7 percent.

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Answer:

Step-by-step explanation:

To find the probability of rolling a 6 on two number cubes, we need to calculate the number of favorable outcomes (rolling a 6 on either or both of the cubes) divided by the total number of possible outcomes.

Each cube has 6 sides, numbered 1 through 6. So, the total number of possible outcomes when rolling two cubes is 6 x 6 = 36.

The number of favorable outcomes is 2, because there are two ways to roll a 6: either rolling a 6 on the first cube and a 6 on the second cube, or rolling a 6 on one of the cubes.

So, the probability of rolling a 6 is:

favorable outcomes / total outcomes = 2 / 36 = 1/18

Therefore, the probability of rolling a 6 on two number cubes is 1/18 or approximately 5.56%.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0) which is not in the given options, so none of them are the correct answer.

Answer:

10.5

Step-by-step explanation:

18/3 = 63/x

18 * x = 63

18 * 3.5 = 63

3 * 3.5 = 10.5

Answer:

f(-7) = 15

Step-by-step explanation:

Subsitute x = - 7 into f (X) = - 3 (x+2)

f(-7) = -3 x (-7+2)

calculate the sum or difference

f(-7) =-3 x (-5)

determine the sign for multiplication or division

f(-7)=3x5

calculate the product or quotient

f(-7)=15

final awnser f(-7)=15

On solving the provided question, we can say that   relation between tangential speed and angular speed, v = r * w; v: tangential speed; r: radius; w: angular speed

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

relation between tangential speed and angular speed

v = r * w

v: tangential speed

r: radius

w: angular speed

the radius is

r = d/2

d is the diameter

[tex]v = (d * w)/2\\w = 2*v/d\\w = (2*9 mile/h)/(58 feet)\\w = (2*9 mile/h)/(0.011 miles) = 1636 rad/h\\w = 1636/60 = 27.2 rad/min\\[/tex]

the angular speed is in radians,

[tex]n = v/(π*d)[/tex]

n = (9 mile/h)/(π*0.011 mile) = 260 rev/h

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Answer:

[tex]\dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}[/tex]

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)).

As h gets smaller, the distance between the two points gets smaller.

The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = sin(x) using first principles, substitute f(x + h) = sin(x + h) and f(x) = sin(x) into the formula:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x+h)-\sin(x)}{(x+h)-x}\right][/tex]

Use the sin addition formula to expand sin(x + h).

[tex]\boxed{\sin(A + B) = \sin A \cos B + \cos A \sin B}[/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)+\cos(x)\sin(h)-\sin(x)}{(x+h)-x}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\cos(h)-\sin(x)+\cos(x)\sin(h)}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)+\cos(x)\sin(h)}{h}\right][/tex]

Separate the sin(x) and cos(x) terms into two fractions:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)(\cos(h)-1)}{h}+\dfrac{\cos(x)\sin(h)}{h}\right][/tex]

When h gets really small, we can use the small angle approximation to rewrite cos(h).

[tex]\boxed{\cos (h) \approx 1-\dfrac{1}{2}h^2}[/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(1-\dfrac{1}{2}h^2-1\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{\sin(x)\left(-\dfrac{1}{2}h^2\right)}{h}+\dfrac{\cos(x)\cdot h}{h}\right][/tex]

Cancel the common factor, h:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[-\dfrac{1}{2}h\sin(x)+\cos(x)\right][/tex]

As h → 0, the first term → 0:

[tex]\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\cos(x)[/tex]

The demonstration of magnitude of power given by 80 kg monkey by climbing a 15 meter tree in half a minute is equal to option b.  392 J/S.

Weight 'm' of the monkey is equal to 80kilogram

Height 'h' of the tree is equal to 15 meter

Time 't' taken by monkey to climb a tree = half a minute

                                                                    = 30 minutes

g = 9.8 m/s²

Magnitude of power = ( m × g × h )/ t

⇒ Magnitude of power = ( 80 × 9.8 × 15 )/ 30

⇒ Magnitude of power = 784 / 2

⇒ Magnitude of power = 392 J/S

Therefore, the magnitude of the power for the given weight , displacement and time is equal to option b. 392 J/S.

The above question is incomplete, the complete question is:

A 80 Kg monkey climbs a 15 meter tree in half a minute. What is the magnitude of power the monkey demonstrated?

a. 13.1 J/S

b. 392 J/S

c. 784 J/s

d. 11760 J/s​

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Answer:

(p o q) = 54

(q o p) = 68

Step-by-step explanation:

Another way to write is (p o q)(3) is p(q(3)).  As you can see, you start with the inner function and 3 is an input in the q(x) function.  Then, the output of this becomes the input of p(x) (the outer function), which yields a final output and the answer:

[tex]p(x) = 4x + 2\\q(x)=5x-2\\\\p(q(3))\\\\q(3)=5(3)-2=13\\p(13)=4(13)+2=54[/tex]

You do the same process for (q o p)(3), which can be written as q(p(3)), where you start with p(3) and then plug in this result as the input for q(x):

[tex]p(x)=4x+2\\q(x)=5x-2\\\\q(p(3))\\\\p(3)=4(3)+2=14\\q(14)=5(14)-2=68[/tex]

By using the substitution method, the value of a is equal to 10 and the value of b is equal to -1.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

2a + 7b = 13      .......equation 1.

8b = 2 - a          .......equation 2.

From equation 2, we have:

a = 2 - 8b         .......equation 3.

By using the substitution method to substitute equation 3 into equation 1, we have the following:

2(2 - 8b) + 7b = 13

4 - 16b + 7b = 13

4 - 9b = 13

9b = 4 - 13

9b = -9

b = -1

a = 2 - 8b

a = 2 - 8(-1)

a = 2 + 8

a = 10.

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Answer: The answers are both B and C

A. There are 25^26 possible simple substitution ciphers.

(a) A simple substitution cipher is a substitution of one letter for another. In a simple substitution cipher, each letter in the alphabet can be mapped to one of the 25 other letters. Therefore, for each letter in the alphabet, there are 25 possible substitutions. The total number of possible simple substitution ciphers is the number of possible substitutions for each letter, raised to the power of the number of letters in the alphabet:

25^26 = 25 × 25 × 25 × ... × 25 (26 times)

So, there are 25^26 possible simple substitution ciphers.

(b) (i) If no letters are fixed, then each letter can be mapped to one of the 25 other letters. Therefore, the number of simple substitution ciphers that leave no letters fixed is:

25 × 24 × 23 × ... × 2 × 1 = 25!

(ii) If at least one letter is fixed, then for each letter in the alphabet, there are 24 possible substitutions. Therefore, the number of simple substitution ciphers that leave at least one letter fixed is:

25 × 24 × 23 × ... × 2 × 1 = 25!

(iii) If exactly one letter is fixed, then there are 26 possible letters that could be fixed. For each of these 26 possibilities, there are 24 possible substitutions for each of the remaining 25 letters. Therefore, the number of simple substitution ciphers that leave exactly one letter fixed is:

26 × 24^25 = 26 × 24 × 24 × ... × 24 (25 times) = 26 × 24!

(iv) If at least two letters are fixed, then the number of ways to choose the two fixed letters, multiplied by the number of ways to arrange the other 24 letters, gives the number of ciphers that have exactly two fixed letters. The number of ways to arrange 24 letters is 24!, and there are 26 choose 2 ways to choose two letters from 26:

26 choose 2 × 24! = 325 × 24!

However, this counts ciphers with exactly two fixed letters twice: once for each of the two fixed letters. So, to find the number of ciphers with at least two fixed letters, we need to subtract the number of ciphers with exactly two fixed letters and divide by 2:

(25! - 325 × 24!) / 2 = (25! - 325 × 24!) / 2.

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Based on the information, it should be noted that the difference between the scores of the girls and boys aren't significant.

From the information, the average score for boys was 48.4 with standard deviation 12.96 and the girls had an average score

of 48.9 with standard deviation 11.85.

The computed upper limit = 2.1119

The computed lower limit = -3.1119

Since the interval (-3.1119, 2.1119) contains the between the value 0 thus the difference of boys and girls scores isn't significant.

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The APY for the account would be 3.045%.

What is continuous compounding?

The formula for continuous compounding is given by:

A = P[tex]e^{(rt)}[/tex]

where:

A = final amount

P = principal amount

e = the mathematical constant e (approximately 2.71828)

r = annual interest rate

t = time in years

In this case, P = $1000, r = 0.03 (since APR is given), and t = 1 year.

Using the formula, we have:

A = 1000[tex]e^{(0.03*1)}[/tex]

A ≈ $1030.45

So the balance in the account after 1 year is approximately $1030.45.

To find the balance after 5 and 20 years, we simply need to plug in the corresponding values for t:

For t = 5:

A = 1000[tex]e^{(0.03*5)}[/tex]

A ≈ $1160.92

For t = 20:

A = 1000[tex]e^{(0.03*20)}[/tex]

A ≈ $1806.11

To find the APY, we use the formula:

APY = (1 + r/n)ⁿ- 1

where:

n = number of compounding periods per year

Since this is continuous compounding, we take the limit as n approaches infinity:

APY = eʳ - 1

APY = [tex]e^{0.03}[/tex] - 1

APY ≈ 0.03045 or 3.045%

Hence, the APY for the account would be 3.045%.

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Answer: 35

Step-by-step explanation: 52-13-4

Answer: The sales tax is $2.5 and her total cost of the shirt is $47.5.

Step-by-step explanation:

The vertical axis of the scatter plot is the height; on the other hand, if the sphere is 6 inches, the height is closer to 5 inches than to 11 inches.

In this scatter plot, the horizontal axis is the width; however, we know the second variable is the height and this should be in the vertical axis.

Following the trend of the graph, it can be concluded the height if the width is six inches is approximately 5 rather than 11 inches.

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The direction and slope of line A'B' would still be the same as that of line AB, but the positioning of A'B' would depend on the location of line AB with respect to the origin and the value of g.

What is a scale factor ?

A scale factor is a number that scales or multiplies the size or dimensions of an object or a geometric figure by the same amount in all directions. It can be used to describe changes in size or magnification of an object or figure, and is often expressed as a ratio or a percentage.

When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, the resulting line A'B' will be three times as long as line AB and will pass through the origin.

The direction and slope of line A'B' will be the same as that of line AB, but it will be positioned closer to the origin.

If line AB were dilated with a scale factor of g, then the resulting line A'B' would be g times as long as line AB and would also pass through the origin.

Therefore, The direction and slope of line A'B' would still be the same as that of line AB, but the positioning of A'B' would depend on the location of line AB with respect to the origin and the value of g.

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No The triangles' are not congruent

The length of the corresponding sides should be equal and the length of sides is gotten using the equation:

The length of line in an ordered pair is calculated using the formula

d = √{(x₂ - x₁)² + (y₂ - y₁)²}

where

d = distance between the points

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

distance between points A(2, -8), B(-5, -2), C(-7, 3); and ΔDEF: D(-9, 7), E(-11, 12), F(-2, 1) are calculated as follows:

AB =√{(-2 + 5)² + (-8 + 2)²} = 6.71

DE = √{(-9 + 1)² + (7 - 12)²} = 9.43

BC = √{(-5 + 7)² + (-2 - 3)²} = 5.39

EF = √{(-11 + 2)² + (12 - 1)²} = 14.21

AC = √{(2 + 7)² + (-8 - 3)²} =  14.21

DF = √{(-9 + 2)² + (7 - 1)²} = 9.22

Examining the figures showing the side lengths shows that the two triangles are not congruent

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The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Let 'x' be the amount of investment at a rate of 4.75%. Then the amount of investment at a rate of 2.75% is ($18,000 - x). Then the equation is given as,

(18,000 - x) × 0.0275 + 0.0475x = 579

495 - 0.0275x + 0.0475x = 579

0.02x = 84

x = $4,200

Then the value of ($18,000 - x) is given as,

$18,000 - x = $18,000 - $4,200

$18,000 - x = $13,800

The amount of investment at a rate of 2.75% and 4.75% will be $13,800 and $4,200m, respectively.

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Answer:15n + 3 = 153

Step-by-step explanation:

15n + 3 = 153

product of 15 and a number n is 15n, and 3 more gets the plus 3, and it said all of this is 153

n=10 also as subtract 3 both sides then get 15n=150 get n by itself by dividing both sides by 15 and get n=10

The required equation in terms of r is r = (W - FB) / F

An equation is a mathematical statement given by connecting two expressions by equal sign.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

For example: 3x=9y, 67x = 90+39y

Given that an equation W = F(r + B) we need to solve the equation for r,

Therefore, rearranging for r,

W = F(r + B)

Using the distributive law,

W = Fr+FB

Transposing FB to the LHS

Fr = W - FB

Diving the equation by F

r = (W - FB) / F

Hence, the equation in terms of r is r = (W - FB) / F

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