Which equation is equivalent to 2^3x =10
log 3x = 2
10?
log 2 = 3x
log₂ 10 = 3x
log₂ 3x = 10

In a quadrilateral with a perimeter of 120 inches, the longest of the four sides has length equal to 33 inches.

A quadrilateral is a two-dimensional figure that has 4 sides and 4 vertices. The perimeter of any two-dimensional figure is the sum of all its sides.

If the lengths of the four sides of a quadrilateral (in inches) are consecutive odd integers, we can express each side as:

x = length of side 1(odd integer)

x + 2 = length of side 2

x + 4 = length of side 3

x + 6 = length of side 4

If the perimeter of the quadrilateral is 120 inches, then the sum of the four sides is equal to 120 inches.

x + (x + 2) + (x + 4) + (x + 6) = 120

Simplifying and solving for x.

4x + 12 = 120

4x = 108

x = 27

Substitute the value of x on the expression for the length of the 4th side(longest side).

longest side = x + 6 = 27 + 6

longest side = 33 inches

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Answer:

visit a nearby farmer ask him about farming such as things to be considered, possible disease, benefits, challenges etc. prepare a short report and present

[tex]\displaystyle\\Answer:\ y=\frac{1}{3}x-2[/tex]

Step-by-step explanation:

(6,0)    (9,1)

[tex]\displaystyle\\The\ slope=\frac{1-0}{9-6} \\\\The\ slope=\frac{1}{3}[/tex]

(0,-2)

[tex]\displaystyle\\y=\frac{1}{3} x+b\\-2=\frac{1}{3}(0)+b\\ -2=0+b\\\\-2=b\\\\Thus,\\\\y=\frac{1}{3} x-2\\\\[/tex]

The value of x for log (5-2 x)=0 is 2.

It is established that the exponential equation x = ay and the logarithmic function y = logax are equal. Only when x = ay, a > 0, and a 1 do y and logax coincide. The base-a logarithmic function is what it is known as. Think about what it means for the exponential function to be inversed: x = ay.

Given,

log (5-2 x)=0

It can be expressed as -

5 - 2x = 10⁰

= 5 - 2x = 1

= x = 2

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45x2.20=99

meaning she spent $99

45x3.75=168.75

shows how much she made

168.75-99=69.75

shows what she profited

your answer is $69.75

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hope this helped :)

The linear function y = 4, perpendicular to x = 3, is graphed at the end of the answer.

A linear function is modeled by the following rule:

y = mx + b

In which:

When two linear functions are perpendicular, they intersect forming an angle of 90º between them.

For this problem, we want a line perpendicular to x = 3.

The line passes through (-2,4), with y-coordinate of 4, hence the line is given by:

y = 4.

On the graph given at the end of the answer, it is shown that the two lines are perpendicular, forming an straight angle. The line y = 4 is graphed in blue.

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Answer: I think it's 7.8.

Answer:

7.8

Explanation:

This number is irrational because it does not terminate.

Terminate

decimal that is expressed in finite figures in which all figures to the right are zero.

The expression is written as a product of binomials as;

a) (x + 2) (5x + 3)

b) (x - 5) ( 3x + 2)

What is Distributive property?

Distributive property is said to be multiplying the sum of two or more number will give the same result as multiplying each addend individually by the number and then adding the products together.

Now, For solving the expression by using the distributive property "backwards" , we can find the GCD of each term using in the expression as;

(a) x(x+2) + 3(x+2) + 4x(x+2)

GCD of x(x + 2), 3(x + 2), 4x(x + 2) = (x + 2)

Hence, Firstly take (x + 2) as common term we get;

x (x + 2) + 3(x + 2)+ 4x(x + 2) = (x +2) ( x + 3 + 4x)

                                            = (x + 2) (5x + 3)

The expression is written as a product of binomials as;

a) x (x + 2) + 3(x + 2)+ 4x(x + 2) = (x + 2) (5x + 3)

And, (b) 2x(x-5) + 3(x-5) + (x-1) (x-5)

GCD of 2x(x-5) , 3(x-5) , (x-1) (x-5) = (x - 5)

Hence, Firstly take (x - 5) as common term we get;

2x(x-5) + 3(x-5) + (x-1) (x-5) = (x - 5) (2x + 3 + x - 1)

                                        = (x - 5) ( 3x + 2)

So, The expression is written as a product of binomials as;

b) 2x(x-5) + 3(x-5) + (x-1) (x-5) = (x - 5) ( 3x + 2)

Therefore, The expression is written as a product of binomials as;

a) (x + 2) (5x + 3)

b) (x - 5) ( 3x + 2)

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The equivalent of the given expression 5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b ) is 2a - b.

Given the expression in the question;

5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b )

To simplify, apply distributive property.

5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b )

5(2a) + 5(b) + 2(a) + 2(2b) − 5(2a) -5(2b )

Perform the multiplication operation.

10a + 5b + 2a + 4b − 10a - 10b

Collect like terms

10a − 10a + 2a + 5b + 4b - 10b

2a + 5b + 4b - 10b

2a + 9b - 10b

2a - 1b

2a - b

Therefore, the equivalent of the given expression 5( 2a + b ) + 2( a + 2b ) − 5( 2a + 2b ) is 2a - b.

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To find Y-intercept

Set X=0

The slope between (-8,4) and (3,-1) is -5/11 and the slope of 4x - 3y = 13 is 4/3

The points are given as

(-8,4) and (3,-1)

The slope between the points is calculated using

Slope = (y2 - y1)/(x2 - x1)

So, we have

Slope = (-1 - 4)/(3 + 8)

Evaluate

Slope = -5/11

Hence, the slope between (-8,4) and (3,-1) is -5/11

The equation of the line is given as

4x - 3y = 13

Make 3y the subject of the formula

So, we have

3y = 4x - 13

Make y the subject of the formula

So, we have

y = 4/3x - 13/3

A linear equation is represented as

y= mx + c

Where

Slope = m

By comparison, we have

m = 4/3

Hence, the slope of 4x - 3y = 13 is 4/3

A graph that represents direct variation is a linear graph that passes through the origin

The slopes of parallel lines are equal

i.e. m1 = m2

The slopes of perpendicular lines are opposite reciprocals

i.e. m1 = -1/m2

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The correct option is (c) 144ft

The maximum height the ball reaches is 144ft.

A quadratic function has the form of equation as ax²+ bx + c, where a, b, and c are the numbers not equal to  zero. In mathematics, the quadratic function, the quadratic polynomials , 2 degree polynomial is a polynomial function with one or more that one variables in which the highest term is of the second degree.

In the question,

h(t)=-16 t²+96 t

and velocity = 96ft/s

out the -16 from the equation.

h(t)= -16 ( t² + 6 t )

h(t) = −16(t² −6t+9−9)

     = −16(t² −6t+9)+144

Factor the equation to get a perfect square ,t = 3 then h(t) = 144. The maximum height is 144.

−16(t−3)² +144

Thus, height is 144 ft.

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The given  logarithmic expression statement is false. Because log₄7- log ₄3 = log₄(7/3).

The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.

Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).

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Answer:first do the exponents thats equal to 9 then times -2 is -16+7 is -11

hope that helps

Step-by-step explanation:

Answer:

-11.

Step-by-step explanation:

7+(-2)•3^2

= 7 - 2*9

= 7 - 18

= -11.

Answer:

T(3, 8)

Step-by-step explanation:

Yes, it can.

Use the midpoint formula with points S and Z, and solve for point T.

M( (x_1 + x_2)/2 , (y_1 + y_2)/2 )

Z(3, 5) = ( (3 + x)/2 , (2 + y)/2 )

(3 + x)/2 = 3

3 + x = 6

x = 3

(2 + y)/2 = 5

2 + y = 10

y = 8

T(3, 8)

A full cycle, if the pendulum is 10 cm, is 0.6 seconds long. A full cycle, if the pendulum is 20 cm, is 0.9 seconds long. A pendulum that takes 2 seconds for one full cycle is 100 cm long.

Given,

The time t in seconds for a swinging pendulum to complete one full cycle is given by the function t as,

t = 0.2 √I

Here, l is the length of the pendulum in centimeters.

For the first part, two lengths are given for the pendulum is given

We can obtain the value of t by substituting the value of l

This implies,

For l =  10 cm

t =  0.2 √10 = 0.632 = 0.6 seconds

For l =  20 cm

t =  0.2 √20 = 0.894 = 0.9 seconds

For the second part, time is given

We can obtain the value of l by substituting the value of t

This implies,

For t = 2 seconds

l = t² / (0.2)² = t² / 0.04 = 2² / 0.04 = 4 / 0.04 = 100 cm

Therefore, A full cycle is 0.6 seconds long if the pendulum is 10 cm long, 0.9 seconds long if the pendulum is 20 cm long, and 100 cm long if the pendulum takes 2 seconds to complete one full cycle.

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Addie is correct because both 2 and 14 are common factors of 56 and 42.

The factor of a number is the number that can perfectly divide another number without leaving any remainder. For example, a factor of 20 is 10 because 10 perfectly divides 20 to 2.

A common factor is a factor that is common to two or more integers. An example of a common factor of 15 and 20 is 5.

A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. The numbers at the intersection of the two circles are common to both numbers.

Factors of 56 =  1, 2, 4, 7, 8, 14, 28 and 56.

Factors of 42 = 1, 2, 3, 6, 7, 14, 21 and 42.

Common factors = 1, 2, 7, 14

This means that Addie is correct because both 2 and 7 are common factors of 56 and 42.

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Answer:

12.

Step-by-step explanation:

y /x = 6/8 = 3/4

y/x = 18/24 = 3/4

The relation is y = 3/4 x.

So, the missing value is 16 * 3/4

= 12.

[tex](4 \times 1) + (4 \times \frac{1}{1000}) \\ (4) + ( \frac{4}{1000} ) \\ 4 + \frac{1}{250 \\} \\ \frac{1000 + 1}{250 } \\ \frac{1001}{250} \\ [/tex]

I guess this is the answer

The logarithm statement log (x - 2) = log x / log 2 is a false statement as log x / log 2 = log x - log 2.

We are given the logarithm as:

log (x - 2) = log x / log 2

We need to tell if it is true of not.

We get that, it is false statement.

We know that log a / log b = log a - log b

So, log x / log 2 = log x - log 2

So, it is not equal to log (x - 2)

Therefore, we get that, the logarithm statement log (x - 2) = log x / log 2 is a false statement as log x / log 2 = log x - log 2.

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Answer: The area of Triangle is A = 43.25

Step-by-step explanation:

In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3 [tex]s^{2}[/tex]* s = √3/4([tex]s^{2}[/tex])

Define Area of Triangle:

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3/4([tex]s^{2}[/tex]) . The perimeter of an equilateral triangle is 3s.

So, we can write,

A = √3/4([tex]s^{2}[/tex])

It means, A = Area of the Triangle

S = length of Triangle = 10inches.

A = √3/4([tex]s^{2}[/tex])

A = √3/4([tex]10^{2}[/tex])

A= √3/4*100

A = 1.73/4*100

A = 0.4325*100

A = 43.25

The area of Triangle is A = 43.25

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Greg will pay $25.99 for one ink cartridge after the rebate

Cost of ink cartridge: $35.99

Rebate on each ink cartridge: $10

A rebate is a portion of the purchase price that is refunded. It serves as a motivator to promote the sale of goods. For instance, if I want to spend $1,000 on a laptop/computer, the shopkeeper can offer me a $100 rebate to sweeten the bargain and convince me to buy the item.

Price Greg will pay after rebate: 35.99 - 10 = $25.99

So, Greg will pay $25.99 for one ink cartridge after the rebate of $10.

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The required solution of the system of equations are x=-6 and y=-10.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.

Given:

The system of equations are

-2x+2y=-8 and -3x+y=8

According to given question we have

Consider the first equation.

-2x+2y=-8

Taking  minus sign common  from both sides we get

-(2x-2y)=-8

2x-2y=8

Taking  2 common  from left sides,  we get

2(x-y)=8

Divide by 2 on both sides we get,

x-y= 4....(i)

-3x+y=8...(ii)

By adding 2 equation we get

-2x=12

x=-6

Put the value of x in Equation (i) we get

x-y= 4

-6-y=4

-y=4+6

y=-10

Therefore, the required solution of the system of equations are x=-6 and y=-10.

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Based on the given parameters, the value of the polynomial function f(8) is -4

Polynomials are mathematical statements that are represented by variables, coefficients and operators

The polynomial function is given as

Polynomial = f(x)

Also, we have the following statement

a remainder of -4 when divided by x-8

To start with, we set the divisor to 0

So, we have

x - 8 = 0

Add 8 to both sides of the equation

So, we have

x = 8

Express as a function

f(x) = f(8)

Set the equation to the remainder

So, we have

f(x) = f(8) = -4

Hence, the value of the polynomial function f(8) is -4

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Answer:

1 : 25.

Step-by-step explanation:

24 : 600

= 24/24 : 600/24

= 1 : 25.

Answer:

The answer is 7

Step-by-step explanation:

The formula you would use is A=bxh

So you would just plug it in

3.5 x 2 which gives you 7

Hope this helps:)

Answer: bofa

Step-by-step explanation:

The solution is 6

Rewriting the given equation

√(4x + 1) - 5 = 0

Now, taking square of the equation to find the solution of equation -

(√(4x + 1))² = 5²

On squaring both sides we get the equation -

4x + 1 = 25

Shifting 1 to the Right Hand Side of the equation

4x = 25 - 1

Performing subtraction on Right Hand Side of the equation

4x = 24

Shifting 4 to the Right Hand Side of the equation as denominator

x = 24 ÷ 4

Performing division on Right Hand Side of the equation

x = 6

Thus, the solution is 6

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The correct question is - sqrt(4x+1)-5=0

Answer:

3*2

Step-by-step explanation: