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What is the length of segment AB when A(-2,2) and
B(5,2)?

The time it would take Kim running the same distance is 15 minutes.

Ratio is used to show the relationship between two or more numbers. It shows the frequency that one value is contained within other value(s). The sign that is used to represent ratio is :.

Speed = distance / time

The first step is to determine the time spent by Richard running:

(4 x 1/8) / 5 = 1/10 or 10 minutes

The second step is to determine the time spent by Kim running:

(2 x 1/10) / 3 = 1/15 =  15 minutes

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For the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.

We are given the logarithm expression as:

1 / 4 log₃ 2 + 1 / 4 log₃ x

Now, take 1 / 4 common from the expression:

1 / 4 ( log₃ 2 + log₃ x)

Now, we know that log₃ a + log₃ b = log₃ ( a b)

So, we get that:

1 / 4 ( log₃ ( 2 x) )

1 / 4 log₃ 2 x

Therefore, for the logarithm expression 1 / 4 log₃ 2 + 1 / 4 log₃ x, we get the single expression as 1 / 4 log₃ 2 x.

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-4 is an extraneous solution.

The equation is

[tex](x - 2)^{1/2}[/tex] - [tex](28-2x^{1/4}[/tex] = 0

To know whether the given equation has an extraneous solution or not we need to find the value of x.

[tex](x-2^{1/2}[/tex]= [tex](28-2x)^{1/4}[/tex]

Multiply both sides with the power of 4, and we get

[tex](x- 2)^{2}[/tex] = 28-2x

[tex]x^{2}[/tex] - 4x + 4 = 28-2x

[tex]x^{2}[/tex] - 2x - 24= 0

[tex]x^{2}[/tex]- 6x + 4x -24=0

x(x-6) +4(x-6)=0

(x-6)(x+4) = 0

x = 6 , -4

Now put both the value of x in the equation

x=6

[tex](6-2)^{1/2}[/tex]-[tex](28- 2* 6)^{1/4}[/tex]= 0

[tex]4^{1/2}[/tex]- [tex]16^{1/4}[/tex]= 0

2-2=0

0=0

Now

x = -4

[tex](-4-2)^{1/2}[/tex]-[tex](28-2*-4)^{1/4}[/tex]=0

[tex](-6)^{1/2}[/tex] -[tex]36^{1/4}[/tex]=0

[tex](-6)^{2}[/tex] - [tex]6^{1/2}[/tex]=0

Which is not possible and a negative integer is not present in the square root.

Therefore we get the extraneous solution of the equation which is x= -4, and x = 6 is the solution of the equation.

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The value of constant  variation is 18.

A key integer with a stable value determined by a clear specification is referred to as a mathematical constant.

connection in mathematics between two variables that may be described by an equation in which the sum of their products equals a constant

Inverse variation is y = k. 1/x

given y = 3

x = 6

So, 3 = k. 1/6

So, the value of k = 18.

We can conclude that the value of constant variation is 18.

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The given 4th order polynomial equation only has real solutions,  x = √7  and x = –√7

The given equation is x⁴-14 x²+49 = 0.

This is a 4th degree polynomial equation.

Let p = x².

Then we can write x⁴-14 x²+49 = 0 as:

p²- 14p +49 = 0

This is a quadratic equation.

There are three ways to find the solutions of a quadratic equation:

Notice that p²- 14p +49 = 0 can be written as a perfect square:

(p - 7)² = 0

Hence, it has only single real solution:

p - 7 = 0

p = 7

Substitute p = 7 into p = x², we get:

x² = 7

x = ± √7

The solutions are, therefore,  x = √7  and x = –√7

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Factor the expression 25-40 x+16 x² is [tex](4x-5)^2[/tex]

On rearranging the equation , we get

   [tex]16x^2-40x+25=0[/tex]        ...(1)

To split the middle term of the quadratic equation, we need to look at the middle term of the quadratic equation under consideration.

Midterm is 40 x  , to split the middle term, use the sum-and-product form which is

" The sum-product form is the product of intermediate terms after splitting and must  equal a × c and the sum must equal b "

    [tex]f(x)=16x^2-40x+25[/tex]

here a = 16 , b = -40 and c = 25

We need to divide into 40x  in two parts

40x = 20x + 20x

The product of the terms is [tex]16\times25=400[/tex]

Now we can rewrite 40x as 20x + 20x

Putting in equation (1) , we get

      [tex]16x^2-(20+20)x+25=0\\\\(16x^2-20x)-(20x-25)=0\\\\4x(4x-5)-5(4x-5)=0\\\\(4x-5)(4x-5)=0[/tex]

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Answer:  22.8888888889 but rounded 22.9

Step-by-step explanation: This is so because when you turn 23 to ninths you get 207/9 - 1/9 then put into decimal form, 22.8888888889 or 2.9

1) m∠4 + m∠7 = 180° (given)

2) ∠4 is congruent to ∠6 (vertical angles)

3) m∠4 = m∠6 (definition of congruent angles)

4) m∠6 + m∠7 = 180° (substitution)

5) c is parallel to d (converse of same side interior angles theorem)

Answer:

270

Step-by-step explanation:

(∛9)³ × (√30)²

9 × 30 = 270

I hope this helps!

Answer:

Answer:

270

Step-by-step explanation:

(∛9)³ × (√30)²

9 × 30 = 270

Step-by-step explanation:

Answer:

y=-3x-17

Step-by-step explanation:

y=mx+b   (slope-intercept form)           b=y-intercept= (0,?)  m=slope

y=-3x+b  substitute values

y+3x=b isolate b to find b

1+3(-6)=b substitute given ordered pair

-17=b

y=-3x-17

Answer:

2 2/4 because i just know the answer

Using the properties of logarithm the value of the expression is   [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]

According to the question the expression that we have been given is

         =  [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75}[/tex]

Now solving it step by step using the properties of logarithm which are

      [tex]log a^{m} = m*loga[/tex] ,  [tex]log \frac{x}{y} = logx - logy[/tex]  and [tex]log_{a} a = 1[/tex]

As √75 is also equal to [tex](75)^{1/2}[/tex]. Thus equating in the equation we get

Therefore ,  

           [tex]= \frac{1}{2}log_{5} 15 - log_{5} 75^{\frac{1}{2} } \\= \frac{1}{2}log_{5} 15 - \frac{1}{2} log_{5}{75} \\[/tex]  

As we can see that 1/2 is common in both the terms we will take out 1/2 common from both terms, by which we get

           [tex]= \frac{1}{2} [log_{5} 15 - log_{5}{75} ] \\= \frac{1}{2} [log_{5} \frac{15}{75} ] \\\= \frac{1}{2} [log_{5} \frac{1}{5} ] \\= \frac{1}{2} [log_{5} 1 - log_{5}{5} ]\\= \frac{1}{2} [0 - 1]\\= -\frac{1}{2}[/tex]

Hence using the properties of logarithm the value of the expression is  [tex]\frac{1}{2}log_{5} 15 - log_{5} \sqrt{75} = -\frac{1}{2}[/tex]

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The equation of the required line parallel to the given line is y = -x - 10.

Slope can be defined as the rate of change.

According to the given question we have to write an equation of a line parallel to the line y = - x - 1 that goes through the point (-2,-8).

We know that lines are parallel because of the same slope they have.

So, the required line also have a slope(m) = -1.

∴ The equation of the required line in slope intercept form can be written as y = mx + b.

Putting the value of given points (-2, -8) in (x,y) t evaluate y intercept b.

So, - 8 = (-1)(-2) + b.

- 8 = 2 + b.

b = -10.

∴The equation of the required line in slope intercept form is  y = -x -10.

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The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)

In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.

Now we proceed to check the expression for each case:

(x, y) = (1, - 5)

- 5 + 4 = (3 / 5) · (1 - 2)

- 1 = (3 / 5) · (- 1)

- 1 = - 3 / 5     (FALSE)

(x, y) = (- 8, - 12)

- 12 + 4 = (3 / 5) · (- 8 - 2)

- 8 = (3 / 5) · (- 10)

- 8 = - 30 / 5

- 8 = - 6    (FALSE)

(x, y) = (- 3, - 8)

- 8 + 4 = (3 / 5) · (- 3 - 2)

- 4 = (3 / 5) · (- 5)

- 4 = - 3    (FALSE)

(x, y) = (12, 10)

10 + 4 = (3 / 5) · (12 - 2)

14 = (3 / 5) · 10

14 = 30 / 5

14 = 6     (FALSE)

(x, y) = (7, - 1)

- 1 + 4 = (3 / 5) · (7 - 2)

3 = (3 / 5) · (5)

3 = 3    (TRUE)

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).

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The area of the rectangle having three identical circles inside is calculated as: (16√3 + 32) mm².

Area of rectangle = (length)(width)

The image of the three identical circles in the rectangle has been labelled as shown in the diagram attached below.

We need to find the measure of the length and width of the rectangle.

Radius = AB = BD = DF = FG = CD = HI = 2 mm

Length of the rectangle = AB + BD + DF + FG = 2 + 2 + 2 + 2

Length of the rectangle = 8 mm

Width of the rectangle = CD + DH + HI

CD = 2 mm

HI = 2 mm

Use the Pythagorean theorem to find the measure of DH

DH = √(FH² - DF²)

FH = 2 + 2 = 4 mm

DF = 2 mm

Substitute

DH = √(4² - 2²)

DH = √(16 - 4)

DH = √12 = 2√3 mm

Width of the rectangle = CD + DH + HI = 2 + 2√3 + 2

Width of the rectangle = 2√3 + 4

Area = (2√3 + 4)(8)

Area = (16√3 + 32) mm²

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Answer:

$37.96

Step-by-step explanation:

$9.49 x 4 = $37.96

The domain of given points are :

IR x ≠ -1 , -2

Points of discontinuity - x = -2 ( non removable / asymptote )

                                         x = -1 ( removable / hole)

x - intercept = -1 , y -  intercept = 1/2

Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).

y=x+1/x²+3 x+2

= x+1/x²+2x+x+2

=  x+1/(x+2)(x+1)

The domain of given points are :

IR x ≠ -1,-2

Points of discontinuity - x = -2 ( non removable / asymptote)

                                       x = -1 ( removable / hole)

x-intercept :

0 = x + 1

x = -1

y - intercept :

0+1 / (0+1)(0+2) = 1/2

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Every conditional has two parts they are hypothesis and conclusion.

The hypothesis is the first part of a conditional statement 'if' and conclusion is the last part of a conditional statement 'then'

According to the given statement every conditional has two parts a hypothesis and a conclusion.

Conditional starts with if and ends with then.It is used to express possible situations.

For example-: if the two angles are complementary then their sum is 90°.

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Answer:

Step-by-step explanation:

39.16 approx. is the value of x in  [tex]e^{\frac{x}{4} -8}[/tex] = 6 solved by using natural logarithm

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to find x in [tex]e^{\frac{x}{4} -8}[/tex] = 6 using natural logarithm

⇒  [tex]e^{\frac{x}{4} -8}[/tex] = 6

⇒ [tex]\frac{x}{4} - 8[/tex] = ㏑6

⇒  [tex]\frac{x}{4}[/tex] = ㏑6 + 8

⇒ x = ln(1296) + 32

      = 39.16 approx.

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Use natural logarithms to solve each equation.

[tex]e^{\frac{x}{4} -8}[/tex] = 6

Answer:

16.3p + (-10)

Step-by-step explanation:

Answer:

170 minutes

Step-by-step explanation:

So if there was two 45 min work outs in a week and she left those 10 mins early that was two 35 min work outs and then there was 4, 30min work outs and she left those 5 mins early so 4, 25min workouts so its 35+35+25+25+25+25.

Answer:

11a^2 + 122a + 11

Step-by-step explanation:

First, multiply a by 11a, which gives you 11a^2. Then you multiply 11 to 11a, which gives you 122a, then last just multiply 11 to 1 and you get 11. Hope this helps.

The real square root of the number 0.49 is 0.7

0.49 can also be presented as, 49* [tex]10^{-4}[/tex]

The square root of   49* [tex]10^{-2}[/tex]

= [tex]\sqrt{49}[/tex] * [tex]\sqrt{10} ^{-2}[/tex]

= 7 * [tex]10^{-2}[/tex]

=0.7

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12

Step-by-step explanation:

n + (2/3)n = 2n - 4

(5/3)n = 2n - 4

(5/3)n - 2n = -4

(-1/3)n = -4

n = 12

With an equilateral triangle, only two circles are formed.

What kind of polygon is carved into the circle?

Therefore, with an equilateral triangle, only two circles are formed.

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