Three cities lie along a perfectly linear route: Springfield, Clarksville, and Allentown. Molly lives in Springfield and works in Allentown. She makes it to work using two gallons of gas in her car. Her friend Edgar lives in Allentown and works in Clarksville. It takes Edgar one gallon of gas to get to work. If Molly's car averages 26 miles per gallon, and Edgar's car averages 17 miles per gallon, about how far apart are Springfield and Clarksville?

Final answer:

Yes, a segment can have more than one bisector. A bisector divides a segment into two equal parts.

Explanation:

Yes, a segment can have more than one bisector. A bisector of a segment is a line, segment, ray, or plane that divides the segment into two equal parts. Each bisector intersects the segment at its midpoint. Since the definition of a bisector doesn't specify uniqueness, there can be infinitely many bisectors of a given segment, especially in a two-dimensional plane.

For example, if you have a horizontal line segment, you could have one vertical bisector that divides it in the middle, but you could also have an infinite number of bisectors at various angles that also pass through the midpoint. Thus, there are multiple bisectors for any given line segment. Thus, consider two points A and B on a straight line segment AB. According to geometric principles, you can draw a perpendicular bisector that would be unique in the sense that it's the only line that both bisects AB and is perpendicular to it

The equation of the line in standard form that has a y-intercept of -3 and passes through the point (3, 0) is y = x - 3.

The standard form of a line can be found using the formula y = mx +b, where 'm' is the slope and 'b' is the y-intercept. The y-intercept in this problem is -3, but we need to find the slope to complete the standard form of the line. Since our line passes through the point (3,0) and (0,-3), the slope, m, can be found by using the formula (y2-y1)/(x2-x1), which gives us a slope of 1. So the equation of our line in standard form is y = x - 3.

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Final answer:

To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation and solve the resulting quadratic equation. The solutions are x = ±√2.

Explanation:

To find the solutions of the equation 4x^4 - 4x^2 = 8, we can rearrange the equation to get 4x^4 - 4x^2 - 8 = 0. This is a quadratic equation in terms of x^2. We can solve this quadratic equation by factoring or by using the quadratic formula.

Factoring the equation, we get (2x^2 - 4)(2x^2 + 2) = 0. Setting each factor equal to zero, we have 2x^2 - 4 = 0 and 2x^2 + 2 = 0.

Solving each equation separately, we get x^2 = 2 and x^2 = -1. Taking the square root of both sides, we get x = ±√2 and x = ±i. Therefore, the solutions of the original equation are x = ±√2.

Final answer:

To solve the student's algebra problem, we defined variables, set up an equation based on the given conditions, and then solved for the larger number. Ultimately, we found the two numbers to be 33 and 16.

Explanation:

The student asked a problem that involves finding two numbers given that their sum is 49 and the smaller number is 17 less than the larger number. To solve this problem, we will use algebra.

Let the larger number be x and the smaller number be x - 17. According to the problem, the sum of these two numbers is 49:

x + (x - 17) = 49

Combine like terms: 2x - 17 = 49

Add 17 to both sides: 2x = 66

Divide by 2: x = 33

Since the larger number is 33, the smaller number is 33 - 17, which is 16.

Therefore, the two numbers are 33 and 16.

Answer:  Option 'C' is correct.

Step-by-step explanation:

Since we have given that

[tex]S_n=\sum^{\infty}_{n=1}4(\dfrac{1}{4})^{n-1}[/tex]

We need to find the value of S₄.

So, it means sum of 4 terms.

Here it form a geometric series:

a = 4 = first term

r = [tex]\dfrac{1}{4}[/tex] = Common ratio

And sum of n terms whose ratio is less than 1 is given by

[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\S_4=\dfrac{4(1-\dfrac{1}{4}^{4})}{1-\dfrac{1}{4}}\\\\S_4=\dfrac{4(1-0.25^4)}{1-0.25}\\\\S_4=\dfrac{4(1-0.0039)}{0.75}\\\\S_4=5.3125\\\\S_4=5\dfrac{5}{16}[/tex]

Hence, Option 'C' is correct.

Answer:  Option 'C' is correct.

Step-by-step explanation:

The solution of the given quadratic equation is x = 1.37, - 1.37.

"A quadratic equation is an algebraic equation of the second degree in any variable."

Given quadratic equation:

9x² = 17

⇒ x² = (17 / 9)

⇒ x = ± √(17 / 9)

⇒ x = ± (√17) / 3

⇒ x = 1.37, - 1.37

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Step-by-step explanation: Apex 9/25/19

Answer:

1.1 × 103 feet per second

The greatest perfect square that is a factor of 650 is 25

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves,

Prime Factorization is defined as any number that may be expressed as a product of prime numbers that has been said to be prime factorized. Any integer with exactly two factors 1 and the number itself. is said to be a prime number.

Given the number is 650

To determine the greatest perfect square that is a factor of the number 650.

We need to write 650 as the product of its prime factors, which is 650.

⇒ 650 = 2×5×5×13

So the pair is 5×5 which is 5² or 25

Hence, the greatest perfect square that is a factor of 650 is 25

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Answer:

that persons work is correct im pretty sure

Step-by-step explanation:

The exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\(\frac{2}{27} (10\sqrt{10} - 1)\)[/tex].

To find the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex], we can use the formula for arc length of a curve:

[tex]\[ L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx \][/tex]

where a and b are the lower and upper bounds of the interval, respectively.

First, we need to find [tex]\(\frac{dy}{dx}\)[/tex], which represents the derivative of y with respect to x:

[tex]\[ \frac{dy}{dx} = \frac{d}{dx}(3 + 2x^\frac{3}{2}) = 0 + 3x^\frac{1}{2} = 3\sqrt{x} \][/tex]

Next, we substitute this derivative into the formula for arc length:

[tex]\[ L = \int_{0}^{1} \sqrt{1 + (3\sqrt{x})^2} dx = \int_{0}^{1} \sqrt{1 + 9x} dx \][/tex]

Now, we need to integrate [tex]\(\sqrt{1 + 9x}\)[/tex]L with respect to \(x\). We can do this by making a substitution. Let u = 1 + 9x, then du = 9dx and \(dx = \frac{du}{9}\). Substituting these into the integral, we get:

[tex]\[ L = \frac{1}{9} \int_{1}^{10} \sqrt{u} du \][/tex]

Now, we can integrate [tex]\(\sqrt{u}\)[/tex]:

[tex]\[ L = \frac{1}{9} \left[\frac{2}{3}u^\frac{3}{2}\right]_{1}^{10} = \frac{2}{27} \left[10^\frac{3}{2} - 1^\frac{3}{2}\right] \][/tex]

[tex]\[ L = \frac{2}{27} (10^\frac{3}{2} - 1) \][/tex]

[tex]\[ L = \frac{2}{27} (10\sqrt{10} - 1) \][/tex]

So, the exact length of the curve [tex]\(y = 3 + 2x^\frac{3}{2}\)[/tex] over the interval [tex]\(0 \leq x \leq 1\)[/tex] is [tex]\( \frac{2}{27} (10\sqrt{10} - 1) \)[/tex].

Answer:

b.1 over 3 to the 5th power.

Step-by-step explanation:

We are given that an expression

[tex]3^4\cdot 3^{-9}[/tex]

We have to find that which expression is equivalent to given expression

[tex]3^4\cdot 3^{-9}[/tex]

We know that [tex]a^b+a^c=a^{b+c}[/tex]

Using this identity

Then, we get [tex]3^4\cdot 3^{-9}=3^{4-9}=3^{-5}[/tex]

[tex]3^4\cdot 3^{-9}=\frac{1}{3^5}[/tex]

Using [tex]a^{-b}=\frac{1}{a^b}[/tex]

Hence, option b is true.

Answer:b.1 over 3 to the 5th power.

Answer:

False it never will

Step-by-step explanation:

Got it right on my test.

Answer-

The first graph represents [tex]f(x)=2(3)^x[/tex]

Solution-

The given function is,

[tex]f(x)=2(3)^x[/tex]

Putting x = 1,

[tex]f(x)=2(3)^1=2(3)=6[/tex]

So, the point (x, f(x)) i.e (1, 6) must satisfy or lie on the curve of the function.

Only in case of the first graph, the point (1, 6) lies on the curve.

Therefore, the first graph represents the function [tex]f(x)=2(3)^x[/tex] correctly.

Answer: the first answer is correct

Answer:

It take 119.954 years to earn $ 3000 without depositing any additional funds.

Step-by-step explanation:

Given:

Principal Amount, P = $ 150

Amount, A = $ 3000

Rate of interest, R = 2.5% compounded monthly.

To find: Time, T

We use formula of Compound interest formula,

[tex]A=P(1+\frac{R}{100})^n[/tex]

Where, n is no time interest applied.

Since, It is compounded monthly.

R = 2.5/12 %

n = 12T

[tex]3000=150(1+\frac{\frac{2.5}{12}}{100})^{12T}[/tex]

[tex]\frac{3000}{150}=(1+\frac{2.5}{1200})^{12T}[/tex]

[tex]20=(1+\frac{2.5}{1200})^{12T}[/tex]

Taking log on both sides, we get

[tex]log\,20=log\,(1+\frac{2.5}{1200})^{12T}[/tex]

[tex]1.30103=12T\times\,log\,(1.002083)[/tex]

[tex]T=\frac{1.30103}{12\times\,log\,(1.002083)}[/tex]

[tex]T=119.954[/tex]

Therefore, It take 119.954 years to earn $ 3000 without depositing any additional funds