A student performed the following steps to find the solution to the equation x^2-2x-8=0. Where did the student go wrong?

Step 1. Factor the polynomial into (x-4) and (x-2)
Step 2. x-4=0 and x-2=0
Step 3. x=4 and x=3

A. The student did not make any mistakes, the solution is correct
B. in step 1
C. in step 2
D. in step 3

We know from physics class that the formula for distance of a linear motion is given as:

d = v t

Where,

d = distance travelled

v = average velocity

t = time it took to reach the destination

Since the distance going to the office and back is just similar, therefore we can simply equate the two:

v1 t1 = v2 t2

Where 1 signifies going to the office and 2 signifies going back from the office. Therefore this yields to:

v1 * 5 hours = 65 mph * 4 hours

v1 = 52 mph

Answer: The average speed going to the office is 52 mph.

The average speed of Jill's trip to the ferry office was 52 mph, calculated by dividing the distance of 260 miles by the time of 5 hours.

To find the average speed of the trip there, we need to know the distance Jill traveled to the ferry office. Since she averaged 65 mph on the return trip which took 4 hours, the distance is calculated as speed x time, which equals 260 miles (65 mph x 4 hours).

The distance to the ferry office is the same as the distance back, so Jill also traveled 260 miles on the trip there. Given that the trip there took 5 hours, we can find the average speed by dividing the distance by the time. The average speed is 260 miles / 5 hours, which equals 52 mph.

Final answer:

The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.

Explanation:

To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:

28 = 2 x 2 x 7

The smallest power of 3 that is common is just 3.

Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.

In a circle, the point of symmetry is the centerpoint; any straight line that passes through this point is a line of symmetry. The standard form of equation of a circle is given as:

(x – h)^2 + (y – k )^2 = r^2

Where,

h = x coordinate of the center

k = y coordinate of the center

In the problem statement, we are given that the equation of the circle is:

(x – 5)^2 + (y + 4)^2 = 25

So identifying the variables from the standard form of equation of a circle:

h = 5

k = - 4

Therefore the point of symmetry is (5, -4).

Answer:

We have to find a graph which represents a  reflection of f(x) = 1/10 (10)x across the y-axis.

As we know that on reflecting the graph across the y-axis the x-coordinate of the point changes to opposite sign nut with same magnitude and the y-coordinate remains same.

Hence, the function f(x) is transformed to:

[tex]f(x)=\dfrac{1}{10}\times 10^{-x}[/tex]

The graph of the function passes through the point (0,0.1) and is a strictly decreasing function.

and the end behavior of the graph is that:

when x→∞    f(x)→ 0

when x→ -∞    f(x) → ∞

In this scenario involving an elevator's movement, the negative velocity indicates downward motion and corresponds to the slope in the equation of a line. By applying the slope and initial conditions, we calculated that Monica was initially 470 feet above the ground, which is the y-intercept in the slope-intercept form.

The student's question involves understanding the implications of negative velocity in a real-world situation involving an elevator, calculating an initial position based on this velocity and elapsed time, and tying these concepts to algebraic representations in slope-intercept form.

The inheritance problem deals with distributing Rs. 300,000 among 4 sons and 3 daughters after a Rs. 80,000 debt is paid. Using algebra and ratios, it is determined that each daughter receives Rs. 20,000 while each son receives Rs. 40,000.

The situation given is that a person dies leaving behind an inheritance of Rs. 300,000, which must be divided among 4 sons and 3 daughters such that each son receives double what each daughter gets. Additionally, a debt of Rs. 80,000 is to be taken out of the inheritance before distribution.

First, we need to consider the debt. Subtracting the debt from the total inheritance, we have:

Total inheritance after debt = Rs. 300,000 - Rs. 80,000 = Rs. 220,000

Now, let's assume each daughter gets x amount. Therefore, each son gets 2x the amount. We can set up the equation accounting for all sons and daughters:

3x (daughters' shares) + 4(2x) (sons' shares) = Rs. 220,000

Simplifying:

3x + 8x = Rs. 220,000

11x = Rs. 220,000

x = Rs. 20,000 (share of each daughter)

Consequently, the share of each son will be double that of a daughter, which is:

2x = 2(Rs. 20,000) = Rs. 40,000 (share of each son)

Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.

What is Scientific notation ?

Scientific notation is the way to express the large value in short form. The number in scientific notation have two parts. The digits (decimal point will place after first digit) × 10 ( the power which put the decimal point where it should be).

Here it is given that The distance between the earth and the sun is approximately 93 million miles and 1 million miles equals 1,00,000 miles.

Now, writing 93 millions Scientific notation by writing 1,00,000 in power of 10 and 93 as 9.3 x 10 :

93 million miles = 9.3 x 10 x 1,00,000

                          = 9.3 x 10^7

Therefore, Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.

Read more about Scientific notation at:

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The distance between the Earth and the Sun (93 million miles) in scientific notation is [tex]9.3 *10^7 miles[/tex].

To write the distance between the Earth and the Sun (93 million miles) in scientific notation, follow these steps:

First, write 93 million as a standard numeral: 93,000,000.

Next, identify how many places to move the decimal point to get a number between 1 and 10. For 93,000,000, the decimal point moves 7 places to the left.

After moving the decimal point in 93,000,000.00 by 7 places, you get 9.3, which is between 1 and 10. This is known as mantissa.

Mantissa = 9.3

Write the number as a coefficient multiplied by 10 raised to the number of places the decimal was moved. This is called the exponent term. Exponent term = [tex]10^7[/tex].

Scientific notation of a number = Mantissa*Exponent term

So, 93,000,000 = [tex]9.3 *10^7[/tex].

Therefore, the distance between the Earth and the Sun in proper scientific notation is [tex]9.3 *10^7 miles[/tex].

The value of the house in 8 years. (D) ≈ $296,282

The given parameters are:

Initial value, a = $225,000

Rate, r = 3.5%

The scenario is an illustration of an exponential growth function.

So, we have:

V(x) = a * (1 + r)^x

Substitute known values

V(x) = 225000 * (1 + 3.5%)^x

This gives

V(x) = 225000 * (1.035)^x

Next, we plot the graph of V(x)

See attachment

From the attached graph

V(x) = $296,282

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Answer:

i) t = 5

ii) a = 3√7

iii)  x =3√13

Step-by-step explanation:

We have right triangles.

Know the two sides of the triangle and need to find the third missing side.

In order to find the third side of the right triangle, we use pythagoras theorem.

It is,

(Hypotenuse)² = (base)² + (height)²

i)

13² = 12² + t²

169 = 144 + t²

t² = 25

t = 5.

ii)

12² = 9² + a²

144 = 81 + a²

144 - 81 = a²

a² = 63

a = √63

iii)

x² = 9² + 6²

x² = 81 + 36

x² = 117

x = √117

x = 3√13

Using the friction equation mg sin A = μmg cos A and the given coefficient of friction (μ) of 0.17, the angle at which a waxed wood block begins to slide on wet snow is calculated to be approximately 9.6°.

To find the angle at which a waxed wood block on an inclined plane of wet snow begins to slide, we can use the equation mg sin A = μmg cos A, where A is the angle of inclination, m is the mass of the block, g is the acceleration due to gravity, and μ is the coefficient of friction. Since the mass (m) and gravity (g) are both common factors on each side of the equation, they can be canceled out, leaving us with tan A = μ, where tan A is the tangent of the angle A, and μ is the coefficient of friction (0.17 in this case). Solving for A gives us A = arctan(μ). So, A = arctan(0.17), which calculates to approximately 9.6°. This is the angle at which the block begins to slide.