Choose the justification for each step in the solution for equation 6X -9 equals 45

The smaller triangular prism's surface area is calculated by squaring the scale factor of 1/5 (which is 1/25) and then multiplying it by the surface area of the larger prism. The result is 2.4 square centimeters.

The question asks about the surface area of a similar but smaller triangular prism given that the larger prism has a surface area of 60 square centimeters and the scale factor of the smaller prism is 1/5. When the size of an object changes by a scale factor, the surface area changes by the square of that scale factor. For the smaller triangular prism, the surface area will be the square of 1/5, which is 1/25, times the surface area of the larger prism.

To calculate it:

Therefore, the surface area of the similar smaller triangular prism by the given scale factor is 2.4 square centimeters.

Answer: c

Step-by-step explanation: hope this helps

The distance that a tortoise will cover in 6 hours is:

                        16.47735 feet.

It is given that :

A tortoise travels 11 feet in one hour.

In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour.

[tex]11+\dfrac{1}{3}\times 11\ feet[/tex]

which is equal to:

[tex]11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11\ feet[/tex]

[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11+\dfrac{1}{3^5}\times 11\ feet=16.47735\ feet[/tex]

                     Hence, the answer is:

                               16.47735 feet

A) Consider the equation [tex]10x^2-3x-1=0[/tex]

We have to describe the solutions to this equation.

We will determine the radicand = [tex]b^2-4ac[/tex]

= [tex](-3)^2 - 4(10)(-1) = 9+ 40 = 49[/tex] which is greater than zero,

Therefore, the given equation ha real roots.

B) Consider the equation [tex]16x^2-2x-5=0[/tex]

We will use middle splitting term method to solve this equation.

[tex]16x^2+8x-10x-5 =0[/tex]

[tex]8x(2x+1) -5(2x+1)=0[/tex]

[tex](2x+1)(8x-5)=0[/tex]

So, [tex]2x+1=0[/tex]

[tex]x = \frac{-1}{2}[/tex] and [tex]x = \frac{5}{8}[/tex]

I chose this method, because this is more easier and takes less time.

Here, we need to find express 0.2444... as a fraction in simplest form.

Let the fraction be expressed as x

Now,

x = 0.2444....

Since, x is recurring in 1 decimal places, we multiply it by 10.

10x = 2.4444....

From left hand-side, x is subtracted and from 0.24444... from right hand side

10x - x = 2.4444.... - 0.24444....

So now,

9x = 2.2

x = [tex] \frac{2.2}{9} [/tex]

x = [tex] \frac{22}{90} [/tex]

x = [tex] \frac{11}{45} [/tex]

Thus, fraction as simplest form = [tex] \frac{11}{45} [/tex]

The marked price of the shoes that Morgan bought at a 25% discount for $1000 is $1333.33. The calculation was done by dividing the discounted price by (1 minus the discount percentage in decimal form).

The question involves finding the marked price of an item given the discounted price and the discount percentage. Morgan paid $1000 for a pair of shoes after getting a 25% discount. To find the original marked price, we can use the formula:

Discounted Price = Marked Price × (1 - Discount Percentage)

Here, the Discounted Price is $1000, and the Discount Percentage is 25%, which is equivalent to 0.25 in decimal form.

By rearranging the formula to solve for the Marked Price, we get:

Marked Price = Discounted Price ÷ (1 - Discount Percentage)

Now we can calculate:

Marked Price = $1000 ÷ (1 - 0.25) = $1000 ÷ 0.75 = $1333.33

Therefore, the marked price of the shoes was $1333.33.

ANSWER

[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]

EXPLANATION

The given rational function is

[tex] \frac{5}{ \sqrt{11} - \sqrt{3}} [/tex]

We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of

[tex] \sqrt{11} - \sqrt{3} [/tex]

which is

[tex]\sqrt{11} + \sqrt{3} [/tex]

When we rationalize we obtain:

[tex] \frac{5( \sqrt{11} + \sqrt{3} )}{(\sqrt{11} - \sqrt{3} )( \sqrt{11} + \sqrt{3} )} [/tex]

The denominator is now a difference of two squares:

[tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]

We apply this property to get

[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{( \sqrt{11}) ^{2} - ( \sqrt{3}) ^{2} )} [/tex]

[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{11 - 3} [/tex]

This simplifies to

[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]

Or

[tex]\frac{5 } {8}\sqrt{11} + \frac{5 } {8}\sqrt{3} [/tex]

Answer:

B

Step-by-step explanation:

Final answer:

To find the area of the floor not covered by the rug, calculate the total floor area (120 square feet), subtract the rug's area (58.5 square feet), resulting in 61.5 square feet of uncovered floor.

Explanation:

To find the area of the floor that is not covered by the area rug, we first need to calculate the area of the entire floor and then subtract the area of the rug.

The area of the floor is calculated by multiplying its length and width. So for a floor that measures 10 feet by 12 feet, the area is 10 feet × 12 feet = 120 square feet.

The area rug measures 6.5 feet by 9 feet, which means its area is 6.5 feet × 9 feet = 58.5 square feet.

Now, subtract the area of the rug from the area of the entire floor to find the part of the floor not covered by the rug:

120 square feet - 58.5 square feet = 61.5 square feet.

Therefore, the area of the floor not covered by the rug is 61.5 square feet.

60 miles per hour
Or
60/1

Answer: The corresponding segments in the in the figure and the image are :

AB and EF,  

AD and EH,

CD and HG,

BC and FG,

Step-by-step explanation:

Given: Polygon ABCD is the result of a translation of polygon EFGH .

AB is parallel to DC in the pre-image.

We know that a translation is a rigid transformation which produces congruent images such that the corresponding segments have equal lengths.

So from the given statements the corresponding segments in the figure and the image are :

AB and EF,  

AD and EH,

CD and HG,

BC and FG,

The third fraction [tex]\frac{10}{80}[/tex] is not equivalent to the other options. The other options,  0.8, 80% and [tex]\frac{24}{30}[/tex] are all equivalent.

In mathematics, a fraction is a composition that represents a part of a whole. Fractions can be written in a few different ways, but the most frequent way is to utilize a numerator and a denominator. The numerator is the number of parts we have, and the denominator is the total number of parts. For illustration, the fraction 1/2 represents one part out of two.

Option 1 is 0.8.

Option 2 is 80% which is in fact equal to [tex]\frac{80}{100}[/tex] .

[tex]\frac{80}{100}[/tex] = [tex]\frac{8}{10}[/tex] = 0.8.

Option 3 is [tex]\frac{24}{30}[/tex] .

[tex]\frac{24}{30}[/tex] = [tex]\frac{8}{10}[/tex] = 0.8.

So, only the third option is not equivalent to the others.

Learn more about fractions here:

https://brainly.com/question/10354322

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