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In a science experiment, a student concluded that a ray has to travel a distance from one corner at the
top of the rectangular prism to the opposite side where the surface touching the floor is intersected. If
the length, width, and height of the prism are given as 24 inches and 8 inches, 6 inches respectively,
what is the distance travelled by the ray?


**TEACHER SAID NOT A OR D**

Answer:

864.

Step-by-step explanation:

1) the required volume can be calculated according to the formula (see also the attachment):

V=Area(BKS)*height;

2) if to see the triangle ABC (see the attachment), then m∠C=90°; m∠A=30° and m∠B=60°;

3) the length of AC=BC*cot(m∠A)=2√3*√3=6 [cm];

4) if AC=6 [cm], then BS=36-2*BC=24 [cm];

5) in the equilateral triangle BKS BS=BK=KS=24 [cm], then the Area(BKS)=BS²√3/4=144√3 [cm²];

6) if the height is 2√3 [cm] and Area(BKS)=144√3 [cm²], then

V=144√3*2√3=864 [cm³].

The value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

For Geometric sequence, the value of  geometric mean can be found out using the following formula,

[tex]x=\sqrt{ab}[/tex]

Here, (a and b) are the two terms of geometric sequence.

The geometric mean of a and 12 is 8√6. Thus,

[tex]x=8\sqrt{6}[/tex]

[tex]b=12[/tex]

Put this value in formula to find the value of a,

[tex]8\sqrt{6}=\sqrt{a\times12}\\[/tex]

Square both side of equation,

[tex](8\sqrt{6})^2=(\sqrt{a\times12})^2\\64\times6=12a\\a=\dfrac{64\times6}{12}\\a=32[/tex]

Thus, the value of a, when the geometric mean of two numbers a and 12 is 8√6 is equal to the number 32.

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1 kilometer = 1000 meters

5000 meters / 1000 = 5 kilometers

5 kilometers x 2 times per day = 10 kilometers per day.

answer: D) 10 kilometers

Answer:

vp=1186380cm^3

Step-by-step explanation:

Answer:

Step-by-step explanation: hi it’

Answer:

  (a) higher by 0.25%

Step-by-step explanation:

The error in the estimate is found by comparing the estimated rate to the actual rate.

__

The rate of estimated closing costs is ...

  (estimated cost)/(home cost) × 100% = 6375/170000×100% = 3.75%

The actual rate is 4.00%.

  actual - estimate = 4.00% -3.75% = 0.25%

The actual closing costs were higher than the estimate by 0.25%.

Answer:

612 centimeters = 612 : 10 = 61,2 decimeters

Answer:

Step-by-step explanation:

f(x) = x/(x-7)

The domain is C

7/(7-7) = 7/0 = undefined

Explanation:

By definition, the floor is assumed to be level and that means the floor is at a 0 degree angle. The shelf must also have this same angle relative to the floor so we have the shelf and floor as parallel planes. For more info, check out the converse of the corresponding angles theorem.

Answer:

A. 90°

Step-by-step explanation:

A perpendicular on a straight line creates 2 right angles.

We know the value of a right angle is 90°.

Hence :

∠2 = 90°

Answer:

[tex]-\dfrac{b^2}{16a^4}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{(2a)^{-2}b^5}{-4a^2b^3}[/tex]

[tex]\textsf{Apply the exponent rule}\quad (ab)^c=a^c \cdot b^c:[/tex]

[tex]\implies \dfrac{2^{-2}a^{-2}b^5}{-4a^2b^3}[/tex]

Separate the variables:

[tex]\implies \dfrac{2^{-2}}{-4}\cdot \dfrac{a^{-2}}{a^2}\cdot \dfrac{b^5}{b^3}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{2^{-2}}{-4}\cdot a^{-2-2}\cdot b^{5-3}[/tex]

[tex]\implies \dfrac{2^{-2}}{-4}\cdot a^{-4}\cdot b^{2}[/tex]

[tex]\textsf{Apply the exponent rule}\quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{-4(2^2)}\cdot \dfrac{1}{a^4}\cdot b^{2}[/tex]

[tex]\implies -\dfrac{1}{16}\cdot \dfrac{1}{a^4}\cdot b^{2}[/tex]

Simplify:

[tex]\implies -\dfrac{b^2}{16a^4}[/tex]

Answer:

b

Step-by-step explanation:

Answer:

Simplified answer = C = $0.65m + $24.65

Step-by-step explanation:

Add the two initial charges together (from the insurance and the standard charge) and you get $24.65.  Then add the two charges together for each mile which is $0.65 per mile.  Therefore, the total charge on the car is $24.65 + 65 cents every mile driven.

Answer:

S = $76 and P = $236

Step-by-step explanation:

Let the sodas be S and the patties P. So

4S + 6P = 840  and 5S + 5P = 800

By substitution method we will have the solution

5S + 5P = 800

5S = 800 - 5P

S = 800 - 5P

          5

We'll sustitute S with this equation

4S + 6P = 840

[tex]4(\frac{800 - 5P}{5})[/tex] + 6P = 80

4(800 - 5P) + 6P(5) = 840

3200 - 20P + 30P = 840

-20P + 30P = 840 - 3200

10P = -2360

P = -2360

        10

P = -236

Since the cost of the patty can't be negative, P = $236

Now that we know the cost of the patty, we can calculate the cost of the soda

S = 800 - 5P

          5

S = 800 - 5(236)

             5

S = 800 - 1180

             5

S = -380

        5

S = -76

Here S can't be negative, so S = $76

Answer:

8%

Step-by-step explanation:

assume simple interest rate = r

interest = 1000 * 4 * r = 320

r = 320/4000 = 0.08 = 8%

The perimeter of the polygon of sides as 9/2, 17/2, 52/5, 52/5, 64/5, 59/4 is 1227 /20.

The perimeter of the polygon is the measure of the sum of the sides of the given figure.

The sides are given as 9/2, 17/2, 52/5, 52/5, 64/5, 59/4

The perimeter of the polygon = 9/2 + 17/2 + 52/5 + 52/5 + 64/5 + 59/4

                                                  = 26/2 + 168/5 + 59/4

                                                  = 111/4 + 168/5

                                                  = 555 + 672 / 20

                                                  = 1227 /20

Thus, The perimeter of the polygon is 1227 /20.

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Answer: 475 Add 5 more.

Step-by-step explanation:

The value of the given expression in terms of s will be [(s + 0.602)/3].

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

If [tex]\log(16) = s[/tex]

Then the value of the given expression in terms of s is given below.

[tex]\dfrac{2}{3} \times \log(6400) - \dfrac{1}{3} \times \log(1600)[/tex]

We know the property of the logarithm.

[tex]\log 100 = 2[/tex]

Then we have

[tex]\rm \rightarrow \dfrac{2}{3} \times \log(6400) - \dfrac{1}{3} \times \log(1600)\\\\\\\rightarrow \dfrac{2}{3} \times ( \log 16 + \log 4 + \log 100 ) - \dfrac{1}{3} \times (\log 16 + \log 100)\\\\\\\rightarrow \dfrac{2}{3} \times (s + 0.602+2) - \dfrac{1}{3} \times (s + 2)\\\\\\\rightarrow \dfrac{2}{3} \times (s + 2.602 ) - \dfrac{1}{3} \times (s + 2)\\\\\\\rightarrow \dfrac{2 (s + 2.602) - (s - 2)}{3} \\\\\\\rightarrow \dfrac{s + 0.602}{3}[/tex]

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Step-by-step explanation:

the error:

it is stated that

[tex]\frac{5x}{x+7} +\frac{7}{x} = \frac{5x}{x+7} +\frac{7(7)}{x+7}[/tex]

subtract (5x)/(x+7) from both sides

[tex]\frac{7}{x} = \frac{7(7)}{x+7}[/tex]

multiply both sides by x + 7

7(x+7) = 49x

7x + 49 = 49x

subtract 7x from both sides to isolate x and its coefficient

49 = 42x

thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must always be true, so this is wrong

the solution:

we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x  by 1.

anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.

(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get

[tex]\frac{7}{x} = \frac{7(x+7)/x}{x+7}[/tex]

substitute this for 7/x in our original problem

[tex]\frac{5x}{x+7} +\frac{7(x+7)/x}{x+7} = \frac{5x}{x+7} +\frac{(7x+49)/x}{x+7} = \frac{5x}{x+7} +\frac{7+49/x}{x+7} = \frac{5x+7+49/x}{x+7}[/tex]

Answer:

Step-by-step explanation:

There are 10 girls in an athletics club.

e ratio of girls to boys is 5:3.

w many boys are there?

we can solve with an equation

10 : x = 5 : 3

x = 10 * 3 : 5

x = 30 : 5

x = 6

---------------

Step-by-step explanation:

1 and 2 are negative

3 and 5 are none

4 and 6 are positive

Answer:

[tex]4.25-\sqrt{3}.[/tex]

Step-by-step explanation:

1) tan45=1; sin60=√3/2; cot30=√3; sec45=√2, then

2) 3-0.75-√3+2=4.25-√3 (it is ≈2.5179492).

Answer:

32.5 hours

Step-by-step explanation:

Total hours

6.5 x 5

32.5 hours

If the dimension of the rectangular prism will be 11 by 8 by 4. Then the volume of the rectangular prism will be 352 cubic yards.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

A rectangular prism and its net are shown below.

Then the volume of the rectangular prism will be

Volume = LWH

where

Width (W) = 8 yd

Length (L) = 11 yd

Height (H) = 4 yd

Then the volume will be

Volume = 11 × 8 × 4

Volume = 352 yd³

Then the volume of the rectangular prism will be 352 cubic yards.

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Answer:

The bigger angle is 57 degrees

The smaller angle is 33 degrees

Step-by-step explanation:

complimentary is that two angles will add up to 90 degrees

Lets say one angle is x, and the other is y.

the smaller angle is x, so it is be x-24degrees

x+(x-24)=90

2x=114

x=57 degrees

y=33degrees

A percentage is a way to describe a part of a whole. The amount of water in the bottle originally is 800 mm.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Let the water in the bottle at the very initial be x.

Given that after reduction the amount of water in the bottle is 120 millimetres, also, the water is reduced by 85%, therefore, the amount of water that will be in the bottle is 15% of the original.

Water in the bottle = 15% of x

120 mm = 0.15 × x

x = 800 mm

Hence, the amount of water in the bottle originally is 800 mm.

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3 1/2 = 7/2

7/2 ÷ 1/4

7/2 × 4/1

14/2

7 pieces

hope it helps...!!!