Simplify: log81/8 + 2log2/3 - 3log 3/2 +log 3/4​

Answer: D

Step-by-step explanation:

On USA test prep the answer is D.

Answer:

They are incorrect. The answer is actually 36.9

Step-by-step explanation:

Answer:

The height of the flagpole is 25 foot.

Step-by-step explanation:

Given:

Height of the stick = 5 foot

Shadow of the stick = 4 foot

Another one:

Height of the flagpole = 'x'

Shadow of the flagpole = 20 foot

Note:The shadows are formed at the same time of the day so the Sun makes an equal angle with both the situation.

Here from both ends it forms two similar triangles.

So,

We can say that:

⇒ [tex]\frac{Height\ of\ the\ flagpole}{Shadow\ of\ the\ flagpole}=\frac{Height\ of\ the\ stick}{Shadow\ of\ the\ stick}[/tex]

⇒ [tex]\frac{x}{20}=\frac{5}{4}[/tex]

⇒ [tex]\frac{x}{20}\times 20=\frac{5}{4}\times 20[/tex]

⇒ [tex]x=25[/tex] foot

So Darius estimated height of the flagpole = 25 foot.

Answer:

8

Step-by-step explanation:

The formula of volume is 4/3 × π × radius3.

volume of smaller sphere = 4/3 x 3.14 x 3*3*3

v = 113.04

volume of larger sphere = 4/3 x 3.14 x 6*6*6

v = 904.32

904.32 / 113.04 = 8

The Answer Is 8 times

Answer:

0.039

Step-by-step explanation:

Answer: 14x^5y^8

Step-by-step explanation:

(-7x^2y^4)(-2x^3y^4)

-7x^2y^4*-2x^3y^4, next take out the constants

−(7×−2)x^2x^3y^4y^4, -(7*-2)=14, so now you just need to add the variables.

(x^2+x^3)+(y^4+y^4)=x^5y^8

14x^5y^8

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤

Answer:

The answer is A)$10.50

Step-by-step explanation:

In order to solve the average amount, you have to add the total amount of money spent and divide it by the total number of times you spent money on food. The total sum of money spent was $63. If you divide that by how many times you ate (6 times) you'll get the dividend/answer of 10.5.

Hope this helps :)

You are spending, on average, A) $10.50 per day on food.

The correct answer is A) $10.50.

To find the average amount spent per day on food, you need to add up the total amount spent over the 6 days and then divide it by the number of days (6).

Total amount spent on food = $8 + $14 + $12 + $11 + $5 + $13

                                               = $63

Average amount spent per day = Total amount spent / Number of days

                                                     = $63 / 6

                                                     = $10.50

So, you are spending, on average, $10.50 per day on food.

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Answer: [tex]245cm^{2}[/tex]

Step-by-step explanation:

The formula for calculating the area of a square is given by :

Area = [tex]l^{2}[/tex]

where [tex]l[/tex] is the length of a side .

Therefore , the area of one of the square given implies :

Area = [tex]7^{2}[/tex]

Area [tex]= 49[/tex]

And since there are 5 squares in all , the area will therefore be :

Area = [tex]5[/tex] x[tex]49[/tex]

Area = [tex]245cm^{2}[/tex]

Therefore: the area of the shape is [tex]245cm^{2}[/tex]

Answer:

78 witch is 15%

Step-by-step explanation:

Answer:

The length of the base the pyramid is 116 feet.

Step-by-step explanation:

See the diagram attached to this answer.

Let Δ OAB is the side triangle of the square pyramid, and A'B' is the mid segment parallel to the ground with length of 58 feet.

Now, Δ OAB and Δ OA'B' are similar triangle and the length of sides of the triangle Δ OA'B' are in the same ratio with the corresponding sides of Δ OAB.

Hence, [tex]\frac{OA'}{OA} = \frac{OB'}{OB} = \frac{A'B'}{AB} = \frac{1}{2}[/tex]

⇒ AB = 2 × 58 = 116 feet.

The length of the base the pyramid is 116 feet. (Answer)  

Final answer:

The length of the base of the pyramid in question, referenced as the Great Pyramid of Cheops, is historically known to be 230 meters on each side.

Explanation:

The student's question relates to finding the length of the base of a pyramid with a known mid-segment length in one of the triangular faces.

Based on the information provided, which references the Great Pyramid of Cheops (or the Great Pyramid of Giza), the original square base length of the pyramid was 230 meters on each side.

This measurement is crucial for answering questions related to the geometry and scale of pyramids in mathematical problems.

Answer:   [tex]Perimeter= 71.75[/tex]

The parameter of a 2-D figure is the total length of its boundaries.

Step-by-step explanation:

In the given figure a hexagon is given with the length of its sides given in mixed fraction.

A mixed fraction can be solved by    [tex]p\frac{x}{y} =\frac{(p*y)+x}{y}[/tex]

So adding the given sides in the figure:

[tex]Perimeter=14\frac{3}{4}+ 4\frac{1}{2}+ 8\frac{1}{2}+10 \frac{2}{5}+10 \frac{2}{5}+12 \frac{4}{5}[/tex]

[tex]=\frac{(14*4)+3}{4} +\frac{(4*2)+1}{2} +\frac{(8*2)+1}{2} +\frac{(10*5)+2}{5}+ \frac{(10*5)+2}{5} +\frac{(12*5)+4}{5}[/tex]

[tex]=\frac{59}{4}+ \frac{9}{2}+ \frac{17}{2}+ \frac{52}{5}+ \frac{52}{5}+ \frac{64}{5}[/tex]

[tex]=14.75+4.5+8.5+10.4+10.4+12.8[/tex]

[tex]Perimeter= 71.75[/tex]

The perimeter of the given figure is 71.75

Answer:

1. 19

Step-by-step explanation:

Answer:

7.1ft

Step-by-step explanation:

The formula for calculating the total surface area of a cube is 2(L²+L²+L²)

=2(3L²)

= 6L²

Where L is the length of the cube

If the total surface area of a cube is 302.46ft², then

302.46 = 6L²

L² = 302.46/6

L² = 50.41

L =√50.41

L = 7.1ft

The length of the side of the cube is 7.1ft

The length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]

To find the length of the side of a cube given its total surface area, we need to use the formula for the surface area of a cube.

The formula for the surface area of a cube is:

[tex]\[ \text{Surface Area} = 6s^2 \][/tex]

where s is the length of a side of the cube.

Given the total surface area is [tex]\( 302.46 \, \text{ft}^2 \)[/tex], we can set up the equation:

[tex]\[ 6s^2 = 302.46 \][/tex]

To solve for s we first divide both sides by 6:

[tex]\[ s^2 = \frac{302.46}{6} \][/tex]

[tex]\[ s^2 = 50.41 \][/tex]

Next, we take the square root of both sides to find s

[tex]\[ s = \sqrt{50.41} \][/tex]

[tex]\[ s \approx 7.1 \, \text{ft} \][/tex]

Thus, the length of the side of the cube is approximately [tex]\( 7.1 \, \text{ft} \).[/tex]

Answer:

1.[tex]x^\circ= 7^\circ[/tex]

2.(a)Therefore , Side LJ =side CA

(b) BC = KL

Step-by-step explanation:

1.

we know that, vertically opposite angles are congruent .

[tex]\therefore (x+16)^\circ= (4x-5)^\circ[/tex]

[tex]\Leftrightarrow 4x^\circ-x^\circ= 5^\circ+16^\circ[/tex]

[tex]\Leftrightarrow 3x^\circ= 21^\circ[/tex]

[tex]\Leftrightarrow x^\circ= 7^\circ[/tex]

2.

(a)SAS = side,angle , side

Given ,side AB = side KJ

and ∠CAB= ∠LJK

All Pythagorean Triples are unique.

Since side AB = side KJ

Therefore , Side LJ =side CA

It satisfies SAS postulate ThereforeΔABC≅ΔKJL

(b)

HL Theorem: If hypotenuse and one leg of of a right triangle are congruent to the hypotenuse and one leg of of other right triangle , then the triangle congruent.

Since,

All Pythagorean Triples are unique.

Then hypotenuse of ΔABC=ΔLKJ ⇔BC = KL

Option C

Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches

Solution:

Anusha needs to find a rectangular container large enough to hold a volume of 130 cubic inches

The volume of rectangular container is:

[tex]volume = length \times width \times height[/tex]

Option A

Container with the dimensions 2 by 5 by 10 inches

Therefore, volume is given as:

[tex]Volume = 2 \times 5 \times 10 = 100[/tex]

Thus volume is 100 cubic inches

Option B

Container with the dimensions 3 by 4 by 10 inches

Therefore, volume is given as:

[tex]Volume = 3 \times 4 \times 10 = 120[/tex]

Thus volume is 120 cubic inches

Option C

Container with the dimensions 3 by 5 by 10 inches

Therefore, volume is given as:

[tex]Volume = 3 \times 5 \times 10 = 150[/tex]

Thus volume is 150 cubic inches

Option D

Container with the dimensions 4 by 2 by 10 inches

Therefore, volume is given as:

[tex]Volume= 4 \times 2 \times 10 = 80[/tex]

Thus volume is 80 cubic inches

Thus Container with the dimensions 3 by 5 by 10 inches has a volume of 150 cubic inches, which is large enough to hold a volume of 130 cubic inches

Answer:C. a container with the dimensions by 5 by 10 inches

Answer:

D:  y = 5x

Step-by-step explanation:

According to Google, a proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if: y=kx. for some constant k , called the constant of proportionality.  So the only one in that form would be the y = kx.  

The constant k = 5

Answer:

19 1/4

Step-by-step explanation:

5 1/2 of 2 1/3

Change mixed fraction to improper fraction

11/2 of 7/2

Of means multiplication

11/2 x 7/2

77/4

19 1/4

Answer:

22.5 weeks

Step-by-step explanation:

y = 1.12x + 28.78 represents the height of the puppy.  Here that height is 54 cm:

Then 54 = y = 1.12x + 28.78

Combining the constants, we get 1.12x = 25.22.  Dividing both sides by 1.12, x turns out to be 22.5 weeks.

Question:

Which summation formula represents the series below? 1 + 2 + 6 + 24

(a) [tex]\sum_{n=2}^{5}(n-1) ![/tex]

(b) [tex]\sum_{n=0}^{3} n ![/tex]

(c) [tex]\sum_{n=1}^{4}(n+1) ![/tex]

(d) [tex]\sum_{n=2}^{5} n ![/tex]

Answer:

Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex] is the correct answer.

Explanation:

Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex](2-1) !+(3-1) !+(4-1) !+(5-1) ![/tex]

Subtracting, we have,

[tex]1 !+2!+3 !+4 ![/tex]

Expanding the factorial,

[tex]1+(2*1)+(3*2*1)+(4*3*2*1)[/tex]

Simplifying, we get,

[tex]1+2+6+24[/tex]

Thus, the summation [tex]\sum_{n=2}^{5}(n-1) ![/tex] represents the series [tex]1+2+6+24[/tex]

Hence, Option a is the correct answer.

Option b: [tex]\sum_{n=0}^{3} n ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex]0!+1!+2!+3![/tex]

Expanding the factorial,

[tex]0+1+(2*1)+(3*2*1)[/tex]

Simplifying, we get,

[tex]0+1+2+6[/tex]

Thus, the summation [tex]\sum_{n=0}^{3} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]

Hence, Option b is not the correct answer.

Option c: [tex]\sum_{n=1}^{4}(n+1) ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex](1+1) !+(2+1) !+(3+1) !+(4+1) ![/tex]

Adding, we have,

[tex]2!+3!+4!+5![/tex]

Expanding the factorial,

[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]

Simplifying, we get,

[tex]2+6+24+120[/tex]

Thus, the summation [tex]\sum_{n=1}^{4}(n+1) ![/tex] does not represents the series [tex]1+2+6+24[/tex]

Hence, Option c is not the correct answer.

Option d: [tex]\sum_{n=2}^{5} n ![/tex]

By substituting the values of n and expanding the summation, we have,

[tex]2!+3!+4!+5![/tex]

Expanding the factorial,

[tex](2*1)+(3*2*1)+(4*3*2*1)+(5*4*3*2*1)[/tex]

Simplifying, we get,

[tex]2+6+24+120[/tex]

Thus, the summation [tex]\sum_{n=2}^{5} n ![/tex] does not represents the series [tex]1+2+6+24[/tex]

Hence, Option d is not the correct answer.

Hence, the correct answer is Option a: [tex]\sum_{n=2}^{5}(n-1) ![/tex]

Answer: A

Step-by-step explanation:

Answer:

A) 28*sqrt(3)

Step-by-step explanation:

Answer:

28√3 is your answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: It has no exact solution

Answer:

-1

Step-by-step explanation:

Slope = (y2 - y1)/(x2 - x1)

= (7 - (-3))/(-2 - 8)

= (7+3)/(-10)

= 10/(-10) = -1

Answer:

C2+17

Step-by-step explanation:

Algebraic expression is 2c + 17

17 more than twice Craig's height

Algebraic expression

We know that;

c = craig's height

So,

twice Craig's height

⇒ 2c

17 more than twice Craig's height

⇒ 2c + 17

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Answer:

Nothing

Step-by-step explanation:

You can't divide by zero

Answer:

ANYTHING DIVIDED BY 0 IS ALWAYS ZERO

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

1

Step-by-step explanation:

13  15  17  x  20  21

Cross out all outer numbers

We are left with 17 and x

With double medians, you add those two together and then divide them by two.

With the median (total) being 18, we will first add 17+x then divide Y/2 = 18

The value of x is 1

Answer:

0.032 Amperes

Step-by-step explanation:

in this question We are given;

We are required to determine the current, I

We need to know that power, P is given by the product of current and voltage.

That is;

Power = VI

But; 1 mW = 0.001 Watts

Thus, 500 mW = 0.5 watts

Rearranging the formula;

I = Power ÷ V

 = 0.5 watts ÷ 15.81 V

 = 0.0316 Amperes

 = 0.032 A

Thus, the current, I is 0.032 Amperes

To solve the equation, you need to isolate/get "y" by itself in the equation:

3y - 4 = 6 - 2y        Add 2y on both sides

3y + 2y - 4 = 6 - 2y + 2y

5y - 4 = 6        Add 4 on both sides

5y - 4 + 4 = 6 + 4

5y = 10          Divide 5 on both sides

[tex]\frac{5y}{5} =\frac{10}{5}[/tex]

y = 2

PROOF

3y - 4 = 6 - 2y        Substitute/plug in 2 for y

3(2) - 4 = 6 - 2(2)

6 - 4 = 6 - 4

2 = 2

After Solving the equation for 3y-4=6-2y, we get y = 2. We must isolate the variable y on one side of the equation in order to get the solution to the equation 3y - 4 = 6 - 2y. Here's a step-by-step procedure:

Start by solving 3y - 4 = 6 - 2y, which is the provided problem.

Add 2y to both sides of similar phrases to combine them: 3y + 2y - 4 = 6 - 2y + 2y.

Simply put, this is: 5y - 4 = 6.

Add 4 to both sides of the variable word to isolate it: 5y - 4 + 4 = 6 + 4.

This may be summarised as 5y = 10.

To find y, multiply both sides of the equation by 5. (5y) / 5 = 10 / 5.

This may be condensed to: y = 2.

Consequently, y = 2 is the answer to the equation 3y - 4 = 6 - 2y.

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Answer:

do you mean x=7

Step-by-step explanation:

this aint a quadratic function a qaudratic function is ax^2+bx+c=c

To create a 30-lb batch of sweets that is 22% nuts and dried fruit, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B.

To find the solution, we can set up a system of equations based on the percentages of nuts and dried fruit in each brand of granola and the desired final percentage.

Let x represent the amount of sweet item A (in pounds) and y represent the amount of sweet item B (in pounds) to be mixed.

The total weight of the mixture is x + y = 30 lbs.

The percentage of nuts and dried fruit in brand A is 25%, so the amount of nuts and dried fruit from A is 0.25x lbs.

The percentage of nuts and dried fruit in brand B is 10%, so the amount of nuts and dried fruit from B is 0.10y lbs.

The desired final percentage in the mixture is 22%, so we have the equation: (0.25x + 0.10y) / 30 = 0.22.

Now, we can solve this system of equations to find x and y.

First, we'll multiply the last equation by 30 to get 0.25x + 0.10y = 6.6.

Then, we can use substitution or elimination to solve for x and y.

In this case, it's simpler to use elimination, and we find that x = 12 lbs and y = 18 lbs.

Therefore, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B to create the desired 30-lb batch with 22% nuts and dried fruit.

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