Write the linear equation in standard form.
12x = -9y+ 7

Hence, the value of the expression is 36.

Solution:

Step 1: Given expression is [tex]4(10-4)^{2} \div 4[/tex].

BODMAS means do Bracket, Of, Division, Multiplication, Addition, Subtraction

Step 2: Using BODMAS rule first simplify the expression which is in bracket.

⇒ [tex]4(10-4)^{2} \div 4=4(6)^2\div4[/tex]

Step 3: Squaring of the number 6.

⇒ [tex]4(6)^2\div4=4\times36\div4[/tex]

Step 4: Using BODMAS rule, divide 36 by 4.

⇒ [tex]4\times36\div4=4\times9[/tex]

Step 5: Using BODMAS rule, multiply 4 with 9.

⇒ [tex]4\times9=36[/tex]

Hence, the value of the expression is 36.

Final answer:

The sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given a 50-foot tree and a 9-foot shadow, is approximately 0.984, calculated using the definition of sine in a right triangle and the Pythagorean theorem.

Explanation:

The question involves finding the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree, given that a 50-foot tree casts a 9-foot long shadow. In this scenario, we can visualize a right triangle where the tree represents the opposite side (height), the shadow represents the adjacent side (base), and the hypotenuse is the line from the top of the tree to the end of the shadow on the ground.

To find the sine of the angle, we use the definition of sine in a right triangle, which is sine(angle) = opposite / hypotenuse. However, before we can do that, we need to determine the length of the hypotenuse using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²).

Let's calculate:

a (opposite) = 50 feet (Height of the tree)

b (adjacent) = 9 feet (Length of the shadow)

c (hypotenuse) = √(50² + 9²) = √(2500 + 81) = √2581 = 50.8 feet (approximately)

Now, we can calculate the sine of the angle:

sine(angle) = opposite / hypotenuse = 50 / 50.8 ≈ 0.984

Therefore, the sine of the angle between the ground and the line connecting the top of the shadow to the top of the tree is approximately 0.984.

Answer:

the third one

Step-by-step explanation:

hope it helps

Answer:        [tex]x=9[/tex]

Step-by-step explanation:

Alright, lets get started.

[tex]log_{6}4x^2-log_{6}x=2[/tex]

Using the property of logs : [tex]log (m) - log(n)=log\frac{m}{n}[/tex]

[tex]log_{6}\frac{4x^2}{x}=2[/tex]

[tex]log_{6}4x=2[/tex]

Using the property of logs : [tex]if \ log_{a}m=n, \ then \ a^n=m[/tex]

So,

[tex]6^2=4x[/tex]

[tex]4x=36[/tex]

Dividing 4 in both sides

[tex]x=9[/tex]   ......................   Answer

Hope it will help :)

Answer:

x = 9

Step-by-step explanation:

Determine the defined range

[tex]log^6 (4x^2) - log^6 (x) = 2, x = (0, + ∞)[/tex]

Use log^a (x) - log^a (y) = log^a (x/y) to simplify the expression

[tex]log6 (\frac{4x^{2} }{x} )= 2[/tex]

Simplify the expression

log^6 (4x) = 2

Convert the logarithm into an exponential form using the fact that log^a (x) = b is equal to x = a^b

[tex]4x=6^{2}[/tex]

Evaluate the power

4x = 36

Divide both sides of the equation by 4

x = 9, x = (0, + ∞)

Check if the solution is the defined range

x = 9

Answer:

Step-by-step explanation:

total capacity = 62.5 GB

available capacity = 35.0 GB

35 is what percent of 62.5

35 = x% * 62.5

35 / 62.5 = x%

0.56 = x%

56% = x <=====

56% of the memory capacity is still available.

To calculate the percentage of memory capacity that is still available, we can use the available capacity and total capacity information provided.

Given:

Capacity: 62.5 GB

Available: 35.0 GB

To find the percentage, we divide the available capacity by the total capacity and multiply by 100:

Percentage = (Available / Capacity) x 100

Percentage = (35.0 GB / 62.5 GB) x 100

Percentage ≈ 56%

Therefore, 56% of the memory capacity is still available.

Learn more about Percentage here:

https://brainly.com/question/32197511

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Answer:

208.85

Step-by-step explanation:

It is 208.85 because when you have .8 + .05 =.85

Answer:

Step-by-step explanation:

the total amount of water used that day = 526.80 - 318.05 = 208.75 gallons.

The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3

Step-by-step explanation:

A symptote is a line that a curve approaches but never touches

∵ f(x) = 3 ㏒(x + 3)

∵ The argument is (x + 3)

- Equate the argument by zero

∵ x + 3 = 0

- Subtract 3 from both sides

∴ x = -3

- The vertical asymptote of a logarithmic function is at the zero

  of the argument

∴ The vertical asympotote of f(x) is x = -3

The vertical asymptote of the function f(x) = 3 log(x + 3) is x = -3

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

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Answer:

-3

Step-by-step explanation:

plato

Answer:

Step-by-step explanation:

The answer is 1.2, you want to replace the x with the 6.3 and then the -7.5 ends up turning into a positive. You then add the two together -6.3 + 7.5 = 1.2

Answer:

7 - 3[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

3 + [tex]\sqrt{x+7}[/tex] - [tex]\sqrt{3x}[/tex] ← substitute x = 9

= 3 + [tex]\sqrt{16}[/tex] - [tex]\sqrt{27}[/tex]

= 3 + 4 - [tex]\sqrt{9(3)}[/tex]

= 7 - 3[tex]\sqrt{3}[/tex]

Answer:

y=-6x-2

Step-by-step explanation:

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

m=(10-(-2))/(-2-0)

m=(10+2)/(-2)

m=12/-2

m=-6

y-y1=m(x-x1)

y-(-2)=-6(x-0)

y+2=-6(x)

y+2=-6x

y=-6x-2

Answer:

200 = 20

470 47

The number of year 10 students over the total number of students

50 square meters is equal to 77500 square inches

Solution:

Given that we have to convert 50 square meters to square inches

Use the following conversion factor

1 meter is equal to 39.3701 inch

That is,

[tex]1\ meter = 39.3701\ inch[/tex]

Now frame the conversion factor for square meters to square inches

[tex]1\ meter\ \times meter = 39.3701 \times 39.3701\ inch\ \times inch\\\\1\ m^2 = 1550\ in^2[/tex]

Now convert 50 square meters to square inches

Muliply both the sides by 50

[tex]1 \times 50\ m^2 = 1550 \times 50\ in^2\\\\50\ m^2 = 77500\ in^2[/tex]

Thus 50 square meters is equal to 77500 square inches

Answer:

Step-by-step explanation:

Answer:

2x+10

Step-by-step explanation:

-3x+5(x+2)

-3*x+5*x+5*2

-3*x+5*x+10

(-3+5)*x+10

(-2)*x+10

2x+10

Answer:

The migration of the African-Americans to Harlem in the USA empowered the African-Americans in the society in the early 1900s. This was one of the greatest accomplishments of the African-Americans in history.

Explanation:

The "Harlem Renaissance" was originally called the "New Negro Movement." During the "Reconstruction Era," many of the African Americans felt a newfound empowerment in the society. They started leaving the South, where most of them were enslaved and maltreated. Many of them moved to other places such as "Harlem" in New York City. It became an ideal destination for many "Negros" and their number increased over time. This then became an African-American neighborhood.

African-Americans started producing plays with actors of their descent. Several Negro poets emerged describing the life of the African-Americans. Negros became more literate and able when it comes to expressing themselves in the society. They even had their own newspaper known as "The New Negro Movement."

Answer:

0=0

Step-by-step explanation:

Simply,there is no solution.

Answer:

The person up there is right just saying:)

Step-by-step explanation:

Answer:

(0, 6)

Step-by-step explanation:

plug each x in and find the y

Answer:

(0, 6)

Step-by-step  explanation:

Answer:theres nothimh here to answer

Step-by-step explanation:

Answer:

x = 28.06

Step-by-step explanation:

-12.11-10.5=75.6-3.5x

Put all the integers on one side and X on the other.

-12.11 - 10.5 - 75.5 = -3.5x

-98.21 = -3.5x

-98.21/-3.5 = x

x = 28.06

Step-by-step explanation:

Input:

Input is generally defined as the information that is sent or passed to a computer or the information what is taken.  The devices that are used to give or offer such information is know as Input devices.

For example:  

We usually use keyboard to type and give a specific data to the computer and hence it can be considered as an Input device.

Output:

Output is generally defined as the source of information that is received or processed by the computer or the information what is given back. The devices that are used to give back such information is know as Output devices.

Example:

Printers takes the input from us,process it and gives back the output in the form of printed sheets,Hence it can be considered as Output device.

Answer:

Ms. Griffiths lives on 3rd floor

Step-by-step explanation:

The elevator moves 10.2 seconds from one floor to another and stops for 45.8 seconds for people to exit. Thus, add: 10.2 seconds + 45.8 seconds = 56 seconds

If it takes her 158 seconds to travel from the lobby to her apartment, then 158 seconds/56 seconds = 2.8 = 3 (approximately).

Therefore, she lives on 3rd floor.

Mathematically, the values ought to be 168 seconds /56 seconds = 3.

Answer

(8-2×2) to the power of 2 is 16

Work: 2×2=4

8-4=4

4 to the power of 2 =16

Answer:

144

Step-by-step explanation:

in pemdas always do parenthesis first so it will be 8-2x2= 144 because

Answer:

25) If f(x) = sin ([1/3] x) , find f(π/2).

Substitute with x = π/2

f(π/2) = sin ([1/3] *[π/2]) = sin (π/6) = 1/2

======================================

26) If f(x) = cos (2x) , find f(3π/4).

Substitute with x = 3π/4

f(3π/4) = cos ( 2 * 3π/4) = cos ( 3π/2) = zero.

======================================

27) If f(x) = sin (2x) + cos (3x) , find f(π/4)

Substitute with x = π/4

f(π/4) = sin ( 2 * π/4) + cos ( 3 * π/4) =

        = sin ( π/2) + cos ( 3π/4)

        =  1  - 1/(√2)

        = 0.293

======================================

28) f(x) = tan (5x) - sin (2x) , find f(π/6).

Substitute with x = π/6

So, f(π/6) = tan (5 * π/6) - sin ( 2 * π/6)

               = tan (5π/6) - sin (π/3)

               = -1/(√3) - (√3)/2

                = -1.443

Answer:

-40/33

Step-by-step explanation:

Answer:

-6/11 > -2/3

Step-by-step explanation:

6/11 = 18/33

2/3 = 22/33

Since 18/33 < 22/33  then 6/11 < 2/3 then -6/11 > -2/3

Answer:

D.  -2.

Step-by-step explanation:

2(x-4) + 3x - x2 for x = 3

= 2(3-4) + 3(3) - 3^2

= 2(-1) + 9 - 9

= -2 + 9 - 9

= -2.

Answer: 4 5/14

Step-by-step explanation:

Answer:

Frosts second mile and steadys 6th mike

Step-by-step explanation:

Part A: The two plans will cost the same amount when the distance to the airport is 12 miles.

Part B: For a 20-mile distance, Mr. Gardner should choose Fost Shuttle, costing $10 compared to $12 for Steady Shuttle.

Let's solve Part A first:

Part A:

Let's denote the distance to the airport as d miles.

For Fost Shuttle:

Cost = Pick-up fee + Cost per mile × Distance

Cost = $5 + $0.25 × d

For Steady Shuttle:

Cost = Pick-up fee + Cost per mile × Distance

Cost = $2 + $0.50 × d

Now, we'll set up an equation to find when the two plans cost the same amount:

[tex]\[5 + 0.25d = 2 + 0.50d\][/tex]

Solving for d:

[tex]\[0.25d - 0.50d = 2 - 5\]\[-0.25d = -3\]\[d = \frac{-3}{-0.25}\]\[d = 12\][/tex]

So, the two plans will cost the same amount when the distance is 12 miles.

For Part B:

Given the distance is 20 miles, let's calculate the cost for each company:

For Fost Shuttle:

Cost = $5 + $0.25 × 20 = $5 + $5 = $10

For Steady Shuttle:

Cost = $2 + $0.50 × 20 = $2 + $10 = $12

Comparing the costs, Mr. Gardner should choose Fost Shuttle as it costs $10 compared to $12 for Steady Shuttle.

The correct answer is: When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0). The true statement is D.

Let's analyze each statement:

A; When triangle ABC is reflected over the y-axis to create triangle A'B'C' , the coordinates for B' are (1, -1) .

To reflect over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. If the coordinates for B are (x, y), then after reflecting, the x-coordinate becomes -x. Since B has coordinates (1, 1), after reflection, B' will have coordinates (-1, 1). So, statement A is false.

B; When triangle ABC is rotated 90 degrees clockwise about point A to create triangle A'B'C' , the coordinates for B' are (3,3]

Rotation of 90 degrees clockwise about a point involves swapping x and y coordinates and negating the new x-coordinate. The point A is not given, but assuming it's (0, 0), if B has coordinates (x, y), then after rotation, B' will have coordinates (y, -x). If A is (0, 0) and B is (3, 1), after rotation, B' will have coordinates (1, -3), not (3, 3). So, statement B is false.

C; When triangle ABC is dilated from the origin by a scale factor of 1/4 to create triangle A'B'C', the coordinates for B' are (4,4)

Dilating by a scale factor of 1/4 means multiplying each coordinate by 1/4. If B has coordinates (x, y), then after dilation, B' will have coordinates (1/4 * x, 1/4 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (1, 1). So, statement C is false.

D; When triangle ABC is translated 2 units to the left and 1 unit down to create triangle A'B'C' , the coordinates for B' are (-1, 0)

Translation involves adding/subtracting values to x and y coordinates. If B has coordinates (x, y), then after translation by (-2, -1), B' will have coordinates (x - 2, y - 1). Since B has coordinates (1, 1), after translation, B' will have coordinates (-1, 0). So, statement D is true.

E; When triangle ABC is dilated from the origin by a scale factor of 5 to create triangle A'B'C', the coordinates for B' are (5,5)

Dilating by a scale factor of 5 means multiplying each coordinate by 5. If B has coordinates (x, y), then after dilation, B' will have coordinates (5 * x, 5 * y). Since B has coordinates (4, 4), after dilation, B' will have coordinates (20, 20), not (5, 5). So, statement E is false.

So, the true statement is D.