Find the area of the quadrilateral EFGH

Remark

The 2 angles are vertically opposite and that means they are equal.

Equation

(3x - 3) = [6(x - 10)]    

Solution

Remove the brackets.

3x - 3 = 6(x - 10)

3x - 3 = 6x - 60             Subtract 3x from both sides

- 3 = 6x - 60 - 3x           Combine like terms

-3 = 3x - 60                    Add 60 to both sides

-3 + 60 = 3x

57 = 3x                           Divide by 3

57 / 3 = 3x / 3

19 = x  Answer

[tex]2x+4=16\\\\2x=12\\\\x=6[/tex]

The solution to the equation 2x + 4 = 16 is x = 6.

Given the equation in the question:

2x + 4 = 16

To solve the equation 2x + 4 = 16, first, isolate the variable term on one side by moving the constant term to the other side of the equation.

2x + 4 = 16

Subtract 4 from both sides of the equation:

2x + 4 - 4 = 16 - 4

2x = 16 - 4

Subtract 4 from 16:

2x = 12

Divide both sides of the equation by 2 to isolate the variable x:

2x/2 = 12/2

x = 12/2

x = 6

Therefore, the value of x is 6.

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Answer:

The slope of line [tex]LM[/tex] is  [tex]-\frac{4}{3}[/tex]

Step-by-step explanation:

Line [tex]JK[/tex] has the slope [tex]\frac{3}{4}[/tex] and is perpendicular to line [tex]LM[/tex]

Suppose, the slope of line [tex]LM[/tex] is  [tex]m[/tex]

We know that, the product of the slopes of two lines which are perpendicular to each other is always [tex]-1[/tex].  So, the equation will be..............

[tex]\frac{3}{4}*m= -1\\ \\\frac{3m}{4}=-1\\ \\ 3m= -4\\ \\ m=-\frac{4}{3}[/tex]

So, the slope of line [tex]LM[/tex] will be [tex]-\frac{4}{3}[/tex]

In this Decimal Point Movement question, Moving the decimal five places to the right in mathematics is a shortcut for multiplication by 105 (one hundred thousand). This uses the principle of powers of ten.

In mathematics, moving the decimal five places to the right is actually a shortcut for multiplying by 105, or 100,000. This concept utilizes the patterns in powers of ten. For instance, for any given number, we can count the zeros in the power of ten and then move the decimal point that same number of places to the right.

Illustrating with an example, let's say we have the number 5.27. If we multiply it by 105, we move the decimal five places to the right to get 527000. This aligns with the multiplication principle: when we multiply by 10, 100, 1000, and so on, each time, we are essentially incrementing the decimal place to the right.

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The answer is D! Aight hope it helped

The value of f in the equation 6f − 12 = −4f + 6 is 1 4/5.

To answer the student's question, we need to solve the algebraic equation 6f − 12 = −4f + 6 for the unknown variable f. First, we want to get all terms with f on one side of the equation, and all constant terms on the other side. Thus, we'll add 4f to each side of the equation to eliminate -4f from the right side of the equation and get 6f + 4f = 6 + 12. This simplifies to 10f = 18, then we divide each side by 10, and we get f = 18/10 which reduces to f = 1 4/5 (Option C).

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The third one is the right answer

Answer:

its a :)

Step-by-step explanation:

There are 13 rungs on the ladder :)

Answer:

23 rungs

Step-by-step explanation:

Let the number of rungs on the ladder be h and make the necessary adjustments based on this

Given that she is on the middle rung of a ladder this is equivalent to

= (h + 1)/2

She climbed up three rungs

= (h + 1)/2 + 3

moved down five rungs

= (h + 1)/2 + 3 - 5

and then climbed up 7 rungs

=  (h + 1)/2 + 3 - 5 + 7

Then she climbed up the remaining 6 rungs to the top of the ladder

(h + 1)/2 + 3 - 5 + 7 + 6 = h

(h + 1)/2 + 11 = h

h + 1 + 22 = 2h

2h - h = 23

h = 23

Using the concept of scale, we find that the distance between Cleveland and Cincinnati on the first map (1 cm to 10 km) is 40 cm, equivalent to 400 km in real-world distance. On the second map with a scale of 1 cm to 50 km, the equivalent distance is calculated to be 8 cm.

To calculate the distance between Cleveland and Cincinnati on the second map, we use the concept of scale. On the first map, the scale is 1 cm to 10 km, and the distance is represented as 40 cm. Scaling this to the real-world distance gives us 40 cm × 10 km/cm = 400 km between the two cities.

Now, let's apply the second map's scale of 1 cm to 50 km. To find the corresponding map distance, we set up a proportion: 10 km/cm (first map) / 50 km/cm (second map) = 40 cm (distance on the first map) / X cm (distance on the second map). Simplifying this, we find that X = 40 cm ×(10 km/cm) / (50 km/cm) = 40 cm × 1/5 = 8 cm.

Therefore, the distance between Cleveland and Cincinnati on the second map, which has a scale of 1 cm to 50 km, would be 8 cm.

The average amount of rain fall is 9.61 inches

The average rainfall in Annette, Alaska is 0.31 inches per day. Over the course of an average September, the total amount of rain that falls is 9.3 inches.

To find out how much rain falls over the course of an average September, we need to know the number of days in September. Let's assume there are 30 days. Given that the average rainfall in Annette, Alaska is 0.31 inches per day, we can calculate the total rainfall by multiplying the average rainfall per day by the number of days in September: 0.31 inches/day * 30 days = 9.3 inches.

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Answer:

38%

Step-by-step explanation:

Given that X,the hours per week the music student practice follow a normal distribution.

X:N(8,4)

We have to find the percentage of students who practice between 6 and 10 hours.

6<x<10 implies converting to z

We know z = (x-mean)/sigma = (x-8)/4

Hence 6<x<10 is equivalent to (6-8/4)<Z<(10-8/4)

= |z|<0.5

From std normal table we find this area equals = 0.1915+0.1915

=0.3830 = 0.38 (rounded off)

Hence required percentage = 0.38x100 = 38%

Final answer:

To determine the percentage of music students practicing between 6 to 10 hours, we convert these hours to z-scores and use the standard normal distribution table, which reveals that approximately 38.2% of students practice within this range.

Explanation:

To find the percentage of music students who practice between 6 to 10 hours per week, we can use the properties of the normal distribution. We first need to convert the range values to z-scores using the formula Z = (X - μ) / σ, where X is the value from the data set, μ is the mean, and σ is the standard deviation.

Converting 6 hours to a z-score:
Z = (6 - 8) / 4 = -0.5

Converting 10 hours to a z-score:
Z = (10 - 8) / 4 = 0.5

Now we use the standard normal distribution table to find the probability corresponding to these z-scores. The area under the curve between z-scores -0.5 and 0.5 gives us the desired percentage. Looking up the z-scores in the standard normal distribution table, we find that the area between these scores is approximately 38.2%. Thus, 38% is the closest option provided.

The answer is 620.6666666666667

The remainder is 620.7 or 620.6

Answer in the attachment.

Solution

f(r) = 3.14[tex]r^{2}[/tex]

Now we have to find the area of the circle when the radius (r) = 4.

Plug in r = 4 in f(r) to get the area of the circle.

f(4) = 3.14[tex](4^{2} )[/tex]

f(4) = 3.14 * 4 * 4

f(4) = 3.14 *16

f(4) = 50.24

The answer is C. 50.24

Tom drank 2.25qt of the jug, in fraction form it would be 2 1/4

To solve the equation 100e^0.125t=200 for t, divide by 100, apply the natural logarithm, and rearrange to find t=ln(2)/0.125, which simplifies to t=ln(16).The Correct Answer is Option. A.

The question involves solving for the variable t in the exponential equation 100e^0.125t=200.

To solve this, we need to isolate the exponent on one side. Here are the steps to find the correct value of t:

The correct answer from the given options is A. t= ln(16), as ln(2) / 0.125 = ln(16).

Hello!

To answer this question we need to find the factors of -120.

The total set (both negative and postive! ) are the following:

After looking over all of these factors, we can see that 10 · -12 is equal to not only -120, but when the multiplication sign is replace by addition, it is equal to -2!

Hope this helps.

Final answer:

The two numbers that multiply to -120 and add to -2 are 10 and -12. These satisfy the given conditions of multiplication and addition.

Explanation:

To find two numbers that multiply to -120 and add to -2, we can set up a system of equations based on the factors of -120. We know that if two numbers multiply to a negative number, one must be positive and the other negative. So we look for two factors of 120 with a difference of 2, given that one will be negative and the other positive.

Considering the factor pairs of 120: (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), (10, 12), we find that 10 and -12 satisfy both conditions: 10 * -12 = -120 and 10 + (-12) = -2.

Answer:

[tex]x=-9[/tex]

[tex]y=4[/tex]

Step-by-step explanation:

[tex]3x+10y=13[/tex] ← Equation 1

[tex]4(-2y+x)-9x=13\\[/tex]

By simplifying the above equation we get,

[tex]-8y+=4x-9x=13[/tex] (Simplifying the brackets)

[tex]-8y-5x=13[/tex] (By subtracting [tex]-9x[/tex] from [tex]+4x[/tex]) ← Equation 2

Multiply Equation 1 by 5 and Equation 2 by 3 and add them together.

Equation 1 multiplied by 5 will give,

[tex]15x+50y=65[/tex]

Equation 2 multiplied by 3 will give,

[tex]-24y-15x=39[/tex]

Add those together,

[tex]15x+50y-24y-15x=65+39[/tex]

[tex]26y=104[/tex] (After simplifying [tex]x[/tex] values)

Therefor [tex]y=4[/tex]

By substituting [tex]y=4[/tex] to Equation 1 we get,

[tex]3x+10*4=13[/tex][tex]3x+40=13\\3x=-27\\x=-9[/tex]

Therefor we can say,

[tex]x=-9[/tex]

[tex]y=4[/tex]

48 times 24 is 1,152.

48x24=672

Hope I helped!

ΩωΩ

Hello!

They should most definitely use meters. Meters are much bigger than centimeters as centimeters are 1/100th of a meter. Meaning, it will take 100 centimeters to get 1 meter. A soccer field is a large surface, and to get a simpler number, you should use meters.

Hope this helps!

Answer:

E, C

Step-by-step explanation:

1.  Curcumfrance 37.68

2.Diameter of 16m

3. Radius of 7m

4. Diameter of 8m

Hope it Helps!!

The circle with the largest area to the circle with the smallest area.

Area of circle with diameter 16 cm >  Area of circle with radius 7 m > Circumference of circle of  37.68 m > Area of circle with diameter 8 cm .

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.

Given:

1. Area of Circle

= πr²

= 3.14 x 4 x 4

= 50.24 m²

2. Area of Circle

= πr²

= 3.14 x 7 x 7

= 153.86 m²

3. Circumference of circle = 2πr

37.68 = 6.28r

r= 6

Area of Circle

= πr²

= 3.14 x 6 x 6

= 113.04 m²

4. Area of Circle

= πr²

= 3.14 x 8 x 8

= 200.96 m²

So, Area of circle with diameter 16 cm >  Area of circle with radius 7 m > Circumference of circle of  37.68 m > Area of circle with diameter 8 cm .

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6-x=5x+30

-x=5x+30-6

-x=5x+24

-x-5x=24

-6x=24

x=24/-6

x=-4

Hello there!

[tex]6-x=5x+30\\[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓

First you had to subtract by 6 from both sides of the equation.

[tex]6-x-6=5x+30-6[/tex]

Simplify

[tex]-x=5x+24[/tex]

Then you subtract by 5x from both sides of the equation.

[tex]-x-5x=5x+24-5x[/tex]

Simplify

[tex]-6x=24[/tex]

Divide by -6 from both sides of the equation.

[tex]\frac{-6x}{-6}=\frac{24}{-6}[/tex]

Simplify it should be the correct answer.

[tex]x=-4[/tex]

Answer⇒⇒⇒⇒⇒x=-4

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Answer:

[tex](\frac{x}{3})(\frac{6}{x})=2[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following multiplication given in the problem above:

[tex](\frac{x}{3})(\frac{6}{x})[/tex]

2. Multiply the numerators and the denominators:

[tex](\frac{x}{3})(\frac{6}{x})=\frac{6x}{3x}[/tex]

3. You can simplify the expression. Then, you have:

[tex]\frac{6x}{3x}=2[/tex]

Answer:

2

Step-by-step explanation:

Because I did it on edge

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