What does K =
2(k-3)/k+9 = 3/5

[tex]x+146=546[/tex]

Subtract 146 from both sides:

[tex]x+146-146=546-146\\[/tex]

[tex]x=400[/tex]

Answer:

x = 400

Step-by-step explanation:

x + 146 = 546

We need to subtract 146 on both sides.

146 - 146 is equal to 0 so we cancel out. 546 - 146 is equal to 400.

So now x is alone and we have our answer.

x = 400

1) Let's sketch this out so that we can better understand it

2) Reminding ourselves of the metric relations of a right triangle we can write out the following:

Note that the radius intersects that chord with a 90º angle so it bisects that chord.

To know if 2/5 and 6/15 are equivalent, we do a multiplication, then,

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times2}{5\times2}=\frac{4}{10} \ \ \longmapsto \ Not \ the \ result } \end{gathered}$} }[/tex]

Since if we try it with number 1, the result would be the same, then we continue with 2 being closer, then we continue with number 3, successively, until we reach the expected answer.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{2}{3}=\frac{2\times3}{5\times3}=\frac{6}{15} } \end{gathered}$} }[/tex]

She invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account

Here, we want to know the amount of money invested in each account

Let the amount invested in the 4% simple interest account be $x ----> (a)

While the amount invested in the 2.5% account be $y -------->(b)

So mathematically;

Both the interests are added to get total interest

x + y = 6,000 ••••••(i)

Let’s now evaluate the interest

for the 4% account , interest = 4/100 * x = 4x/100

For the 2.5% account, interest = 2.5/100 * y= 2.5y/100

The addition of both  interests gives the total simple interest;

4x/100 + 2.5y/100 = 204

Multiply through by 100

4x + 2.5y = 20,400 •••••••(ii)

From i, x = 6,000 - y

Putting this into equation ii

4(6,000-y) + 2.5y = 20,400

24,000 - 4y + 2.5y = 20,400

24,000-20,400 = 4y - 2.5y

1.5y = 3,600

y = 3,600/1.5

y = $2,400

Recalling it again,

x = 6000 - y

x = 6,000 - 2,400

x = $3,600

Therefore, Nina invested $2,400 in the 2.5% account and $3,600 in the 4% simple interest account

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The value of BC is 60.6.

According to the segment addition postulate, if we have two locations on a line segment, A and C, a third point B lies on the line segment AC if and only if the lengths between the points match the requirements of the equation AB + BC = AC.

Given:

BC = 6x+6

AB = 8x+9  

AC = 142

We need to find BC.

As AB and BC combine to form AC, we add them together and equate them with the value of AC to determine the value of x.

Using the property of segment addition,

AB + BC = AC

8x + 9 + 6x + 6 = 142

Combine the variable terms and constants together,

14x + 15 = 142

14x = 142 - 15 (Subtracting both sides by 15)

14x = 127

x = 9.1

Hence the value of BC is,

BC = 6x + 6 = 6(9.1) + 6 = 60.6

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The equation of line in point - slope form will be;

⇒ y + 2 = 10 (x - 1)

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line = (1, -2)

And, The slope of the line = 10

Now,

Since, The equation of line in point-slope form is;

⇒ y - y₁ = m (x - x₁)

Where, (x₁ , y₁) is the point on the line and m is slope of the line.

Hence, The equation of line in point-slope form passing through the points (1, -2)  with slope 10 is;

⇒ y - y₁ = m (x - x₁)

⇒ y - (-2) = 10 (x - 1)

⇒ y + 2 = 10x - 10

⇒ y = 10x - 10 - 2

⇒ y = 10x - 12

Thus, The equation of line in point - slope form will be;

⇒ y + 2 = 10 (x - 1)

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EXPLANATION

Given the circle, we can see the following facts:

Diameter= 24 ft ----> radius= 12 ft

Total arc length = 360°

The arc of a semi-circle is equal to 360/2 = 180 degrees

The red labeled arc is given by the difference between 360, the other 60 degrees and the semi-circle,

360° - 180° - 60° = 120°

So, representing this as a radian form:

Multiplying terms:

Simplifying:

So, the answer is 8π ft

The expression for volume is (28-2x)(22-2x)x and when x=6, the volume is 840 inch^3.

A 3D object's volume is the amount of actual space it occupies. It is a 2D shape's 3D equivalent of area. It is quantified in cubic units like cm3. It means that the amount of space a closed form can occupy in three dimensions depends on its volume. Volume is a gauge of a thing's potential. For instance, a cup is said to have a 100 ml capacity if the brim can hold 100 ml of water. Another way to measure volume is the amount of space a three-dimensional item takes up.

According to question,

Let x be the height of the cubic box

Length = (28-2x)

Breadth = (22-2x)

Volume = x(28-x)(22-x)

When x =6

Volume = 6(28-6×2)(22-6×2)

=6(10)(14)

=840 inch^3

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Answer: 12%

Step-by-step explanation:

12%

Explanation:

If has 176 £1 coins then 176 drivers paid £1 and 20 p coins.

The rest of the driver paid with 20 p coins.

So the number of 20 p coins is:

320 - 176 = 144

Since £1 and 20 p need 6 coins of 20 p, the number of drivers who paid only for 20 p coins is:

144 / 6 = 24

The total number of drivers is:

176 + 24 = 200

The percentage of drivers who paid only with coins id 20 p is:

24 / 200 • 100% =

0.12 • 100% = 12%

Factors of 50 are the numbers which on dividing 50 leave no remainder. 50 is a composite number, therefore, it has more than 2 factors.

We can get the factors of 50 by Prime Factorization. We can draw a factor tree to get the prime factors of 50 as shown below:

Therefore, the prime factors are:

Hence, the other factors are:

Therefore, the factors of 50, including 1 and 50, are:

The question asks to sum all the factors between 1 and 50. This means that 1 and 50 are not included in the sum.

Therefore, the sum will be:

The correct option is OPTION A.

Answer:

explain  15/256

Answer:

y = 6m - 13

Step-by-step explanation:

Parallel lines have the same slope.  The slope in the equation y = 6x -2 is 6.

To write an equation in the slope intercept form, we need a slope and a y-intercept.  We have the slope, we need to find the y-intercept.

To find the y intercept, we need a slope, and x on the line and a y on the line.  The point (3,5) gives us the x and the y.

slope = 6

x = 3

y = 5

y = mx + b  plug in what we know and solve for b

5 = 6(3) + b

5 = 18 + b  Subtract 18 from both sides of the equation

-13 = b

y = mx  + b

y = 6m - 13

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 9 5/8, where 9 is the quotient and 5 is the remainder.

Remain length = 13.2' = 13' 2 2/5 ".

Length of black steel pipe is 21'-0".

7' 9 5/8" =7.8 '

Remain length = 13.2' = 13' 2 2/5 ".

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The enlarged node that the nurse should suspect that the client has a blockage within the right lymphatic duct is the right cervical node

A network of tissues, blood arteries, and organs called the lymphatic system collaborates to transport lymph, a colorless, watery fluid, back into your circulatory system. Every day, your body's arteries, smaller arteriole blood vessels, and capillaries circulate about 20 liters of plasma.

The right lymphatic duct receives drainage from the right cervical node. The thoracic duct receives drainage from the superficial popliteal, superficial inguinal, and lumbar nodes. The sides and back of the neck include the cervical lymph nodes.

Typically, these glands are incredibly tiny. A lymph node, however, is swollen if its diameter is higher than 1 centimeter. Deep inside the neck, the cervical lymph nodes are located.

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we have the expression

Remember that

Evaluate

For x=2i

substitute

Answer: no equation can pass through those points

Step-by-step explanation:

the x value -4 has two y values, 5 and -2. a function needs at most 1 y value to be considered a function.

Answer:

The biker's pace is 25 miles per hour and the walker's speed is 50/3 miles per hour.

Answer:The speed of the walker is 16.67 miles per hour.

The speed of the cyclist is 25 miles per hour.

How to calculate the value?

Let the speed of a walker = x

Biker's speed = 1.5x

Their relative speed will be:

= 1.5x - x = 0.5x

Distance between them = 12.5 miles

Time taken = 1.5 hours.

It should be noted that distance will be:

= Speed × Time

12.5 = 1.5 × 0.5x

Divide through to get x

12.5 = 0.75x

x = 16.67 miles per hour.

Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.

The given polynomial 6+3x⁴ +7x⁵ +7x² is a quadrinomial.

So, 6+3x⁴ +7x⁵ +7x²:

Therefore, the given polynomial 6+3x⁴ +7x⁵ +7x² is a quadrinomial.

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Answer:

I believe it stands for Side, Side, Side

Step-by-step explanation:

When two triangles with all three sides are equal they're SSS

The solution to the inequality problem is represent by the graph attached below.

To solve this problem we simply need to use a graphing a calculator to plot the graph of the two inequalities. The points of intersection represents the solution of the graph.

The broken purple line represents the first inequality and the second straight line represents the second inequality.

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The length of the original sides of the rectangle are 72m and 24m.

The area of a rectangle formula is used to calculate the area occupied by the rectangle within its boundaries. A rectangle's area is calculated by multiplying its length and breadth.

Given:

One side is 3 times as long as the other in a rectangle.

Let the length of the rectangle be 3x and the breadth of the rectangle be x.

Area of original rectangle = length × breadth

                             = 3x² m²

Now, the longest side is extended by 4m.

Length of rectangle = 3x + 4

Area of rectangle = length × breadth

                             =  x(3x + 4) m²

It is given that this area will be 96 square meters larger than the former.

So, x(3x + 4) - 3x² = 96

⇒ 3x² + 4x - 3x² = 96

⇒ 4x = 96

⇒ x = 24 m

Original length of the rectangle = 3x = 3×24 = 72m

Therefore, the original length of the rectangle is 72m and the original breadth of the rectangle is 24m.

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the probability that Ron will get in trouble with Professor Snape at least two times in one day is 0.7

We are given

  X    0         1        2         3        4

P(X)    0.15   0.20   0.20   0.30   0.15

we want Ron Weasley to get in trouble at least two time in one day

that mean X 2

P(X 2) = P(X=2) + P(X=3) + P(X=4)

= 0.20+0.30+0.15

= 0.65= 0.7 (rounded to nearest tenth)

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If the sum of two angles is 180 then the angles are supplementary.This is true.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.

If the total of two angles is 180 degrees, they are considered to be supplementary angles since they form a linear angle when combined. If the total of two angles is 90 degrees, they are considered to be complimentary angles since they produce a right angle when combined.

If two angles add up to 180 degrees, they are considered to be supplementary angles in geometry. For example, if A + B = 180°, A and B are referred to as supplementary angles. When supplementary angles are combined, they always yield a straight angle (180 degrees).

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The change that increases the loudness is a > 1

From the question, the equation of the function that represents the musical note is given as

y = a sin(1320πx)

Where

In sound, the sound loudness is directly proportional to the amplitude.

This means that an increment in the amplitude, would cause the note to become louder

This change is represented as a > 1

This is so because a represents the amplitude, and the initial value is 1

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Trina is closer to the surface of the ocean. She will not fly higher than Jessie did.

Consider the provided information.

The distance is the absolute value of a number.

Part (A) : It is given that Trina went scuba diving and reached an elevation of -85.5 meters, which is below sea level.

That means the distance she covers is: |-85.5| = 85.5 meters

Thus Trina covers 85.5 meters.

Jessie went hang gliding and reached 87.9 meters which is above sea level.

That means the distance she covers is: |87.9| = 87.9 meters

We know that 85.5 < 87.9

So, we can say that Trina is closer to the surface of the ocean as she covers less distance.

Part (B) : Trina wants to hang glide at the same number of meters above sea level as she scuba dived below sea level.

That means she will hang the glide at a height of 85.5 meters.

As we know 85.5 < 87.9

Thus, she will not fly higher than Jessie.

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The angles ∠4 and ∠6  are found to be supplement angles.

For the given question;

∠5 ≅ ∠6 ( both are congruent means equal)

As, ∠4 and ∠5 are forming on the straight line. Thus,

∠4 + ∠5 = 180 (linear pair)

But, ∠5 ≅ ∠6 , replacing ∠5 with ∠6 .

∠4 + ∠6 = 180 supplement angles.

Thus, ∠4 and ∠6 are found to be supplement angles.

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Work Shown:

1 foot = 12 inches

3*1 foot = 3*12 inches

3 feet = 36 inches

I multiplied both sides by 3 so that the "12" turns into "36".

Answer:3 feet

36/12=3

3x12=36

so 36 inches= 3 feet

hope it helps

Answer: x= 11

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

im assuming u r trying to find x

you need to solve the bracket first (2×x =2x , 7×2= 14)

After that move numbers with x to ur left, to make life easier

3x-2x= x

14-3 = 11

x=11