2X + 10 = -2
3X -4 311
X=__
X =
4X - 1 = -5
X =
I!!!
X =
2X + 5 = 21
-3x - 2 = -17
X =

Answer:

2m/s south

Step-by-step explanation:

p = mv

Where p is the momentum, m is the mass, while v is the velocity.

Given that

m = 25kg

v = ?

p = 50kgm/s

Substituting the values into the formula.

50kgm/s = 25×v

50kgm/s = 25v

Divide both sides by 25

v = 50/25

v = 2m/s

From the option list, the answer is

2m/s south

Answer:

16) x=13.5 17) x=17

Step-by-step explanation:

*The sum of the interior angles of a 5 sided polygon is 540 degrees.

16) The angle measures are 10x-1, 6x+5, 6x+5, 8x+9, and 8x+9. We add these values up to get 38x + 27. Because the sum of the interior angles must be 540, we set an equation of 38x + 27 = 540. From here, we can make it 38x = 513. Then we divide out the 38 and that leaves us with x = 13.5.

17) In this 5 sided polygon, the angle measures are 139, 5x, 92, 71, and 9x. Like number 16, we add these up to get a sum of 14x + 302 = 540. We subtract out the 302, leaving us with the equation 14x = 238. Finally, we divide out the 14 to get x = 17.

I hope the numbers are right since the values are a bit blurry! If not, just use the same work process to get your answer :)

#16

\(\\ \sf\longmapsto 2(6x+5)+2(8x+9)+10x-1=540\)

\(\\ \sf\longmapsto 12x+10+16x+18+10x-1=540\)

\(\\ \sf\longmapsto 38x+27=540\)

\(\\ \sf\longmapsto 38x=513\)

\(\\ \sf\longmapsto x=13.5\)

#17

\(\\ \sf\longmapsto 5x+9x+139+71+92=540\)

\(\\ \sf\longmapsto 14x+302=540\)

\(\\ \sf\longmapsto 14x=238\)

\(\\ \sf\longmapsto x=17\)

Answer:

$3240

Step-by-step explanation:

2700x.20=540

2700+540=3240

Therefore ,The marked point will now have the updated coordinates P' (2, 7).

When a figure is transferred from one area to another without altering its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Here,

On an X-Y coordinate plane, a figure is plotted.

When translating a figure 7 units to the down, we must provide the coordinates of the indicated point in the original figure

"(x, y)" = "(x + m, y + n)"

In response to the query, we have

The specified point's coordinates are: P (5,4).

The new coordinates of the indicated spot after this figure is translated 6 units to the right will be -

P'( 5,4- 7) = P'(5, -3) (5, -3)

As a result, the designated point's new coordinates are P' (5, -3)

The new coordinates of the marked point will be - P'(5, -3)

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Answer:

Yes

Step-by-step explanation:

When the greatest common factor of two numbers is 1 or -1, the numbers are known as relatively prime. This means there are no numbers that can be factored out of both of the numbers, meaning if the numerator and denominator are relatively prime, they can not be simplified any further.

The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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The largest number that divides two or more numbers evenly is greatest common divisor (GCD).

The biggest positive number that divides any non-zero integer by two or more is known as the greatest common divisor.

The greatest common divisor is the biggest number that divides two or more numbers proportionally (GCD).

Using the LCM method, the steps to calculate the GCD of (a, b) are as follows:

Find the result of a and b in step 1.

Find a and b's least common multiple (LCM) in step two.

Step 3: Dividing the results of Steps 1 and 2.

Step 4: The value that results from division is the most significant common divisor of (a, b).

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Answer:

  B.  61

Step-by-step explanation:

The sum of arcs around a circle is 360°. This means ...

  110° +128° +c° = 360°

  c° = 122° . . . . . . . . . . . . . subtract 238°

__

An inscribed angle in a circle has half the measure of the arc it subtends.

  a° = 1/2c° = 1/2(122°) = 61°

__

The other angles in the diagram are ...

  b° = 1/2(110°) = 55°

  d° = 1/2(128°) = 64°

Length of AB = 8.06 units

Length of BC = 8.94 units

Length of AC = 9.22 units

What is a Scalene Triangle?

A scalene triangle is a type of triangle with three different length sides and three interior angles that add up to 180 degrees. Scalene triangles have no equal of parallel sides , hence there is no line of symmetry. The interior angles of a scalene triangle can be acute , right or obtuse angles.

Given data ,

Triangle ABC with vertices

A( 5 , 12 ) , B( 13 , 13 ) and C( 11 , 5 )

From the coordinates , we can see that

Now ,

When two points are given P( x₁ , y₁ ) and Q( x₂ , y₂ ) , the distance between the two points is given by distance formula

D = √( x₂ - x₁)² + ( y₂ - y₁)²

So , Length of AB is given by

AB = √( 13 - 5 )² + ( 13 - 12 )²

AB = √( 64 + 1 )

AB = √65

AB ≈ 8.0622

So , Length of AB = 8.06 units

And , Length of BC is given by

BC = √ ( 11 - 15 )² + ( 5 - 13 )²

BC = √ ( 16 + 64 )

BC = √ 80

BC ≈ 8.944

So , Length of BC = 8.94 units

And , Length of AC is given by

AC = √ ( 11 - 5 )² + ( 5 - 12 )²

AC = √ ( 36 + 49 )

AC = √85

AC ≈ 9.219

So , Length of AC = 9.22 units

Since , the lengths of AB , BC and AC all are different , we can say that the triangle ABC is a scalene triangle

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Answer:

(-5,2)

Step-by-step explanation:

x=-5

-5-5y=-15

plus 5 on both sides you get

-5y=-15

divide by -5y to get

y=2

Answer:

0.00636

Step-by-step explanation:

The limit of 5x²/sin(6x)sin(x) as x approaches 0 is 5/6.

In the given expression, we have a fraction with multiple terms involving trigonometric functions. Our goal is to simplify the expression so that we can evaluate the limit as x approaches 0.

First, we observe that as x approaches 0, both sin(6x) and sin(x) approach 0. This is because sin(θ) approaches 0 as θ approaches 0. So, we can use this property to rewrite the expression.

Next, we use the fact that sin(x)/x approaches 1 as x approaches 0. This is a well-known limit in calculus. Applying this property, we can rewrite the expression as:

limx→0 5x²/sin(6x)sin(x)

= limx→0 (5x²/6x)(6x/sin(6x))(x/sin(x))

Now, we can simplify the expression further. The x terms in the numerator and denominators cancel out, and we are left with:

= (5/6) (6/1) (1/1)

= 5/6

Thus, the limit of 5x²/sin(6x)sin(x) as x approaches 0 is 5/6.

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Ans: 55°

Let's draw two parallel line intersecting angle x° and 45° as shown in the photo.

i) a=25° [Being Alternative Angle]

ii) d=15° [Being Alternative Angle]

iii) c= 45°-d[45°=c+d]

=45°-15°

=30°

iv)b=c[Being Alternative Angle]

v)x=a+b[Combining Angle a & b]

=25°+30°

=55°

Answer:

7.987

Step-by-step explanation:

  1 4

×     5 7 0 5

+         7 0

+ 0 0 0 0 0  

+     9 8    

+   7 0      

=  7 9 8 7 0

Rewrite the product with 4 total decimal places.

Answer = 7.9870

Therefore:

0.14 × 57.05 = 7.9870

Answer:

You can’t add 3x with 2x because to get term to the other side of the equal sign, you need to do the inverse (opposite) of the number. Since 3x is positive (basically with a + in the front) you SUBTRACT 3x for it to get to the other side. Which will get u -1x or just -x.

Answer:

135

Step-by-step explanation:

m(abc)= m(abd) +m(dbc) = 65+60 =135

Answer:

A is the correct answer

Step-by-step explanation:

∂g/∂u is equal to 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v)).

To find the indicated derivative, we need to use the chain rule. Let's differentiate step by step:

Given:

g(u, v) = f(x(u, v), y(u, v))

f(x, y) = 7x³y³

x(u, v) = ucos(v)

y(u, v) = usin(v)

To find ∂g/∂u, we differentiate g(u, v) with respect to u while treating v as a constant:

∂g/∂u = (∂f/∂x) * (∂x/∂u) + (∂f/∂y) * (∂y/∂u)

To find ∂f/∂x, we differentiate f(x, y) with respect to x:

∂f/∂x = 21x²y³

To find ∂x/∂u, we differentiate x(u, v) with respect to u:

∂x/∂u = cos(v)

To find ∂f/∂y, we differentiate f(x, y) with respect to y:

∂f/∂y = 21x³y²

To find ∂y/∂u, we differentiate y(u, v) with respect to u:

∂y/∂u = sin(v)

Now, we can substitute these partial derivatives into the equation for ∂g/∂u:

∂g/∂u = (21x²y³) * (cos(v)) + (21x³y²) * (sin(v))

To find the simplified form, we substitute the given values of x(u, v) and y(u, v) into the equation:

x(u, v) = ucos(v) = u * cos(v)

y(u, v) = usin(v) = u * sin(v)

∂g/∂u = (21(u * cos(v))²(u * sin(v))³) * (cos(v)) + (21(u * cos(v))³(u * sin(v))²) * (sin(v))

Simplifying further, we get:

∂g/∂u = 21u⁵cos⁴(v)sin⁴(v)(cos(v) + u³cos⁴(v)sin²(v)sin(v))

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Answer:

y

=

−

1

3

x

+

22

3

Step-by-step explanation:

Hello!

The perimeter is the sum of all sides of the figure. As we know, this is rectangular parking with a length equal to 69m. Look at the figure below:

As we know the definition of the perimeter, we can sum all sides, look:

Answer for A:

width of the parking lot = 58m.

We'll solve it in a similar way.

The area of a rectangle is obtained using the formula:

Replacing the values, we'll obtain:

Answer for B:

length of the pool = 78m.

Answer:hi

Step-by-step explanation:

Answer:

Origin of common law

The English common law originated in the early middle ages in the King's court. It did not have substantive rights but it consisted of procedural remedies. Until the 19th century, the English common law continued to be developed primarily by the judges rather than the legislature.

Answer:6.56

Step-by-step explanation:

Answer:

Step-by-step explanation:

Length of the third board = Total length - ( sum of other two boards)

                                         = 21.35 - ( 8.2 + 6.42)

                                        = 21.35 - 14.62

                                       =      6.73 m

The average time it takes to rent a video tape is 0.141 minutes.

Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.

Thus, the average time it takes to rent a video tape is 0.141 minutes.

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Theorem 9.11 states that the p-series ∑_(n=1)^∞ 1/n converges if p > 1 and diverges if p ≤ 1.
In the given series, we can see that each term is of the form n^3, which can be written as (n^p)^3 where p=1/3.

Since p=1/3 is less than or equal to 1, we can conclude that the series diverges by applying Theorem 9.11.

Therefore, the given series diverges.
Using Theorem 9.11, we can determine the convergence or divergence of the given p-series. This theorem states that a p-series ∑_(n=1)^∞ 1/n^p converges if p > 1 and diverges if p ≤ 1.

If you meant to write the series as 1/8 + 2/27 + 3/64 + 4/125 + ... (with terms of the form n/n^3), then it is a p-series with p = 3 > 1. In this case, according to Theorem 9.11, the series converges.

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The number of ways for filling 4 positions out 17 applicants is 57120

For the local dry cleaner 17 candidates were interviewed.

There are four positions available cashier, washer, salesperson, and delivery driver.

To calculate number of ways by which they can fill those 4 positions first we need to find the no of ways to select 4 candidates out of 17 candidates.

No of ways to select r candidates out of n

= nCr

=( n!) / (r!)(n-r)!

= 17!/( 4! ) ( 17-4)!

17Cr = 2380.

For assigning the four positions to the four candidates there are

17C4 x 4! ways.

So, The number of ways for filling 4 positions out 17 applicants = 2380 x 4!

The answer to this problem is 57120.

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Answer:

Step-by-step explanation:120

The perimeter is :

Work:

Assuming you're asked to find the perimeter of a rectangle, I set to work.

The formula is A = LW, where A is the area, L is the length and W is the width.

Diagram

\(\boxed{\begin{tabular}{c}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\\\\\end{tabular}}}\sf{~~42\:ft}\\\sf{~~~~~~18~ft}\)

Plug in the values.

You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The relationship between the two variables in a bivariate data set is graphically represented by a scatter plot. Consider them to be the graphic depiction of two data sets that have been combined by allocating each axis in the plot to a distinct variable.

Due to the presence of two variables, this type of data is known as bivariate data. Only 1 variable may be displayed on a line plot. You can use scatter plots to present bivariate data. The data can be used to create coordinate pairs.

The standard deviation of each variable and the covariance between them must first be determined in order to calculate the Pearson correlation. Covariance is subtracted from the product of the standard deviations of the two variables to get the correlation coefficient.

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The magic ratio for muffins in 2:2:1:1.

The magic muffin ratio is 2:2:1:1. This equates to 2 parts flour, 2 parts liquid, 1 part fat, and 1 part eggs. The most crucial aspect is to remember to utilize the same unit of weight for each component!

Rinse frozen blueberries many times in cold water until the water turns lighter in color to prevent your batter and baked items from developing a purple-blue tint. Then, blot them dry with a paper towel and gently fold them into the batter. The goal of this procedure is to maintain fast breads light and delicate by limiting the quantity of gluten produced during the mixing process. To do this, the dry components are mixed in a one bowl, the wet ingredients are combined in a separate bowl, and then the two mixtures are combined together.

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