A square playground has an area of 175 m2. What is the approximate length of each side of the playground? Round your answer to the nearest meter

Well, 50% of 15 is 7.5 , so you should say something a little less than that. The real answer is 7.35

Try this solution (see the attachment).

Final answer:

The general solution to the differential equation (8 + x)y' = 3y is y = C(8+x)³, where C is a constant and can be found by integrating and rearranging the separated variables.

Explanation:

To find the general solution of the differential equation (8 + x)y' = 3y, we can separate variables and integrate both sides. First, we divide both sides by (8 + x) and then by y to get [tex]\frac{ y'}{y} = \frac{3}{8 + x}[/tex]

Next, we integrate both sides:

Integrate LHS: [tex]\int \frac{dy}{y} = ln|y| + C_1[/tex]

Integrate RHS: [tex]\int \frac{3dx}{8 + x} = 3ln|8+x| + C_2[/tex]

Now, we can combine the two constants (C₁ and C₂) into a single constant C by writing C = C₂ - C₁. So our solution looks like ln|y| = 3ln|8+x| + C. We can exponentiate both sides to solve for y:

[tex]y = e^{3ln|8+x|+C}[/tex]

Remembering that [tex]e^{ln|a|} = a[/tex], we can simplify this to:

y = C(8+x)³ where C is a constant.

This is the general solution to the differential equation.

1/2 divided by 3 is 1/6.
So your answer is 1/6 pounds each person.

3 friends equally shared 1/2 pound of trail mix, during the hike.

Total quantity of trail mix = 1/2 pound

Quantity shared by each friend is 1/3 rd of the trial mix

= 1/3 * 1/2 pound

= 1/6 pound

Therefore, during the hike, each friend shared 1/6 pound of the trail mix.

Hope this helps ..!!

Thank you :)

She read 5 pages

8÷4=2+3=5

Final answer:

To find the total number of pages they have read so far, add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class. The total number of pages they have read so far is 5 pages.

Explanation:

To find the total number of pages they have read so far, we need to add the number of pages Mrs. Ross read to the class and the number of pages Mrs. M read to the class.

Mrs. Ross read 1/4 of the chapter, which is 8 x 1/4 = 2 pages.

Mrs. M read 3 pages to the class.

Therefore, the total number of pages they have read so far is 2 + 3 = 5 pages.

subtract:
189.95 - 45.00 = 144.95

the cost = 144.95

Answer:

Cost price of an item = $144.95

Step-by-step explanation:

Cost price is the price at which the article is purchased .

It includes all the expenses incurred on that item till the time it is owned by us .

Selling price is the price at which the item is sold to the customer .

Market price is the price marked on the product . It is basically the current price of the item .

We know that selling price - market price = cost price

Given :

Market price of an item =  $45.00

Selling price of an item = $189.95

To find : cost price of an item

Solution :

Cost price = $189.95 - $45.00 = $144.95

Note: The explanation of problems b) and c) are attached as images because of the maximum limit of 5,000 characters.

Answers:

a) [tex]y = -\frac{1}{32} x^2 + \frac{49}{8}[/tex]
b) [tex] \frac{49}{8} \text{ meters} [/tex]
c) [tex]y = -\frac{1}{32} (x-14)^2 + \frac{49}{8}[/tex]

Explanations:

a) Note that the path where the ball travels when kicked off the ground is the parabola. 
Let (h,k) be the vertex of the parabola. Since the vertex is in y-axis, the x-coordinate of the vertex is 0. So, h = 0. 
The equation of the parabola with vertex (h, k) is given by
 [tex]y = a(x - h)^2 + k[/tex]   (1) Since h = 0, we can replace this to equation (1) so that 
 [tex]y = a(x - h)^2 + k\\ y = a(x - 0)^2 + k\\ y = ax^2 + k[/tex]   (2)

To solve for a and k, we need to get the coordinates of the points of parabola. In the problem, it is possible to determine the coordinates of the points where the ball is kicked off from the ground and where the ball ended hitting the ground and the point where the ball hits the tree which are points of the parabola.
Since the ground is in x-axis and the ball is kicked off from the ground and ended hitting the ground, the parabola intersects the x-axis at the points where the ball is kicked off from the ground and where the ball ended hitting the ground. 
Let

A = point where the ball is kicked off from the ground
B =  point where the ball ended hitting the ground
M be the midpoint of A and B.

Note that the x-coordinate of the vertex of the parabola is the same as the x-coordinate of M. Since the x-coordinate of the vertex of the parabola is 0, the x-coordinate of M is 0. Moreover, since the ground is in x-axis, A and B are in the x-axis and so M is in x-axis. So, the y-coordinate of M is 0 because the y-coordinate of any points of x-axis is 0. Thus, the coordinates of M are (0,0).
As mentioned earlier, the y-coordinate of any points in x-axis is 0. Since A and B both lie in x-axis, their y-coordinate is 0. Now, we let j be the x-coordinate of A and k be the x-coordinate of B so that (j, 0) are the coordinates of A and (k, 0) are the coordinates of B.

Since the ball traveled with a horizontal distance of 28 meters when it is kicked off until it hit the ground, the horizontal distance from A to B is 28. Since the coordinates of A and B are (j, 0) and (k, 0) respectively, using the distance formula the distance from A and B is given by 

[tex]d = \sqrt{(j-k)^2 + (0 - 0)^2} \\ 28 = \sqrt{(j-k)^2} \\ (j-k)^2 = 28^2 \\ \boxed{j - k = \pm 28}[/tex]

Since A is the point where the ball is kicked off and B is the point where the ball hits the ground, A is in the left of B. Since A and B are both in x-axis and j and k are the x-coordinates of A and B respectively, j < k. Thus, j - k is negative and so

j - k = -28      (3)

Because M is the midpoint of A and B, the x-coordinate of M is [tex] \frac{j+k}{2}[/tex]. Since the x-coordinate of M is 0,

[tex]\frac{j+k}{2} = 0[/tex]     (4)

Multiplying both sides of equation (4) by 2, we have

j + k = 0   (5)

Now, we add equations (3) and (5) so that 

2j = -28
j = -14

Substituting the value of j in (5), we have

j + k = 0
-14 + k = 0
k = 14

Hence the coordinates of A are (-14,0) and the coordinates of B are (14,0). Since point A is in parabola, we can substitute its coordinates of A in equation (2) with x = -14 and y = 0 so that 

[tex]y = ax^2 + k \\ 0 = a(-14)^2 + k \\ 0 = 196a + k \\ \boxed{196a + k =0} [/tex]      (6)

Note that, if we substitute the coordinate of B, we also arrive at equation (6), which is useless.

So, we need to determine the coordinates of another point of parabola, which is the point where the ball hits the tree. We call this point C. Since the tree is 3 meters high and the ground is in x-axis, the y-coordinate of point C is 3. Let c be the x-coordinate of C. Since the ball hits the tree after travelling a horizontal distance of 24 meters, the horizontal distance from A to C is 24. Moreover, the horizontal distance is the difference of x-coordinates of two points. Since C is the right of A and the x-coordinate of A is -14

c - (-14) = 24
c + 14 = 24
c = 10

Hence, the coordinates of C are (10, 3). Substituting this to equation (2), we have

[tex]y = ax^2 + k \\ 3 = a(10)^2 + k \\ 3 = 100a + k \\ \boxed{100a + k =3} [/tex]       (7)

Subtracting equation (6) to (7), we have

[tex](196a + k)-(100a + k) = 0-3 \\ 96a = -3 \\ \boxed{a = -\frac{1}{32} }[/tex]

Substituting the value of a in equation (6) we have

[tex]196a + k = 0 \\ 196(-\frac{1}{32}) + k = 0 \\ \\ -\frac{49}{8} + k =0 \\ \\ \boxed{k = \frac{49}{8} } [/tex]

Using equation (2) and the values of a and k, the equation of the parabola is given by 

[tex]\boxed{y = -\frac{1}{32} x^2 + \frac{49}{8} }[/tex]

sally can have 3 pairs of full outfits

Answer:

150

Step-by-step explanation:

Because, 5 x 3 x 10 = 150.

10 x 3

10 20 30

1    2   3

( add 10 every time )

30 60 90 120 150

1    2   3     4     5

( add 30 every time )

I tried to explain well.

Lucky for you, 18.84 is already rounded to the nearest hundredth.

When rounding 18.84 to the nearest hundredth, the result is 18.84 that means the number 18.84 remains unchanged when rounded to the nearest hundredth.

Given information:

The number is 18.84 and need to round it to the nearest hundredth.

Steps to round to the nearest hundredth:

Look at the digit in the thousandth place (the third decimal place). In this case, it is 4.Determine if the digit is 5 or greater. If it is, round up; if it is less than 5, round down.Since the digit in the thousandth place is 4, which is less than 5, there is no need to round.

Therefore, the number 18.84 remains unchanged when rounded to the nearest hundredth.

Therefore, when rounding 18.84 to the nearest hundredth, the result is 18.84.

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x= total pounds bagged

Multiply the number bagged by the number of pounds of each bag.

x= (5 * 1/4 lb) + (2 * 1/2 lb)
x= [(5*1)/4] + [(2*1)/2]
x= 5/4 + 1
convert fraction to mixed number
x= 1 1/4 + 1
x= 2 1/4 total pounds bagged

ANSWER: Libby bagged 2 1/4 pounds of crackers.

Hope this helps! :)

when a number is a composite it has more than two factors so, therefore, the answer is no it is a prime because it only has one factor

The number 127 is a prime number as it has no divisors other than 1 and itself.

The number 127 is a prime number. A prime number is defined as a number that is greater than 1 and has no positive divisors other than 1 and itself. To determine if 127 is prime, we must check if it can be divided evenly by any number other than 1 and 127. When we perform this check, we find that 127 does not have any divisors other than 1 and itself, confirming that it is indeed a prime number.

50 -7 1/4 -13 1/2 -15 1/4 = 14 . . . . gallons remain

14 gallons would remain in the gas tank after the third part of his journey.

Each frame costs $12. Since you are ordering 15 frames, the price of the frames is 15 * $12 = $180.
Shipping is $8 for the entire order, not for each frame, so just add $8 to the price of the frames.
$180 + $8 = $188
Answer: The total cost of the order is $188.

Answer:

$188

Step-by-step explanation:

Since you requested I answer this, I will do my best, but I'm not sure I can explain it well. 

45° clockwise from due east is just 45° from the east. Moving clockwise, which is the direction the hands of a clock move, you're going to the south, and since it's by 45°, you're halfway between east and south, so you're southeast.

Final answer:

A direction of 45 degrees clockwise from due east would put you in the South-East quadrant of a compass or geometric plane.

Explanation:

When discussing directions in terms of degrees, it's commonly understood with the idea of a compass rose or a unit circle in mind. Here, 'Due East' is represented as 0 or 360 degrees. A clockwise rotation would mean we are moving in a positive direction.

Therefore, if you start from Due East which is 0 degrees and rotate 45 degrees in the clockwise direction, you would end up in the south-east direction. This is because in the coordinate system, the +x direction is East and moving in the clockwise direction, the next quadrant would be the South-East quadrant. So, 45 degrees clockwise from due east would be considered as South-East direction on a compass rose or geometrically on a plane if you are looking at it in terms of degrees on a circle.

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Final answer:

OPTION B.

The rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6) shows the new position of the original rectangle after a translation of 2 units upwards on the y-axis.

Explanation:

In mathematics, a translation moves an object without changing its shape or orientation. You simply move it to another position in the plane. To find the new position of the rectangle after a translation, we need to find which set of coordinates matches those of our original rectangle but is located in a different spot.

Looking at the options given, the only rectangle that represents a translation of the original is the rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6). This rectangle is similar in shape and orientation to our original rectangle, but it is shifted 2 units upwards on the y-axis.

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A graph that shows the new position of the rectangle after a translation include the following: C. Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4).

How to transform the preimage and image of a quadrilateral?

In Mathematics, a translation is a type of transformation that is typically used for shifting every point of a geometric object in the same direction on the cartesian coordinate, as well as for the same distance.

In this scenario and exercise, we would apply a translation of 2 units to the right and 2 units up to the given rectangle, in order to determine the new position of the rectangle after a translation as follows;

(x, y)                        →           (x + 2, y + 2)

Point (1, 0)               →    (1 + 2, 0 + 2) = (3, 2).

Point (1, 2)                →    (1 + 2, 2 + 2) = (3, 4).

Point (6, 0)               →    (6 + 2, 0 + 2) = (8, 2).

Point (6, 2)               →    (6 + 2, 2 + 2) = (8, 4).

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Complete Question:

Which graph shows the new position of the rectangle after a translation?

Rectangle with coordinates: (1, 0), (1, 2), (6, 0), and (6, 2).

A. Rectangle with coordinates: (0, negative 1), (0, negative 6), (2, negative 1), and (2, negative 6).

B. Rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6).

C. Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4).

D. Rectangle with coordinates: (0, negative 0.5), (1, negative 0.5), (0, negative 3), and (1, negative 3).

The above is an estimation question. Estimation is when you judge the results obtained from a sample and make a rough calculation. The answer obtained might not be exactly right, its based on a judgement.

In this a sample was taken and out of 80 books, 6 of them were history books.
The assumption made then is that for every 80 books taken randomly , 6 of them will be history. Using this assumption ;
21 360 books in the library,
for every 80 books - 6 history books
then for 21 360 books - 6 / 80 * 21360
                                   =  1602 history books

You take ten percent of 33, which is 3.3, and subtract it from the original price.
33-3.3=29.7 which means the final price is $29.70

Answer:

$29.70

Step-by-step explanation:

The word of in an equation or expression = multiply.

10 percent of $33 =  1/10 x 33/1 or 33/10 ($3.30)

$33 - $3.30 = $29.70

I have attached a picture that shows the computation with an explanation for each number. The main idea is to represent the situation with the retail price, multiplied by the percent you'll pay after 20% has been deducted, multiplied by the percent you will pay after the additional 15% is taken off for store A. For store B it will be the retail price multiplied by the price you pay after the 35% has been taken off. You can see that store C will be a lower price after the discounts.

The obtuse angle is 165 degrees.

You find this by subtracting 15 from 180
180 - 15 = 165
This works because the two angles (15 and 165) are supplementary. They add to 180 degrees and form a straight angle.

FIND LOT AREA:
Area = length * width
A= 18 feet * 45 feet
A= 810 feet squared

FIND # OF YARDS:
1 yard= 3 feet

Divide number of square feet by number of feet per yard.
Yards= 810 ÷ 3
Yards= 270

FIND PRICE OF SOD:
multiply number of yards by price per square yard.
Price= 270 yards * $12/yard
Price= $3,240

ANSWER: Cindy will pay $3,240 to cover the lot with sod.

Hope this helps! :)

25% times 80 = 20. 20 students have green eyes.:) :)

Answer:

The ratio is a fraction that tells us how many times longer a thing is compared to another thing. In mathematics, we express a ratio as the relationship between two numbers, namely [tex]a \ and \ b[/tex], so the ratio can be written as:

[tex]r=\frac{a}{b}[/tex]

If we can change this number without changing the ration we need to multiply  both the numerator and the denominator by the same number. For instance, if we have the following ratio:

[tex]r=\frac{2}{3}[/tex]

We can multiply both the numerator and denominator, say, by 7. Then:

[tex]r=\frac{7\times 2}{7 \times 3}=\frac{14}{21}[/tex]

As you can see, the ratio's number has changed but without changing the ratio itself because:

[tex]\frac{2}{3}=\frac{14}{21}[/tex]

6050(.14)=847
150+847=997
He made $997

Answer: -135

Explanation:

1) I will use synthetis division

2) Write the coefficients of the divisor in order

   1    -3    7    5

3) Dividing by x + 4 => use x = - 4

4) Division:

      | 1     -3       7       5
      |
 - 4 |       -4    +28   - 140
-------------------------------
        1    -7      35    - 135

5) The last number is the remainder: - 135

Let's use syntethic division
The dividend is x^3-3x^2+7x+5
Write the coefficients in decresing order:
x^3   x^2   x   Independent term
1       -3     7      5

Let's do the synthetic division with x=-4
    ! 1   -3      7          5
-4 !___-4__28__-140_
      1   -7    35     -135

The remainder is the last term: -135

I think your answer might be 19.5

Angle 1 = 8x + 45
Angle 2 = x

x + 8x  + 45 = 180
combine like terms

9x + 45 = 180
subtract 45 from both sides

9x = 135
divide both sides by 9 to isolate x

x = 15

Angle 1 = 8(15) + 45 = 165 degrees
Angle 2 = 15 degrees

Just remember in Law of cosines: 

[tex] a^{2} = b^{2} + c^{2} - 2bccosA[/tex]

The A there is the angle opposite of side a.

In the case of the formula given to you for triangle RST instead of A, S was used and that means the letter in the left side of the equation would be s, so S = 5.

If you look at the base formula given to you, 5 is S. With that alone you can eliminate the first three choices because none of them shows that S = 5. 

1/2
1/4:1/2=1/4•2/1=2/4=1/2

To understand 1/4 dividend by 1/2 lets start with understanding what division does;

1/4 dividend by any number greater than 1 will make smaller quantities than 1/4 because you cut that 1/4 to make out of it 2 or 3 or 4...etc. equal groups

1/4 : 2 = 1/8
1/4 cut to make 2 groups =2 groups of 1/8

1/4 dividend by a number smaller than 1 like 1/2 will make you bigger quantity than 1/4 because because you don’t make not even a whole group yet a half (1/2) a group.

1/4: 1/2= 1/4 •2= 1/2

In a regression analysis, you look at the relationship between two or more variables. Your question is very vague. But whenever you have a negative coefficient it means that dependent variable is negatively correlated to the independent variable.

3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?

The domain of a function is the complete set of possible values of the independent variable.

The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.

2x+3y=18

For this equation, domain and range both would be all real numbers.

3x-4y>16

Here domain and range both will be all real numbers.

55 degrees is your answer

Answer:

55 degree

Step-by-step explanation:

By the Law of cosines: a2 = b2 + c2 – 2bccos(A)

That is the image. :-）