The city wants to build a football field. Each wheelbarrow full of dirt covers an area of 10x squared. Determine how many wheelbarrows full of dirt they need for the field below. One side of the rectangle is just 5x squared. The other side is 10x square plus 90x.

QUESTION POSTED AT 18/01/2020 - 07:33 AM

Answered by admin AT 18/01/2020 - 07:33 AM

As this is a unitless problem, let us try to deal with it as if it does have units. Since we are already given the length and width of a rectangle, we can solve for the area by multiplying. After getting the area, we divide this by the area a wheelbarrow can cover to obtain the expression for how many wheelbarrows we need.

Rectangle length = 10x^2 + 90x
Rectangle width = 5x^2
Rectangle area = length * width = 5x^2(10x^2 + 90x)

Rectangle area = 50x^4 + 450x^2

Dividing:

          _5x^2_+_45____10x^2|50x^4 + 450x^2           50x^4          --------                        450x^2                        450x^2                         ---------                                  0

Therefore, the expression for how many wheelbarrows are to be used is 5x^2 + 45 wheelbarrows.

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Related questions

What is the conjugate of the square root of -15 ? ...?

The answer to the problem is as follows:


The square root of -15 is equal to i*sqrt(15). Therefore, the conjugate of this complex number is -i*sqrt(15).


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!



ANSWERED AT 16/02/2020 - 06:43 PM


QUESTION POSTED AT 16/02/2020 - 06:43 PM

True or false. The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. ...?

Answer:  The given statement is FALSE.

Step-by-step explanation:  We are given to check whether he following statement is true or false :

"The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. "

Let us consider the right-angled triangle ABC as shown in the attached figure below.

With respect to acute angle C, we can see that

perpendicular, p = AB

base, b = BC

and

hypotenuse, h = AC.

We know that

sine of an angle in a right-angled triangle is equal to the ratio of the perpendicular to the base.

So, we must have

\sin \angle C=\dfrac{p}{h}\\\\\\\Rightarrow \sin \angle C=\dfrac{AB}{AC}.

Since AB is the opposite side to angle C, not adjacent, therefore

sine of any angle in a right-angled triangle is the ratio of the length of the OPPOSITE SIDE to length of the hypotenuse.

Thus, the given statement is FALSE.

ANSWERED AT 16/02/2020 - 06:38 PM


QUESTION POSTED AT 16/02/2020 - 06:38 PM

Find the area of the regular polygon. Give the answer to the nearest tenth. dodecagon with a perimeter of 108 cm ...?

A regular dodecagon is a polygon with 12 equal sides.
Length of each side = 108/12 = 9 cm.

Length of the apothem = (9/2)/tan 15 = 9/2tan 15 = 16.79 cm

Area of each triangle = 9/2(16.79) = 75.57 cm^2

Therefore, area of the dodecagon = 12(75.57) = 906.9 cm^2

ANSWERED AT 16/02/2020 - 06:36 PM


QUESTION POSTED AT 16/02/2020 - 06:36 PM

A rectangular table is two times as long as it is wide. If the area is 50ft^2, find the length and the width of the table.

10ftx5ft .........................................................................................................................................................................................................................................................................................

ANSWERED AT 16/02/2020 - 06:32 PM


QUESTION POSTED AT 16/02/2020 - 06:32 PM

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7-x^2 . What are the dimensions of such a rectangle with the greatest possible area?

If the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2
the area of a rectangle = length * width
thus, area = x*(7-x^2)= 7x-x^3
in order to maximize the area, you would need to take the derivative of the area and set it equal to 0
Area = 7x-x^3Area' = 7 - 3x^2
7-3x^2 = 0thus, x = 1.5275
this x represents the x needed to create the largest possible area with the given parameters.
Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667

ANSWERED AT 16/02/2020 - 05:35 PM


QUESTION POSTED AT 16/02/2020 - 05:35 PM

Fill in the blank: To find the values of p, q, r and s, you should start by finding all factor ___ of the leading coefficiant and constant term. Then try them to determine which ones give you the correct product ...?

I can be wrong, but I think that the answer is: To find the values of p, q, r and s, you should start by finding all factor pairs of the leading coefficiant and constant term. 

ANSWERED AT 16/02/2020 - 05:35 PM


QUESTION POSTED AT 16/02/2020 - 05:35 PM

determine whether multiplication by A is one to one linear transformation a)A=[ 1 -1 2 0 3 -4] b) A=[ 1 2 3 -1 0 4] ...?

To know if the given matrix is one to one linear transformation, Row reduce the Matrix A and if it has free variables in it it means it is not a one to one linear transformation.

So, we take A and apply Row Operation and get the following matrix
 
1 0 0
0 1 0
0 0 0

As, it has free variables in it, it means it is not a one to one linear transformation.

Hope it helps :)

ANSWERED AT 16/02/2020 - 05:34 PM


QUESTION POSTED AT 16/02/2020 - 05:34 PM

The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side. Find the lengths of the medians of the triangle with vertices at A=(0,0), B=(6,0), C=(4,4) ...?

Answer:

\sqrt{29} , \sqrt{20} , \sqrt{17}

Step-by-step explanation:

Consider ΔABC with vertices A\left ( 0,0 \right )\,,\,B\left ( 6,0 \right )\,,\,C\left ( 4,4 \right ) such that P , Q , R are midpoints of sides BC , AC and AB .

We know that midpoint of line segment joining points \left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right ) is equal to \left ( \frac{x_1+x_2}{2}\,,\,\frac{y_1+y_2}{2} \right )

Midpoints P , Q , R :

P\left ( \frac{6+4}{2}\,,\,\frac{0+4}{2} \right )=P\left ( 5\,,\,2 \right )\\Q\left ( \frac{0+4}{2}\,,\,\frac{0+4}{2} \right )=Q\left ( 2\,,\,2 \right )\\R\left ( \frac{6+0}{2}\,,\,\frac{0+0}{2} \right )=R\left ( 3\,,\,0 \right )

We know that distance between points \left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right ) is given by \sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}

Length of AP :

AP = \sqrt{\left ( 5-0 \right )^2+\left ( 2-0\right )^2}=\sqrt{25+4}=\sqrt{29}

Length of BQ :

BQ = \sqrt{\left (2-6 \right )^2+\left ( 2-0 \right )^2}=\sqrt{16+4}=\sqrt{20}

Length of CR :

\sqrt{\left (3-4\right )^2+\left ( 0-4 \right )^2}=\sqrt{1+16}=\sqrt{17}

ANSWERED AT 16/02/2020 - 05:32 PM


QUESTION POSTED AT 16/02/2020 - 05:32 PM

Angle ABD and angle BDE are supplementary. Find the measures of both angles. m angle ABD =5x degrees, m angle BDE = (17x-18)degrees

By definition of supplementary angles,
∠ABD + ∠BDE = 180
5x + 17x - 18 = 180
22x = 198
x = 9

∠ABD = 5(9) = 45°
∠BDE = 180 - 45 = 135°

ANSWERED AT 16/02/2020 - 05:29 PM


QUESTION POSTED AT 16/02/2020 - 05:29 PM

When working with the square root of a number, when would you have only a positive answer and when would you have both a positive and negative answer?

Lets make it clear: You would have a positive answer when the value you are looking for has to be a positive number. On the other hand you would have a positive and a negative answer when you take the square root of something that doesn't have to be positive. it could be either because when a negative number is squared it becomes positive and when a positive number is squared it stays positive as well.

ANSWERED AT 16/02/2020 - 05:24 PM


QUESTION POSTED AT 16/02/2020 - 05:24 PM

Find Dxy using the rules for finding derivatives. =(5x^2−8)(9x^2−3x+5)

You can do foil method first, to make it easier and to avoid product rule,
y= 45x^4 - 15x³ + 25x² - 72x² + 24x - 40
Simplify like terms,
y= 45x^4 - 15x³ - 47x² + 24x - 40
Now, find derivative,
dy/dx  = 180x³ - 45x² - 94x + 24 

ANSWERED AT 16/02/2020 - 05:13 PM


QUESTION POSTED AT 16/02/2020 - 05:13 PM

If x = 4 calculate the value of x squared 2x

x² × 2x = 16 × 8 = 128

ANSWERED AT 16/02/2020 - 04:51 PM


QUESTION POSTED AT 16/02/2020 - 04:51 PM

What is the perimeter of Elisa's second rectangle

Um, do you have the side lengths and some information about the problem? Without that, The perimeter could be almost any random number. 

ANSWERED AT 16/02/2020 - 04:40 PM


QUESTION POSTED AT 16/02/2020 - 04:40 PM

What is the square root of 97? for my younger friend

Square root of 97 is originally 9.848857802 when you punch it in a calculator , so you have to move the decimal two loops to the right which gives you 9.84 & that's the square root of 97 :)

ANSWERED AT 16/02/2020 - 04:39 PM


QUESTION POSTED AT 16/02/2020 - 04:39 PM

Roberto measured his garden to be 10' x 12.5' he plants vegetables in one half of the garden what is the area of the vegetable garden

Well, if half of the garden's area is 10' x 12.5' (which is equal to 125 inches^2), then we add 125+125 which gets us 250 inches^2 .

ANSWERED AT 16/02/2020 - 04:36 PM


QUESTION POSTED AT 16/02/2020 - 04:36 PM

What is the solution of x+3y=-12 and 5x-3y=-6

Look at the picture.........

ANSWERED AT 16/02/2020 - 04:30 PM


QUESTION POSTED AT 16/02/2020 - 04:30 PM

Two similar prisms have heights 4 cm and 10 cm. What is the ratio of their surface areas? A) 2:5 B) 4:25 C) 4:10 D) 8:125

H 1 : H 2 = 4 : 10
H 1 = 2/5 H 2
and also for the base: L 1 = 2/5 L 2 and W 1 = 2/5 L 2
 A 1 = 2 L 1 x W 1 + 2 L 1 x H 1 + 2 W 1 x H 1
A 2 = 2 L 2 x W 2 + 2 L 2 x H 2 + 2 W 2 x H 2
A 1 / A 2 = 4/25 *( 2 L 2 x W 2 + 2 L 2 x H 2 + 2 W 2 H 2 ) /
                 / ( 2 L 2 x W 2 + 2 L 2 x H 2 + 2 W 2 x H  2 ) =
= 4/5
A 1 : A 2 = 4 : 25
Answer:  B ) 4 : 25

ANSWERED AT 16/02/2020 - 04:08 PM


QUESTION POSTED AT 16/02/2020 - 04:08 PM

A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 a foot, while the remaining two sides will use standard fencing selling for $2 a foot. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $6000?

Ok lets do this like this:
Let x = length Let y = width
From this we know that area A=xy.
Now, perimeter is P=2x+2y
cost would be 3(2x)+2(2y) or 6x +4y=$6,000.00.
From this cost equation we solve for x in terms of y 6x=6000-4y x=1000-(4y)/6.
now lets substitute this value in the area equation A=xy. A=(1000-4y/6)y A=1000y−4y2/6=1000y−2y2/3 differentiate and set to equal zero (0) 1000−(−4y/3)=0 Solve for y and obtain y=750ft

ANSWERED AT 16/02/2020 - 04:07 PM


QUESTION POSTED AT 16/02/2020 - 04:07 PM

A ferris wheel is 35 meters in diameter and boarded at ground level. The wheel makes one full rotation every 8 minutes, and at time t = 0 you are at the 9 o'clock position and descending. Let f(t) denote your height (in meters) above ground at t minutes. Find a formula for f(t).

F(t) = -17.5sin((t/4)*pi) + 17.5
Because the ferris wheel is a circle you can use sine and cosine. As we are descending and in the middle of the descent the use of negative sine makes the most sense.
Period = 2pi.
Our period is 8 minutes.
8 minutes*w = 2pi
w = (t/4) * pi.
The 17.5 at the end is to take into account that we are 17.5 meteres up in the air at the start.

ANSWERED AT 16/02/2020 - 04:07 PM


QUESTION POSTED AT 16/02/2020 - 04:07 PM

Show that det(A) = 0 without directly evaluating the determinant. A = [-4 1 1 1 1; 1 -4 1 1 1; 1 1 -4 1 1; 1 1 1 -4 1; 1 1 1 1 -4]

Answer:You could interpret them as system of equation and answer the question easily

from A 

-4x + y + x + w =1

write in same form from A 

as this system has five variables and four of them are unknowns it means the unique solution is not possible 

So, det (A) = 0

Read more on Brainly.com - brainly.com/question/2253943#readmore

ANSWERED AT 16/02/2020 - 04:06 PM


QUESTION POSTED AT 16/02/2020 - 04:06 PM

Which statement is false? Explain. A. An equiangular polygon has all angles congruent. B. A regular polygon is both equilateral and equiangular. C. An equilateral polygon has all sides congruent. D. A polygon is concave if no diagonal contains points outside the polygon

The false option is D) : "A polygon is concave if no diagonal contains points outside the polygon"  because polygon is only concave if diagonal contains points outside the polygon (its has to be convex instead of concave)

ANSWERED AT 16/02/2020 - 04:06 PM


QUESTION POSTED AT 16/02/2020 - 04:06 PM

How many solutions does the equation 4x + 8 = − 2 − 2 + 5x have? Two One Zero Infinitely many

The answer is B) One.

ANSWERED AT 16/02/2020 - 04:02 PM


QUESTION POSTED AT 16/02/2020 - 04:02 PM

Group the terms with variables on one side of the equal sign,solve and simplify.5/8a +6=3/4a

5/8a +6=3/4a 5\8a-3\4=-6 -1\8a=6 then multiply both sides by 8 -8a=48 then divide both sides by -8 a=6

ANSWERED AT 16/02/2020 - 06:05 AM


QUESTION POSTED AT 16/02/2020 - 06:05 AM

What is the substitution for 5x-2y=14, 2x-y=5

Okay so
5x-2y=14
2y=5x-14
y=(5x-14)/2
2x-y=5
y=2x-5
2(2x-5)=5x-14
4x-10=5x-14
x=4

y=(5[4]-14)/2
y=(20-14)/2
y=6/2
y=3

Answer: x=4, y=3

ANSWERED AT 16/02/2020 - 05:58 AM


QUESTION POSTED AT 16/02/2020 - 05:58 AM