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Oxana [17]
2 years ago
5

Compare these rational numbers. Which of the following are true?

Mathematics
1 answer:
Inessa [10]2 years ago
6 0

Answer:

i. false

ii. true

iii. true

iv. false

When comparing negative numbers, if you disregard the negative sign, the apparent greater value will actually be the smaller.

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A 50-foot ladder leans against a wall, as shown in the figure below. If the base of the ladder is 30 feet away from the wall, ho
notka56 [123]

50^2 + 30^2 = x^2

2500 + 900 = x^2

3400 = x^2

x = sqrt(3400)

x = 58.31

 height is 58.31 feet ( round answer as needed)

4 0
3 years ago
You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river
inn [45]

Answer:

The length and width of plot is L=300\:ft, W=150\:ft

Largest area of the plot is A=45000 ft^{2}

Step-by-step explanation:

Assume width as x and length as y. Given that length of fencing is 600 feet and fencing is enclosed on 3 sides. So perimeter is given as,

Perimeter = width + length + width

Substituting the value,  

600=x+y+x

600= 2x+y  ….1

Now area of fence of rectangular box is given as follows,  

A=xy  ….2

Solving equation 1 for y, subtracting 2x from both sides,  

600-2x= y

Substituting the value in equation 2,  

A=x\left (600-2x  \right )

Simplifying

A=600x-2x^{2}

Rewriting,  

A=-2x^{2}+600x

Above equation looks like quadratic equation f\left ( x \right )=ax^{2}+bx+c whose graph looks like parabola.  

Comparing equation f(x) and A values of a, b and c are, a=-2,b=600 and c=0.  

Now maximum of f\left ( x \right ) occurs at vertex.  

The x coordinate of the vertex is given as -\dfrac{b}{2a}

Substituting the values,  

x=-\dfrac{600}{2\left (-2  \right )}

Simplifying,  

x=\dfrac{600}{4}

x=150

So width of plot is 150 feet.  

Now to calculate value of length by using equation 1,

600= 2x+y

Substituting the values,

600= 2\left (150  \right )+y

600= 300+y

Subtracting 300 from both sides,

300= y

So length of plot is 300 ft.

The y coordinate of the vertex is given as y=f\left ( -\dfrac{b}{2a} \right ) which also means, y=f\left ( 150 \right )

\therefore A=-2\left (150  \right )^{2}+600\left (150  \right )

Simplifying,  

\therefore A=-2\left (22500  \right )^{2}+600\left (150  \right )

\therefore A=-45000+90000

\therefore A=45000

So, area of the plot will be A=45000 ft^{2}

7 0
3 years ago
A dog kennel charges $40 to board a dog for one night and $35 per night each night after that. Henry
Lostsunrise [7]

Answer: 6 nights

Step-by-step explanation:Step-by-step

Minus 40 from 215 then divide it by 35

8 0
2 years ago
Jamie takes at random a counter from the bag and records the colour. Red : blue : green = 1:3:7 Jamie does this a number of time
Sonbull [250]

Answer: There are 249 times Jamie takes a counter from the bag.

Explanation:

Since we have given that

Ratio of colour of red to blue to green is 1:3:7.

Number of blue counters = 68

Let the total number of times Jamie does from the bag be x.

So, According to question,

\frac{3}{11}\times x=68\\\\x=\frac{11}{3}\times 68\\\\x=249.33\\\\=249\ approx.

Hence, there are 249 times Jamie takes a counter from the bag.

8 0
3 years ago
A hexagonal pyramid that has a slant height of 39 cm and its hexagonal base has a radius of 10√3 cm.
VMariaS [17]

Answer: 225

Step-by-step explanation:

Volume of the pyramid is calculated as 1/3 bh, where b is base and h is height

Given height as 39cm and a base of 10√3cm = 10 x √3, where √3= 1.73; base = 10 x 1.73 = 17.3

Slot the values into the formula:

Volume = 1/3 × 17.3 x 39

= 1/3 × 674.7 = 674.7/3

Volume = 224.9 approximately 225.

I hope this helps.

3 0
2 years ago
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