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2 years ago

5

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

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

3 years ago