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4 years ago

169 as sum of odd numbers

Mathematics

2 answers:

Vitek1552 [10]4 years ago

5 0

Answer:

3 odd numbers can make 169, for an example,

33 + 63 + 73

If my answer helped, then kindly mark me as the brainliest!!

Thank You!!

Ad libitum [116K]4 years ago

5 0

Answer:

Step-by-step explanation:

Sum of first n odd numbers=n²

13²=169

Therefore sum of 13 odd numbers is 13²

1+3+5+7+9+11+13+15+17+19+21+23+25=169=13²

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What is the relationship between capacity and fluid ounces

horrorfan [7]

Capacity is the maximum that the object can hold.

Fluid Ounce is a U.S Customary Unit Measurement for liquid.

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3 years ago

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The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

NemiM [27]

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

$60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120$

Let's find h with the quadratic formula:

$\fbox {Quadratic formula:} \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}$

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation

$\fbox {Pythagorean equation:}$ <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

$H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17$

H = 17

If we decrease the base and the height by 2 centimeters, we have

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

$H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3$

$H' \approx 14.3$

So, the hypotenuse decreases $H - H' \approx 17 - 14.3 = 2.7$

3 0

3 years ago

Find the length of the height of the right trapezoid shown below, if it has the greatest possible area and its perimeter is equa

Artyom0805 [142]

Answer:

The height of the right trapezoid is $\frac{6}{5+\sqrt{3}}\ units$

Step-by-step explanation:

Let

x ----> the height of the right trapezoid in units

we know that

The perimeter of the figure is equal to

$P=AB+BC+CD+DH+HA$

we have

$P=6\ units$

$AB=BC=CH=HA=x$ ---> because is a square

substitute

$6=x+x+CD+DH+x$

$6=3x+CD+DH$ -----> equation A

<em>In the right triangle CDH</em>

$sin(30\°)=\frac{CH}{CD}$

$sin(30\°)=\frac{1}{2}$

Remember that $CH=x$

$\frac{1}{2}=\frac{x}{CD}$

$CD=2x$

$tan(30\°)=\frac{CH}{DH}$

$tan(30\°)=\frac{\sqrt{3}}{3}$

$\frac{\sqrt{3}}{3}=\frac{x}{DH}$

$DH=x\sqrt{3}$

substitute the values in the equation A

$6=3x+CD+DH$ -----> equation A

$CD=2x$

$DH=x\sqrt{3}$

$6=3x+2x+x\sqrt{3}$

$6=5x+x\sqrt{3}$

$6=x[5+\sqrt{3}]$

$x=\frac{6}{5+\sqrt{3}}\ units$

5 0

3 years ago

The weights of a certain dog breed are approximately normally distributed with a mean of μ = 55 pounds, and a standard deviation

weqwewe [10]

Answer:

(a)z=-1

(b)48.5 pounds

Step-by-step explanation:

$z-score=\dfrac{x-\mu}{\sigma}$

Given:

Mean, μ = 55 pounds

Standard deviation,σ = 6 pounds.

(a)For a dog that weighs 49 pounds.

x=49 pounds

The z-score

$=\dfrac{49-55}{6}\\=\dfrac{-6}{6}\\\\=-1$

(b)When a dog has a z-score of -1.09

$-1.09=\dfrac{x-55}{6}\\x-55=-6.54\\x=55-6.54\\x=48.46 \approx 48.5$ pounds (to the nearest tenth)$

The weight of a dog with a z-score of -1.09 is 48.5 pounds.

(c)When a dog has a z-score of 1.09

$1.09=\dfrac{x-55}{6}\\x-55=6.54\\x=55+6.54\\x=61.54 \approx 61.5$ pounds (to the nearest tenth)$

The weight of a dog with a z-score of 1.09 is 61.5 pounds.

3 0

3 years ago

Help me plssssssssssssssssssssssssssss

Rama09 [41]

Answer:

D. 2750

Step-by-step explanation:

22/200 = 0.11

0.11*25000=2750

5 0

3 years ago