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2 years ago

3

a folded napkin has a triangular cross section of sides x cm ,x +1 cm and x+2 cm if one of the angles of the triangle is 90 degr

ees find x

1 answer:

Scorpion4ik [409]2 years ago

4 0

The value of x is 3 cm.

Step-by-step explanation:

Given : A folded napkin has a triangular cross section of sides x cm, x +1 cm and x+2 cm if one of the angles of the triangle is 90 degrees.

To find : The value of x ?

Solution :

One of the angle is 90 degrees i.e. it is a right angled triangle.

Applying Pythagorean theorem,

$H^2=P^2+B^2$

Where, H is the hypotenuse the largest side i.e. H=x+2 cm

P is the perpendicular i.e. P=x+1 cm

B is the perpendicular i.e. B=x cm

Substitute the value,

$(x+2)^2 = x^2+ (x+1)^2$

$x^2+ 4x + 4 = x^2+ x^2+ 2x + 1$

$x^2+ 4x + 4 = 2x^2+ 2x + 1$

$2x^2- x^2+ 2x - 4x + 1 - 4 = 0$

$x^2- 2x - 3 = 0$

$x^2- 3x + x - 3= 0$

$x(x-3) + 1(x-3) = 0$

$(x-3)(x + 1) = 0$

$x = 3,-1$

Reject x=-1 as it is not possible.

So, x=3

The sides are 3,4,5 cm.

Therefore, the value of x is 3 cm.

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Let's say the number of days library book is late is X, and the total fee is Y.

Liability charges $0.30 dollars as a fee for being 1 day late,

For being 1 day late, fee charge is: 1* $0.30
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Total charge for being X days late is Y, Which means: Y= 0.30 * X.

Now We would have to check all the viable solutions in the answer to see if they satisfy the equation Y= 0.30 * X

Option one(-3, -0.9) and two (-2.5, -0.75) Would not be a viable solution because the value of number of days can not be negative and in option one and two, value of days -3 and -2.5 is negative.

Option three(4.5, 1.35) can not be correct because library charges fee for a full day so the number for days would be a whole number. Library would not charge for 4.5 days, they would either charge of 4 days or 5 days because 4.5 is not an whole number.

Option four(8, 2.40) is the correct answer because it satisfies our equation;

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2.40= 0.30 * 8

2.40 = 2.40.

Fourth option (8, 2.40) is the only viable solution to this question.

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2 years ago

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Hannah is designing containers to hold 300 cm3 of juice. Which container is more efficient?

Lubov Fominskaja [6]

Answer:

a) 2nd container is more efficient and contains the elements for a container.

b) The cylinder has a........A)Smaller surface area B)bigger C)equal

And will cost.....A)Less to produce B)more C)The same

Step-by-step explanation:

a) The 2nd container has these elements:

Width 20.5cm

Length 6.5cm

side 3.25cm

So, the volume in cubic cm is 20.5 x 6.5 x 3.25 = 433cm3.

This container can hold the 300cm3 of juice.

b) A cylinder is a geometric solid common in everyday life. Examples of a cylinder are soup cans, food tins, drink cans, candles, toilet paper rolls, cups, aerosol cans, flower vases, test tubes, fire extinguishers, plant containers, salt shakers and pencil holders. The two ends are called bases, and are usually circular. Though, they can take other shapes. When a cylinder is unrolled and flattened out, the side is actually a rectangle.

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6 0

2 years ago

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is la

nikdorinn [45]

Answer:

f(x) = 3(2)^x

Step-by-step explanation:

The Table is:

<u>x</u> <u>f(x)</u>

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0 3

1 6

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The exponential funtion has the next form:

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At x = 0, f(x) = a. Then, a = 3

Isolating b from the equation:

f(x)/a = b^x

ln(f(x)/a) = x*ln(b)

[ln(f(x)/a)]/x = ln(b)

At x = 1, f(x) = 6. Then:

[ln(6/3)]/1 = ln(b)

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2 = b

Therefore, the function is f(x) = 3(2)^x

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2 years ago

in one week, 128 cell phones were sold. The following week 37 more cell phones were sold than the week before. How many cell pho

Pani-rosa [81]

$\large\bf{\underline{Given :}}$

128 cellphones were sold in a week
37 more cellphones more were sold than the week before

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ $\large\bf{⟹128+37=165}$

__________________________________________

$\large\bf{\underline{Therefore:}}$

$\bf{Total\: number\:of\: cellphones\:sold\:in\:two\:weeks}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large{⟹128 + 165}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large{⟹293}$

__________________________________________

$\large\bf{\underline{Hence}}$

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2 years ago

Two planes, which are 3400 miles apart, fly toward each other. Their speeds differ by 80mph. If they pass each other in 5 hours,

Andreas93 [3]

Answer : The speed of both planes is 61.25 mph and 18.75 mph respectively.

Explanation:

Let the speed of first plane be x mph

Let the speed of second plane be y mph

Since we have given that difference of speeds is 80 mph

i.e. x - y= 80 ( $Eq^n$ 1)

Distance between two planes = 3400 miles

As they are flying towards each other i.e. they are in the opposite direction.

So, Relative speed will be the sum of their speeds i.e.

Relative speed = x + y

And we know speed = $\frac{Distance}{Time}$

Speed= $\frac{3400}{80}$

⇒ Speed = 42.5 mph

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Now, by using the elimination method of solving the system of equation, we have ,

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2 years ago