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3 years ago

What is the length of a hypotenuse when the legs are 5 and 12

1 answer:

8 0

By using pythagoras theorem where
(Base)^2 +(perpedicular)^2 = (hypotenuse)^2
So,
(5)^2 +(12)^2 = (hypotenuse)^2
25 + 144 = (hypotenuse)^2
169 = (hypotenuse)^2
13 = hypotenuse

So, hypotenuse = 13

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The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec

igomit [66]

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 $m^{2}$

From there

x * (2x - 4) = 70

$2x^{2}$ - 4x = 70

$2x^{2}$ - 4x - 70 = 0

$x^{2}$ - 2x - 35 = 0

Now we have a quadratic equation, which is a $x^{2}$ + bx + c = 0, where a $\neq$ 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = $-2^{2}$ - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are $\frac{- b - \sqrt{D} }{2a}$ and $\frac{- b + \sqrt{D} }{2a}$

$x_{1}$ = $\frac{- (-2) - \sqrt{144} }{2}$ = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

$x_{2}$ = $\frac{- (-2) + \sqrt{144} }{2}$ = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

8 0

3 years ago

Calculate (A⃗ ×B⃗ )⋅C⃗ for the three vectors A⃗ with magnitude A = 5.08 and angle θA = 25.6 ∘ measured in the sense from the +x

alexgriva [62]

Answer:

(A⃗ ×B⃗ )⋅C⃗ = - 76.415

Step-by-step explanation:

First we need to calculate (A⃗ ×B⃗ ) :

(A⃗ ×B⃗ ) = A.B.sin (α).n

Where A is the magnitude of A⃗

Where B is the magnitude of B⃗

Where α is the angle between A⃗ and B⃗ = 63.9 - 25.6 = 38.3

Finally n is the vector orthogonal to A⃗ and B⃗

n magnitude is 1 and his direction is given by the right hand-rule

so n = ( 0 , 0 , 1 )

(A⃗ ×B⃗ ) = A.B.sin (α).n = 5.08 . 3.94 . sin (38.3) . (0 , 0 , 1 ) = (0,0,12.4)

C⃗ can be written as C.(0,0,-1) because of his +z - direction

C.(0,0,-1) = 6.16.(0,0,-1) = (0,0,-6.16)

(A⃗ ×B⃗ )⋅C⃗ = (0,0,12.4).(0,0,-6.16) = -76.41480787 = -76.415

8 0

3 years ago

Andy and Jordan's are playing a game that involves tossing two dice numbered one to six, and recording the sum of the two how ma

Ne4ueva [31]

Answer:

there are 11 diffrent sums and the greatest sum is 12

Step-by-step explanation:

5 0

2 years ago

Please help I don’t understand math

andrew-mc [135]

Answer:

x = 12

Step-by-step explanation:

The sum of the two smaller angles is 140

80+5x = 140

Subtract 80 from each side

80+5x-80 =140-80

5x = 60

Divide each side by 5

5x/5 = 60/5

x = 12

6 0

2 years ago

If i had 10 pound then i times that by 4 then divide by 2 then take 5 away what is it

Lemur [1.5K]

15 because 10x4 is 40 divided by 2 is 20 and 20-5 =15

3 0

2 years ago

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