All categories

3 years ago

Find the area of quadrilateral with vertices at points (3,0)(4,5)(-1,4)(-2,-1)

Mathematics

2 answers:

marissa [1.9K]3 years ago

6 0

Step-by-step explanation:

$Let the points be A(3,0),B(4,5),C(−1,4) and D(−2,−1)Area of a rhombus =21×(diagonal1×diagonal2)Hence, the distance between the points A(3,0) and C(−1,4)=(−1−3)2+(4−0)2=16+16=32And, Distance between the points B(4,5) and D(−2,−1)BD=(−2−4)2+ (−1−5)2=36+36=72So, Area of the rhombus =21×32×72=21×32×72=21×4×8×36×2=21×2×68×2=62×4×2=6×2×2=24 sq units$

guapka [62]3 years ago

4 0

Answer: 20

Step-by-step explanation:

Let 's complete our quadrilateral to a rectangle ; and subtract from it the area highlighted in red

$\displaystyle \rm S_{\diamond}=6\cdot 5 =30 \\\\ S_{ABCD}=30-(5:2+5:2+5:2+3:2+1\cdot1)=30-(7,5+1,5+1)=\\\\30-10=20 \\\\ S_{ABCD}=20$

You might be interested in

Question 2: Please help. If m∠EKT=(5x+65)∘, what is the value of x?

lina2011 [118]

Answer:

The answer is 5.

8 0

4 years ago

Y=x.arctan(x)^1/2. find dy/dx. pls show steps

Whitepunk [10]

$y=x(\arctan x)^{1/2}$

Use the product rule first:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dx}{\mathrm dx}(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

Use the chain rule to compute the derivative of $(\arctan x)^{1/2}$ . Let $z=(\arctan x)^{1/2}$ and take $u=\arctan x$ , so that by the chain rule

$\dfrac{\mathrm dz}{\mathrm dx}=\dfrac{\mathrm dz}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm dz}{\mathrm du}=\dfrac{\mathrm du^{1/2}}{\mathrm du}=\dfrac12u^{-1/2}$

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\mathrm d\arctan x}{\mathrm dx}=\dfrac1{1+x^2}$

$\implies\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}(1+x^2)}$

So we have

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+\dfrac x{2(\arctan x)^{1/2}(1+x^2)}$

You can rewrite this a bit by factoring $(\arctan x)^{-1/2}$ , just to make it look neater:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}}\left(2\arctan x+\dfrac x{1+x^2}\right)$

3 0

3 years ago

Jonny has 9 apples. If he eats one and then splits the apples evenly for him and his friend, how much will he have now?

il63 [147K]

Well if he has 9 then eats one that would have 8 so they both would get 4

Hope it helped! :)
And cool pic

8 0

4 years ago

Read 2 more answers

In the figure, angle D measures 71º and angle G measures 37º. What is the measurement of angle A?

leva [86]

check the picture below.

recall that the sum of all interior angles in a triangle is 180°, and that a flat-line like the line C, D and E are sitting on, is always 180°.

4 0

4 years ago

Read 2 more answers

Nathaniel can't remember exactly how many cupcakes Haley and Virgil made for the Halloween party but he did remember that all to

amid [387]

Answer:

Haley = 62

Nathaniel = 48

Virgil = 46

Step-by-step explanation:

According to question ,

Haley + Virgil + Nathaniel had made total of = 156 cupcakes ..... 1

Haley + Nathaniel had made total of = 110 cupcakes ..... 2

Virgil + Nathaniel had made total of = 94 cupcakes ..... 3

So, from above three equations ,

From eq 2 and 3

(Haley + Nathaniel) - (Virgil + Nathaniel ) = 110 - 94

So, Haley - Virgil = 16 ..... 4

From eq 1 and 4

(Haley + Virgil + Nathaniel ) + ( Haley - Virgil ) = 156 + 16

2 Haley + Nathaniel = 172 ...... 5

From eq 2 and 5

( 2 Haley + Nathaniel ) - ( Haley + Nathaniel ) = 172 - 110 = 62

so, Haley = 62

In eq 5 put the Haley make value

so, Nathaniel = 172 - ( 2 × 62)

Nathaniel = 48

In eq 4 , put the value of Haley make value

So, Virgil = Haley - 16

Virgil = 62 - 16 = 46

Hence the value of all the three persons make is

Haley = 62

Nathaniel = 48

Virgil = 46 Answer

4 0

3 years ago