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3 years ago

A really simple question that I just don't understand.

Mathematics

2 answers:

ollegr [7]3 years ago

5 0

It is a right-angle triangle because one of the angles is 90 degrees.

Scrat [10]3 years ago

3 0

The key is that Pythagoras' Theorem works in both directions.

-- IF it's a right triangle, THEN [ A² + B² = C² ].
and
-- IF [ A² + B² = C² ], THEN it's a right triangle.

Look at the triangle on the sheet.

Left side:
length of the side is 0.75
square of the left side = (0.75)² = 0.5625

Bottom side:
length of the side = 1
square of the bottom side = (1)² = 1

Sum of the squares = (0.5625 + 1) = 1.5625

Square root of that sum = √1.5625 = 1.25

Is that the length of the third side ? Yes !
Then [ A² + B² = C² ].
Then it's a right triangle.
You proved it.
yay

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A bottle of jam contains 10 pints of jam. How many 1/3 pint servings can you get out of one bottle?

Sergeeva-Olga [200]

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3 years ago

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4 years ago

The vertices of a backyard are W(10,30),X(10,100),Y(110,100),Z(50,30). The coordinates are measured in feet. The line segment XZ

MariettaO [177]

Given vertices W(10,30), X(10,100), Y(110,100), Z(50,30) of a backyard, find distances WX, XY, YZ, ZW and XZ:

1. $WX=\sqrt{(10-10)^2+(30-100)^2}=\sqrt{70^2}=70\ ft;$

2. $XY=\sqrt{(110-10)^2+(100-100)^2}=\sqrt{100^2}=100\ ft;$

3. $YZ=\sqrt{(110-50)^2+(100-30)^2}=\sqrt{60^2+70^2}=10\sqrt{85}\ ft;$

4. $ZW=\sqrt{(50-10)^2+(30-30)^2}=\sqrt{40^2}=40\ ft;$

5. $XZ=\sqrt{(10-50)^2+(100-30)^2}=\sqrt{40^2+70^2}=10\sqrt{65}\ ft.$

Then:

1. the area

$A_{WXZ}=\sqrt{\frac{70+40+10\sqrt{65}}{2}\\\cdot (\frac{70+40+10\sqrt{65}}{2}-70)\cdot (\frac{70+40+10\sqrt{65}}{2}-40)\cdot (\frac{70+40+10\sqrt{65}}{2}-10\sqrt{65})}=\\ \\=1400\ ft^2.$

2. the area

$A_{XYZ}=\sqrt{\frac{100+10\sqrt{85}+10\sqrt{65}}{2}\cdot (\frac{100+10\sqrt{85}+10\sqrt{65}}{2}-100)}\cdot\\ \\\cdot\sqrt{(\frac{100+10\sqrt{85}+10\sqrt{65}}{2}-10\sqrt{85})\cdot (\frac{100+10\sqrt{85}+10\sqrt{65}}{2}-10\sqrt{65})}=3500\ ft^2.$

Then

$\dfrac{A_{XYZ}}{A_{WXZ}}=\dfrac{3500}{1400}=2.5$ times greater.

6 0

4 years ago

What is 9.66 rounded to the nearest tenth

nikitadnepr [17]

9.66
^ This is the tenths place.

Look at the number after it, if it's 5 or more we round up, if it's 4 or less we round down.

The number is 6, so we round up to 9.7.

6 0

3 years ago

Read 2 more answers

The graph is of a function in the form p(t) = a*b^t. What is the function?

DanielleElmas [232]

Answer:

p(t) = 5*2^t

Step-by-step explanation:

We can solve for 'a' and 'b' using the point coordinates shown on the graph.

<h3>Setup</h3>

Substituting for (t, p(t)), the two equations we can make from the given points are ...

p(t) = a*b^t

5 = a*b^0 . . . . . . . (t, p(t)) = (0, 5)

10 = a*b^1 . . . . . . . (t, p(t)) = (1, 10)

<h3>Solution</h3>

The first equation tells you ...

5 = a

The second equation tells you ...

10 = 5*b

2 = b

<h3>Equation</h3>

The function is ...

p(t) = a*b^t

p(t) = 5*2^t

5 0

2 years ago