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3 years ago

Calculate the length of the diagonal AB

Mathematics

2 answers:

wolverine [178]3 years ago

8 0

25
EXPLANATION:
No ok

Arisa [49]3 years ago

7 0

Answer:

AB = $5\sqrt{3}$ cm

Step-by-step explanation:

The diagonal of the bottom square is the hypotenuse of two right triangles with legs 5 and 5

So, the length of that diagonal, say x, of a 45-45-90 triangle where x is the hypotenuse is x = $5\sqrt{2}$

Now that diagonal is a leg of the right triangle where AB is the hypotenuse and 5 is the length of the other leg.

So, $x^{2} + 5^{2} = AB^{2}$ = $(5\sqrt{2} )^{2}$ + 25

= 50 + 25

= 75

Therefore AB = $\sqrt{75}$ = $5\sqrt{3}$

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Answer:

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Step-by-step explanation:

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3 years ago

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Randy is walking home from school. According to the diagram above, what is his total distance from school to home? Show your wor

In-s [12.5K]

Answer:

First, when he walks, we can see in the image that between the school and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.

Then he needs to walk 2km.

Now if he has a jet-pack, he can ignore the buildings and just take the shorter path, here we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.

One of the catheti is the vertical distance (two blocks of 0.5km, so this catheti has a length of 2*0.5km = 1km), and the other one is the horizontal distance, also 1km.

The actual distance of this path is given by the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse, then:

H^2 = 1km^2 + 1km^2

H = (√2)km = 1.41km.

Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, in this case the distance and the displacement would be the same.

This is because the definitions of distance and displacement are:

Distance: "how much ground an object has covered"

Displacement: "Difference between the final position and the initial position"

When he walks, the distance is 2km and the displacement is 1.41km , but when he uses the jet pack, the distance is equal to the displacement, both are 1.41km.

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4 years ago

PLEASE HELP IF YOUR GOOD AT ALGEBRA

LUCKY_DIMON [66]

9514 1404 393

Answer:

lower left

Step-by-step explanation:

We notice that the answer choices have only the first equation changed. The equivalent of the first equation must have the same ratios of coefficients.

x-coefficient : y-coefficient : constant

= 2 : 1 : -15 . . . . . in the given equation

2 : -2 : 30 = 1 : -1 : 15 . . . upper left — not the same

-4 : -2 : -15 = 4 : 2 : 15 . . . upper right — not the same

-4 : -2 : 30 = 2 : 1 : -15 . . . lower left — same as the given equation

-4 : 1 : 30 = 4 : -1 : -30 . . . lower right — not the same

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3 years ago

Enter the values for the highlighted variables to complete the steps to find the sum: (see picture)

dangina [55]

Answer:

a = -1

b = -9

c = 9

d = 3

e = 3

f = 2

g = 3/2

Step-by-step explanation:

* Lets explain how to solve the problem

∵ $\frac{3x}{2x-6}+\frac{9}{6-2x}$ are rational fractions

- To add or subtract the rational fractions they must have same

denominator

∵ 6 - 2x must be written 2x - 6, take (-1) as a common factor from 6 - 2x

∴ - 1(-6 + 2x) = - 1(2x - 6)

∴ $\frac{3x}{2x - 6}+\frac{9}{6-2x}=\frac{3x}{2x-6}+\frac{9}{-1(2x-6)}$

∴ a = -1

∵ 9 ÷ -1 = -9

∴ = $\frac{3x}{2x-6}+\frac{-9}{2x-6}$

∴ b = -9

∵ The denominators of the two fractions are 2x - 6

∴ We can add them by adding their numerator

∵ 3x + -9 = 3x - 9

∴ = $\frac{3x-9}{2x-6}$

∴ c = 9

∵ 3x - 9 has a common factor 3

∴ 3x - 9 = 3(x - 3)

∵ 2x - 6 has common factor 2

∴ 2x - 6 = 2(x - 3)

∴ = $\frac{3(x-3)}{2(x-3)}$

∴ d = 3 , e = 3 , f = 2

- The fraction has same factor (x - 3) up and down then we can cancel

them together

∴ = $\frac{3}{2}$

∴ g = 3/2

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3 years ago

I need extreme help with this.<br><br>

irga5000 [103]

The first way i.e. the 4(x)

Step-by-step explanation:

Its because there's no gap in between and the letter is surrounded by brackets on both sides so it cant be divided and it's the only letter . There's no rule in mathematics that allows you to multiply a single number surrounded by brackets at both sides.

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