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3 years ago

Which Roman numeral is equivalent to the number below?

Mathematics

1 answer:

In-s [12.5K]3 years ago

7 0

I = 1

II = 1 + 1 = 2

V = 5

VI = 5 + 1 = 6

IV = 5 - 1 = 4

X = 10

A. XVIII = 10 + 5 + 1 + 1 + 1 = 18

B. VII = 5 + 1 + 1 = 7

C. XXVII = 10 + 10 + 5 + 1 + 1 = 27

D. XVII = 10 + 5 + 1 + 1 = 17

Answer: D. XVII

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The hypotenuse of a right triangle is 1 centimeter longer than one side and 4 centimeters longer than three times the other side

snow_tiger [21]

Answer:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

Step-by-step explanation:

Represent:

The opposite with a
The adjacent with b
The hypotenuse with c

Given that:

$c = 1 + a$

$c = 4 + 3b$

Required

Solve for a, b and c

$c = c$

So, we have:

$1 + a = 4 + 3b$

Subtract 1 from both sides

$a = 4 -1 + 3b$

$a = 3 + 3b$

Apply Pythagoras Theorem

$c^2 = a^2 + b^2$

Substitute 3 + 3b for a and 4 + 3b for c

$(4 + 3b)^2 = (3 + 3b)^2 + b^2$

Open brackets

$16 + 12b+12b+9b^2 = 9 + 9b+9b+9b^2 +b^2$

$16 + 24b+9b^2 = 9 + 18b+10b^2$

Collect Like Terms

$10b^2 - 9b^2 + 18b - 24b + 9 - 16 = 0$

$b^2 - 6b -7 = 0$

Expand

$b^2 +b-7b-7=0$

Factorize:

$b(b+1)-7(b+1) =0$

$(b-7)(b+1) = 0$

Split:

$b - 7 = 0\ or\ b+1=0$

$b = 7\ or\ b=-1$

But the adjacent of a triangle can't have a negative measurement.

So:

$b = 7$

Recall that:

$c = 4 + 3b$

$a = 3 + 3b$

Substitute 7 for b in the above expressions

$c = 4 + 3 * 7$

$c = 4 + 21$

$c = 25$

$a = 3 + 3 * 7$

$a = 3 + 21$

$a = 24$

Hence, the dimensions of the triangle are:

$Hypotenuse = 25cm$

$Opposite = 24cm$

$Adjacent = 7cm$

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2 years ago

What is the slope of the line perpendicular to the given line?<br> 5x - 2y = 14

motikmotik

Answer:

$-\frac{2}{5}.$

Step-by-step explanation:

1) if to re-write the given equation into slope-interception form, then:

$y=\frac{5}{2}x-7;$

the slope of the given line is 5/2;

2) according to the rule of perpendicular, the required slope should be:

s*(5/2)=-1;

3) if to solve this equation (s*5/2=-1), then s=-2/5 or -0.4.

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Answer:

Step-by-step explanation:

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