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disa [49]
2 years ago
15

What is the measure of x?

Mathematics
1 answer:
Sveta_85 [38]2 years ago
4 0

Answer:

Hello!

After reviewing the problem you have provided I have come up with the correct solution:

x= 9

Step-by-step explanation:

To come up with this solution you have to first realize that the smaller triangle is a proportionally scaled down version of the entire larger triangle! (I will show what I mean in a linked picture)

So after we have realized that the smaller triangle is a scaled down version of the larger one, we can then create a formula or ratio to calculate the value of the missing side of the larger triangle (being x+6=??).

To create the formula/ratio I divided 10inches by 4inches. Thus the larger triangle is 2.5 times larger than the smaller one.

I then use this ratio to figure out the missing length of the larger triangle by doing:

6inches x 2.5 = 15inches.

I then inputed the 15inches into the formula of the missing side:

x+6=15

Subtracted 6 from both sides to simplify, and came up with the solution!

x=9

Let me know if this helps!

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The hypotenuse of an isosceles right triangle is centimeters longer than either of its legs. Find the exact length of each side.
Varvara68 [4.7K]

Question

The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.

Answer:

Hypotenuse:37.56

Other\ Legs: 26.56

Step-by-step explanation:

Let the hypotenuse be y and the other legs be x.

So:

y = 11 + x

Required

Determine the exact dimension of the triangle

Using Pythagoras theorem;

y^2 = x^2 + x^2

y^2 = 2x^2

This gives:

(11+x)^2 = 2x^2

Open bracket

121 + 22x + x^2= 2x^2

Collect like terms

2x^2 - x^2 -22x - 121 = 0

x^2 -22x - 121 = 0

Using quadratic formula:

x = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}

x = \frac{-(-22)\±\sqrt{(-22)^2 - 4*1*-121}}{2*1}

x = \frac{-(-22)\±\sqrt{968}}{2*1}

x = \frac{22\±31.11}{2}

Split

x = \frac{22+31.11}{2}\ or\ x = \frac{22-31.11}{2}\\

x = \frac{53.11}{2}\ or\ x = \frac{-9.11}{2}

x can not be negative.

So:

x = \frac{53.11}{2}

x = 26.56

Recall that:

y = 11 + x

y = 11 + 26.56

y = 37.56

Hence, the dimensions are:

Hypotenuse:37.56

Other\ Legs: 26.56

6 0
3 years ago
Simplify I know I spelled it wrong
givi [52]

Answer:A

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Find the missing side length
DochEvi [55]
Tan=o/adj
Tan=60/b
B=60/tan(68)
I don't have a calculator on me but you should be able to do it from there
3 0
3 years ago
12 and 3000 as decimals full equation
ICE Princess25 [194]

Answer:

12=0.12x100

3000=0.3x10000

3 0
2 years ago
The symbol ⊕ is used to denote exclusive or, so p ⊕ q ≡ (p v q) ^ ~ (p ^ q).
Elan Coil [88]

I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

⊕ = XOR

∨ = OR

∧ = AND

~ = NOT

↔ = IFF (meaning "if and only if")

→ = IMP (short for "implies")

and for logical equivalence I'll use a regular equal sign.

Then

p XOR q = (p OR q) AND NOT (p AND q)

(a) By definition of XOR, we have

p XOR p = (p OR p) AND NOT (p AND p)

= p AND NOT p

and this is tautologically FALSE.

(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

NOT (p AND q) = NOT p OR NOT q

Then we can interchange the AND and ORs using their respective distributive properties. That is,

p XOR q = (p OR q) AND (NOT p OR NOT q)

= (p AND (NOT p OR NOT q)) OR (q AND (NOT p OR NOT q))

= ((p AND NOT p) OR (p AND NOT q)) OR ((q AND NOT p) OR (q AND NOT q))

Both (p AND NOT p) and (q AND NOT q) are tautologically FALSE, so the truth value of either OR depends only on the other statements, so we have

p XOR q = (p AND NOT q) OR (q AND NOT p)

Recall the definition of IFF:

p IFF q = (p IMP q) AND (q IMP p)

Also recall that IMP is logically equivalent to

p IMP q = p OR NOT q

Then we have

p IFF q = (p OR NOT q) AND (q OR NOT p)

so that its negation is

NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

= NOT (p OR NOT q) OR NOT (q OR NOT p)

= (NOT p AND q) OR (NOT q AND p)

The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

3 0
3 years ago
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