The legs are 5 inches long.
Use the Pythagorean theorem:
![5^2+5^2=c^2 \\ 25+25=c^2 \\ 50=c^2 \\ c=\sqrt{50} \\ c=\sqrt{25 \times 2} \\ c=5 \sqrt{2} \\ c \approx 7](https://tex.z-dn.net/?f=5%5E2%2B5%5E2%3Dc%5E2%20%5C%5C%0A25%2B25%3Dc%5E2%20%5C%5C%0A50%3Dc%5E2%20%5C%5C%0Ac%3D%5Csqrt%7B50%7D%20%5C%5C%0Ac%3D%5Csqrt%7B25%20%5Ctimes%202%7D%20%5C%5C%0Ac%3D5%20%5Csqrt%7B2%7D%20%5C%5C%0Ac%20%5Capprox%207)
The length of the hypotenuse of the triangle is approximately 7 inches long.
Answer:
and ![y = -5\cdot t +21](https://tex.z-dn.net/?f=y%20%3D%20-5%5Ccdot%20t%20%2B21)
Step-by-step explanation:
Given that
and
, the parametric equations are obtained by algebraic means:
1)
Given
2)
Given
3)
Associative and modulative properties
4)
Existence of multiplicative inverse/Commutative property
5)
Associative property
6)
/ ![(-1)\cdot a = -a](https://tex.z-dn.net/?f=%28-1%29%5Ccdot%20a%20%3D%20-a)
7)
Modulative property
8)
Existence of additive inverse
9)
Associative and commutative properties
10)
Distributive property
11)
![(-a)\cdot (-b) = a\cdot b](https://tex.z-dn.net/?f=%28-a%29%5Ccdot%20%28-b%29%20%3D%20a%5Ccdot%20b)
12)
By 1)
13)
/Result
14)
Compatibility with addition
15)
Compatibility with addition
16)
Associative property
17)
Associative property
18)
Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is
and
.
Answer:
yes it is correct
Step-by-step explanation:
subtract |p| from |p+q| to get |q|
Answer:
$10278
Step-by-step explanation:
Given data
P= $6000
R= 8%
T= 7 years
The compound interest formula is
A=P(1+r)^t
substitute
A=6000(1+0.08)^7
A=6000(1.08)^7
A=6000*1.713
A=$10278
Answer:
1. 9 < s < 17
2. 5 < MN < 19
3. AD > BD
Step-by-step explanation:
1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:
- the sum of the shortest two sides is greater than the length of the longest side
- the length of any side lies between the sum and the difference of the other two sides
Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...
9 < s < 17
(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)
__
2. Same as (1) using different numbers.
12 -7 < MN < 12 +7
5 < MN < 19
__
3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:
AD > BD