Answer:
![\boxed{\bold{\huge{\boxed{497}}}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cbold%7B%5Chuge%7B%5Cboxed%7B497%7D%7D%7D%7D)
Step-by-step explanation:
=> ![\sf 249^2 - 248^2](https://tex.z-dn.net/?f=%5Csf%20249%5E2%20-%20248%5E2)
<u>Using Formula</u> ![\sf a^2 - b^2 = (a+b)(a-b)](https://tex.z-dn.net/?f=%5Csf%20a%5E2%20-%20b%5E2%20%3D%20%28a%2Bb%29%28a-b%29)
<u><em>Where </em></u>
a = 249
b = 248
=> ![\sf (249+248)(249-248)](https://tex.z-dn.net/?f=%5Csf%20%28249%2B248%29%28249-248%29)
=> ![\sf (497)(1)](https://tex.z-dn.net/?f=%5Csf%20%28497%29%281%29)
=> 497
Answer:
They do not equal eachother
Step-by-step explanation:
-4(2+9) + 3 = 6 - 4(-3)
-12 - 36 + 3 = 6 + 12
-45 = 18
Answer:
The equation of the circle is
(x + 2)² + (y + 2)² = 9
Centered at (-2, -2), with radius of 3 units.
Step-by-step explanation:
The general equation of a circle is given as
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle, and r is the radius.
Looking at the graph, the center is the red dot. It corresponds to -2 on the y-axis, and -2 on the x-axis. So, the center (h, k) is (-2, -2).
The radius is the distance from the center of the circle to the edge of the circle. The red dot is the edge of the circle, there are 3 lines that represent 3 units, so we have a radius of 3 units.
Using these in the general equation, we have
[x - (-2)]² + [y - (-2)]² = 3²
(x + 2)² + (y + 2)² = 9
And this is the equation.
Answer:
Distributive property
Step-by-step explanation:
Think of Distributive property being a party. the host is outside of the house (the parenthesis) and wants to greet everyone at the party. so 2x3k=6k and 2x5=10. so you replace 2(3k+5) with 6k+10
<h2>
Answer:</h2>
The equation that is used to model the length of ladder in terms of x is:
![x^2-7x-60=0](https://tex.z-dn.net/?f=x%5E2-7x-60%3D0)
<h2>
Step-by-step explanation:</h2>
We can model this problem with the help of a right angled triangle whose hypotenuse is 13 meters and the other two legs are x meters and (x-7) meters.
where x is the distance between the top of the ladder and the ground.
and (x-7) is the distance between the foot of the ladder and the wall.
Hence, using Pythagorean Theorem we have:
![13^2=x^2+(x-7)^2\\\\i.e.\\\\169=x^2+x^2+49-14x\\\\i.e.\\\\169=2x^2-14x+49\\\\i.e.\\\\2x^2-14x+49-169=0\\\\i.e.\\\\2x^2-14x-120=0\\\\i.e.\\\\x^2-7x-60=0](https://tex.z-dn.net/?f=13%5E2%3Dx%5E2%2B%28x-7%29%5E2%5C%5C%5C%5Ci.e.%5C%5C%5C%5C169%3Dx%5E2%2Bx%5E2%2B49-14x%5C%5C%5C%5Ci.e.%5C%5C%5C%5C169%3D2x%5E2-14x%2B49%5C%5C%5C%5Ci.e.%5C%5C%5C%5C2x%5E2-14x%2B49-169%3D0%5C%5C%5C%5Ci.e.%5C%5C%5C%5C2x%5E2-14x-120%3D0%5C%5C%5C%5Ci.e.%5C%5C%5C%5Cx%5E2-7x-60%3D0)
Hence, the answer is:
![x^2-7x-60=0](https://tex.z-dn.net/?f=x%5E2-7x-60%3D0)