So remember that the distance formula is
.
1.
![\sqrt{(4-4)^2+(-2-(-5))^2}\\ \sqrt{0^2+3^2}\\ \sqrt{0+9}\\ \sqrt{9}\\ 3](https://tex.z-dn.net/?f=%20%5Csqrt%7B%284-4%29%5E2%2B%28-2-%28-5%29%29%5E2%7D%5C%5C%20%5Csqrt%7B0%5E2%2B3%5E2%7D%5C%5C%20%5Csqrt%7B0%2B9%7D%5C%5C%20%5Csqrt%7B9%7D%5C%5C%203%20)
Distance between (4,-5) and (4,-2) is 3 units.
2.
![\sqrt{(1-(-1))^2+(1-4)^2}\\ \sqrt{2^2+(-3)^2}\\ \sqrt{4+9}\\ \sqrt{13}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%281-%28-1%29%29%5E2%2B%281-4%29%5E2%7D%5C%5C%20%5Csqrt%7B2%5E2%2B%28-3%29%5E2%7D%5C%5C%20%5Csqrt%7B4%2B9%7D%5C%5C%20%5Csqrt%7B13%7D%20)
Distance between (1,1) and (-1,4) is √13 (or 3.61 rounded to the hundreths) units.
Answer:
C
Step-by-step explanation:
it describes how much the shown graph extends left and right.
Note that 4 is included, but -2 itself not. that's why it's empty and A isn't correct.
B and D are completely inapplicable
pls brainliest
Answer:
The distance you are from the base of plateau = ![99.97\ m\approx 100\ m](https://tex.z-dn.net/?f=99.97%5C%20m%5Capprox%20100%5C%20m)
Step-by-step explanation:
Given:
Height of plateau = 70 m
Angle of elevation to the top of plateau = 35°
To find the distance you are from the base of plateau.
We will construct a triangle ABC to model the given situation. The triangle would be a right triangle for which we know an angle and its opposite side. We need to find the adjacent side of the triangle.
We will apply trigonometric ratio to find the adjacent side.
![\tan\theta=\frac{Opposite\ Side}{Adjacent\ Side}](https://tex.z-dn.net/?f=%5Ctan%5Ctheta%3D%5Cfrac%7BOpposite%5C%20Side%7D%7BAdjacent%5C%20Side%7D)
where
represents the angle of reference.
Plugging in the values from the triangle.
![\tan 35\° =\frac{BC}{AC}](https://tex.z-dn.net/?f=%5Ctan%2035%5C%C2%B0%20%3D%5Cfrac%7BBC%7D%7BAC%7D)
![\tan 35\° =\frac{70}{AC}](https://tex.z-dn.net/?f=%5Ctan%2035%5C%C2%B0%20%3D%5Cfrac%7B70%7D%7BAC%7D)
Multiplying both sides by AC.
![AC\times \tan 35\° =AC\times \frac{70}{AC}](https://tex.z-dn.net/?f=AC%5Ctimes%20%5Ctan%2035%5C%C2%B0%20%3DAC%5Ctimes%20%5Cfrac%7B70%7D%7BAC%7D)
![AC\times \tan 35\° =70](https://tex.z-dn.net/?f=AC%5Ctimes%20%5Ctan%2035%5C%C2%B0%20%3D70)
Dividing both sides by ![\tan 35\°](https://tex.z-dn.net/?f=%5Ctan%2035%5C%C2%B0)
![\frac{AC\times \tan 35\°}{\tan 35\°} =\frac{70}{\tan 35\°}](https://tex.z-dn.net/?f=%5Cfrac%7BAC%5Ctimes%20%5Ctan%2035%5C%C2%B0%7D%7B%5Ctan%2035%5C%C2%B0%7D%20%3D%5Cfrac%7B70%7D%7B%5Ctan%2035%5C%C2%B0%7D)
∴ ![AC=99.97\ m\approx 100\ m](https://tex.z-dn.net/?f=AC%3D99.97%5C%20m%5Capprox%20100%5C%20m)
The distance you are from the base of plateau = ![99.97\ m\approx 100\ m](https://tex.z-dn.net/?f=99.97%5C%20m%5Capprox%20100%5C%20m)
Answer:
13 cm × 12 cm
Step-by-step explanation:
The diagonal of the top or bottom faces of the box is the hypotenuse of a triangle with legs 12 cm and 5 cm. The Pythagorean theorem tells you that diagonal length is ...
d = √(12² +5²) = √(144 +25) = √169 = 13 . . . cm
The width of the divider is 13 cm.
The height of the divider is shown as 12 cm.
The dimensions of the dividing rectangle are 13 cm by 12 cm.
Answer:
a) x=18
b) 36 (2*18)
c) 54 (3*18)
d) I'm not exactly sure what it's asking for, so I don't know
Step-by-step explanation:
triangle sum theorem means the sum of every triangle is 180 degrees
so we can make this equation: 180 = 90 + 2x + 3x
solve and you get 18.