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Mathematics

1 answer:

zaharov [31]3 years ago

7 0

Answer:

B. x = 7; AB = 9, AC = 12

Step-by-step explanation:

12/4 = (x + 2)/(x - 4) (similar triangles theorem)

3 = (x + 2)/(x - 4)

Cross multiply

3(x - 4) = (x + 2)

3x - 12 = x + 2

Collect like terms

3x - x = 12 + 2

2x = 14

x = 14/2

x = 7

✔️AB = x + 2 = 7 + 2

AB = 9

✔️AC = (x + 2) + (x - 4) = (7 + 2) + (7 - 4)

AC = 9 + 3

AC = 12

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the sum of two numbers is 70. the larger number is five less than twice the smaller number . what are the two numbers

earnstyle [38]

X+y=70
x=2y-5
x=larger number
y=smaller number
now plug in the value of x to only have one variable in the equation...
Way to solve for y:
(2y-5)+y=70
3y-5=70
add 5 on both sides...
3y=75
divide by 3 on both sides
y=25
1st way to solve for x:
now plug in y in the original equation...
x+25=70
subtract 25 on both sides...
x=45
2nd way to solve for x:
plug in y for the second equation...
x=25(2)-5
x=50-5
x=45
answer: the two numbers are 45 and 25.

3 0

3 years ago

A submersible traveling at a depth of 250 feet dives at an angle of 15 degrees with respect to a

kipiarov [429]

Answer:

$\boxed{\text{652 ft}}$

Step-by-step explanation:

The submersible is diving at a down angle of 15° along the hypotenuse AC of triangle ABC.

Its horizontal track along the surface AB is 1500 ft.

$\begin{array}{rcl}\tan A & = &\dfrac{BC}{AC}\\\\\tan 15^{\circ} & = & \dfrac{a}{1500}\\\\0.2679 & = & \dfrac{a}{1500}\\\\a & = & 1500 \times 0.2679\\& = & \textbf{402 ft}\\\end{array}$