What is the solution of the system? Use any method. 3x + 2y = 7 y = –3x + 11

Mathematics

1 answer:

Gnom [1K]2 years ago

6 0

Answer:

$(5,-4)$

Step-by-step explanation:

SOLVE BY SUBSTITUTION:

STEP 1: Replace all occurrences of $y$ with $-3x+11$ in each equation.

$-3x+22=7\\y=-3x+11$

STEP 2: Solve for $x$ in the first equation.

$x=5\\y=-3x+11$

STEP 3: Replace all occurrences of $x$ with $5$ in each equation.

$y=-4\\x=5$

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A 10-foot ladder is to be placed Against the side of the building. The base of the latter must be placed in an angle of 72° With

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Answer:

Distance of foot of ladder from building: 37.2 inches

Distance of top of ladder from building's base: 114 inches

Step-by-step explanation:

Please refer to the figure attached in the answer area.

A right angled triangle $\triangle ABC$ is formed by the ladder with the building where hypotenuse is the length of ladder.

Hypotenuse, AC = 10 foot

Also, we are given that angle made by the base of ladder with the ground is $72^\circ$ .

We have to find AB and BC.

$\angle BAC = 72^\circ$

Using trigonometric functions:

$cos \theta= \dfrac{Base}{Hypotenuse}\\cos 72^\circ= \dfrac{AB}{AC}\\\Rightarrow 0.309 = \dfrac{AB}{AC}\\\Rightarrow AB = 10 \times 0.309\\$\approx$ 3.1 foot\\$\approx$ 37.2 inches$

$sin \theta = \dfrac{Perpendicular}{Hypotenuse}\\\Rightarrow sin72^\circ = \dfrac{BC}{AC}\\\Rightarrow 0.95 = \dfrac{BC}{AC}\\\Rightarrow AB = 10 \times 0.95\\$\approx$ 9.5 foot\\$\approx$ 114 inches$