Solve Systems by Substitution 2x+5y=-3 x+8y=4 and 2x+y=7 x-2y=-14

1 answer:

4 0

2x + 5y = -3 ⇒ 2x + 5y = -3
1x + 8y = 4 ⇒ 2x + 16y = 8
 -11y = -11 
 -11 -11
 y = 1
 2x + 5(1) = -3
 2x + 5 = -3
 -5 -5
 2x = -8
 2 2
 x = -4
 (x, y) = (-4, 1)

2x + 1y = 7 ⇒ 2x + 1y = 7
1x - 2y = -14 ⇒ 2x - 4y = -28
 5y = 35
 5 5
 y = 7
 2x + 7 = 7
 -7 -7
 2x = 0
 2 2
 x = 0
 (x, y) = (0, 7)

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Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B

Anna71 [15]

Answer:

The length of side b is 179 ft

Step-by-step explanation:

Given triangle ABC in which

∠A = 33°, ∠B = 63°, c=200

we have to find the length of b

In ΔABC, by angle sum property of triangle

∠A+∠B+∠C=180°

33°+63°+∠C=180°

∠C=180°-33°-63°=84°

By sine law,

$\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}$

$\frac{\sin 63^{\circ}}{b}=\frac{\sin 84^{\circ}}{200}$

$b=200\times \frac{\sin 63^{\circ}}{\sin 84^{\circ}}=179.182887\sim 179 ft$

The length of side b is 179 ft

Option C is correct.

7 0

3 years ago

Please help on this question?

svlad2 [7]

Well we know these two angles are congruent, so we set their angles equal to each other.
5w - 69 = w + 3
4w = 72
w = 18
Now we plug w back into one of the equations, and then multiply whatever number we get by 2.
18 + 3 = 21
21 x 2 = 42
The measure of STU is 42°

4 0

3 years ago

What is the maximum number of turns for the graph of f(x)=x^4+3x^2?

Stels [109]

Answer:

The turns of a graph is represented by the number of maximum or minimum that the function has.

If we differenciate f(x) we get:

f'(x)=4x^3+6x

f'(x)=2x(2x^2 + 3)

Therefore f'(x) =0, when x=0. Given that negative roots are not defined.

Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.

Attached you find the graph of the function which confirms the number of turns.

If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!