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Allushta [10]
3 years ago
13

.A ladder is leaning against a wall. The top of the ladder is 4 feet above the ground

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
8 0

Step-by-step explanation:

The ladder forms a triangle with the wall and ground.

The side of the triangle opposite of the 60° angle is 4 feet.

To find the length of the ladder (the hypotenuse), use sine.

sine = opposite / hypotenuse

sin 60° = 4 / L

L = 4 / sin 60°

L = 4 / (√3 / 2)

L = 8 / √3

L = 8√3 / 3

L ≈ 4.619 feet

To find the distance from the wall, use tangent.

tangent = opposite / adjacent

tan 60° = 4 / x

x = 4 / tan 60°

x = 4 / √3

x = 4√3 / 3

x ≈ 2.309 feet

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Which ordered pair is a solution of the equation?<br> y = -3x-4.
geniusboy [140]

Answer:

B. Only (-3,5)

Step-by-step explanation:

1. Plug in the x values from the answer choices  and see if it gives you the y-value in the answer choices.

A. y=-3(-2) - 4

= 6 - 4

y = 2

The ordered pair for answer A is (-2,4) where the y-value is 4. Well, when you plugged in -2 for x you got 2, not 4. So A can't be the right answer.

B. y=-3(-3) - 4

= 9- 4

y = 5

The y-value in this ordered pair (-3,5) is indeed 5, so this answer holds true.

Therefore, the answer is B because it is the only ordered pair that has the correct solution.

8 0
3 years ago
Which letter accurately describes how w(x) = log4(x + 5) – 3 is translated from p(x) = log4(x).
Irina-Kira [14]

Answer:

B. Left 5 units and down 3 units

5 0
2 years ago
X - 2y &lt; 2<br> graph the inequality
Korvikt [17]

Answer:

y > 1/2x - 1

First, draw the dashed line y = 1/2x - 1 (slope intercept ; y = mx + b).

Start at -1 on the y-axis, and continue going 2 units to the right, and 1 unit up for the right side of the graph.

Then starting at -1 on the y-axis, continue going 2 units to the left, and 1 unit down for the left side of the graph.

Explanation:

Convert standard form (Ax + By = C) by isolating y from the rest of the equation.

Ax + By = C → y = -Ax/B + C/B → y = mx + b.

Given a standard form equation in inequality form,

x - 2y < 2.

Set it to slope-intercept as an inequality to find the slope and y-intercept.

When negating (making opposite) a variable, you flip the inequality.

x - 2y < 2 → x - 2y - x < 2 - x → -2y < -x + 2 → 2y > x - 2 → <u>y > 1/2x - 1</u><u>.</u>

3 0
2 years ago
Find z1z2 if z1 = 2/5(cos63° + isin63°) and z2 = 10/3(cos117° + isin117°).
Airida [17]

Answer:

-10/3 is the answer

Step-by-step explanation:

Given are two complex numbers as

z1=\frac{2}{5} (cos63  + isin63)\\z2=\frac{10}{3} (cos 117 + isin117})

Recall Demoivre theorem as

(cosA+isinA)(cos A+isin B) = cos(A+B)+isin(A+B)

Hence here we have sum of angles  as

A+B = 63+117 =180

z1z2=\frac{2}{5} \frac{10}{3} (cos180+isin180)

=\frac{-10}{3}

Since sin180=0 and cos 180=-1

7 0
3 years ago
1. Which of the following points is a solution of y &gt; |x| + 5?
Dennis_Churaev [7]
1.   iThis  is shaped like a V with its vertex at the point (0,5)
( its ( 1,7)

2. -3 <= -1-1 = =2

so its (-1, -3)

7 0
3 years ago
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