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Alex73 [517]
3 years ago
6

In the coordinate plane, ABCD has vertices with coordinates A(1,-1), B(-5,3), C(-3,6),

Mathematics
1 answer:
Nana76 [90]3 years ago
6 0

Answer:

C

Step-by-step explanation:

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A 10 foot tree create a shadow that is 15 feet long. Find the angle of elevation of the sun
Solnce55 [7]

Answer:

The angle of elevation of the sun is 33.7⁰

Step-by-step explanation:

let the height of the tree, T = 10 foot

length of the shadow created by the tree, B = 15 feet long

Height of the tree and the shadow of the tree forms a right angle triangle with the remaining side that joins the two which is known as hypotenuse.

Let the remaining side, hypotenuse, L = ?

Apply Pythagoras theorem;

L ² = T² + B²

L ² = 10² + 15²

L ² = 325

L = √325

L = 18.03 ft

The angle of elevation of the sun, is the angle facing the height of the tree with the length of the shadow of the tree as adjacent of the triangle.

Let the angle of elevation = θ

tan θ = opp / adj

tan θ  = 10 / 15

tan θ  = 0.66667

θ = tan ⁻¹ (0.66667)

θ = 33.7⁰

Therefore, the angle of elevation of the sun is 33.7⁰

5 0
4 years ago
Hich function has a range of {y|y ≤ 5}?
marshall27 [118]

Answer:

f(x)=-(x-4)^{2}+5

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

y=a(x-h)^{2}+k

where

(h,k) is the vertex of the parabola

if a>0 -----> the parabola open upward (vertex is a minimum)

if a<0 -----> the parabola open downward (vertex is a maximum)

<u>Verify each case</u>

case A) f(x)=(x-4)^{2}+5

The vertex is the point (4,5)

a=1

a>0 -----> the parabola open upward (vertex is a minimum)

The range is the interval--------> [5,∞)

y\geq5

case B) f(x)=-(x-4)^{2}+5

The vertex is the point (4,5)

a=-1

a<0 -----> the parabola open downward (vertex is a maximum)

The range is the interval--------> (-∞,5]

y\leq 5

case C) f(x)=(x-5)^{2}+4

The vertex is the point (5,4)

a=1

a>0 -----> the parabola open upward (vertex is a minimum)

The range is the interval--------> [4,∞)

y\geq4

case D) f(x)=-(x-5)^{2}+4

The vertex is the point (5,4)

a=-1

a<0 -----> the parabola open downward (vertex is a maximum)

The range is the interval--------> (-∞,4]

y\leq 4

4 0
3 years ago
Which of the following is equal to (2x/3 - 7) + 7?. A. (2x - 7) + 21. B. 2x - 21/3. C. 3x/2. D. 2x/3.
Setler79 [48]

For this case we have the following expression:

(\frac{2x}{3} - 7) + 7

What we must do in this case is to use one of the properties of the sum.

In this case, we must use the associative property.

The associative property states:

(a + b) + c = a + (b + c)

We have then:

(\frac{2x}{3} - 7) + 7 = \frac{2x}{3} + (- 7 + 7)

Simplifying we have:

(\frac{2x}{3} - 7) + 7 = \frac{2x}{3} + (0)

(\frac{2x}{3} - 7) + 7 = \frac{2x}{3}

Answer:

the following is equal to (2x / 3 - 7) + 7

D. 2x / 3.

7 0
4 years ago
Read 2 more answers
Express 2.58 x 10^-2 in standard form​
Alisiya [41]

Answer:

2.5 x 10^{-2] = 0.025

Step-by-step explanation:

If you mean standard DECIMAL form, then you move the decimal point 2 places to the left because of the negative power of 10:

8 0
4 years ago
Read 2 more answers
I need helpppppppppppp
ratelena [41]
The answer to question 3 is D. 15(4a+3). And the answer to question 4 is A. 90. Have a great day
7 0
3 years ago
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