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vagabundo [1.1K]

3 years ago

7

Bamboo plants grow rapidly. A bamboo plant is 113 inches tall. Tomorrow it will be 120 inches tall, the next day it will be 127

inches tall, and on the next day it will be 134 inches tall. Write a rule to represent the height of the bamboo plant as an arithmetic sequence. How tall will the plant be in 18 days? A ; 232 inches B ; 239 inches C ; 239 inches D ; 232 inches

1 answer:

Allisa [31]3 years ago

3 0

18 x 7 = 126
113 + 126 = 239

239 inches

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Find the exact value of cos 157.5°.

Nonamiya [84]

Cos 157.5º=-cos (180º-157.5º)=-cos 22.5=-cos(45/2)

cos Ф/2=⁺₋√((1+cosФ)/2).

In this case 157.5º is in the second quadrant, therefore we use the following equation:
cos Ф/2=-√((1+cosФ)/2). (we will have a negative number)

cos 157.5º=-cos (45/2)=-√((1+cos 45º)/2)
=-√((1+√2/2)/2)
=-√((2+√2)/4)
=-√(2+√2) / 2 (≈-0.92387...)

Answer: cos 157.5º= -√(2+√2) / 2

3 0

4 years ago

Extra points!!no links tho

Naddik [55]

Answer:

<h3> a. the vertex represents a minimum point</h3><h3> b. f(x) = (x + 5)² - 5</h3>

Step-by-step explanation:

a.

a = 1 > 0 ← that means the parabola opens up, so the vertex is minimum of the function

b.

$f(x)=x^2+10x+20\\\\f(x)=\underline{x^2+10x+25} - 25+20\\\\f(x)=(x+5)^2-5$

5 0

3 years ago

Find the coordinates of the circumcenter of △PQR with vertices P(−2,5), Q(4,1), and R(−2,−3).

mel-nik [20]

Answer: (1/3,2)

Step-by-step explanation:

Let O(x,y) be the circumference of the triangle PQR,

Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.

Thus, PO = QO

By the distance formula,

$(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2$

$\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y$

$\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y$

$\implies 4x +8x-10y+2y = 16 + 1 -25-4$

$\implies 12x - 8y = 17 - 29$

$\implies 12 x - 8 y = - 12$ ---------(1)

Similarly, QO = RO

$\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2$

$\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y$

$\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y$

$\implies - 8x -4x-2y-6y=4+9-16-1$

$\implies -12 x - 8 y = 13 - 17$

$\implies 12 x + 8 y = 4$ ------------(2)

By adding equation (1) and (2),

24 x = - 8

x = 1/3

By putting this value in equation (1),

We get,

Thus, 4 - 8 y = -12

8 y = 16

y = 2

7 0

3 years ago

The graph of a proportional relationship passes through the point (6, 21). What is the equation for the relationship?

Kipish [7]

Answer:

The equation for the relationship is $y = \frac{7}{2}\cdot x$ .

Step-by-step explanation:

Given that point $(x,y) = (6, 21)$ is part of a direct relationship. That is:

$y \propto x$

$y = k\cdot x$ (1)

Where $k$ is the proportionality constant.

If we know that $x = 6$ and $y = 21$ , then the proportionality constant is:

$k = \frac{y}{x}$

$k = \frac{21}{6}$

$k = \frac{7}{2}$

Lastly, the equation for the relationship is $y = \frac{7}{2}\cdot x$ .

7 0

3 years ago

Point A is located at (2, 6), and D is located at (−4, 10). Find the coordinates of the point that lies halfway between A and D.

valina [46]

$(( \frac{1}{2} (( - 4) - 2) + 2and( \frac{1}{2} (10 - 6)) + 6$
the answer is(-1,8)

8 0

3 years ago

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