What is the quotient? x + 1)3x2 − 2x + 7

Use the information that sin⁡θ=35 and 90°<θ<180° to answer the following questions. Part A: Which equation shows cos2θ+sin

gizmo_the_mogwai [7]

Answer:

(a) $cos\theta = \sqrt{1-sin^2\theta}$

(b) $cos\theta = \frac{4}{5}$

(c) $cos\theta = -\frac{4}{5}$

Step-by-step explanation:

Given that 90°< θ<180° and $sin\theta= \frac{3}{5}$

Since 90°< θ<180° so θ lies in second quadrant where sinθ is positive but cosθ is negative.

(a) The identity,

Sin²θ+cos²θ= 1

⇒cos²θ=1-sin²θ

$\Rightarrow cos\theta = \sqrt{1-sin^2\theta}$

(b)

$cos\theta = \sqrt{1-sin^2\theta}$ [ Since the quadrant is not considered]

$\Rightarrow cos\theta = \sqrt{1-(\frac{3}{5})^2 }$

$\Rightarrow cos\theta = \sqrt{1-(\frac{9}{25}) }$

$\Rightarrow cos\theta = \sqrt{(\frac{25-9}{25}) }$

$\Rightarrow cos\theta = \sqrt{\frac{16}{25} }$

$\Rightarrow cos\theta = \frac{4}{5}$

(c)

$cos\theta = -\sqrt{1-sin^2\theta}$ [ since cos θ is negative in second quadrant]

$\Rightarrow cos\theta = -\sqrt{1-(\frac{3}{5})^2 }$

$\Rightarrow cos\theta = -\sqrt{1-(\frac{9}{25}) }$

$\Rightarrow cos\theta = -\frac{4}{5}$

8 0

3 years ago

Steven is comparing the cost of a fresh lobster dinner at two different restaurants. The first

Anarel [89]

Answer:

Step-by-step explanation:

2x+51=4x+19

32=2x

x=16. The weight is 16 pounds

plug it back in to find the cost

32+51=83. 64+19 = 83. The cost is 83 dollars

6 0

3 years ago

Match each table with its corresponding function type.

mario62 [17]

The first table that starts with -1,2 is exponential

The second table that starts with -2,-7 is linear

The last table is quadratic

5 0

3 years ago

Elliott has some yarn that she wants to use to make hats and scarves. Each hat uses 0.2, point, 2 kilograms of yarn and each sca

sp2606 [1]

Answer:

Elliot will make 4 hats and 16 scarves

Step-by-step explanation:

Let x be the number of hats and y be the number of scarves Elliot will make.

Elliott wants to make a total of 20 items, then

x + y = 20

Each hat uses 0.2 kilograms of yarn, so x hats use 0.2x kilograms of yarn and each scarf uses 0.1 kilogram of yarn, then y scarves use 0.1y kilograms of yarn. Elliott wants to use twice as much yarn for scarves as for hats, then

0.1y = 2(0.2x)

Thus,

0.1y = 0.4x

y = 4x

Substitute it into the first equation:

x + 4x = 20

5x = 20

x = 4

y = 20 - 4

y = 16

Hence, Elliot will make 4 hats and 16 scarves

4 0

3 years ago

which statements are true about the graph of the function f(x) = 6x – 4 x2? check all that apply. the vertex form of the functio

Brut [27]

Answer:

The vertex of the function is the point $(-3,-13)$

The graph increase over the interval--------> (-3,∞)

Step-by-step explanation:

we have

$f(x)=6x-4+x^{2}$

1) Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)+4=x^{2}+6x$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)+4+9=x^{2}+6x+9$

$f(x)+13=x^{2}+6x+9$

Rewrite as perfect squares

$f(x)+13=(x+3)^{2}$

$f(x)=(x+3)^{2}-13$ -----> function in vertex form

2) Find the vertex

The vertex of the function is the point $(-3,-13)$

3) Find the axis of symmetry

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

The x-coordinate of the vertex in this problem is equal to $x=-3$

therefore

the equation of the axis of symmetry is $x=-3$

4) Find the increase-decrease intervals

The graph increase over the interval--------> (-3,∞)

The graph decrease over the interval--------> (-∞,-3)

see the attached figure to better understand the problem

5) Find the x-intercepts of the function

we know that

the x-intercepts are the values of x when the value of the function is equal to zero

In this problem the x-intercepts are

$(-6.61,0)$ and $(0.61,0)$

so

The function cross the x-axis twice

see the attached figure

5 0

4 years ago

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