1. Find the sum of csc230° and cot2 45°.​

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as some coordinates to transform are not given.

I will, however, give a general explanation.

Rotate circle 270 degrees counterclockwise

This implies that, we rotate the center of the circle and the rule of this rotation is:

[tex](x,y) \to (y,-x)[/tex]

Assume the center is: (5,3), the new center will be: (3,-5)

Reflect square across y-axis

The rule is:

[tex](x,y) \to (-x,y)[/tex]

If the square has (3,5) as one of its vertices before rotation, the new point will be (-3,5).

Reflect triangle across y-axis, then 3 units up and 2 units left

The rule of reflection is:

[tex](x,y) \to (-x,y)[/tex]

If the triangle has (3,5) as one of its vertices before rotation, the new point will be (-3,5).

The rule of translating a point up is:

[tex](x,y) \to (x,y+h)[/tex] where h is the unit of translation

In this case, h = 3; So, we have:

[tex](-3,5) \to (-3,5+3)[/tex]

[tex](-3,5) \to (-3,8)[/tex]

The rule of translating a point left is:

[tex](x,y) \to (x-b,y)[/tex] where b is the unit of translation

In this case, b = 2; So, we have:

[tex](-3,8) \to (-3+2,8)[/tex]

[tex](-3,8) \to (-1,8)[/tex]

The L shape

[tex]A = (3, 8)[/tex]       [tex]A" = (-3, 1)[/tex]

[tex]B = (6, 8)[/tex]       [tex]B"= (-6, 1)[/tex]

[tex]C = (6, 3)[/tex]       [tex]C" = (-6, -4)[/tex]

[tex]D = (5, 3)[/tex]       [tex]D" = (-5, -4)[/tex]

Required

The transformation from ABCD to A"B"C"D"

First, ABCD is reflected across the y-axis.

The rule is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]A' = (-3,8)[/tex]

[tex]B' = (-6,8)[/tex]

[tex]C' = (-6,3)[/tex]

[tex]D' = (-5,3)[/tex]

Next A'B'C'D' is translated 7 units down

The rule is:

[tex](x,y) \to (x,y-7)[/tex]

So, we have:

[tex]A"= (-3,8-7) = (-3,1)[/tex]

[tex]B"= (-6,8-7) = (-6,1)[/tex]

[tex]C"= (-6,3-7) = (-6,-4)[/tex]

[tex]D"= (-5,3-7) = (-5,-4)[/tex]

Answer:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Step-by-step explanation:

This question is asking for the function's end behavior. An even degree power function with a negative leading coefficient forms a parabola concave down. This means, its vertex represents the maximum and the parabola opens downward (towards negative infinity).

Thus,

[tex]\lim_{x\rightarrow \infty}f(x)=-\infty,\\\lim_{x\rightarrow-\infty}f(x)=-\infty[/tex]

This corresponds with the first answer choice listed:

[tex]\text{As }x\rightarrow \infty, f(x)\rightarrow -\infty,\\\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

Answer:

First choice

Step-by-step explanation:

It gives you the endpoints of the included side, F and R. Therefore, the side is FR or RF.

1/6 = 1 batch, 2/6 = 2 batches and so on

if the factory used 1/2, the factory used 3/6 of a barrel, which equals to 3 batches.

hope it helps :)

Answer:

Yes

Step-by-step explanation:

Answer:

k=10

Step-by-step explanation:

Brainliest please~

Answer:

K=10

Step-by-step explanation:

Correct on Plato

Answer:

The y-intercept of the parent function, f(x), is 0

The y-intercept of the child function, g(x), is  7

Step-by-step explanation:

Since the parent function passes through the origin, its y-intercept is 0. Once the function is translated 7 units up, its y-intercept is 7.

The solution is :

Vertex is (-2, 0)

y-intercept is 4.

In geometry, a vertex is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.

here, we have,

to find the function translated 2 units left, we just need to substitute the 'x' in the equation by 'x+2':

f(x) = (x+2)^2 = x2 + 4x + 4

Then, to find the vertex, we can use the formula:

x_v = -b / 2a

x_v = -4 / 2 = -2

Now, finding the y_vertex, we have:

f(x_v) = (-2)^2 + 4*(-2) + 4 = 0

So the vertex is (-2, 0)

To find the y-intercept, we make x = 0 and then find f(x):

f(0) = 0 + 0 + 4 = 4

So the y-intercept is 4.

To learn more on vertex click:

brainly.com/question/12563262

#SPJ2

complete question:

Identify the vertex and y-intercept of the graph of the function translated 2 units left from the parent function f(x) = x².

vertex: ( ? , ? )

y-intercept: ?

To solve this question, we need to solve an exponential equation, which we do applying the natural logarithm to both sides of the equation, both to find the needed time and to find the inverse function. From this, we get that:

Number of trees infected after t years:

The number of trees infected after t years is given by:

[tex]f(t) = e^{0.4t}[/tex]

Question 1:

We have to find the number of years it takes to have 21 trees infected, that is, t for which:

[tex]f(t) = 21[/tex]

Thus:

[tex]e^{0.4t} = 21[/tex]

To isolate t, we apply the natural logarithm to both sides of the equation, and thus:

[tex]\ln{e^{0.4t}} = \ln{21}[/tex]

[tex]0.4t = \ln{21}[/tex]

[tex]t = \frac{\ln{21}}{0.4}[/tex]

[tex]t = 7.6[/tex]

Thus, it will take 7.6 years for 21 of the trees to become infected.

Question 2:

We have to find the inverse function, that is, first we exchange y and x, then isolate x. So

[tex]f(x) = y = e^{0.4x}[/tex]

[tex]e^{0.4y} = x[/tex]

Again, we apply the natural logarithm to both sides of the equation, so:

[tex]\ln{e^{0.4y}} = \ln{x}[/tex]

[tex]0.4y = \ln{x}[/tex]

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

Thus, the logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

For an example of a problem that uses exponential functions and logarithms, you can take a look at https://brainly.com/question/13812761

Factorize the numerator:

4r + 20 = 4r + 4×5 = 4 (r + 5)

I think you meant to say r ≠ -5, which means r + 5 ≠ 0, so that the denominator is never zero and so the expression is defined (no division by zero). This lets you cancel the factor of r + 5 in the numerator with the one in the denominator:

(4r + 20)/(r + 5) = 4 (r + 5)/(r + 5) = 4

Please look at the scanned picture.

Answer:

I'm pretty sure you are intended to pick AAS.

Step-by-step explanation:

As it stands, AAS. But this can be an unreliable theorem. If you show that the third angles are equal (which they are) using the fact that if two angles of a triangle are equal to the corresponding angles of another triangle, then the third angle is as well. That means that you can use the much more reliable ASA.

Answer:

Step-by-step explanation:

Given:

27 + 2/3 ÷ 3 + 9/10

In division, compatible numbers are numbers that can be divided mentally.

27 + 2/3 ÷ 3 + 9/10

27 + 0.67 ÷ 3 + 0.9

27.67 ÷ 3.9

= 7.0948717948717

Approximately

= 7

But, alternatively

27.67 ÷ 3.9

27.67 is closer to 28

3.9 is closer to 4

Therefore,

28 ÷ 4

= 7

The quotient of 27 + 2/3 ÷ 3 + 9/10 using compatible numbers is around 7

Answer:

The first fraction is between 27 and 28, closer to 28. The second fraction is between 3 and 4, closer to 4. Compatible numbers in division are numbers that can be divided mentally. 28 divided by 4 is 7. The quotient will be around 7.

Step-by-step explanation:

Answer:

$0.5

Step-by-step explanation:

A + B = 1.10

A=1 +B

now A + B = 1.10

A - B = 1 (B cancels out)

2A = 2.10

A= 1.05

A + B = 1.10

substitute A value

1.05 + B = 1.10

B= 1.10-1.05

B=$ 0.5

Answer:

y = 2/5x +24/5

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

y = 2/5 x +b

Substitute the point into the equation and solve for b

4 = 2/5(-2)+b

4 = -4/5 +b

Add 4/5 to each side

20/5 +4/5 = b

24/5 = b

y = 2/5x +24/5

Answer:

-3

Step-by-step explanation:

because as you vo more to the negative side the less.it gets and more to the positive side it gets moe

Answer: [tex]\frac{11}{12}[/tex]

Step-by-step explanation:

Use trigonometry (shown in image below) to find the 3 side-lengths:

According to right triangle trigonometry:

cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Substitute in the values:

cos θ = [tex]\frac{11}{12}[/tex]

Answer:

b20

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

s² + s² = 2²

2s² = 4 ( divide both sides by 2 )

s² = 2 ( take the square root of both sides )

s = [tex]\sqrt{2}[/tex]

Answer:

E.

Step-by-step explanation:

we know the diagonal of the square : 2

as you can see in the picture, there is a right-angled triangle with the baseline of Hypotenuse being the diagonal, and 2 times s being the 2 sides.

that means we can use Pythagoras to calculate s :

2² = s² + s²

4 = 2s²

2 = s²

s = sqrt(2)

Answer:

It is c

Step-by-step explanation:

3/z when z = 2

= 3/2

= 1.5

This is the answer

Answer:

[tex]3/z\: when\:z=2[/tex]

[tex]\frac{3}{z}=2[/tex]

[tex]\frac{3}{z}z=2z[/tex]

[tex]2z=3[/tex]

[tex]\frac{2z}{2}=\frac{3}{2}=z=\frac{3}{2}[/tex]

[tex]z=1.5\right[/tex]

OAmalOHopeO

Answer:

4/3

Step-by-step explanation:

Using the given points

(0,-2) and (3,2)

We can use the slope formula

m = (y2-y1)/(x2-x1)

    = ( 2- -2)/(3-0)

   = (2+2)/(3-0)

   =(4/3

Answer:

f(x) = x² + 2x + 1

Step-by-step explanation:

you know how to multiply 2 expressions ?

let's say in general we have

(a + b)(c + d)

you take one part of one expression and multiply it with all parts of the other expression, then you take the second part of the first expression and multiply it with all parts of the other expression, then a potential third part, then a fourth part and so on, and you add all these things together (well, depending on the actual signs, of course).

so, we get for this simple generic example

a×c + b×c + a×d + b×d

now we use that understanding for our question here.

(x+1)(x+1) = x×x + 1×x + x×1 + 1×1 = x² + x + x + 1 = x² + 2x + 1

Answer: Third Choice. 9

Step-by-step explanation:

Concept:

Here, we need to understand the idea of evaluation.    

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given

4x + 2y -1

x = 3, y = -1

Substitute the value of x and y

4(3) + 2(-1) - 1

Simplify by multiplication

12 - 2 - 1

Simplify by subtraction

9

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Hello!

4x= 4*3 = 12

2y = 2*-1 = -2

12-2  -1= 9

Answer:

θ ≈ 35.7°

Step-by-step explanation:

His mistake was in using the wrong trig. ratio

Instead of using cosine he should have used the sine ratio

sinθ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7}{12}[/tex] , then

θ = [tex]sin^{-1}[/tex] ([tex]\frac{7}{12}[/tex] ) ≈ 35.7° ( to the nearest tenth )

below

Step-by-step explanation:

all real numbers

[0,∞]

increasing

decreasing

Answer:

XN = 22

Step-by-step explanation:

Recall: the Centroid theorem states that the Centroid of a triangle is ⅔ of the distance any vertex of the triangle to the midpoint of the side opposite to it.

This implies that:

XN = ⅔(XG)

XG = 33

Substitute

XN = ⅔(33)

XN = 2*11

XN = 22

Do it by your self  ok ???

Answer:

Step-by-step explanation:

te da x<3/2 y x<2, pero la segunda solucion abarca la primera. Por lo tanto creo q seria x<2

4x - 7 = 3x + 9

x = 16

they're equal because they are opposites by the vertex.

hope it helps :)

Answer:

216 cm^2

Step-by-step explanation:

15^2 -3^2 = 225 -9

= 216