One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0). Which transformations could have taken place? Select two options. R0, 90° R0, 180° R0, 270° R0, –90° R0, –180°

Answer:

Y=(-1,0)

G=(0,1)

F=(-1,3)

Step-by-step explanation:

Answer:

[tex]f(theta)=sin(theta) - cos(theta)[/tex] + C

This is my first time doing a double integral, so im only 90% sure in my answer

Step-by-step explanation:

You pretty much want to take the double integral of sinx + cosx

The anti-derivative of sinx = -cosx

The anti-derivative of cosx = sinx

So f' = -cosx + sinx

Now lets take the integral of f':

The anti-derivative of -cosx = sinx

The anti-derivative of sinx = -cosx

So, f(x) = sinx - cosx

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Work Shown:

I'll use x in place of theta since its easier to type on a keyboard.

f '' (x) = sin(x) + cos(x)

f ' (x) = -cos(x) + sin(x) + C ..... integrate both sides; dont forget the plus C

f ' (0) = 1

f ' (0) = -cos(0) + sin(0) + C

-cos(0) + sin(0) + C = 1

-1 + 0 + C = 1

C = 1+1

C = 2

So,

f ' (x) = -cos(x) + sin(x) + C

turns into

f ' (x) = -cos(x) + sin(x) + 2

----------------------------

Now integrate both sides of the first derivative to get the original f(x) function

f ' (x) = -cos(x) + sin(x) + 2

f(x) = -sin(x) - cos(x) + 2x + D .... apply integral; D is some constant

f(0) = -sin(0) - cos(0) + 2(0) + D

f(0) = 0 - 1 + 0 + D

f(0) = D - 1

f(0) = 2

D-1 = 2

D = 2+1

D = 3

We have f(x) = -sin(x) - cos(x) + 2x + D update to f(x) = -sin(x) - cos(x) + 2x + 3

----------------------------

So f '' (x) = sin(x) + cos(x) becomes f(x) = -sin(x) - cos(x) + 2x + 3 when f(0) = 2 and f ' (0) = 1

The last step is to replace every x with theta so that we get back to the original variable.

f(x) = -sin(x) - cos(x) + 2x + 3   turns into   f(θ) = -sin(θ) - cos(θ) + 2θ + 3

Answer:

Step-by-step explanation:

Area of a sector = [tex]\frac{\theta}{360} * \pi r^{2}\ where\ \pi r^{2} \ is\ the\ area\ of\ the\ circle[/tex]

theta is the sector's central angle

Area of the sector = [tex]\frac{\theta}{360} * \ area\ of\ a\ circle[/tex]

Given area of a circle = 18πin² and area of a sector = 6πin²

On substituting;

6π = [tex]\theta/360 * 18 \pi[/tex]

Dividing both sides by 18π we have;

1/3 = [tex]\theta/360[/tex]

[tex]3 \theta = 360\\\theta = 360/3\\\theta = 120^{0}[/tex]

The sector's central angle is 120°

Answer:

  42.67%

Step-by-step explanation:

The annual growth factor for interest at annual rate r compounded quarterly is ...

  (1 +r/4)^4

You want that value to be 1.5:

  1.5 = (1 +r/4)^4

  1.5^(1/4) = 1 +r/4

  (1.5^(1/4) -1) = r/4

  4(1.5^(1/4) -1) = r ≈ 0.426728

The rate r must be about 42.67%.

_____

Comment on the wording

We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."

The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."

Answer:

x = 22

x = 4,6

Step-by-step explanation:

3x - 22 = 44

3x = 44 + 22

3x = 66

x = 66/3

x = 22

5/6 = 10/2x - 3

5/6 + 3 = 10/2x

5/6 + 18/6 = 10/2x

23/6 = 10/2x

23/6 * 2 = 10x

46 = 10x

x = 46/10

x = 4,6

Answer:

The 85% confidence interval is ( 7.7 , 8.0 )

Step-by-step explanation:

In order to find the 85% confidence interval you use the following formula:

[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]       (1)

where

[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8

σ: standard deviation = 2.2

n: sample size = 967

α: 1 - 0.85 = 0.15

Zα/2: Z factor of the density distribution = 1.44

You replace the values of all parameters in the equation (1):

[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]

Then, the confidence interval is:

[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]

Answer:

B=25

Step-by-step explanation:

Answer:

y=cosx

Step-by-step explanation:

cosx has a domain of all real numbers

Answer:

8

Step-by-step explanation:

just do the comparation

Vb : Vs

b for big and s for small

4/3 π rb³ : 4/3 π rs³ (since there are 4/3 and π on both side, we can eliminate them so)

Vb : Vs = rb³ : rs³

Vb : Vs = (2rs)³ : rs³

Vb : Vs = 8rs³ : rs³ (delete the r³ on both side)

Vb : Vs = 8 : 1

so Vb is 8 times larger in volume than the small one

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

Answer=6 . S/R . 4T

This is the answer because u have to simplify so to do this u have to divide all of this by R

Answer:

x = 15

Step-by-step explanation:

3x = 45

x = 45/3

x = 15

Answer:

15

Step-by-step explanation:

3x = 45

Dividing 3 from both sides gives you

[tex]x = 45/3\\\\[/tex]

Now that isolated x.

[tex]45/3 = 15[/tex]

So x = 15

:D

Answer:

A right triangle consists of two legs and a hypotenuse.

Step-by-step explanation:

The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle. There are a couple of special types of right triangles, like the 45°-45° right triangles and the 30°-60° right triangle.

Answer:

X = 2 and Y = -3

Step-by-step explanation:

2x+5y=-11    - equation 1

10x+3y=11    - equation 2

from equation 1, 2X = -11 - 5y

                           X = -11/2 - 5Y/2

                           X = -5.5 - 2.5Y

insert X = -5.5 - 2.5Y into equation 2

     therefore, 10x+3y=11

                       10(-5.5 - 2.5Y) + 3y = 11

                       -55 -25Y +3Y = 11

                        -22Y = 11+55

                      Y = -66/22

                      Y = -3

insert Y = -3 into equation 1

      thus 2x + 5(-3) = -11

              2x - 15 = -11

              2x = -11 + 15

              2x = 4

              x = 4/2

              x = 2

ordered pair: X = 2 and Y = -3

Answer:

Population = 34.27336

Step-by-step explanation:

Given:

Population function (t) = 34(1.00804)^t

Number of year = 2000

Find:

Number of citizen in year 2000

Computation:

We know that, base year is 2000

So, t = 1

Population function (t) = 34(1.00804)^t

Population function (1) = 34(1.00804)^1

Population = 34(1.00804)

Population = 34.27336

Therefore, Population is 34.273636 million

Answer:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Step-by-step explanation:

Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:

[tex] X \sim Unif (a=0, b =12)[/tex]

And we want to find the following probability:

[tex] P(X<11)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Answer:

The quantity of salt at time t is [tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex], where t is measured in minutes.

Step-by-step explanation:

The law of mass conservation for control volume indicates that:

[tex]\dot m_{in} - \dot m_{out} = \left(\frac{dm}{dt} \right)_{CV}[/tex]

Where mass flow is the product of salt concentration and water volume flow.

The model of the tank according to the statement is:

[tex](0.5\,\frac{pd}{gal} )\cdot \left(6\,\frac{gal}{min} \right) - c\cdot \left(6\,\frac{gal}{min} \right) = V\cdot \frac{dc}{dt}[/tex]

Where:

[tex]c[/tex] - The salt concentration in the tank, as well at the exit of the tank, measured in [tex]\frac{pd}{gal}[/tex].

[tex]\frac{dc}{dt}[/tex] - Concentration rate of change in the tank, measured in [tex]\frac{pd}{min}[/tex].

[tex]V[/tex] - Volume of the tank, measured in gallons.

The following first-order linear non-homogeneous differential equation is found:

[tex]V \cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]

[tex]60\cdot \frac{dc}{dt} + 6\cdot c = 3[/tex]

[tex]\frac{dc}{dt} + \frac{1}{10}\cdot c = 3[/tex]

This equation is solved as follows:

[tex]e^{\frac{t}{10} }\cdot \left(\frac{dc}{dt} +\frac{1}{10} \cdot c \right) = 3 \cdot e^{\frac{t}{10} }[/tex]

[tex]\frac{d}{dt}\left(e^{\frac{t}{10}}\cdot c\right) = 3\cdot e^{\frac{t}{10} }[/tex]

[tex]e^{\frac{t}{10} }\cdot c = 3 \cdot \int {e^{\frac{t}{10} }} \, dt[/tex]

[tex]e^{\frac{t}{10} }\cdot c = 30\cdot e^{\frac{t}{10} } + C[/tex]

[tex]c = 30 + C\cdot e^{-\frac{t}{10} }[/tex]

The initial concentration in the tank is:

[tex]c_{o} = \frac{10\,pd}{60\,gal}[/tex]

[tex]c_{o} = 0.167\,\frac{pd}{gal}[/tex]

Now, the integration constant is:

[tex]0.167 = 30 + C[/tex]

[tex]C = -29.833[/tex]

The solution of the differential equation is:

[tex]c(t) = 30 - 29.833\cdot e^{-\frac{t}{10} }[/tex]

Now, the quantity of salt at time t is:

[tex]m_{salt} = V_{tank}\cdot c(t)[/tex]

[tex]m_{salt} = (60)\cdot (30 - 29.833\cdot e^{-\frac{t}{10} })[/tex]

Where t is measured in minutes.

Answer:

Option (2).

Step-by-step explanation:

In the figure attached,

A, C and B are the points lying on a straight line.

2 lines EC and DC have been drawn by extending the lines from C to E and D respectively.

Ray CE is the angle bisector of ∠ACD.

That means CE divides ∠ACD in two equal parts.

m∠ACE = m∠DCE

Since m∠ACD = m∠ACE + m∠DCE

                        = 2(m∠ACE)

          m∠ACE = [tex]\frac{1}{2}(\angle ACD)[/tex]

Therefore, option (2) will be the answer.

Answer:

b

Step-by-step explanation:

took test

Answer:

The volume of the space outside the pyramid but inside the prism is 225 cubic centimeters.

Step-by-step explanation:

To find this, you subtract the volume of the pyramid from the volume of the rectangular prism.

The prism and pyramid's bases is 25 cm²

The pyramid's height is 12÷2 or 6 cm

The volume formula for a prism is l×w×h

The volume formula for a pyramid is [tex]\frac{1}{3}[/tex] ×b×h

The area of the prism is 5×5×12 or 300 cm³

The area of the pyramid is [tex]\frac{1}{3} *25*6[/tex] or 75 cm³

300 cm³-75 cm³=225 cm³

The volume outside the pyramid but inside the prism is 225 cm³.

Answer:

  θ = ±2π/3 +2kπ . . . . . for any integer k

Step-by-step explanation:

  2·cos(θ) +1 = 0

  cos(θ) = -1/2 . . . . . subtract 1, divide by 2

The cosine function has the value -1/2 for θ = ±2π/3 and any integer multiple of 2π added to that.

  θ = ±2π/3 +2kπ . . . . . for any integer k

Answer: A

Step-by-step explanation:

You want to make them both have common denominators. What number does the denominators both go into? Thats easy, its 60.

Multiply 7/12 by 5/5 to get 35/60

Now multiply 4/15 by 4/4 to get 16/60

You need to add a negative number to 35/60 in order to get 16/60

Do 16-35 to get -19/60

Answer:

d. no solution

Explanation:

Step 1 - Subtract nine from both sides of the equation

[tex]|x| + 9 \leqslant 7 \\ |x| + 9 - 9 \leqslant 7 - 9 \\ |x| \leqslant - 2[/tex]

Step 2 - Remove the absolute value

[tex] |x| \leqslant - 2 \\ 2 \leqslant x \leqslant - 2 \\ 2 \leqslant - 2[/tex]

Therefore, since positive two is not less than or equal to negative two, there is no solution.

Answer:

Step-by-step explanation:

What function ?

Answer:

Step-by-step explanation:

The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.

The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.

The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.

If possible, please mark brainliest

The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The important features for the graph of a quadratic function will be

The parabola is symmetric about the line which is passing through focus.

The quadratic function can be expressed in the form of vertex form.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

#SPJ2

Answer:

$3,485.48

Step-by-step explanation:

For computing the money required at the end of the account term we need to apply the Future value formula i.e be to shown in the attachment below:

Given that,  

Present value = $3,000

Rate of interest = 3% ÷ 365 days  = 0.00821917

NPER = 5 years × 365 days  = 1,825

PMT = $0

The formula is shown below:

= FV(Rate;NPER;PMT;PV;type)

So, after applying the above formula

the amount of future value is $3,485.48

Answer:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Step-by-step explanation:

For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Answer:

10

-5

Step-by-step explanation:

5 - -5

Subtracting a negative is like adding

5+5 = 10

-9 - -4

-9+4

-5

Answer:

Step-by-step explanation:

5+5 = 10

-9+4 = -5

Answer:

The volume of the prism is 75 cubic inches

Step-by-step explanation:

The volume of the prism is the amount of space contained on the interior of the prism.

Now we have that this entire space is filled with cubes of defined volumes. Therefore, to get the volume of the prism, we can simply get the total volume occupied by all the cubes. This should give us our answer.

From the information we are given, we know that the there are 3 layers of cubes each containing 25 cubes.

This gives the total number of cubes to be 3 X 25 = 75 cubes in total

We also know that the volume of 1 cube is 1 cubic inch.

Hence the volume of 75 cubes will be 75 X 1 cubic inch = 75 cubic inches.