What is the equation for the translation of x2 + y2 = 16 seven units to the right and five units up?
(x + 7)2 + (y – 5)2 = 16
(x - 7)2 + (y + 5)2 = 16
(x + 7)2 + (y + 5)2 - 16
(x - 72 + (y – 5)2 = 16

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(t)=-16t^2+\stackrel{\stackrel{v_o}{\downarrow }}{19}t+110~\hspace{10em}19~\frac{ft}{sec}[/tex]

The initial velocity of the rock when thrown from the cliff is represented by the coefficient of the t term in the quadratic equation, which is 19 feet per second.

The equation h(t) = -16t² + 19t + 110 describes the height of a rock in feet, as a function of time in seconds after it is thrown from a cliff. To find the initial velocity of the rock when it is thrown, we look at the coefficient of the linear term in this equation, which represents the initial velocity in feet per second (since the equation is quadratic and the coefficient of the t2 term corresponds to half the acceleration due to gravity in feet per second squared).

The initial velocity of the rock is given by the coefficient of the t term, which is 19 feet per second.

Answer:

4a. About 54 times NOT INCLUDING THE FIRST TRIAL

4b. About 60 times NOT INCLUDING THE FIRST TRIAL

Step-by-step explanation:

I say about because we don't know if it's ALWAYS going to be the same results.

4a. Also 12*4 because it's 20 times so 20*4=80 then you add half of it to become 90 and you get 54

4b. 12*5 because 100/5=20 for the 20 trials of them

Answer:

x^3 -6x^2 +18x-10

Step-by-step explanation:

f-g (x) = f(x) -g(x)

f(x) = x^3 -2x^2 +12x-6

g(x)  =4x^2 -6x +4

f(x) -g(x) =x^3 -2x^2 +12x-6 - (4x^2 -6x +4)

Distribute the minus sign

            x^3 -2x^2 +12x-6 - 4x^2 +6x -4

Combine like terms

           x^3 -2x^2- 4x^2 +12x+6x-6  -4

            x^3 -6x^2 +18x-10

Answer:

The discriminant D=0

Step-by-step explanation:

For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is

[tex]D=b^2-4ac.[/tex]

In your case, for the polynomial [tex]4x^2-20x+25,[/tex]

Answer:

The answer is 0 D

Answer:

23) option c

    JL ≈ 9.3

25) option c

      y ≈ 9.6

Step-by-step explanation:

Given in the question that,

cos(21°) = 9 / y

y = 9/cos(21°)

y = 9.64

y ≈ 9.6(nearest tenth)

Given in the question that the hypotenuse of right angle triangle = 12

To find,

height of the right angle triangle

angle k = 39°

so by using trigonometry identity

cos(39) = opp/hypo

cos(39) = JL / KL

JL = cos(39)(12)

JL = 9.32

JL ≈ 9.3

Answer:

Q 23.  Last option 7.6

Q 25 Third option

Step-by-step explanation:

To solve Q 23

From the figure we can write,

Sin 39 = Opposite side/Adjacent side

 = JL/KL

 = JL/12

JL= 12 * Sin 39

 = 12 * 0.629  = 7.55

 = 7.6

To solve Q 25

Cos 21 = 9/y

y = 9/Cos 21 = 9/0.9335

= 9.64

 = 9.6

Answer:

56 cm

Step-by-step explanation:

The tangents from the 90° angle will form a square with the radii that has a side length of 4. If we call the length of the short side of the right triangle "x", then the tangent lengths are ...

on the short side of the triangle: 4, x-4

on the hypotenuse side of the triangle: x-4, 24-(x-4) = 28-x

on the long side of the triangle: 4, 28-x

The perimeter is twice the sum of the unique tangent lengths:

P = 2(4 + (x-4) + (28-x)) = 2·28

P = 56 . . . . . the perimeter is 56 cm.

_____

Using the Pythagorean theorem on side lengths x and 32-x and hypotenuse 24, we find x = 16-4√2 ≈ 10.34, the length of the short side (in cm).

Answer:

[tex]4800+183x\geq 8000[/tex]

She must sell at least 18 policies to make an annual income of at least $8,000

Step-by-step explanation:

Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell

We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:

[tex]\frac{3*6,100}{100} =183[/tex]

Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.

We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:

[tex]4800+183x[/tex]

Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:

[tex]4800+183x\geq 8000[/tex]

Let's solve the inequality:

1. Subtract 4800 from both sides

[tex]4800-4800+183x\geq 8000-4800[/tex]

[tex]183x\geq 3200[/tex]

2. Divide both sides by 183

[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]

[tex]x\geq 17.48[/tex]

Since she can't sell a fraction of a policy, we must round the result to the next integer:

[tex]x\geq 18[/tex]

We can conclude that she must sell 18 policies to make an annual income of at least $8,000.

Answer:

$ 38,824

Step-by-step explanation:

Total Area of land that was bought = [tex]4\frac{2}{8}[/tex] acres

Total Cost of this area = $ 165,000

We have to find the cost of 1 acre of land.

Cost of [tex]4\frac{2}{8}[/tex] acres of land = $ 165,000

Dividing both sides by [tex]4\frac{2}{8}[/tex], we get:

Cost of 1 acre of land = $ 165,000 ÷ [tex]4\frac{2}{8}[/tex]

= $ 38,824

Thus the cost of each acre of land  is $ 38,824 (rounded to nearest dollar)

Answer: $38,824

Step-by-step explanation:

Convert the mixed number [tex]4\ \frac{2}{8}[/tex] as a decimal number.

Divide the numerator by the denominator and add it to the whole number 4. Then:

[tex]4+0.25=4.25acres[/tex]

Then, knowing that 4.25 acres cost $165,000 , divide this amount by 4.25 acres to find the cost of each acre.

Therefore, you get that the cost of each acre rounded to nearest dollar is:

[tex]cost=\frac{\$165,000}{4.25}\\cost=\$38,824[/tex]

Answer:

  none of the above

Step-by-step explanation:

The transformation ...

  g(x) = k·f(x -a) +b

vertically stretches the function f(x) by a factor of "k", translates it to the right by "a" units and up by "b" units. There won't be any reflection across the x-axis unless the stretch factor (k) is negative.

You have k=2, a=2, b=-2, so the function is stretched by a factor of 2, then translated to the right and down by 2 units each.

_____

The stretch is done first. If it is done last, then the translation factor(s) are also stretched. All the answer choices given in your problem statement list the stretch last, so none is correct. (You are probably expected to choose d.)

Answer:

x intercept= 3

y=-2

Step-by-step explanation:

the intercept is the point when the line crosses the axis

g(4)=2×4_1

8-1

=9

hence the answer is 9

hope it helps you!!!!!!!!!

Answer:

g(4) = 7

Step-by-step explanation:

To evaluate g(4) substitute x = 4 into g(x), that is

g(4) = (2 × 4) - 1 = 8 - 1 = 7

Answer:

15 inches

Step-by-step explanation:

The longest side of the right triangular window frame is 39 inches

The height is 36 inches

Let the base of the window frame be x inches

So according to Pythagoras theorem,

x² + 36² = 39²

x² = 39² - 36² = 225

x = [tex]\sqrt{225}[/tex] = 15 inches

The third side of the window frame is therefore equal to 15 inches.

The length of the third side of the window frame will be 15 inches. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The longest side has a length labeled as 39 inches. The height of the frame is labeled as 36 inches.

Let x be the length of the third side of the window frame. Then we have

39² = x² + 36²

 x² = 39² - 36²

 x² = 1521 - 1296

 x² = 225

  x = 15 inches

Then the correct option is A.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

Answer:

• domain: x ≥ 0

• range: y ≥ 0

Step-by-step explanation:

The graph shows a ray that starts at the origin and extends to infinity in both the +x and +y directions. The domain (horizontal extent) is [0, ∞), as is the range (vertical extent).

Answer:

The equation of the line into point slope form is [tex]y-32=3(x-10)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

In this problem we have

[tex]m=3[/tex]

[tex](x1,y1)=(10,32)[/tex]

substitute

[tex]y-32=3(x-10)[/tex] ---> equation of the line into point slope form

[tex]y=3x-30+32[/tex]

[tex]y=3x+2[/tex] ---> equation of the line into slope intercept form

Answer:

  (x, f(x)) ≈ (5.5, 4)

Step-by-step explanation:

You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...

  4 = 8/(1 +3e^(-0.2x))

  1 +3e^(-0.2x) = 8/4 = 2

  e^(-0.2x) = 1/3

  x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5

We already know the value of f(x) is 4 there.

The point of maximum growth is about (5.5, 4).

Answer:

1.8 represents the initial number of the club members in hundreds.

Step-by-step explanation:

* Lets revise the exponential grows

- If a quantity grows by a fixed percent at regular intervals,

 the pattern can be depicted by this function.

- The function of the exponential growth is:

  y = a(1 + r)^x

# a = initial value (the amount before measuring growth)

# r = growth rate (most often represented as a percentage and

  expressed as a decimal)

# x = number of time intervals that have passed

* Now Lets study the problem to solve it

- The club's total number of members will grow exponentially

  each month

- The expression to model the number of club members, in

  hundreds, after advertising for t months is

  1.8(1.02)^12t

* Lets compare between this model and the function above

# a = 1.8 ⇒ initial number of members in hundreds

# r = 1.02 - 1 = 0.02 ⇒ growth rate

# x = 12t ⇒ number of time intervals

* 1.8 represents the initial number of the club members in hundreds.

Answer:

A and C are correct because the farther its is to 1 the stronger it is

Answer:

The answer is A and C

Step-by-step explanation:

Answer:

E. 44 meters

Step-by-step explanation:

The function that models the distance covered by the object is

[tex]s(t)=t^2+5t[/tex]

where s(t) is in meters and t is in seconds.

The distance covered by the object after 1 second is

[tex]s(1)=1^2+5(1)=6m[/tex]

The distance covered by the object after 1 second is

[tex]s(1)=5^2+5(5)=50m[/tex]

The distance covered between 1 second and 5 seconds is

50-6=44m

Answer:

person above is right

Step-by-step explanation:

right on plato

Answer:

Option C is correct.

Step-by-step explanation:

The equation used to represent the slop-intercept form is

y= mx + b

where m is the slope

and b is the y-intercept.

So, in the given question y-intercept = (0,8)

b= 8 and

slope =m= 1/2

the equation will be:

y = mx + b

y= (1/2)x + 8

So, Option C is correct.

Answer:

㏒3(14) = 2.402 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some rules of the logarithmic functions

- log(a^n) = n log(a)

-  log(a) + log(b) = log(ab) ⇒ vice versa

- log(a) - log(b) = log(a/b)  ⇒ vice versa

* Lets solve the problem

- We have the value of ㏒3(2) and ㏒3(7)

- We must change the problem to these logarithm to solve

∵ 14 = 2 × 7

∴ We can write ㏒3(14) as ㏒3(2 × 7)

∴ ㏒3(14) = ㏒3(2 × 7)

* Now lets use the rules above

∵  log(ab) = log(a) + log(b)

∴ ㏒3(2 × 7) = ㏒3(2) + ㏒3(7)

∵ ㏒3(2) = 0.631 and ㏒3(7) = 1.771

∴ ㏒3(2 × 7) = 0.631 + 1.771 = 2.402

* ㏒3(14) = 2.402

Answer:

   c.  {(–4, 8.5)}

Step-by-step explanation:

A plot of the equation and the offered points is attached.

__

It might be helpful to put the equation into slope-intercept form.

  2y = -5x -3

  y = -5/2x -3/2

This shows you that y will be an odd multiple of 1/2 only for even values of x. So, we only need to check the points (-2, 9.5) and (-4, 8.5).

At x=-2, y = -5/2(-2) -3/2 = 5 -3/2 < 9.5 . . . . . (-2, 9.5) is not a solution

At x=-4, y = -5/2(-4) -3/2 = 10 -3/2 = 8.5 . . . . (-4, 8.5) is a solution

Of the offered choices, the only one in the solution set is (-4, 8.5).

I think it’s C sorry if I’m wrong

For this case we have a system of sos equations with two unknowns:

[tex]x-5y = -3\\-7x + 8y = -33[/tex]

We clear "x" from the first equation:

[tex]x = -3 + 5y[/tex]

We substitute in the second equation:

[tex]-7 (-3 + 5y) + 8y = -33\\21-35y + 8y = -33\\-27y = -33-21\\-27y = -54\\y = \frac {-54} {- 27}\\y = 2[/tex]

We find the value of "x":

[tex]x = -3 + 5 (2)\\x = -3 + 10\\x = 7[/tex]

ANswer:

(7,2)

Option C

Answer:

  338 in

Step-by-step explanation:

If each of the measures shown is the measure from the vertex to the point of tangency, then that measure contributes twice to the perimeter (once for each leg from the vertex to a point of tangency).

  2(22 in + 27 in + 22 in + 98 in) = 2(169 in) = 338 in

Answer:

According to the given question if one of the angle of the triangle is 75 degree and the other two sides are of length 2 and 3 units respectively then option C is correct. Only One triangle can be formed where Angle B will be 40 degree. You can figure it out from the steps mentioned below first of all draw an Arc with the length either 3cm or 2 cm that will be the base of a triangle and then from the ending point again cut an arc then after from the starting point that is the point draw  an angle of 75 degree with the help of protactor and extend it to meet the Arc finally you can get the 40 degree.

Hope this helps. Name me brainliest please

Answer:

  (x, y) = (-6, -7)

Step-by-step explanation:

Substitute for y:

  2x +5 = 3x +11 . . . . . use the first expression for y in the second equation

  0 = x +6 . . . . . . . . . . subtract 2x+5

  -6 = x . . . . . . . . . . . . add -6

  y = 2(-6) +5 = -7 . . . .substitute for x

The solution is x = -6, y = -7.

Answer:

y=1/2x+5 or d

Step-by-step explanation:

Answer is D

Step-by-step explanation:

you cannot show too much "work"

basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...

you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2

Answer:

40 (cm)

Step-by-step explanation:

0. make up a new picture with additional elements (radius of the inscribed circle, it's 'x'; and some elements as shown in the attached picture);

1. the formula of the required perimeter is P=a+b+c, where c- hypotenuse.

2. apply the Pythagorean theorem: a²+b²=c², where c - hypotenuse, then calculate value of 'x' (attention! x>0, the length is positive value !)

3. substitute 'x' into the formula of the required perimeter. The result is 40.

PS. All the details are in the attached picture, answer is marked with red colour.

ANSWER

The correct choice is A

EXPLANATION

The given inequality is

y < -|x|

We substitute each point into the inequality to determine which one is a solution.

Option A

-2 < -|1|

-2 < -1.

This statement is true.

Hence (1,-2) is a solution.

Option B.

-1 < -|1|

-1 < -1.

This statement is false.

Option C

0 < -|1|

0 < -1.

This statement is also false.

Answer:

y = -3

Step-by-step explanation:

Following the directions, we have ...

y = 2·(-1) -1 = -2-1 . . . . . . put -1 where x is in the equation

y = -3