100 POINTS! Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.

The distance that Kelli can swim will be about 6.11 kilometers per hour.

Here is the complete question:

Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth. Kelli can swim about km/hour.

To solve for x, you need to follow SADMEP. SADMEP is subtraction, addition, division, multiplication, exponents, and parentheses.

It follows the same rules as PEMDAS, but SADMEP is only used when solving algebraic equations.

x - 5 = 0.1(x + 5) (use the distributive property)

x - 5 = 0.1x + 0.5 (subtract 0.1x to both sides)

0.9x - 5 = 0.5 (add 5 to both sides)

0.9x = 5.5 (divide both sides by 0.9)

x = 6.11 km/hour.

Therefore, Kelli can swim about 6.11 kilometers per hour.

Learn more about distance on:

https://brainly.com/question/17273444

#SPJ1

Answer:

It's the first one for upstream and the other one for downstream

Step-by-step explanation:

See below for the properties of the functions

The function f(x)

We have:

f(x) =  –7(x + 2)^3(x – 1)^2(x – 3)

From the graph, we have the following features:

The function m(x)

We have:

m(x) =  x^3 - 4x^2

Factor out x^2

m(x) = x^2(x - 4)

Factor out x

m(x) = x(x)(x - 4)

From the graph, we have the following features:

Read more about functions at:

https://brainly.com/question/12431044

#SPJ1

The original value of the piece of equipment is 700000

The resale value is given as:

V=700,000e^(-0.02t)

The original value is when t = 0.

So, we have:

V=700,000e^(-0.02 *0)

Evaluate the product

V=700,000e^0

This gives

V=700,000 * 1

Evaluate

V=700000

Hence, the original value of the piece of equipment is 700000

Read more about exponential functions at:

https://brainly.com/question/11487261

#SPJ1

Using the given exponential function, the age of the skull is 6,733 years old.

It is given by:

[tex]N(t) = N(0)e^{-kt}[/tex]

In which:

In this problem, the parameters are given as follows:

N(t) = 0.51N(0), k = 0.0001.

Hence we solve for t to find the age.

[tex]N(t) = N(0)e^{-kt}[/tex]

[tex]0.51N(0) = N(0)e^{-0.0001t}[/tex]

[tex]e^{-0.0001t} = 0.51[/tex]

[tex]\ln{e^{-0.0001t}} = \ln{0.51}[/tex]

[tex]-0.0001t = \ln{0.51}[/tex]

[tex]t = -\frac{\ln{0.51}}{0.0001}[/tex]

t = 6,733 years old.

More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1

Answer:

10.  Left 5

11.   Horizontal stretch by a factor of 5

12.  Horizontal reflection

Step-by-step explanation:

Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Identify the transformations that take the parent function to the given function.

Question 10

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(x+5)^3[/tex]

Comparing the parent function with the given function, we can see that 5 has been added to the x-value of the parent function.

Therefore, the transformation is:

[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]

Question 11

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=\left(\dfrac{1}{5}x\right)^3[/tex]

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by ¹/₅.

Therefore, the transformation is:

[tex]y=f\left(\dfrac{1}{5}x\right) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{\frac{1}{5}}[/tex][tex]\textsf{As }\dfrac{1}{\frac{1}{5}}=5 \implies \textsf{horizontal stretch by a factor of 5}[/tex]

Question 12

[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]

[tex]\textsf{Given function}: \quad f(x)=(-x)^3[/tex]

Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by -1.

Therefore, the transformation is:

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

Learn more about graph transformations here:

https://brainly.com/question/27845947

Answer:

(1,0)

Step-by-step explanation:

Since log (x+y) = 0        you should know  x+y = 1

                                            so y = (1-x)

then   2 logx = log (y+1)

          log x^2 = log (1-x   +1) = log (2-x)

                x^2 = 2-x

                 x^2 + x-2 = 0

                 (x+2)(x-1) = 0      so x = -2  or   +1

                                               then y = 3  or 0

-2,3    and   1,0       since you cannot have a log of a negative number

                                     the only answer is (1,0)  

the transformation from f(x) to g(x) is (c) the graph of g(x) is horizontal compression of the graph f(x) by a factor of 1/3 and a reflection across the x-axis.

The functions are given as:

f(x) =x^3

g(x) = -(3x)^3

The minus sign in g(x) = -(3x)^3 implies that the function f(x) is reflected across the x-axis

The 3 in g(x) = -(3x)^3 implies that the function f(x) is stretched horizontally by 1/3

Hence, the transformation from f(x) to g(x) is (c)

Read more about transformation at:

https://brainly.com/question/13810353

#SPJ1

Limit, can be defined as the every nearby  the value of a variable for a function exists, is called limits|

⇒ [tex]\lim_{h \to0 \zero} 46x^11+32xh^3+6x^15h+23[/tex]

When putting  h = 0

⇒  [tex]46x^11+23[/tex]

Thus, the value of a function of its limit is given by [tex]46x^11+23[/tex]

Learn more about limits here:
https://brainly.com/question/18008819

#SPJ1

Answer:

  2448 ft²

Step-by-step explanation:

The surface area of the triangular prism is the sum of the areas of the triangular bases and the lateral area of the rectangular faces.

The two right triangle bases together form a rectangle that is 24 ft wide and 18 ft tall. The total base area is ...

  A = (24 ft)(18 ft) = 432 ft²

The rectangular faces of the prism are each 28 ft wide and have a total width of 18 +24 +30 = 72 ft. Their total area is ...

  LA = (28 ft)(72 ft) = 2016 ft²

The sum of the base area and lateral area is ...

  total area = (432 ft²) +(2016 ft²) = 2448 ft²

The surface area of the triangular prism is 2448 ft².

__

Additional comment

The area formula for the triangular base is ...

  A = 1/2bh . . . . . . area of one triangle with base b and height h

Then the area of the two congruent triangular bases is ...

  A = 2(1/2bh) = bh

This is the formula we used above. It skips the work of dividing by 2, then multiplying by 2 again.

I think it is 49123.52

Step-by-step explanation:

The coefficients [tex]a_0,a_1,a_2,a_3[/tex] could be chosen to be the coefficients in the Maclaurin series of [tex]\sin(x)[/tex].

We have

[tex]y = \sin(x) \approx a_0 + a_1 x + a_2 x^2 + a_3 x^3 \\\\ \implies y(0) = 0 = a_0[/tex]

[tex]y' = \cos(x) \approx a_1 + 2a_2 x + 3a_3 x^2 \\\\ \implies y'(0) = 1 = a_1[/tex]

[tex]y'' = -\sin(x) \approx 2a_2 + 6a_3 x \\\\ \implies y''(0) = 0 = 2a_2[/tex]

[tex]y''' = -\cos(x) \approx 6a_3 \\\\ \implies y'''(0) = -1 = 6a_3[/tex]

It follows that [tex]a_0=0[/tex], [tex]a_1=1[/tex], [tex]a_2=0[/tex], and [tex]a_3 = -\frac16[/tex].

Answer:

2^25

Step-by-step explanation:

Given

On first day bag contained 1 kernels

on second bag contained 2 kernels of corn

on third day bag contained 4 kernels of corn

on n th day bag contains 2n-1  kernels of corn

thus on 26 th day bag contains 2^26= 2^25=33,554,432 kernel

Each kernel weigh  0.07 gm

Therefore 2^25  kernels weighs = 2^25 x 0.07

Therefore on 26 th day 2^25 kernel weighs 23,488.1024 kg

The average rate, in miles per hour, of the rail portion of the trip is; D: 75

Since exactly 1/3 of the distance travelled was by rail, then we can say that;

(1/3) * (90) = 30 miles

We are told that part of the trip took 1/5 of the travel time. Thus;

Time it takes to travel that distance is:

(1/5) * (2) = 2/5 of an hour

Average rate is;

30/(2/5) = 150/2 = 75 mph

Read more about Average speed at; https://brainly.com/question/4931057

#SPJ1

Answer:

[tex]\displaystyle \frac{\pi}{6}[/tex]

Explanation:

According to the unit circle, [tex]\displaystyle \frac{\pi}{3}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are the radian measures you are looking for because all y-coordinates are associated with the sine function, so when evaluating, you will arrive at this:

[tex]\displaystyle \boxed{\frac{\pi}{3}} = \frac{\pi}{3} - \frac{\pi}{6}[/tex]

I am joyous to assist you at any time.

Answer:

Monomial - one term
Binomial - two terms
Trinomial - three terms
Polynomial - any polynomial with more than three terms

Brainliest, please :)

The polygon with 128.57° as every interior angle is a septagon.

If the interior angle = 128. 57°

Using ( n-2) × 180 = sum of interior angles

Let's say n= 7

We have that,

(7-2) × 180 = 900

Let's find out the polygon

= 7 × 128.57

= 900

A polygon with seven sides is a septagon

Thus, the polygon with 128.57° as every interior angle is a septagon.

Learn more about polygons here:

https://brainly.com/question/1592456

#SPJ1

Considering the stem-and-leaf plot, the range of the data-set is given as follows:

C. 45,79

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

Considering the key format, the smallest value in this problem is 4|5 = 45, and the highest is 7|9 = 79, hence the range is given by:

C. 45,79

More can be learned about an stem-and-leaf plot at https://brainly.com/question/8649311

#SPJ1

The ratio of circle to triangles is; 3:4 and the number of circles which should be added to make the ratio 1:1 is; 3.

It follows from the task content that the total number of circles and triangles in all 4 rows and can be counted and concluded as; 9 and 12 respectively.

Hence, the ratio of circles to triangles is 9 to 12 and in its simplest form is; 3:4.

However, to make the ratio 1:1, the number of circles and triangles must be equal. Hence, 3 circles must be added to make the ratio 1:1.

Read more on ratios;

https://brainly.com/question/13513438

#SPJ1

Based on the Congruent Supplements Theorem, <1 = <3 are congruent, given that <1 and <2 and <2 and <3 are supplements.

The Congruent Supplements Theorem shows that when two angles are considered to be supplements of a certain angle, then those two angles must be congruent.

Filling in the chart would therefore be:

<1 and <2 are

supplementary                                               <1 = <3

GIVEN                                           Congruent Supplements Theorem

<2 and <3 are

supplementary

GIVEN

Find out more on the Congruent Supplements Theorem at https://brainly.com/question/17385360.

#SPJ1

Answer:

the law of cosines with ABC

[tex]\angle R[/tex] and [tex]\angle S[/tex] are supplementary by the same-side interior angles theorem, and [tex]\angle S \cong \angle T[/tex] because of the properties of an isosceles trapezoid, meaning that [tex]\angle R[/tex] and [tex]\angle T[/tex] are supplementary.

[tex]4x+11+2x-5=180\\\\6x+6=180\\\\6x=174\\\\x=\boxed{29}\\\\\implies m\angle S=m\angle T=2(29)-5=\boxed{53^{\circ}}[/tex]

The value of x in the right triangle is 4 units.

The side x of the right triangle can be found using trigonometric ratios.

Therefore,

sin 30° = opposite / hypotenuse

sin 30 = x / 8

1 / 2 = x  /8

cross multiply

8 = 2x

divide both sides by 2

8 / 2 = 2x / 2

x = 4

learn more on right triangle here: https://brainly.com/question/10060696

#SPJ1

Answer:

there is no x-intercept

Step-by-step explanation:

The graph of the equation y = -1 is a horizontal line that passes through (0, -1). The line is parallel to the x-axis. It never intersects the x-axis. There is no x-intercept.

The effectiveness depends on your score of working.

How effective is it to go to your manager to request others take on some activities?

Certainty implies, indeed, that favorable things will happen and uncertainty  implies favorable things won't happen.

If we go to our manager, requesting that others should take some activities. It certainly depends upon the our score in the office. if we are hard working than in situations manager could approve our request and if our score is low or we are not a hard worker than result may no be in our favor.

Thus, the effectiveness depends on your score of working.

Learn more about certainty and uncertainty here:
https://brainly.com/question/23422212

#SPJ1

Answer:

22

Step-by-step explanation:

Hello!

We can convert it into slope-intercept form.

Slope - Intercept Form: [tex]y = mx +b[/tex]

The y-intercept of the line is 22.

Answer:

394.13cm²

Step-by-step explanation:

Formula: The area of a circle is found by A = πr²

Given:

Plug in:

A = πr² → A = (3.142)(11.2)²

            → A = (3.142)(125.44)

            → A = 394.13248

"2 decimal places",  round up to 394.13

Learn more about Circles here: https://brainly.com/question/10368742

Answer:

D. 5^6

Step-by-step explanation:

[tex]5^2*5^4\\5^2^+^4\\5^6[/tex]

Answer: Option (1)

Step-by-step explanation:

The line y = 2x is shaded above and is dotted, so it represents [tex]y > 2x[/tex].

This eliminates all the options except for option (1).

The graph of a system of inequalities is shown. The following system of inequations represents the graph:

y ≥ 2x;

x + 2y ≤ -8:

Inequality refers to a condition in which there's a lack of equivalency or aesthetics, frequently panning out in disparities or differences in chances, resources, treatment, or outcomes among individuals, groups, or associations. It encompasses various forms, including economic inequality, colonial inequality, and political inequality.

The blue region is on the left of the blue line of equation y = 2x so the region is represented by the line y ≥ 2x. The equality holds in this inequality as the region also includes the origin (0, 0).

The second option only has the inequality y ≥ 2x in its system of inequalities.

So, the correct answer is the second one. The system of inequation is

y ≥ 2x;

x + 2y ≤ -8:

Learn more about Inequality here:

https://brainly.com/question/30013680

#SPJ7