The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n +c.what does the graph tell you about the value of a in this function?

The Graph Shown Below Expresses A Radical Function That Can Be Written In The Form F(x)=a(x+k)^1/n +c.what

Answers

Answer 1

Answer:

a is less than 0

Step-by-step explanation:

Answer 2

The value of a in this function is a is less than 0 .

What is  radical function?

A radical function contains a radical expression with the independent variable (usually x) in the radicand. Usually radical equations where the radical is a square root is called square root functions. An example of a radical function would be. y=√x.

According to the question

Radical function that can be written in the form

[tex]f(x)=a(x+k)^{1/n} +c.[/tex] ------------------------(1)

By solving this equation we will get value of a and c

differentiating the equation

[tex]f'(x)=\frac{1}{n}* (a(x+k)^{1/n-1})[/tex]

therefore

[tex]((x+k)^{1/n-1}) > 0[/tex]

As graph is decreasing monotonically  

[tex]\frac{a}{n} < 0[/tex]

as n will be always n>0 ,

so a < 0

Now taking value of f(x)= 0 in equation (1)

[tex]f(x)=a(x+k)^{1/n} +c[/tex]

[tex]0 =-a(x_{0} + k)^{1/n} +c[/tex]   as (a < 0)

[tex]0=-a(k)^{1/n} +c[/tex]

[tex]-c =-a(k)^{1/n}[/tex]  multiplying (-1) both side

[tex]c =a(k)^{1/n}[/tex]  

i.e

c > 0

Hence, the value of a in this function is a is less than 0 .

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Related Questions

Of the last 20 trains to arrive at Wildgrove Station, 12 were on time. Considering this data, how many of the next 5 trains would you expect to be on time?

Answers

Answer:

Late because 12 were on time so 5 would be late

Find the surface area of a square pyramid with side length 3 cm and slant height 4 cm

Answers

Answer:

Image result for Find the surface area of a square pyramid with side length 3 cm and slant height 4 cm

The surface area of a square pyramid is the sum of the areas of all its 4 triangular side faces with the base area of the square pyramid. If a, h, and l are the base length, the height of the pyramid, and slant height respectively, then the surface area of the square pyramid = a2+ 2al (or) a2+2a √a24+h2 a 2 4 + h 2 .

Step-by-step explanation:

Please help me with this problem

Answers

Answer:

-36

Step-by-step explanation:

6^2+(y-x)

=>                 6^2+[-77 - (-5)]

=>                 6^2+[-77+5]

=>                 6^2+(-72)

=>                 36+(-72)                            [6^2 = 36]

=>                 -36

 

can you mark me brainliest?

Hello-

6² + (y - x) is our equation. And wonder of wonders, our x and y values are given! What a beautiful thing, having both given to us.

x = -5

y = -77

Let's plug our given values into our equation for x and y. Like so-

6² + (y - x) becomes 6² + (-77 - (-5))

In math, we must do whatever operations are contained within parentheses first and foremost. So we must subtract -5 from -77. That, by the way, equals -72.

6² + -72

Now we do our exponents, or powers.

6² = 36

36 + -72

Now we do the easiest part - adding.

32 + -72 = -36

So the answer to this problem (if I've done my algebra correctly) is -36.

Hope this helps.


What is the approximate area of the shaded region?
Use 3.14 for pi
12.6 units
28.3 units
50 2 units
78.5 units

Answers

Answer:

A

Step-by-step explanation:

Find the area of the window.

Answers

Answer:

2512

Step-by-step explanation:

Formula=πr^2/2

(3.14×40×40)/2

=2512

help me find the area please

Answers

Answer:

I'm not a hundred percent sure how to answer this one, because you need the height to solve but the other two tick marks would also be twenty because all of the sides are equal to one another.

Select all that apply. (30 points)


Which pairs of angles are supplementary?




1 and 6
5 and 7
5 and 8
2 and 3

Answers

Answer:

1 and 6

5 and 7

Step-by-step explanation:

Supplementary angles equal 180degrees. 1 = 60 and 6=120. 60+120=180.

5 = 60 and 7=120. 60+120=180

1/2 of 4/5 as a fraction

Answers

Answer:

4/10 is the answer

( 1 * 4 ) / ( 4 * 5 ) = 4 / 10

4 / 10 = 2 / 5

can someone explain this pls

brainliest

Answers

You need to add up the sides in order to find your answer

Find the missing side of the right triangle.

options:

6.5 ft


7 ft


5.5 ft


6 ft

Answers

Answer:

6ft, the missing side is the base(b), 10ft is the hypotenuse(h) and 8ft is the perpendicular(p). The formula for base is root over h²-p² and root over 10²-8² equals 6.

I need help with this

Answers

Ok so to find the mode

To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!

So the mode is 5

Hope this helps :)

You roll a number cube 120 times. How many times can you expect the number cube to land on a six?​

Answers

Answer:

10 or 6

Step-by-step explanation:

pls tell me if im wrong

Write an expression that is equivalent to 110% of a quantity, n

Answers

Answer:

[tex]\displaystyle 1\frac{1}{10}n[/tex]

Explanation:

Convert [tex]\displaystyle 110\%[/tex]to a mixed number, then set [tex]\displaystyle n[/tex]up next to it.

I am joyous to assist you at any time.

how much would $500 invested at a 4% interest compounded continuosly be worth after 7 years round your answer to the nearest cent

Answers

Answer: F = 661.56

Step-by-step explanation: interest formula: F = Pe^(rt)

F = future value

P = present value = 500

r = interest rate = 0.04

t = years = 7

F = 500e^(0.04 * 7)

A triangular swimming area is marked off by a rope.

a. If a woman swims around the perimeter of the swimming area, how far will she swim?
b. What is the area of the roped off section?

Answers

#a

Perimeter=Sum of sides

400+200√6+200+200√3600+200(√6+√3)600+200(2.6+1.7)600+200(4.3)600+8601460m

#b

Area:-

1/2×Base×Height1/2(200+200√3)(200√3)(200+200(1.7))100√3(200+340)(170)540(170)91800m²

Answer:

Perimeter = 1436.3 m (nearest tenth)

Area = 94641.0 m² (nearest tenth)

Step-by-step explanation:

The perimeter is the sum of the lengths of all the sides.

[tex]\begin{aligned}\sf \implies perimeter & =400+200\sqrt{6}+200\sqrt{3}+200\\ & =1436.30811\\ & = 1436.3 \: \sf m\:(nearest\:tenth)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area of a triangle} & =\sf \dfrac12 \times base \ height\\ & = \sf \dfrac12 \times (200+200\sqrt{3}) \times 200\sqrt{3}\\ & =94641.01615\\ & = 94641.0\: \sf m^2\:(nearest\:tenth)\end{aligned}[/tex]

SOMEONE PLEASE HELP ME WITH THIS!!
IMAGE DOWN BELOW!!
ILL GIVE YOU BRAINLIST ANSWER!!

Answers

Answer:

okay so i think the length of CD is 16cm

identify which of the following sequences is a geometric sequence. check all that apply. from math nation test yourself

Answers

A geometric sequence is any sequence that has a common ratio and a non-zero initial value

The sequence 2, 6, 18, 54, ..... is a geometric sequence

How to determine the geometric sequence?

A geometric sequence is represented as:

Tn = ar^(n - 1)

Where:

n represents the number of termsa represents the initial valuer represents the common ratioTn represents the current term

Assume that:

a = 2 and r = 3.

The terms of the sequence would be:

T1 = 2 * 3^0 = 2

T2 = 2 * 3^1 = 6

T3 = 2 * 3^2 = 18

T4 = 2 * 3^3 = 54

So, we have:

2, 6, 18, 54, .....

Hence, the sequence 2, 6, 18, 54, ..... is a geometric sequence

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PLSS I NEED HELP!!
1). To make a full rotation, 59 days, 19 h, and 45 min goes by for Mercury. It only takes Earth 1 day! How many hours does it take Mercury to complete a full rotation? Show your work using the correct conversion factors.

2). Some plants grow quickly. An invasive weed species can grow quickly. One variety grows up to 0.89 ft per day. How fast in inches per hour can this weed grow? Show your work using the correct conversion factors.

3). David’s watch broke. He decides to get it fixed instead of replacing it. The total cost to repair the watch can be represented by 0.07(45h) + 45h, where h represents the number of hours it takes to repair the watch.
a). What part of the expression represents the cost of the repair before tax?
b) Explain what your answer in Part A means in the context of the problem.

Answers

1) It takes 1435.75 hours for Mercury to complete a full rotation.

2) The weed can grow at 0.445 inches per hour.

Time calculation

1) Given that to make a full rotation, 59 days, 19 h, and 45 min goes by for Mercury, to determine how many hours does it take Mercury to complete a full rotation, the following calculation must be performed:

59 x 24 + 19 + 0.75 = X1416 + 19.75 = X1435.75 = X

2) Given that a plant grows up to 0.89 ft per day, to determine how fast in inches per hour can this weed grow, the following calculation must be performed:

0.89 / 24 = ft per hour0.037 = ft per hour1 ft = 12 inches0.037 x 12 = 0.445

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Answer:

1) It takes 1435.75 hours for Mercury to complete a full rotation.

2) The weed can grow at 0.445 inches per hour.

Step-by-step explanation:

I don't understand this

Answers

Answer:

Step-by-step explanation:

what is the area of a trapezoid with coordinated (0.0), (1,3), (4,3), (2,0)? (no picture given)
a. 2
b. 6
c. 9
d. 8

Answers

The area of the trapezoid, to the nearest whole number is: D. 8 units²

What is the Area of a Trapezoid?

Area of trapezoid = 1/2(a + b)h, where:

h = height of trapezoida and b = lengths of the bases of the trapezoid.

Using the coordinates of the trapezoid, (0,0), (1,3), (4,3), (2,0), the points have been plotted on a coordinate plane as shown in the image attached below, and we have the following dimensions of the trapezoid:

h = 3 unitsa = 3 unitsb = 2 units

Area of the trapezoid = 1/2(a + b)h = 1/2(3 + 2)3

Area of the trapezoid = 7.5 ≈ 8 units²

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what is 1,455.8 x 4,628.9?

Answers

Answer:

6738752.62

Step-by-step explanation:

1,455.8 x 4,628.9=6738752.62

Answer:

6738752.62

hope this helps

Line t is tangent to the circle. Find the measure of arc DEF.

Answers

Answer: 234 degrees

Step-by-step explanation:

Angle formed by a chord and a tangent has half the measure as the arc formed by the chord

The value of measure of arc DEF is,

⇒ 234 degree

What is mean by Angle?

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Line t is tangent to the circle.

Hence, We know that;

The angle formed by a chord and a tangent is equal to 1/2 the measure of the intercepted arc.

Thus, The value of measure of arc DEF is,

⇒ 2 x 117 degree

⇒ 234 degree

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3 1/4 - 1 3/5 | please help !!

Answers

Answer:

Step-by-step explanation:

Step: 1: Convert mixed fraction to improepr fraction.

Step: 2 : Find the LCM of 4 , 5 = 20

Step 3: Find equivalent fractions with denominator as 20

Step 4: Now subtract.

[tex]3\dfrac{1}{4}-1\dfrac{3}{5}=\dfrac{13}{4}-\dfrac{8}{5}[/tex]

             [tex]\sf = \dfrac{13*5}{4*5}-\dfrac{8*4}{5*4}\\\\\\ = \dfrac{65}{20}-\dfrac{32}{20}\\\\\\ = \dfrac{65-32}{20}\\\\\\ = \dfrac{33}{20}\\\\ \\ = 1 \dfrac{13}{20}[/tex]

solve pls brainliest

Answers

= 29/6 ×4

=29/3 ×2

=58/3

=19(1/3)

What is the 30th term of the following arithmetic sequences
17, 21, 25, ...

Answers

Answer:

133

Step-by-step explanation:

an = a1 + f × (n-1)

an= 17+4 x (30-1)

an= 17+4 x 29

an= 17+116

an=133

Find YW, would it just be 6?

Answers

Answer:

6

Step-by-step explanation:

AX=1/2XY,. BX=1/2WX

=) AB||WY and AB=1/2WY. [Midpoint theorem]

=) 2AB=WY

=) 2×3=WY

=)6=WY

PLA MARK IT AS BRAINLIEST (•‿•)(•‿•)(•‿•)

THE MIDLINE THEOREM OF A TRIANGLE

This works for triangles with a Midline having two of these properties:

The midline should be parallel to the third sideThe midline is half as long as the third side

The third side of the triangle (the one parallel to its midline) is twice the length of its midline.

Example:

The given question above:

ΔWYX

(Midline) AB = 3

YW = ?

Solution:

[tex]\frac{1}{2}[/tex] YW = AB

[tex]\frac{1}{2}[/tex] YW = 3

YW = (2)3

YW = 6

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What is the equivalent expression of 3(7e+1)=

Answers

Answer:

210 i hope i helped you with this question

answer might seem complicated though it's not if u try, well the answer is..

How do you solve 2. 310x/4y times 8y/5x =

Answers

Answer: 0.924

Step-by-step explanation:

Given

[tex]\frac{2.310x}{4y} *\frac{8y}{5x}[/tex]

Simplify  [tex]\frac{2.310x}{4y}[/tex] to [tex]\frac{0.5775x}{y}[/tex]


[tex]\frac{0.5775x}{y}*\frac{8y}{5x}[/tex]

Cancel y

[tex]0.5775x* \frac{8}{5x}[/tex]

Cancel x

[tex]0.5775* \frac{8}{5}[/tex]

Use the rule, [tex]a*\frac{b}{c} =\frac{ab}{c}[/tex]

[tex]\frac{0.5775*8}{5}[/tex]

Simplify

[tex]\frac{4.62}{5}[/tex]

Simplify

0.924

We have a shape that has an area of 112 inches squared. Convert the units to centimeters squared. (HINT: Perform multiple conversions). Don’t forget to show your work.

Answers

Answer:

722.5792 cm²

Step-by-step explanation:

1 in ≈ 2.54 cm

Squaring both sides:

⇒ (1 in)² ≈ (2.54 cm)²

Apply exponent rule (ab)² = a²b²

⇒ (1)² in² ≈ (2.54)² cm²

⇒ 1 in² ≈ 6.4516 cm²

Therefore, to convert an area measured in inches squared to centimeters squared, multiply by 6.4516:

⇒ 112 in² ≈ (112 × 6.4516) cm²

               = 722.5792 cm²

HELP ASAP! WILL MARK BRAINLIEST
Identify each number as rational or irrational by circling the word that describes it:

Rational or Irrational:
Rational or Irrational: 0.46
Rational or Irrational: √100
Rational or Irrational: -16
Rational or Irrational: √21
Rational or Irrational: 10

Answers

Question 1
Answer
0.46 : rational(/ ); irrational(x);
Solving Steps

Question 2
Answer
1100 : rational(/): irrational(x);
Solving Steps
Categorize the number :

Question 3
Answer
-16 : rational(V); irrational(x);
Solving Steps
Categorize the number:
-16 : rational(/); irrational(x);


Question 4

Answer
V21: rational (×); irrational(r);
Solving Steps
Categorize the number
V21 : rational(×): irrational():
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