1. What is the radical form of the expression 4 2/3?

2. What function equation is represented by th graph?

Answer: Choice B)

an = 15 + a(n-1)

a1 = 250

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The variable "a" is used to represent the terms. Since we have infinitely many terms to worry about, we won'd use "b, c, d, etc" for the other terms or else we'd run out of letters. So instead, we just stick a number next to "a" to help keep track of the terms

a1 = first term, a2 = second term, a3 = third term, etc

The first term is 250 because Chenoa starts off with $250, so a1 = 250. The answer is between A and B at this point.

The recursive step is how we generate each term. In plain english, the recursive step would be "add 15 to each term to get the next term". In an informal equation, it would look like this

term = (previous term) + 15

So that is why the nth term is

[tex]a_n = 15 + a_{n-1}[/tex]

which means "to get the nth term, we add 15 to the previous (n-1)st term"

This is why choice B is the answer

Answer:105

Step-by-step explanation:

the question says it prints 75 pages in 5 minutes.

to find out how much it prints in 7 minutes you must find how much it prints in 1 minute.

1 minute=75/5=15

it prints 15 pages in 1 minute.

15*7=105 pages.

so it prints 105 pages in 7 minutes.

please mark brainliest if it helps and please like.

welcome!

Answer:

105 pages

Step-by-step explanation:

It prints 75/5 = 15  pages per minute.

So in 7 minutes 15*7 = 105 pages are printed.

Answer:

a=21, b=24, c=27

Step-by-step explanation:

a= side 1, b= side 2, c= side 3

a+b+c=72

a/b=7/8 and b/c=8/9 (proportion it)

then cross multiply to get 8a=7b and 9b=8c---> divide to get a=7/8b and c=9/8b

put that into the first equation--> 7/8b+8/8b+9/8b=72

add the fractions to get 24/8b=72 (24/8 equals 3) so 3b=72 (divide to get b=24)

then fill that in to the above equations (8a=7b, 9b=8c)

8a=7(24) and 9(24)=8c---> 8a=168 and 8c=216

divide all that and get a=21 and c=27

with all the measurements, you can check the proportion to make sure it works (7:8:9-->21:24:27)

if you multiple 7, 8, and 9 by 3 then you get the numbers found so it works

The sides of the triangle in question, which are in a 7:8:9 ratio, are 21 cm, 24 cm, and 27 cm respectively when the perimeter is 72 cm.

The subject of this question is Mathematics, specifically related to the concept of ratios and the calculation of triangle side lengths. The triangle in question has sides in the ratio of 7:8:9. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, the perimeter is 72 cm. This means that the total ratio units (7+8+9 = 24 units) represent 72 cm in real lengths.

To find out how much each ratio unit represents, we divide the total perimeter by the total units. This gives us 72 cm / 24 units = 3 cm/unit. This means that each ratio unit represents 3 cm. Thus, the lengths of the sides following the 7:8:9 ratio would be 7*3=21 cm, 8*3=24 cm, and 9*3=27 cm respectively.

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Answer:

d= 10.44030651

Step-by-step explanation:

The diameter is the length  between the endpoints.  We can find it using the distance formula.

d= sqrt((x2-x1)^2+(y2-y1)^2 )

d = sqrt((-6-4)^2+ (-1-2)^2)

d = sqrt((-10)^2+(-3)^2)

d= sqrt(100+9)

d = sqrt(109)

d= 10.44030651

Answer:

The answer for fraction part is 6/7

If this helps please mark brainliest

[tex](x^{2} +8x+16)(x^{2} -8x+16)\\(x+4)^{2} (x-4)^{2} \\(x^{2}-16)^{2} \\[/tex]

it is true; just work them out, you should get what they got :))

Answer:

True.

Step-by-step explanation:

We have been given an equation [tex][x^2 + 8x + 16]\cdot [x^2- 8x+16] = (x^2-16)^2[/tex]. We are asked to determine whether our given equation is true or false.

To answer our given problem, we will simplify left side of our given equation using distributive property as:

[tex]x^2(x^2- 8x+16)+ 8x(x^2- 8x+16)+16(x^2- 8x+16)[/tex]

[tex]x^4- 8x^3+16x^2+ 8x^3-64x^2+128x+16x^2-128x+256[/tex]

Combine like terms:

[tex]x^4- 8x^3+ 8x^3+16x^2+16x^2-64x^2+128x-128x+256[/tex]

[tex]x^4-32x^2+1256[/tex]

Now, we will expand right side of our given equation using perfect square formula as:

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

[tex](x^2-16)^2=x^4-32x+256[/tex]

Since both sides of our given equation are equal, therefore, our given statement is true.

Answer:

Option D is correct.

as the particle always moves to the right

Step-by-step explanation:

Given the function:  [tex]s(t) = \frac{t^3}{3} - \frac{12t^2}{2} + 36t[/tex] , 0<t<15;

where

s(t) represent the distance in feet.

t represents the time in second.

Since, when the particle is moving to the right,

⇒ s(t) is increasing.

so, [tex]v(t) =\frac{ds}{dt} > 0[/tex]

Find the derivative of s(t) with respect to t;

Use derivative formula:

[tex]\frac{dx^n}{dx} = nx^{n-1}[/tex]

[tex]\frac{ds}{dt} = \frac{3t^2}{3}-\frac{24t}{2}+36[/tex]

Simplify:

[tex]\frac{ds}{dt} = t^2-12t+36[/tex]

As [tex]\frac{ds}{dt} > 0[/tex]

⇒[tex] t^2-12t+36 > 0[/tex]

[tex](t-6)^2 >0[/tex]               [[tex](a-b)^2 = a^2-2ab+b^2[/tex] ]

⇒ this is always true because square of any number is always positive

Therefore, it means that the particle always moves to the right.

Answer:   " 7√6 " .

__________________________________________________

                →   The answer is:  " 7√6 units " .

__________________________________________________

Step-by-step explanation:

__________________________________________________

Method 1:

__________________________________________________

This will be a "45-45-90" triangle;

which means that in:

(two sides for triangle will be the same).

which is consistent with the information give:

(the two side of the triangle are sides of a "square" ,

 and ALL sides of a square have the "square length" ;

and one side with be 90 degrees (a right triangle);

and the other angles will be 45 degrees (which is 1/2 of 90 degrees because the will cut into "1/2" of each of the "two other 90 degree angles" when a diagonal is drawn to form the "hypotenuse".

So, for "45-45-90" triangles, the side lengths, are:  

     "x, x, x√2 " ;  in which "x√2" represents the side length of the "hypotenuse" ;  and the two "x" values represent the equal values for the other 2 (two) side lengths.,

We are asked to find the "diagonal" of the square;  in which:  "x = 7√3" ;

 That is, we are ask to find the hypotenuse:  "x√3"  ;

 Note:  We are given:  " x = 7√3 " ;

So:  " x√3 " =  " 7 *√3 *√2 = 7 *√6 = " 7√6 ".

____________________________________________

The answer is:  " 7√6 units " .

__________________________________________________

Method 2:

__________________________________________________

Use the Pythagorean theorem (for right triangles):

 "  a² + b² = c² " ;  

      in which: "c" represents the "side length" of the "hypotenuse" ;

                or:  the "diagonal" of the "square" ; for which we shall solve.

                      "a" and "b" represent the other sides of the right triangle.

                     In this case, "a" and "b" are equal;

                            since "a" & "b" are the side lengths of a square.

                    We are given:  a = b = " 7√3 " .

                      We are to find "c" .

__________________________________________________

"  a² + b² = c²  " ;  

↔   " c²  = a² + b²  " ;

__________________________________________________

 →  c²  = (7√3)² + (7√3)²  ;

 →  c²  = (7²) * (√3)² + (7²) (*√3)²  ;

 →  c²  = ( 49*3)    +  (49*3) ;

 →  c²  = (147) + (147) ;

 →  c²  = 294 ;

Take the "positive" square root of each side of the equation;

    to solve for "c" ;

 →  ⁺ √(c²) = ⁺ √294 ;

→  c = ⁺ √294

⁺ √294 =  ⁺ √3 ⁺ √98 ;

                         →   √98 = ⁺ √49⁺ √2 ;

⁺ √294  =  7√3√2  =  7√6 .    

__________________________________________________

  c = 7√6

__________________________________________________

The answer is:  " 7√6 units " .

__________________________________________________

The values obtained by using "both" methods/ match!

__________________________________________________

Hope this helps!

 Best wishes in your academic pursuits

          — and within the "Brainly" community!

__________________________________________________

Answer:

Seth has 21 nickels

Step-by-step explanation:

Let n represent the number of nickels. Since Seth has 8 more nickels than dimes, then (n-8) is the number dimes.

Nickel is worth 5 cents and dime is worth 10 cents.  Thus, n nickels are worth 5n cents and (n-8) dimes are worth 10(n-8) cents. The total value of Seth's coins is $2.35 that is 235 cents, then

[tex]5n+10(n-8)=235.[/tex]

Solve this equation:

[tex]5n+10n-80=235,\\ \\15n=235+80,\\ \\15n=315,\\ \\n=21.[/tex]

Answer:

The number of gallons of gas Karl used is 15 gallons.

Option (C) is correct.

Step-by-step explanation:

As given

Karl drove 617.3 miles.

For each gallon of gas, the car can travel 41 miles.

i.e

1 gallons = 41 miles

[tex]1\ miles = \frac{1}{41}\ gallons[/tex]

Now find out for the  617.3 miles.

Thus

[tex]617.3\ miles = \frac{617.3}{41}\ gallons[/tex]

[tex]617.3\ miles = 15.1\ gallons[/tex]

[tex]617.3\ miles = 15\ gallons\ (Approx)[/tex]

Therefore the number of gallons of gas Karl used is 15 gallons.

Option (C) is correct.

Answer:

A

Step-by-step explanation:

We find the ratio by dividing two y-values from 2 consecutive x values (1 unit apart). Notice that in the table, all x-values are 1 unit apart. We can choose any pair of consecutive points.

Let's choose: (2,-4) and (1,-2). We divide -4/-2=+2.

Answer A.

Answer:

Use demos it is reaaly helpful with this

To solve the equation 2x-7= 1/3x-2, we multiply both sides by 3, subtract x from both sides, add 21 to both sides, and then divide by 5 to isolate x, resulting in x = 3.

For the given equation 2x-7= 1/3x-2, the goal is to prove x = 3. Here's how to approach it step-by-step:

After solving the equation, it is important to check if the answer is reasonable by substituting x back into the original equation to see if both sides equal.

The height of the Kite from the ground is √19 feet.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

Given, A kite flying in the air has a 10-ft line attached to it and its line is pulled taut and casts a 9-ft shadow.

The line can be thought of as a hypotenuse and the shadow as the base.

So, We have to find the height of the kite.

Therefore, From the Pythagoras theorem,

Base² + Height² = Hypotenuse².

9² + Height² = 10².

Height² = 100 - 81.

Height² = 19.

Height = √19.

learn more about Pythagoras' theorem here :

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Answer:

C. (X-9)^9 + (y+9)^2= 16

D. (X-9)^2 + (y+5)^2= 9

Step-by-step explanation:

The formula for a circle is

(X-h)^2 + (y-k)^2= r^2

where (h,k) is the center of the circle and r is the radius

The 4th quadrant is where x is positive and y is negative

Add r to the y coordinate of the center and if it is still negative, the circle is still completely in the 4th quadrant

A. (X-12)^2 + (y+0)^2= 72

The center is at 12,0 and the radius is sqrt(72) = 6sqrt(2)

This will be positive so it goes into the 1st quadrant

B. (X-2)^2 + (y+7)^2= 64

The center is at 2,-7  and the radius is 8

-7+8=1 so it goes into the 1st quadrant

C. (X-9)^9 + (y+9)^2= 16

The center is at 9,-9  and the radius is 4

-9+4 = -5  so it is completely in the 4th quadrant

D. (X-9)^2 + (y+5)^2= 9

The center is at 9,-5 and the radius is 3

-5+3 = -2 so it is completely in the 4th quadrant

Answer:

C and D

Step-by-step explanation:

The fourth quadrant is the bottom, right quadrant. In the fourth quadrant, the x-coordinate is positive, and the y-coordinate is negative.

For a circle to be completely within the fourth quadrant, the circle must have its center in the fourth quadrant, and the center has to be far away enough from the positive x-axis and from the negative y-axis, that no points on the circle are outside the fourth quadrant.

Choice A has center (12, 0), so it cannot be.

Choice B has center (2, -7) and radius 8. Many points will be past the axes.

Choice C has center (9, -9) and radius 4. All points will be in the fourth quadrant.

Choice D has center (9, -5) and radius 3. All points will be in the fourth quadrant.

Answer:

online

Step-by-step explanation:

insert the subject that is into the search bar on google and look for the pdf document. it will contain all the work and information needed

Answer:

Step-by-step explanation:

2. Conclusion: U is the mid point of RN.

Justification: From the figure, you can see that RU=UN which means U divides the line segment RN in two equal halves, thus by definition of mid point theorem, U is the mid point of RN.

3. From the given figure,

Conclusion: ∠7=∠5

Justification: From the figure, you can see that \overrightarrow{IK} bisects∠MIE. Therefore by the definition of bisector angle property, ∠MIK=∠KIE that is ∠7=∠5.

4. Conclusion: if l║m, and t is the transversal, then ∠3=∠7.

Justification: Since l║m and t is the transversal, then ∠3=∠7 as the alternate angles made by the transversal are equal.

5. Conclusion:    If \overrightarrow{BD} bisects ∠ABC, then ∠ABD=∠DBC

Justification: Since,  \overrightarrow{BD} bisects ∠ABC, then by the bisector angle property,  \overrightarrow{BD} divides ∠ABC in two equal angles that is ∠ABD=∠DBC.

6. Conclusion: If ∠2+∠3= 180°,then ∠2 and ∠3 are supplementary angle pairs.

Justification: Since, ∠2 and ∠3 are supplementary angle pairs which are on the same side of the transversal t, their sum is equal to 180° that is ∠2+∠3= 180°.

Answer: If Tara puts 4 pennies in for every one Sam does then after he puts in 10 she would of put 40.

She put in 40 pennies. Hope this helps ;)

When a 20-foot length of wire is cut into 6 pieces of equal length, each piece would be approximately 3.33 feet long. Rounding to the nearest whole numbers, this means the length of each piece will fall between 3 feet and 4 feet.

To find the length of each piece of wire when a 20-foot length of wire is cut into 6 pieces of equal length, you divide the total length by the number of pieces. So, you calculate:

Since we're looking for whole-number lengths that the length of each piece falls between, we can round 3.33 feet down to the nearest whole number (3 feet) and up to the next whole number (4 feet). Thus, the length of each piece will fall between 3 feet and 4 feet.

Answer:15

Step-by-step explanation:

Answer: Fertilizer A = 20, Fertilizer B = 56

Step-by-step explanation:

Step 1: Set up the equations

[tex]\begin{array}{c|c|c|c}& FertilizerA&FertilizerB&Quantity Required\\Nitrogen&8&5&440\\Phosphorous&2&5&260\\Potassium&4&5&360\\\end{array}[/tex]

Nitrogen: 8x + 5y ≥ 440

Phosphorous: 2x + 5y ≥ 260

Potassium: 4x + 5y ≥ 360

Step 2: Find the vertices

It is easiest to graph the equations to find the vertices. (see attachment).  You can also solve each system of equations to find the intersected points.

The following satisfy the "greater than or equal to" requirement:

Step 3: Use vertices in cost function C(x) to find the minimum

C(x) = $30x + $20y

(0, 88): $30(0) + $20(88) = $1760

(20, 56): $30(20) + $20(56) = $1720    ← This is the minimum!

(50, 32): $30(50) + $20(32) = $2140

(130, 0): $30(130) + $20(0) = $3900

The minimum cost occurs when 20 bags of Fertilizer A and 56 bags of Fertilizer B are purchased.  

This is a linear programming problem. The farmer needs to solve the system of inequalities that define the minimum nutrient requirements for the field and the cost function of the fertilizers to determine the least expensive way to meet the nutrient requirements.

The subject of this problem lies in the realm of linear programming—a mathematical method for determining a way to achieve the best outcome in a given mathematical model.

To solve this problem, we need to find the quantities of Fertilizer A and Fertilizer B that meets the minimum requirements for the field at minimum cost. Let x be the quantity of Fertilizer A and y be the quantity of Fertilizer B. Then, based on the information provided in the problem, we can set up the following inequalities:

Given that a 50-lb bag of Fertilizer A costs $30 and a 50-lb bag of Fertilizer B costs $20, the total cost of the fertilizers can be represented by the equation C = 30x + 20y, where C is the total cost.

The goal is to minimize the cost C = 30x + 20y, subject to the constraints above.
Using graphing or mathematical software, we can construct a graph of these inequalities and find the solution that lies on the feasible region where the cost is minimized.

The farmer needs to solve this system to determine the least amount of each fertilizer to use while still meeting the minimum soil nutrient requirements.

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Hi there! :)

Answer:

The area of the carpet is 3m².

Step-by-step explanation:

First off, the formula to calculate the area of a rectangle is this: A = L × W

Where "A" is the area, "L" the length and "W" the width.

Now that you have that, replace all the information you know in the equation in order to find the value of "A", which is what we are looking for:

- Just keep in mind that 1 1/2 is the same thing as 1.5

- The term "wide" is used to give the "width"

- The term "long" is used to give the "length"

A = L × W

A = 2 × 1.5

A = 3

There you go! I really hope this helped, if there's anything just let me know! :)

The area of the rectangular flying carpet is [tex]$\frac{15}{4} \text{ m}^2}$[/tex] or [tex]3.75 { m}^2}[/tex]

To find the area of a rectangle, one multiplies the length by the width. The width of the carpet is given as [tex]$1 \frac{1}{2}$[/tex] meters, which can be expressed as a fraction [tex]$\frac{3}{2}$[/tex] of meters. The length of the carpet is given as 2 meters.

Using the formula for the area of a rectangle [tex]A = l \times w$,[/tex] where [tex]$l$[/tex] is the length and [tex]$w$[/tex] is the width, we substitute the given values:

[tex]\[ A = 2 \text{ m} \times \frac{3}{2} \text{ m} \][/tex]

[tex]\[ A = \frac{2 \times 3}{2} \text{ m}^2 \][/tex]

[tex]\[ A = \frac{6}{2} \text{ m}^2 \][/tex]

[tex]\[ A = \frac{15}{4} \text{ m}^2 \][/tex]

[tex]\[ A = 3.75 \text{ m}^2 \][/tex]

Therefore, the area of the carpet is [tex]$\frac{15}{4}$[/tex] square meters or 3.75 square meters.

Answer: 75

Step-by-step explanation:

    [tex]2^A3^B5^{13}=20^D18^{12}[/tex]

⇒ [tex]2^A3^B5^{13}=(2^2\cdot5^1)^D(2^1\cdot3^2)^{12}[/tex]

⇒ [tex]2^A3^B5^{13}=(2^{2D}\cdot5^D)(2^{12}\cdot3^{24})[/tex]

⇒ [tex]2^A3^B5^{13}=2^{2D+12}\cdot3^{24}\cdot5^D[/tex]

Now compare the like bases:

[tex]2^A=2^{2D+12}[/tex] ⇒ A = 2D + 12

[tex]3^B=3^{24}[/tex] ⇒ B = 24

[tex]5^{13}=5^D[/tex] ⇒ D = 13

Next, let's solve for A:

A = 2D + 12

  = 2(13) + 12

  = 26 + 12

  = 38

LAST STEP: Find the sum of A, B, and D

S = A + B + D

  = 38 + 24 + 13

  = 75

Hi there! :)

Answer:

The answer is B) 17/30

Step-by-step explanation:

In order to find your answer you need to subtract 1/3 from 9/10:

9/10 - 1/3 = chocolate left

Since theses fractions do not have the same denominators (bottom number), the key here is to rewrite both of the fractions so that they have the same denominator:

The denominator is going to be a common multiple of "10" and "3". Ideally it's going to be the least common multiple of "10" and "3".

Let's start with the larger of the two denominators, which is "10". You have to go through its multiples and and see when we get to one that's divisible perfectly by 3.

So 10 is not divisible perfectly by 3, neither is 20. 30 on the other hand is divisible perfectly by 3. 30 is three times 10.

So you can rewrite both of these fractions as something over 30.

1/3 = ?/30

To get from 3 to 30, we have to multiply by 10. So if you multiply the denominator by 10, if you don't want to change the value of the fraction, you have to multiply the numerator (top number) by 10 also.

1/3 = 10/30

Same thing with the other fraction:

9/10 = ?/30 → 3 × 10 = 30 / SO, you need to multiply the numerator by three also → 9 × 3 = 27

9/10 = 27/30

Now that your fractions both have the same denominator, you can subtract the numerators together and put the answer on 30.

27/30 - 10/30 = ?

27 - 10 = 17 → 17/30

Since the fraction is simplified, you are now done.

There you go! I really hope this helped, if there's anything just let me know! :)

9514 1404 393

Answer:

  (b)  f(x) = 2^x -3

Step-by-step explanation:

The horizontal asymptote is y=-3, eliminating the first and last choices.

The curvature is upward, eliminating the third choice.

The graph is a representation of ...

  f(x) = 2^x -3

Answer:

Point slope intercept form: The equation for line is given by; [tex]y-y_1=m(x-x_1)[/tex] ......[1] ; where m is the slope and a point [tex](x_1, y_1)[/tex] on the line.

Let x represents the number of days and y represents the number of friends.

As per the statement:  After day three, he has 25 friends; after day eight, he has 40 friends.

⇒ We have two points i.e,

(3, 25) and (8, 40)

First calculate slope(m);

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given values we get;

[tex]m = \frac{40-25}{8-3}=\frac{15}{5}[/tex] = 3

now, substitute the given values of m=3 and a point (3, 25) in [1] we get;

[tex]y-25=3(x-3)[/tex]

Using distributive property; [tex]a \cdot(b+c) = a\cdot b + a\cdot c[/tex]

[tex]y-25 = 3x - 9[/tex]

Add 25 on both sides, we get;

[tex]y-25+25 = 3x - 9+25[/tex]

Simplify:

y =3x + 16

if  x = 18 days, then;

y = 3(18) + 16 = 54+16 = 70

Therefore, he will have on day 18, if he continues to add the same number of friends each day is, 70 friends.

Answer:

The y-intercept is at y = 10.

Step-by-step explanation:

It will be between y = 14 and y = 7 because the corresponding x values are -2 and 1.

An increase of 3 units of x  gives a decrease of 6 units of y fro the above values.

Then an increase of 1 ( 1 to 2) in x gives decrease in y of 2 (8 to 6). The other values show the same pattern.

So very unit increase in x,  the y values change by -2.

So  from x = -2 to 0 is +2 units for x and this will be -4 units for y  so the y-intercept ( when x = 0) will be at y = 14-4 = 10

y-intercept  is (0,10).