Which exponential function grows the fastest?
A) f(x) = 5·2x
B) f(x) = 4·3x
C) f(x) = 3·4x
D) f(x) = 2·5x

Answer:

Step-by-step explanation: the cost of one donut is $0.59 because when you divide 3.54 by 6, you get 0.59.

The cost for one donut will be the sixth part of $3.54 thus it will be $0.59 or 59 cents.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Division = divide any two numbers or variables called division.

For example 4/8

As per the given,

Six donuts cost a total of $3.54

Cost of one donut = $3.54/6 = $0.59 = 59 cents

Hence "The cost for one donut will be the sixth part of $3.54 thus it will be $0.59 or 59 cents".

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Solution:

In order to be considered proportional , a line must pass through Origin.

Equation of any line passing through origin is given by:

 → y = k x,    k -= Slope of any line passing through origin.

[tex]\frac{y}{x}=k[/tex], Considering k as a proportionality constant.

Special Point = Origin (0,0)

Answer:

3 hours

Step-by-step explanation:

$50-$18=$32

$32/$10.50=3.04761904762--->3 hours

Answer:Sample Response: The points are on a horizontal line, parallel to the x-axis. The absolute value of −3 represents the distance from (−3, −5) to the y-axis, and the absolute value of 9 represents the distance from the y-axis to (9, −5).

Step-by-step explanation:

|-3| + |9| represents the distance between the points (-3,-5) and (9,-5) because the two points form a horizontal line

The line passes through the points (-3,-5) and (9,-5)

That is, [tex]x_1=-3, y_1=-5, x_2=9, y_2=-5[/tex]

Since [tex]y_1=y_2=-5[/tex], the line is a horizontal line

For a horizontal line passing though the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_1)[/tex], the distance(D) between the two points is given as:

[tex]D=|x_1|+|x_2|\\\\ D=|-3|+|9|[/tex]

Therefore, |-3| + |9| represents the distance between the points (-3,-5) and (9,-5) because the two points form a horizontal line

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Answer: There are 184 total number of CDs they own.

Step-by-step explanation:

Since we have given that

Ratio of rock music to total CDs that Ella Owens is

[tex]15:40\\\\=3:8[/tex]

Now, Number of rock music CDs Paolo has = 50

According to question, the ratio of rock music to total CDs in his collection is equivalent to the ratio of rock music to total music to total CDs in ours collection,

[tex]15:40=3:8[/tex]

Let the total number of CDs be x

So, our equation becomes,

[tex]\frac{3}{11}\times x=50\\\\x=\frac{50\times 11}{3}\\\\x=\frac{550}{3}\\\\x=183.34[/tex]

Hence, there are 184 total number of CDs they own.

Answer:

1. h Multiplication property for inequality

2. b Addition property for inequality.

3. i Set builder

4. f Intersection

5. k Union

6. j Subtraction property for inequalities

7. d Division property for inequality.

8. e Greater than

9. g less than

10. c compound

11. a Absolute value inequality.

Step-by-step explanation:

1/2x ≤ -5    Multiplying by 2 on both sides of the inequality

x ≤ -10

2)  8 > 4         Adding 5 on both sides of the inequality.

     8 + 5 > 4+5

      13 > 9

3)  {h/h > 43}  set builder

4) x ≥ -3  or x < -10   Intersection

5)  x ≥ -4 and x < 2

6) 4x - 1 < 7     Subtract 3 on both sides

   4x - 1 - 3 < 7 - 3

  4x - 4 < 4

7)  -3x < 9   Divide by -3 on both sides

    x > -3

8)  >  This sign means greater than

9)  < This an operation sign means less than

10) 7 > x > 1 This means that x x, 7 and x > 1.

11) /x + 6/ > 12

  This means that:

   (x + 6) > 12   or - (x + 6) > 12.   Absolute value inequality.

Answer:

a = 35°; b = 50°; c = 85°; d = 30°

Step-by-step explanation:

a = 35° because a + 80 + 65 = 180.

b = 50° because b+ 35 + 95 = 180.

c = 85° because c + 95 = 180.

d = 30° because d + 85 + 65 = 180.

57

95% is 19/20 as a fraction. 60/20 is 3. Multiply 19 by 3 to get 57. At least that how I do it. Hopefully this helped you.

Answer: D

Step-by-step explanation:

A. False

f(x): x → -∞, y → -∞

g(x): x → -∞, y → 1  

B. False

at x = -1, f(x) = -7

at x = -1, g(x) = 1.5

C. False

refer to A

g(x) → 1 and f(x) → -∞   so g(x) > f(x)

D. TRUE

It is hard to tell from the graph so plug in a value to check.

f(10) = 5(10) - 2

       = 50 - 2

       = 48

g(10) = 2¹⁰ + 1

        = 1024 + 1

        = 1025

g(10) > f(10)

Answer: 42 cookies/1 hour

Step-by-step explanation: Since Gretchen made 189 cookies in 4.5 hours, we set the equation up as 189/4.5. To get cookies per hour, we divide 189 by 4.5, which is 42/1. This means that Gretchen can make 42 cookies in 1 hour.

Answer:

(-10, 0) and (0,-5)

Step-by-step explanation:

For the function [tex]f(x)=-\dfrac{1}{2}x-5,[/tex] find x-intercept and y-intercept:

1. when y=0, then

[tex]0=-\dfrac{1}{2}x-5,\\ \\\dfrac{1}{2}x=-5,\\ \\x=-10;[/tex]

2. when x=0, then

[tex]y=-\dfrac{1}{2}\cdot 0-5,\\ \\y=-5.[/tex]

You get two points (-10, 0) and (0,-5). Plot them on the coordinate plane and connect, obtained line is the graph of the linear function [tex]f(x)=-\dfrac{1}{2}x-5.[/tex]

Answer: 12 texts per dollar.

The slope of the line is 1/5

Step-by-step explanation: If Ruby can send 48 text messages for $4, we divide 48 by 4 to get amount of texts per dollar: 12. Ruby can send 12 text messages for $1.

To figure out the slope of a line, use the formula y2 - y1 / x2 - x1.

-4 - (-9) / 22 - (-3) = 5 / 25 (rise over run)

Simplify to 1/5

Answer:

i would say the last choice

The disadvantage of using cash as a payment method is the requirement to hand deliver all payments. This method is less convenient and secure compared to electronic payments, highlighting the shift towards a cashless society.

The question asked is, "Which is a disadvantage of using cash as a payment method?" The correct answer to this question is that one must hand deliver all payments when using cash. This is a significant disadvantage compared to electronic forms of payment. In our increasingly digital world, methods like credit cards, online banking, and mobile payment platforms like Apple Pay introduced in 2014 offer the convenience of making payments from virtually anywhere without the need to physically handle currency.

This shift towards a cashless society highlights the limitations of cash transactions, especially in terms of convenience and security. Moreover, in scenarios such as paying bills, shopping for large purchases, or conducting business transactions, the logistical challenges of using cash become even more apparent. Electronic payments, on the other hand, allow for easier transaction tracking and less physical risk, making them more appealing for both consumers and businesses.

Answer:

[tex]A(x)=5\cdot 2^x[/tex]

Step-by-step explanation:

The given scenario can be represented by an exponential growth function. The general form if the exponential growth function is,

[tex]y=a(1+r)^x[/tex]

where,

y = the future amount after time x,

a = initial amount,

r = rate of growth.

As here A(x) represents the amount of money after x years with initial deposit of  $5 and in each year the amount doubles or duplicates itself i.e r=100% = 1, so the function would be,

[tex]A(x)=5(1+1)^x=5\cdot 2^x[/tex]

At the beginning the amount was $5, so the y intercept of the graph will be at 5.

Answer:

It’s Z Bc that’s the only one that starts at 5 and then doubles each year

Answer:9 is the only one

Step-by-step explanation:

Answer:

The above result is proved with the help of Pythagoras theorem and explained below.

Step-by-step explanation:

Given figure ABCD in which AD=BC and all angles intersect at right angle. Hence, the triangle formed inside ADC and ABC are right angled triangle.

In triangle ADC,

By applying Pythagoras theorem, we get

[tex]AC^{2}=AD^{2}+DC^{2}[/tex]    →  (1)

In triangle ABC,

[tex]AC^{2}=AB^{2}+BC^{2}[/tex]    →  (2)

Now, from eq (1) and (2)

Peach Tree Dr. is the same distance as Sycamore Ln.

[tex]AD^{2}+DC^{2} = AB^{2}+BC^{2}[/tex]

⇒ [tex]DC^{2} = AB^{2}[/tex]              (∵ AD=BC)

⇒ DC=AB                    (∵Distance can never negative)

Therefore, Peach Tree Dr. is the same distance as Sycamore Ln.

Step by step explanation: 12.5 x 4

Answer: 50.

[tex]\text{If x and y are proportional, then the quotient of x and y is constant}\\\\\dfrac{y}{x}=const.=a\to y=ax\\\\x=3,\ y=18\to\dfrac{y}{x}=\dfrac{18}{3}=6\\\\\text{therefore}\ \boxed{y=6x}\\\\\text{Check:}[/tex]

[tex]x=0\to y=6(0)=0\\\\x=3\to y=6(3)=18\\\\x=8\to y=6(8)=48\\\\x=13\to y=6(13)78\\\\\boxed{y=6x}[/tex]

Answer:  The volume of the cuboid  is:  " 11 ,200 cm³ " .

_________________________________________________

Step-by-step explanation:

____________________________________________________

The formula for the volume of a "cuboid" ;

      which is given in:  "cubic units" ;  or,  "units³ " ;  is:

____________________________________________________

        →    Volume, "V" = length (L)  * width (w) * (height)  ;

____________________________________________________

 →  The 3 (three given values are "4m" , "4 cm" and "7cm" .

We need the units of measurement to be equal;  so we need to convert the " 4m " to "cm" :

 Note that:  " 1 m = 100 cm " ; {exact conversion} ;

 So:   4m ( 100 cm / 1 m) = (4 * 100) cm = 400 cm.

_____________________________________________________

Now, we can plug these values and solve for the volume; in units of "cm³ " ;

_____________________________________________________

 V = 400 cm * 4 cm * 7 cm ;

    =  400 * 4 * 7 * cm * cm * cm ;

    =  400 * 4 * 7 cm³ ;

    =  1600 * 7 cm³ ;

     =  11, 200 cm³

_____________________________________________________

The answer is:  " 11 ,200 cm³ " .

_____________________________________________________

Answer:

The number of bricks is 16 and the number of blocks is 12

Step-by-step explanation:

Let the number of bricks be x and blocks be y.

Cost of each brick = $0.38

Total cost of x bricks = 0.38*x

Cost of each block = $1.56

Total cost of y blocks = 1.56*y

Total amount spent for the brickyard = $24.80

So,

Total cost of x bricks + Total cost of y blocks = Total amount spent for the brickyard

=> 0.38x + 1.56y = 24.80 ____equation (1)

Total number of items (bricks+blocks) = 28

So,

Number of bricks + Number of blocks = Total number of items

=> x + y= 28 ____equation (2)

We will solve the two equations by the method of elimination.

Let's multiply equation 2 by -0.38

(-0.38)*x + (- 0.38)*y  = (-0.38)*(28)

=> -0.38x - 0.38y  = -10.64 ____equation (3)

Adding equation 1 to the equation 3, we get

-0.38x - 0.38y + 0.38x + 1.56y = -10.64 + 24.80

Cancelling out -0.38x and +0.38x on the left side, we get

1.56y - 0.38y = 24.80-10.64

=> 1.18y = 14.16

Dividing both sides by 1.18, we get

[tex]\frac{1.18y}{1.18}[/tex]  =[tex]\frac{14.16}{1.18}[/tex]

=> y = 12

Plugging in y=12 in the equation 2, we get

x + y= 28

=> x + 12 =28

Subtracting 12 from both sides, we get

x+ 12 -12 = 28- 12

Cancelling out the +12 and -12 from the left side, we have

x = 16

So, the number of bricks is 16 and the number of blocks is 12.

Answer:

1:2

Step-by-step explanation:

She uses 1 cup of water and 2 cups of sugar so

1:2 or 1/2.

1. 800 divided by 4 equals 200.

2. 4 divided by 800 equals 0.005.

3. 440 divided by 24 equals 18 remainder 2, which can also be written as 18.2 as a decimal.

Each division problem is solved below:

1. 800 divided by 4:

To divide 800 by 4, you divide the dividend (800) by the divisor (4):

200

-------

4 | 800

- 8

---

0

Therefore, 800 divided by 4 equals 200.

2. 4 divided by 800:

To divide 4 by 800, you divide the dividend (4) by the divisor (800):

0.005

----------

800 | 4.000

- 0

-----

4.000

Therefore, 4 divided by 800 equals 0.005.

3. 440 divided by 24:

To divide 440 by 24, you divide the dividend (440) by the divisor (24):

18

------

24 | 440

- 24

------

20

- 18

------

2

Therefore, 440 divided by 24 equals 18 remainder 2, which can also be written as 18.2 as a decimal.

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Answer:

x=8

Step-by-step explanation:

15+x = 23

Subtract 15 from each side

15-15 +x = 23-15

x = 8

Answer:

7 minutes

Step-by-step explanation:

you have to set up a proportion

The degree of the polynomial is 4.

To determine the degree of a polynomial, we look for the highest power of the variable present in any of its terms. Let's break down the given polynomial and identify the terms:

[tex]\[ -3.1ax^4 + 2.5ax + 2ax^4 + 1.1ax^4 - 0.5ax - 2ax \][/tex]

Here, we have terms with different powers of [tex]\( x \): \( x^4 \), \( x \),[/tex] and constant terms.

Combine like terms:

[tex]\[ (-3.1a + 2 + 2.1 + 1.1 - 0.5 - 2)ax^4 \][/tex]

[tex]\[ = (-3.1a + 2 + 2.1 + 1.1 - 0.5 - 2)ax^4 \][/tex]

[tex]\[ = (-0.4a)ax^4 \][/tex]

Now, let's analyze the combined term [tex]\( (-0.4a)ax^4 \)[/tex].

The highest power of ( x ) in this term is 4. So, the degree of the polynomial is 4.

Therefore, the degree of the polynomial is 4.

Answer:

Area of the base = [tex]2x^2+5x-18[/tex]

Step-by-step explanation:

We know that volume of rectangular prism = (Area of base) x (Height)

or [Area of base] = [Volume]/[Height]

So basically we need to divide given area by given height to find the answer.

given height is (x+2) that means (x+2) must be factor of volume equation

or x=-2 must be root of volume equation so write down coefficients of volume equation then we divide by -2 as shown in attached picture.

Last digit on the right is always remainder.

Remaining coefficients {2, 5, -18} will give the area equation: [tex]2x^2+5x-18[/tex]

Hence final answer is:

Area of the base = [tex]2x^2+5x-18[/tex]

Answer:

16 2/3 %

Step-by-step explanation:

To put this in a percentage, they need to have the same units.

Let convert days to hours

1 day = 24 hours

Multiply by 3

3 days = 72 hours

The percentage is part over whole

12 hours / 72 hours

We can simplify by dividing top and bottom by 12

1/6

This is a fraction, change this to a decimal

.166666666

Now multiply by 100

16.666666 %

16 2/3 %

Answer:

24.

Step-by-step explanation:

So you need to fine 30% of 80.

I did the following method:

-Break it down, and do, 80 -/- 10 which is 8, now you have 10%, and you need to find 30, times your 10% by 3, so 24.

-Therefore, 24 out of 80 rides at the amusement park are water-related.

Hope this helps!

--Emilie Xx

By using the percentage given, we can calculate that there are 24 water-related rides at the amusement park out of the total 80 rides.

The question is asking how many of the total rides at the amusement park are water-related. This is a problem related to percentage. We know that 30% of the park's 80 rides are water-related. To find out the exact number, we multiply the total number of rides (80) by the percentage of water rides (30%), but since percentage is in terms of 100, we first convert the 30% to a decimal by dividing it by 100. This gives us 0.30. We then multiply 80 (the total number of rides) by 0.30.

Here's the calculation: 80 rides * 0.30 = 24 rides.

So, there are 24 water-related rides at the amusement park.

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Answer: 22 cm

Step-by-step explanation: