A certain shampoo is available in two sizes. A 14.2 ounce bottle costs $3.98. A 33.9 ounce bottle costs $9.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent. Thank you!

Answer:

f(x) = 3.33x - 7

Step-by-step explanation:

We are suppposed to write the slope intercept form of the line . The slope intercept form of the line is ,

[tex]\rm\implies y = mx + c [/tex]

where ,

Here we can see that the line is passing through (0,-7) . Therefore ,

[tex]\rm\implies y- intercept = -7[/tex]

Also we can see that the line is passing through (2.1,0) . Therefore we can find the slope as ,

[tex]\rm\implies Slope =\dfrac{y_2-y_1}{x_2-x_1}\\\\\rm\implies Slope =\dfrac{ -7-0}{0-2.1}\\\\\rm\implies \bf Slope = 3.33 [/tex]

Using Slope Intercept Form :-

[tex]\rm\implies y = mx + c \\\\\rm\implies y = 3.33x + (-7) \\\\\rm\implies\underline{\boxed{\rm\blue{f(x) = 3.33x - 7 }}}[/tex]

Let n be the smallest of the three numbers. Then

n + (n + 1) + (n + 2) = 5 ((n + 1) - 22)

Solve for n :

3n + 3 = 5 (n - 21)

3n + 3 = 5n - 105

2n = 108

n = 54

Then the three numbers are 54, 55, and 56.

Answer:

The system has one solution,

Both lines have the same y-intercept,

The solution is the intersection of the 2 lines.

Step-by-step explanation:

Answer:

6x+6y-5 distributive property

Step-by-step explanation:

6(x+y)-5

Distribute using the distributive property

6x+6y-5

Answer:

false

Step-by-step explanation:

If it was at least 2, it would show x>= 2 which includes 2. However, that question doesn't include 2 so if it is true, it would have said "X is greater than 2"

Answer: False

Step-by-step explanation:  When x is at least 2, x would be greater than or equal to 2.  X cannot be less than 2.  So, it should be x >= 2.

Hope this helped.

Hi there!

[tex]\large\boxed{4x - 2}[/tex]

7x - (3x + 2)

Simplify by distributing the negative sign:

7x - (3x) - (2)

Combine like terms:

4x - 2

Answer:

2(2x - 1)

Step-by-step explanation:

opening the parenthesis and distributing the - sign to both 3x and 2

= 7x - 3x - 2

= 4x - 2

taking 2 common

= 2 (2x - 1)

Answer:

5

Step-by-step explanation:

the absolute value of a number is its distance from zero on a number line. so the absolute value of 5 is 5.

Answer:

Yes, r and h can be changed to produce same volume by;

Increasing "r" and decreasing "h" or by decreasing "r" and increasing "h".

Step-by-step explanation:

What the question is simply asking is if we can get same volume of a particular cylinder if we change the radius and height.

Now, volume of a cylinder is;

V = πr²h

Now, for the volume to remain the same, if we increase "r", it means we have to decrease "h", likewise, if we decrease "r", we now have to increase "h".

Answer: A

Step-by-step explanation:

(22)(21)=(14)(33)

Answer:

-7/5

Step-by-step explanation:

I think let me know

Answer:

7/-5  or -7/5

Step-by-step explanation:

This shall be quite an easy problem, I shall be doubting that this is high school, however, I am happy to aid :)

We shall begin by labeling the points given to us to prepare for inputting the values in the slope formula

(3,4).     (8,-3)

x1,y1     x2,y2

Slope Formula:

y1 - y2

x1 - x2

Inputting the values:

4 - (-3)

3 - 8

Solve:

7

-5

The slope of the line passing through the points (3,4) and (8,-3) shall be 7/-5 or -7/5 negatives shall go both ways of fractions

Answer:

12

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

18 = 2 * 3 * 3

42 = 2 * 3 * 7

96 = 2 * 2 * 2 * 2 * 2 * 3

Greatest common factor = 2 * 3 = 6

Answer:

1st,2nd,3rd, and 5th option

Step-by-step explanation:

Let convert the intergers into radical numbers

[tex] \sqrt{7} > \sqrt{4} [/tex]

[tex] \sqrt{7} < \sqrt{49} [/tex]

[tex] \sqrt{7} < \sqrt{8} [/tex]

[tex] \sqrt{8 } < \sqrt{4} [/tex]

[tex] \sqrt{8} < \sqrt{64} [/tex]

As radical numbers approaches, positive infinity, the answer of the radical gets bigger. So using this explanation,

The first option, Second Option, Third Option, and Fifth Option are true.

Answer:

A, B, C, E

Step-by-step explanation:

Did on edg.  its right

Answer: 540 ft³

Step-by-step explanation:

The volume of pyramids is [tex]\frac{1}{3} Bh[/tex], where:

Therefore, the volume = [tex]\frac{1}{3} (135)(12)=\frac{1}{3}(1620)=\frac{1620}{3} =540[/tex]

Answer:

8

Step-by-step explanation:

The maximum area will be a square. Everything else will have a height less than one of the sides of the square.

Use Pythagoras to find the length of the side of the square.

s^2 = 2^2 + 2^2

s^2 = 8

s = 2sqrt(2)

s^2 = 8

the square will have 8 cm^2

Answer:

1/12

Step-by-step explanation:

Answer:

3.8

Step-by-step explanation:

3*60=180

180+48=228

228/60=3.8

Answer:

no solution

Step-by-step explanation:

Answer:

Step-by-step explanation:

I get no solution also (the answer is imaginary).

Answer:

- 0.25

Step-by-step explanation:

Sine -1/4 is a fraction, you can think of it as quarters in this case. there are 4 quarters in a dollar. 1/4 = 25/100.  

s(x) is continuous and has a horizontal asymptote at y = -9

We know that we have a function r(x) that has a horizontal asymptote at y = -8

Then, what can we say about the function s(x) = r(x + 2) - 1 ?

Ok, first remember that a horizontal asymptote means that as x, the variable, increases (or decreases), the function eventually tends to a given value, but never actually reaches it.

So as x tends to infinity, we should see an almost horizontal line that tends to y = -8.

So if that happens when x tends to infinity, the same thing will happen when x + 2 tends to infinity, because that "+2" does not add a lot.

Then is easy to conclude that:

r(x + 2) also has a horizontal asymptote at y = -8

And our function is:

s(x) = r(x + 2) - 1

So we are subtracting one, then that horizontal asymptote will be at:

y = -8 - 1 = -9

The function s(x) has a horizontal asymptote at y = -9

And because r(x) is continuous, then:

s(x) = r(x + 2) - 1

is also continuos, as there is nothing added that could change the continuity (we do not have any zero in the denominator or something like that)

Then the correct option is D.

"s(x) is continuous and has a horizontal asymptote at y = -9"

If you want to read more, you can see:

https://brainly.com/question/4084552

Answer:

[tex]\huge\boxed{s=17}[/tex]

Step-by-step explanation:

ΔADB is the right triangle with a right angle in vertex B. We can use the Pythagorean theorem.

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have:

[tex]leg=15\\leg=8\\hypotenuse=s[/tex]

Substitute:

[tex]s^2=15^2+8^2\\\\s^2=225+64\\\\s^2=289\Rightarrow s=\sqrt{289}\\\\s=17[/tex]

Step-by-step explanation:

fng-mrxb-dop p.l.e.a.s.e join

Answer:

10 years old :)

Answer:

Amount cubic metres of gravel need = 1.5 cubic meter

Step-by-step explanation:

Given:

Parts

cement = 1 part

sand = 2 parts

gravel = 3 parts

Find:

Amount cubic metres of gravel need

Computation:

Amount cubic metres of gravel need = 3[Part of gravel / Total of all parts]

Amount cubic metres of gravel need = 3[3 / (1+2+3)]

Amount cubic metres of gravel need = 3[3 / 6]

Amount cubic metres of gravel need = 3[0.5]

Amount cubic metres of gravel need = 1.5 cubic meter

Answer:

Zoe was 32 years old, which was 4 years ago.

Step-by-step explanation:

When Zoe was 36 years old, her daughter was 1/3 her age, or 12 years old. Therefore, the difference in ages is 24 years.

So, our equation becomes:

4(Z-24) = Z

4Z - 96 = Z

3Z = 96

Z = 32

Assuming Zoe is 36 years old right now, our answer is 4 years ago.

Hope this helped,

~cloud

Since the daughter is 1/3 Zoe's age, she must be 12 since 1/3 of 36 is 12.

Then make a chart like I have done in the image attached.

Since the problem says "how many years ago", we use

our x years ago column in our chart to setup the equation.

If you need any additional help or are confused on a step, let me know!

Answer:

The 2nd one is 3x+1

The 3rd answer is x+3

Step-by-step explanation:

Given g(x)=4x-1 and f(x)=x-2

Subtracting both

4x-1-(x-2)=4x-1-x+2=x(4-1)+(2-1)=3x+1

The next one is 3x+1-(2x-2)=3x+1-2x+2=x+3

Answer:

1.98*1/8=0.2475

0.2475=0.25

Answer:

x = 13.75

Step-by-step explanation:

a right-angled triangle.

so, we use Pythagoras

c² = a² + b²

where c is the Hypotenuse (the side opposite of the 90 degree angle).

so, in our case

17² = 10² + x²

289 = 100 + x²

189 = x²

x = 13.75

Answer:

98, 68, 44, 20

Step-by-step explanation:

we can write the other two-digit number as:

a*10 + b

Where both a and b are single-digit numbers.

When we "attach" this at the right of 55, the number that we get is:

5500 + a*10 + b

And this number is divisible by 24 if it is divisible by 3 and 8.

A number is divisible by 8 if the sum of its digits is divisible by 3, then we must have:

5 + 5 + a + b = multiple of 3 = n*3

A number is divisible by 8 if the last 3 digits are divisible by 8, then:

500 + b*10 + a = multiple of 8 = m*8

First we can use the second relation to find the value of b:

500 + b*10 + a = m*8

so we need to find a multiple of 8 that is in the range (500, 599)

for example, if we use:

8*65 = 520

Then we have:

b = 2

a = 0

5504, 5512, 5520, 5528, 5536, 5544, 5552, 5560, 5568, 5576, 5584, 5582, 5590, 5598.

Now we just need to see if these are divisible by 4.

5504:

5 + 5 + 0 + 4 = 14

not divisible by 3.

5512:

5 + 5+ 1 + 2 = 13

not divisible by 13

5520:

5 + 5 + 2+ 0 = 12

divisible by 3, then 20 is a option.

5528:

5 + 5 + 2 + 8 = 20

not divisible by 3

5536:

5 + 5 + 3 + 6 = 19

not divisible by 3

5544:

5 + 5 + 4 + 4 = 18

is divisible by 3, then 44 is a option.

5552:

5 + 5 + 5+ 2 = 17

not divisible by 3

5560:

5 + 5 + 6 + 0 = 16

not divisible by 3

5568:

5 + 5 + 6 +8 = 24

divisible by 3, then 68 is an option

5576:

5 +5 + 7 + 6 = 23

not divisible by 3

5582:

5 +5 + 8 + 2 = 20

not divisible by 3

5590:

5 +5 +9 + 0 = 19

not divisible by 3

5598:

5 + 5 + 9 + 8 = 27

is divisible by 3, thus 98 is an option.

Then the possible options are:

98, 68, 44, 20