I sell cookies for $3 and muffins for $7. Yesterday, I made $129. I sold a total of 27 items. How many of each did I sell?

Answers

Answer 1

Answer: You sold 15 cookies and 12 muffins.

c - cookies
m - muffins

c + m = 27

3c + 7m = 129

I don’t know how to explain how to do efficiently but I just plugged in numbers until it worked:

3(15) + 7(12) = 129

45 + 84 = 129

Answer 2

Answer:

Answer:

You sold 15 cookies and 12 muffins

Step-by-step explanation:

So you're given that 1 cookie is sold for $3 and 1 muffin is sold for $7

You're also given that in total you made $129, and sold 27 items

Let's make equations from that, letting c stand for amount of cookies and m for amount of muffins.

3c + 7m = 129 (equation for amount of money made)
c + m = 27 (equation for amount of items sold)

Now we can use the second equation to find m:

c + m = 27

m = 27 - c

Not we can substitute m into the first equation to find c:

3c + 7m = 129

3c + 7(27-c) = 129 [substitute m for (27-c)]

3c + 189 -7c = 129 [distribute 7 into (27-c)]

-4c + 189 = 129 [combine like terms]

-4c = -60 [subtract 189 from both sides]

c = 15 [divide both sides by -4]

Now we can substitute c into the second equation to find m:

c + m = 27

15 + m = 27

m = 12

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Which of the following is not a name of a valid chemical formula? Select one:
a. carbon chloride
b. nitrogen monoxide
c. copper (II) carbonate
d. chloric acid

Answers

Among the compounds given, the one that is not valid is a. carbon chloride. a compound composed of non-metals should have prefixes that is related to the number of atoms of the elements present. In this case, the other cmopounds are considered valid but not A

The correct answer is: Option (a) Carbon Chloride

Explanation:
Carbon has four valence electrons; therefore, it would require 4 more electrons to become stable. Chlorine, however, has seven (7) valence electrons. So it would require only one electron to become stable. In this case, as in the name, carbon chloride, the word chloride refers to the compound that is stable, which in this case cannot be possible (as carbon requires 4 electrons, and chlorine only has 7). If chlorine had 4 valence electrons, then it would be possible. Hence, the correct option is (a) Carbon Chloride.

(4u^3+6u^2+7)+(6u^3-2u+7)
Simplify the sum'

Answers

Hi Nova

(4u³+6u²+7)+(6u³-2u+7)

= 4u³+6u²+7+6u³-2u+7

Combine like terms

( 4u³+6u³)+(6u²)+(-2u)+(7+7)

= 10u³+6u² -2u+14

There no like terms so you can not simplify the sum

I hope that's help and if you have questions please ask !

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π?

Answers

recall that to get the x-intercepts, we set the f(x) = y = 0, thus

$\bf \stackrel{f(x)}{0}=-4cos\left(x-(\pi )/(2) \right)\implies 0=cos\left(x-(\pi )/(2) \right)\n\n\ncos^(-1)(0)=cos^(-1)\left[ cos\left(x-(\pi )/(2) \right) \right]\implies cos^(-1)(0)=x-\cfrac{\pi }{2}\n\n\nx-\cfrac{\pi }{2}=\begin{cases}(\pi )/(2)\n\n(3\pi )/(2)\end{cases}$

$\bf -------------------------------\n\nx-\cfrac{\pi }{2}=\cfrac{\pi }{2}\implies x=\cfrac{\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{2\pi }{2}\implies \boxed{x=\pi }\n\n-------------------------------\n\nx-\cfrac{\pi }{2}=\cfrac{3\pi }{2}\implies x=\cfrac{3\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{4\pi }{2}\implies \boxed{x=2\pi }$

Find the value of x when 6 - 3x = 5x - 10x + 10.

Answers

6 - 3x = 5x - 10x + 10

you’re answer would be :

x = 2

Answer:

x= 2

Step-by-step explanation:

Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4

Answers

Answer:

The length and width that maximize the area are:

W = 2*√8

L = 2*√8

Step-by-step explanation:

We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.

Remember that the area of a rectangle of length L and width W, is:

A = L*W

You can see the image below to see how i will define the length and the width:

L = 2*x'

W = 2*y'

Where we have the relation:

4 = √(x'^2 + y'^2)

16 = x'^2 + y'^2

Now we can isolate one of the variables, for example, x'

16 - y'^2 = x^'2

√(16 - y'^2) = x'

Then we can write:

W = 2*y'

L = 2*√(16 - y'^2)

Then the area equation is:

A = 2*y'*2*√(16 - y'^2)

A = 4*y'*√(16 - y'^2)

If A > 1, like in our case, maximizing A is the same as maximizing A^2

Then if que square both sides:

A^2 = (4*y'*√(16 - y'^2))^2

= 16*(y'^2)*(16 - y'^2)

= 16*(y'^2)*16 - 16*y'^4

= 256*(y'^2) - 16*y'^4

Now we can define:

u = y'^2

then the equation that we want to maximize is:

f(u) = 256*u - 16*u^2

to find the maximum, we need to evaluate in the zero of the derivative:

f'(u) = 256 - 2*16*u = 0

u = -256/(-2*16) = 8

Then we have:

u = y'^2 = 8

solving for y'

y' = √8

And we know that:

x' = √(16 - y'^2) = √(16 - (√8)^2) = √8

And the dimensions was:

W = 2*y' = 2*√8

L = 2*y' = 2*√8

These are the dimensions that maximize the area.

Need help solving this
-3 + y = 0

Answers

The answer would be +3 because in order to get the equation to equal 0 the you would need to add 3 to -3

fue answer is poseitive3

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