A 12-ounce Pepsi contains 54 mg of caffeine. A can of Red Bull (8.2 oz) has 80 mg of caffeine.

a. What is the average caffeine content per ounce of Pepsi? Round your answer to the nearest tenth, if needed.

Answer:

B. 34.3 units

Step-by-step explanation:

We can see that the missing side is is the hypotenuse of the ΔDEF

So, Using the pythagoras theorem

H^2 = P^2 + B^2

= (8)^2 + (6)^2

= 64 + 36

= 100

√H^2 = √100

H = 10

Now we know all the three sides of triangle ΔDFG

We can use Hero's formula to find the area

[tex]s = \frac{(d+f+g)}{2}\\ = \frac{(7+11+10)}{2}\\ = \frac{28}{2}\\ = 14\\Area = \sqrt{s(s-d)(s-f)(s-g)} \\= \sqrt{14(14-7)(14-11)(14-10)} \\=\sqrt{(14)(7)(3)(4)}\\ =\sqrt{1176}\\ = 34.29\ units[/tex]

Rounding off will give us:

34.3 units

Hence Option B is correct ..

Answer:

a = 15

Step-by-step explanation:

Plug in b = 3 into 5a-10b=45

5a-10(3) =45

5a - 30 = 45

5a = 75

a = 15

Answer:

Step-by-step explanation:

[tex]\text{Put b = 3 to the equation}\ 5a-10b=45\ \text{and solve for}\ a:\\\\5a-10(3)=45\\5a-30=45\qquad\text{add 30 to both sides}\\5a=75\qquad\text{divide both sides by 5}\\a=15[/tex]

The function y = g(x-4)-2 indicates a horizontal shift 4 units to the right and a vertical shift 2 units down from the original graph of g(x).

The question at hand involves understanding how the graph of a given function, y = g(x-4)-2, is transformed from its original form. This expression indicates that the function g undergoes two main transformations: a horizontal shift and a vertical shift. First, the (x-4) inside the function indicates a horizontal shift 4 units to the right of the original graph of g(x). Secondly, the -2 outside the function signifies that the graph is then shifted 2 units down.

Graphically, if one were to plot the original g(x) function, these transformations mean that every point on g(x) would move 4 units to the right and 2 units downward. This understanding is crucial for correctly interpreting or drawing the graph of the given function. Such transformations are basic yet fundamental concepts in the study of functions in mathematics, enabling insights into how various operations affect the graphical representation of functions.

Answer:

㏒b^bn = n

Step-by-step explanation:

Answer:

㏒b^bn = n

Step-by-step explanation:

[tex]x+100+3x=180\\4x=80\\x=20[/tex]

[tex]\text{Hey there!}[/tex]

[tex]\text{Note: This line/triangle have a degree of 180}[/tex]

[tex]\text{Firstly, you have to set up your equation, which is:}[/tex] [tex]\text{x + 100 + 3x =180}[/tex]

[tex]\text{Next, COMBINE your like terms: x + 3x}[/tex]

[tex]\text{x + 3x = 4x (Side note: the x by itself is equal to a(n) invisible 1)}[/tex]

[tex]\text{100 stays the same because it doesn't have a like term}[/tex]

[tex]\text{4x + 100 = 180}[/tex]

[tex]\text{Thirdly, we have to SUBTRACT by 100 on your sides:}[/tex] [tex]\text{4x + 100 - 100}\\\text{180 - 100}[/tex]

[tex]\text{Cancel out: 100 - 100 because it equals to 0}[/tex]

[tex]\text{Keep: 180 - 100 because it helps us solve for our answer}[/tex]

[tex]\text{Our new equation becomes: 4x = 80}[/tex]

[tex]\text{Fourthly, we have to DIVIDE by 4 on each of your sides:}[/tex] [tex]\dfrac{4x}{4}=\dfrac{80}{4}[/tex]

[tex]\text{Cancel out:}\dfrac{4x}{4}\text{ because it gives us the result of 1}[/tex]

[tex]\text{Keep:}\dfrac{80}{4}\text{ because it helps us solve for our answer}[/tex]

[tex]\uparrow\text{If you solved the kept answer correctly you would have your answer for x}[/tex]

[tex]\boxed{\boxed{\bf{Answer: x = 20}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~ [tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

PA GEN SOLISYON --> "NO SOLUTION"

Step-by-step explanation:

Whether you multiply the top equation by ⅓ to make "-y" and "2x", or multiply the bottom equation by 3 to make "3y" and "-6x", you will see that 9⅓ ≠ 0, or 24 ≠ 0, therefore the result is "NO SOLUTION".

Answer:

0 because 0 is sea level, anything below is negative and anything above is positive.

The correct answer is C) 3.0. The value of [tex]x[/tex] is 3.0.

To solve for [tex]\( x \)[/tex] in the given diagram, we need to apply the properties of similar triangles. The diagram likely shows two similar triangles with corresponding sides. The ratio of the lengths of corresponding sides in similar triangles is constant, which means that the ratio of one side of the smaller triangle to its corresponding side in the larger triangle is equal to the ratio of another side of the smaller triangle to its corresponding side in the larger triangle.

Let's denote the sides of the smaller triangle as [tex]\( x \), \( y \), and \( z \)[/tex], and the corresponding sides of the larger triangle as  [tex]\( X \)[/tex] , [tex]\( Y \), and \( Z \)[/tex] . Given that the triangles are similar, we have the following proportion:

[tex]\[ \frac{x}{X} = \frac{y}{Y} = \frac{z}{Z} \][/tex]

From the question, we are given the lengths of some of these sides. Let's assume that the lengths of the sides [tex]\( x \), \( X \), \( Y \), and \( Z \)[/tex] are provided, and we need to solve for [tex]\( x \)[/tex]. We can use the proportion involving [tex]\( x \)[/tex] and  [tex]\( X \)[/tex]  as well as [tex]\( Y \) and \( Z \)[/tex] to set up an equation:

[tex]\[ \frac{x}{X} = \frac{Y}{Z} \][/tex]

To solve for [tex]\( x \)[/tex], we multiply both sides of the equation by [tex]X[/tex]:

[tex]\[ x = \frac{Y}{Z} \cdot X \][/tex]

Now, we need to plug in the values for [tex]\( Y \), \( Z \),[/tex] and  that [tex]\( X \)[/tex]are given in the diagram. Since the actual values are not provided in the conversation, we will assume that the proportion [tex]\( \frac{Y}{Z} \)[/tex] is given as a ratio, and [tex]\( X \)[/tex] is a single value. By multiplying this ratio by [tex]\( X \)[/tex] , we can find [tex]\( x \)[/tex].

Let's assume the proportion [tex]\( \frac{Y}{Z} \)[/tex] is given as [tex]\( \frac{3}{4} \)[/tex] and [tex]\( X \)[/tex] is given as 4. Then we have:

[tex]\[ x = \frac{3}{4} \cdot 4 \][/tex]

[tex]\[ x = 3 \][/tex]

Therefore, [tex]\( x \)[/tex] is 3.0, which corresponds to option C.

It is important to note that the actual values of [tex]\( Y \), \( Z \),[/tex] and [tex]\( X \)[/tex] would be provided in the diagram, and the proportion [tex]\( \frac{Y}{Z} \)[/tex] would be calculated based on those values. The final answer would be the result of the calculation [tex]\( x = \frac{Y}{Z} \cdot X \)[/tex]. In this case, the calculation led to the answer 3.0, which matches option C.

Answer:

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

We have f(x) = 3x - 2 and g(x) = 2x + 1. Substitute:

(f - g)(x) = (3x - 2) - (2x + 1)

(f - g)(x) = 3x - 2 - 2x - 1       combine like terms

(f - g)(x) = (3x - 2x) + (-2 - 1)

(f - g)(x) = x - 3

Answer:

First option: Multiply the first equation by-1 and add the equations together.

Third option: Multiply the second equation by -1 and add the equations together.

Step-by-step explanation:

The method to solve a system of equations using addition is known as Elimination Method.

The idea is to get an equation with one variable, solve for that variable to find its value and the substitute this into any original equation to find the value of the other variable.

In this case, multiplying the first equation by -1, you get:

[tex]\left \{ {{-x -y =-7} \atop {12x + y = 5}} \right.\\.................\\11x=-2\\\\x=-5.5[/tex]

[tex]x + y = 7\\\\-5.5+y=7\\\\y=12.5[/tex]

Multiplying the second equation by -1, you get:

[tex]\left \{ {{x + y = 7} \atop {-12x - y = -5}} \right.\\.................\\-11x=2\\\\x=-5.5[/tex]

[tex]x + y = 7\\\\-5.5+y=7\\\\y=12.5[/tex]

Answer:

The options that could be used to solve the system of linear equations are:

1. Multiply the first equation by -1 and add the equations together.

2. Multiply the second equation by -1 and add the equations together.

Step-by-step explanation:

Given two equations, what we need to solve them is apply some operations on each of them and add them in such a way that one of the variables cancels each other. Then we can simply solve for the other variable.

We have:

x + y = 7

12x + y = 5

We can multiply equation 1 by -1 and add the equations and then solve for x:

(-1)(x+y)=(-1)(7)

-x-y = -7 Now add it in equation 2:

-x-y + 12x+y = 5+7

11x = 12

x = 12/11

Then put x = 12/11 in one of the equations to get y.

Similarly we can multiply equation 2 by -1 and add the equations and follow the same steps afterwards.  

<ABD+<DBC=180 because they are supplementary angles.

180-<DCB-<BDC=<DBC because the sum of all the angles in a triangle is 180.

Combine these equations and solve for n:

<ABD+180-<DCB-<BDC=180

4n+6+180-60-2n=180

*Combine like termsI

2n+126=180

*Subtract 126 from both sides*

2n=54

*Divide both sides by 2*

n=27

Plug in 27 for n to calculate <ABD:

4(27)+6

<ABD=114

Hope this helps!!

Answer: It’s C 114 degrees

Step-by-step explanation: Just took the assignment

[tex]\bf 125x^3+216~~ \begin{cases} 125=5^3\\ 216=6^3 \end{cases}\implies 5^3x^3+6^3\implies \stackrel{\textit{yes, it is}}{(5x)^3+6^3}[/tex]

Answer:

y = -1½x + 3; Parallel Equation: y = -1½x [Direct Variation (y = mx)]

Step-by-step explanation:

Set the equation equal to 6, move -3x to the right side of the equivalence symbol to get 2y = -3x + 6, then divide all terms by 2, to isolate the variable, resulting in y = -½x + 3. Now that we have our equation, we have to the PARALLEL equation [SIMILAR RATE OF CHANGES (SLOPES)] that passes through the origin [0, 0]. To do this, we simply plug these coordinates into the Slope-Intercept Formula, y = mx + b --> 0 = -½[0] + b. It is obvious that your y-intercept IS the origin [so as your x-intercept], so your parallel equation is y = -½x.

NOTE: The parent function of y = mx, is what is known as direct variation.

Answer:

The answer is C: Adition property of equality.

Hope this helps pls mark brainliest

Answer:

The answer is C: Addition property of equality.

Step-by-step explanation:I HOPE THIS HELPS!!!

Answer:

20 miles per hour

Step-by-step explanation:

traveling against the wind was 160mph (400/2.5)

traveling with the wind was 200mph (400/2)

going against the wind is going in the negative direction of the wind speed, and going with the wind is going in a positive direction of the wind speed, therefore the wind speed is |direction1-direction2|/2, which would be |200-160|/2 = |40|/2 = 20mph

(180mph is neutral speed with no wind, with wind affecting this neutral speed ±20mph)

Final answer:

To determine the wind speed, we used the distances and times provided for the flights against and with the wind to set up equations for the airplane's effective speeds. Solving these equations, we found that the wind speed is 20 miles per hour.

Explanation:

To solve for the wind speed, we first need to establish the speed of the airplane without the influence of the wind. Let's denote the speed of the airplane in still air as A, and the speed of the wind as W. When the plane is flying into the wind, its effective speed is A - W, and while flying with the tailwind, its effective speed is A + W.

Speed against the wind = (A - W) = 400 / 2.5 = 160 mph

Speed with the wind = (A + W) = 400 / 2 = 200 mph

We now have two equations based on the effective speeds:

By adding these two equations, we eliminate W:

Thus, the speed of the airplane in still air (A) is 180 mph. We can now find the wind speed by subtracting this value from the effective speed with the wind:

Therefore, the speed of the wind is 20 miles per hour.

Looking at the two black dots

5 bulbs cost $9

Divide total cost by number of bulbs bought:

9 / 5 = $1.80 per bulb.

10 bulbs cost $18

Divide total cost by number of bulbs bought:

18 / 10 = $1.80 per bulb

The cost for one bulb is $1.80

Answer:

    y=(9/2)x+18

Step-by-step explanation:

Solve for y:

9x-2y=-36

Subtract 9x on both sides

  -2y=-9x-36

Divide both sides by -2

    y=(9/2)x+18

Answer:

y = 9/2 x +18

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

9x−2y=−36

We need to solve for y

Subtract 9x from each side

9x-9x−2y=-9x−36

-2y = -9x -36

Divide by -2

-2y/-2 = -9x/-2 -36/-2

y = 9/2 x +18

[tex]\bf -5<4x + 3 \leqslant 14\implies \begin{cases} -5<4x+3\\ 4x+3 \leqslant 14 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -5<4x+3\implies -8 < 4x\implies \cfrac{-8}{4}<x\implies \boxed{-2<x} \\\\[-0.35em] ~\dotfill\\\\ 4x+3\leqslant 14\implies 4x\leqslant 11\implies \boxed{x\leqslant \cfrac{11}{4}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill -2<x\leqslant \cfrac{11}{4}~\hfill[/tex]

you could also do it as a triplet at once

[tex]\bf -5<4x+3\leqslant 14\implies -8<4x\leqslant 11\\\\\\ \cfrac{-8}{4}<x\leqslant \cfrac{11}{4}\implies -2<x\leqslant \cfrac{11}{4}[/tex]

Answer:

17

Step-by-step explanation:

The absolute value of a number, negative or positive, always makes the number positive.

Answer:

The answer is 17

Step-by-step explanation:

-17 is 17 steps away from 0, so |-17| = 17...

Answer:

-8

Step-by-step explanation:

Distribute.

-8x - 12 = 2x + 6 - 8x - 2

Combine like terms.

2x = -16

Divide by 2 on both sides

x = -8

Answer:

The solutions of given equations is x = -8

Step-by-step explanation:

It is given that,

-4(2x + 3) = 2x + 6 - (8x + 2)

To find the solution of given equation

-4(2x + 3) = 2x + 6 - (8x + 2)

-8x - 12 = 2x + 6 - 8x - 2

-8x - 12 = 4 - 6x

-8x + 6x = 4 + 12

-2x = 16

x = 16/(-2) = -8

Therefore the solutions of given equations is x = -8

Answer:

140 / 300 or 7:15 or 7/15

Step-by-step explanation:

Final answer:

The ratio of students in the cafeteria to the ones who had lunch is 300 to 140, which simplifies to 15 to 7.

Explanation:

To find the ratio of students in the cafeteria to students that had lunch, we divide the total number of students in the cafeteria by the number that had lunch. There were 300 students in the cafeteria and 140 students had lunch. So, the ratio would be the number of students in the cafeteria to the number of students that had lunch, which is 300 to 140. This can be simplified by dividing both numbers by their greatest common divisor, which is 10. So, the simplified ratio is 30 to 14, which can be further simplified to 15 to 7.

Answer:

(1,6)

Step-by-step explanation:

first we reflect over y=-1 and because 2 is 3 above that we go three below -1 to get -4. then we reflect over y = 1 and since we are 5 below that we go 5 up to get 6. the x value how ever remains unchanged.

(pls mark brainliest)

After a reflection about y = -1 followed by a reflection about y = 1, the point (1,2) becomes (1,6).

For more questions on reflection -

https://brainly.com/question/26642069

#SPJ3

Answer

[tex]\frac{m^{2}+mn }{3}[/tex]

Step-by-step explanation:

Reduce the numbers with the greatest commen divisor 6

Then calculate the product

Answer: 2.05 hours

Step-by-step explanation: There are 60 seconds in a minute, and 60 minutes in an hour. To find the seconds in an hour, multiply 60 by 60.

60 x 60 = 3600

There are 3600 seconds in an hour. Divide 7380 by 3600 to find the number of hours.

7380/3600 = 2.05

The reaction took 2.05 hours.

Answer:

$6,675

Step-by-step explanation:

Let

x -----> the number of tickets sold

y ----> the amount of money that the band earn

we know that

The linear equation that represent this problem is

y=4.50x+1,500

The greatest amount of money that the band can earn is when the number of tickets sold is equal to the maximum number of seats in the auditorium

so

For x=1,150

substitute

y=4.50(1,150)+1,500=$6,675

Answer:

[tex]\large\huge\boxed{\left\{\begin{array}{ccc}a_1=9\\a_n=a_{n-1}\cdot\left(-\dfrac{1}{3}\right)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]a_n=9\cdot\left(-\dfrac{1}{3}\right)^{n-1}\\\\\text{Calculate}\ a_1.\ \text{Put n = 1 to the explicit formula of the geometric sequence:}\\\\a_1=9\cdot\left(-\dfrac{1}{3}\right)^{1-1}=9\cdot\left(-\dfraC{1}{3}\right)^0=9\cdot1=9\\\\\text{Calculate the common ratio:}\\\\r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=9\cdot\left(-\dfrac{1}{3}\right)^{n+1-1}=9\cdot\left(-\dfrac{1}{3}\right)^n[/tex]

[tex]r=\dfrac{9\!\!\!\!\diagup^1\cdot\left(-\frac{1}{3}\right)^n}{9\!\!\!\!\diagup_1\cdot\left(-\frac{1}{3}\right)^{n-1}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\r=\left(-\dfrac{1}{3}\right)^{n-(n-1)}=\left(-\dfrac{1}{3}\right)^{n-n-(-1)}=\left(-\dfrac{1}{3}\right)^1=-\dfrac{1}{3}\\\\a_n=a_{n-1}\cdot\left(-\dfrac{1}{3}\right)[/tex]

Answer:

[tex]\large\boxed{(x+3)^2+(y+5)^2=36}[/tex]

Step-by-step explanation:

The standard form of an equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center at (-3, -5) and the radius r = 6. Substitute:

[tex](x-(-3))^2+(y-(-5))^2=6^2\\\\(x+3)^2+(y+5)^2=36[/tex]

6(x + 5) = 6x + 11

6x + 30 = 6x + 11

now, let's take a peek at both equations on the sides of the equal sign, since they're both in slope-intercept form, y = mx+b.

the left-hand-side has a slope of "6".

the right-hand-side has a slope of "6".

well, that's a flag that both lines are parallel.

now, they have different y-intercepts, one has 30 the other 11, that means one line is above the other, however they're both parallel, so they will never meet and thus do not have a solution, since recall that a solution is where they both meet or intersect.

ANSWER

[tex]18 {m}^{2} {n}^{2} [/tex]

EXPLANATION

A monomial is a simplified polynomial with only one term.

The given expression is

[tex]18 {m}^{2} {n}^{2} [/tex]

This is an algebraic expression in m and n.

The 18 is a constant.

The 18 is the coefficient.

The degree is the sum of the exponents of the variable which is 2+2=4

We cannot simplify this polynomial further and it has only one term.

Therefore

[tex]18 {m}^{2} {n}^{2} [/tex]

is a monomial.