Sam spent $16 on a large pizza and two drinks. If the pizza was 75% of the cost, how much did each drink cost?

Answer:

Part 1) The system of equations that represent this situation is

[tex]12x+6y=180[/tex] and [tex]x=2y[/tex]

Part 2) The number of hardcover books sold was [tex]12[/tex] and the number of paperback books sold was [tex]6[/tex]

Step-by-step explanation:

Part 1) What is the system of equations that represents this situation?

Let

x---->  number of hardcover books sold

y----> number of paperback books sold

we know that

The system of equations that represent this situation is equal to

[tex]12x+6y=180[/tex] -----> equation A

[tex]x=2y[/tex] -----> equation B

Part 2) What is the solution to the system and what does it represent in the context of this situation?

Substitute equation B in equation A and solve for y

[tex]12(2y)+6y=180[/tex]

[tex]24y+6y=180[/tex]

[tex]30y=180[/tex]

[tex]y=6[/tex]

Find the value of x

[tex]x=2y[/tex]

[tex]x=2(6)=12[/tex]

The solution of the system of equations is the point (12,6)

That means

The number of hardcover books sold was [tex]12[/tex]

The number of paperback books sold was [tex]6[/tex]

Answer:

Retailer

Step-by-step explanation:

A retailer buys goods from the manufactures and wholesalers and then sell these products directly to the consumers or users.In the supply chain retailers are the ones who connect with the customers to obtain information on goods and servicers delivered.

1st one is 0

2nd one is -3

3rd one is -2

4th one is 5

Combine like terms, isolate the variable, and make the slope of the variable 1 to find all the answers.

Answer:63Minutes

Step-by-step explanation:

Answer: 63.

Step-by-step explanation: In order to find how fast she runs 6 miles, it'd be convenient to know how fast she runs in 1 mile. So:

8 miles = 84 minutes.

8/8 = 1

84 / 8 = 10.5

6 x 1 = 6

10.5 x 6= 63.

Answer:

b 93

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets gets started.

The dimensions of the given triangle is 24 , 52 and 17.

The another triangle is given congruent to this triangle.

It means the dimensions of another triangle will also be 24, 52 and 17.

So the perimeter will be addition of these sides.

Hence the perimeter will be = [tex]24+52+17[/tex]

Hence the perimeter will be = 93 feet   :    Answer

Hope it will help :)

ANSWER

[tex]3{a}^{4 } [/tex]

EXPLANATION

The cube root of

[tex]27 {a}^{12} [/tex]

is

[tex] \sqrt[3]{27 {a}^{12} } [/tex]

This is the same as:

[tex](27 {a}^{12} )^{ \frac{1}{3} } [/tex]

[tex]( {3}^{3} ({a}^{4})^{3} )^{ \frac{1}{3} } [/tex]

[tex] = (3{a}^{4} )^{3 \times \frac{1}{3} } [/tex]

[tex] = 3{a}^{4 } [/tex]

Answer:

x=2i/3

All you have to do is just to find the square root.

Answer:

x = ±(2/3)i

Step-by-step explanation:

Subtract 4, divide by 9, and take the square root.

9x^2 = -4

x^2 = -4/9

x = ±√(-4/9) = ±(2/3)i . . . . . . the solutions are imaginary numbers

Hello There! The answer is 12w - 12y + 3.

Here's a step by step on how to solve  3(2w-4y+3)+6w-6.

Step 1: Multiply the 3 by the numbers in the parenthesis.

3(2w-4y+3)+6w-6 ⇒ 6w - 12y + 9 + 6w - 6

Step 2: Rearrange the numbers so like terms are next to each other.

6w - 12y + 9 + 6w - 6 ⇒ 6w + 6w - 12y - 6 + 9.

Step 3: Combine like terms. (6w + 6w and - 6 + 9).

6w + 6w - 12y - 6 + 9 ⇒ 12w - 12y + 3

This is your final answer since you cannot simplify any further. I hope this helps and have a great day!

Answer:

12 w - 12 y + 3

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

3 ( 2 w - 4 y + 3 ) + 6 w - 6 =

6 w - 12 y + 9 + 6 w - 6 =

12 w - 12 y + 3

Answer:

28

Step-by-step explanation:

We start by doing 28 - 14 which equals 14.

We do this because we want to find out the amount of books before he bought 14. We have 14 which is after he sold half of his comics. A half is 1/2, that means you multiply 14 by 2. You get 28.

Final answer:

Julio initially had 28 comic books, sold half, then purchased 14 more, which resulted in him having a total of 28 comic books. We used a simple algebraic equation to determine the original amount.

Explanation:

Let's denote the original number of comic books that Julio had as x. According to the problem, Julio sold half of his comic books (x/2) and then bought 14 more. Consequently, he now has 28 comic books in total.

To express this situation mathematically, we can create the following equation to represent the changes in the number of comic books Julio has:

x/2 + 14 = 28

If we simplify this equation by subtracting 14 from both sides, we get:

x/2 = 28 - 14

x/2 = 14

By multiplying both sides of the equation by 2, we can find the original number of comic books Julio had:

x = 14 * 2

x = 28

Therefore, Julio began with 28 comic books before he sold half and bought 14 more.

Answer:

The Numerator is 6x + 4y - 3z

Step-by-step explanation:

Step  1  :

           z

Simplify   —

           4

Equation at the end of step  1  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  2  :

           y

Simplify   —

           3

Equation at the end of step  2  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  3  :

           x

Simplify   —

           2

Equation at the end of step  3  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  4  :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple  

     The left denominator is :       2  

     The right denominator is :       3  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 1 0 1

3 0 1 1

Product of all  

Prime Factors  2 3 6

     Least Common Multiple:  

     6  

Calculating Multipliers :

4.2    Calculate multipliers for the two fractions  

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 3

  Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.  

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      x • 3

  ——————————————————  =   —————

        L.C.M               6  

  R. Mult. • R. Num.      y • 2

  ——————————————————  =   —————

        L.C.M               6  

Adding fractions that have a common denominator :

4.4       Adding up the two equivalent fractions  

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 3 + y • 2     3x + 2y

—————————————  =  ———————

      6              6    

Equation at the end of step  4  :

 (3x + 2y)    z

 ————————— -  —

     6        4

Step  5  :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple  

     The left denominator is :       6  

     The right denominator is :       4  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 1 2 2

3 1 0 1

Product of all  

Prime Factors  6 4 12

     Least Common Multiple:  

     12  

Calculating Multipliers :

5.2    Calculate multipliers for the two fractions  

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 2

  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

5.3      Rewrite the two fractions into equivalent fractions

  L. Mult. • L. Num.      (3x+2y) • 2

  ——————————————————  =   ———————————

        L.C.M                 12      

  R. Mult. • R. Num.      z • 3

  ——————————————————  =   —————

        L.C.M              12  

Adding fractions that have a common denominator :

5.4       Adding up the two equivalent fractions  

(3x+2y) • 2 - (z • 3)     6x + 4y - 3z

—————————————————————  =  ————————————

         12                    12      

Final result :

 6x + 4y - 3z

 ————————————

      12    

Answer:

Step 2, he didn't add the values he completed the square with to both sides.

Step-by-step explanation:

When you complete the square, you need to add the values to both sides, not just one.

So when Homer added 49 + 1 or 50 to the left side of the equation, he should've also added 50 to the right side of the equation.

Hence, the equation would now be :

(x-7)^2 + (y+1)^2 = 75

I think it's B

[tex] - 11 \geqslant n + 0 \\ 1. \: - 11 \geqslant n \\ 2. \: n \leqslant - 11 \\ \\ - 11 \geqslant n \\ 1. \: n \leqslant - 11[/tex]

Answer:

The answer is B. Identity property of Addition

Step-by-step explanation:

Answer:

(4, -3)

Step-by-step explanation:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is changed to the opposite sign.

The reflection of the point (x, y) across the x-axis is the point (x, -y).

The reflected point across the x-axis of the original point (4,3) would have the coordinates (4, -3), where the x-coordinate remains the same and the y-coordinate changes sign. Hence correct option b.

When a point is reflected across the x-axis, the y-coordinate changes sign, but the x-coordinate remains the same. The reflection of the point across the x-axis means that the x-coordinate (4) does not change, but the y-coordinate (3) becomes its opposite (-3). Thus, the new coordinates of the reflected point are (4, -3).

Answer:

Step-by-step explanation:

Pythagoream theorem applies.

The long wires are [tex]\sqrt{45^2+30^2}m[/tex] long, or about 54m long.

The short ones are [tex]\sqrt{20^2+30^2}m[/tex], or about 36m long. You will need 4 of each, so it's [tex]4* 54m + 4*36m = 540m[/tex] of wire

Answer:

Interest earned at 3.9 percent rate is $31.2

Interest earned at 2 percent rate is $5.8

Step-by-step explanation:

A = P(1 + rt)

Where 'A' is the amount, 'r' is the rate and 't' is the time in years

When;

P = $1200

r = 3.9%

t = [tex]\frac{8}{12}[/tex] years

Then,

A = $1200(1 + 0.039([tex]\frac{8}{12}[/tex]))

A = $1200 + $31.2 = $1231.2

Interest = Amount - Principal

Interest earned at 3.9 percent rate is $1231.2 - $1200 = $31.2

When;

P = $580

r = 2%

t = [tex]\frac{6}{12}[/tex] years

Then,

A = $580(1 + 0.02([tex]\frac{6}{12}[/tex]))

A = $580 + $5.8 = $585.8

Interest earned = Amount - Principal

Interest earned at 2 percent rate = $585.8 - $580 = $5.8

Thesimple interest, you use the formula I = PRT, with P representing principal, R the annual interest rate in decimal form, and T the time in years. For $1200 at 3.9% over 8 months, the interest is $37.20. For $580 at 2% over 6 months, the interest is $5.80.

The simple interest earned on two separate principals with different interest rates and time periods. To calculate simple interest, we use the formula I = PRT, where I is the interest earned, P is the principal amount, R is the annual interest rate (in decimal form), and T is the time in years. If the time is given in months, we must convert it into years by dividing by 12.

Example 1:
Principal (P) = $1200
Annual Interest Rate (R) = 3.9% = 0.039
Time (T) = 8 months = ({8}{12}) years

Simple Interest (I) = $1200 (times) 0.039 (times) \(frac{8}{12}) = $37.20 to the nearest cent

Example 2:
Principal (P) = $580
Annual Interest Rate (R) = 2% = 0.02
Time (T) = 6 months = ({6}{12}) years

Simple Interest (I) = $580 (times) 0.02 (times) \({6}{12}) = $5.80 to the nearest cent

In conclusion, we have two amounts of simple interest for the different principals, rates, and times provided. To find the total future amount with simple interest, we would add the interest earned to the principal amount.

Answer:

QC=16 this is correct on usa testprep

Step-by-step explanation:

The centroid of a triangle is the point of concurrency of the median lines of

the triangle.

The length of segment [tex]\overline{QC}[/tex] is C) 16

Reasons:

The given parameters are;

Point C = The centroid of ΔPQR

[tex]\overline{CZ}[/tex] = 8

Required:

The length of  segment QC

Solution;

Given that point C is the centroid of the triangle ΔPQR, we have;

[tex]\overline{QC} = \dfrac{2}{3} \times \overline{QZ}[/tex]

[tex]\overline{CZ}= \dfrac{1}{3} \times \overline{QZ}[/tex]

Therefore;

[tex]\overline{CZ}= \dfrac{1}{2} \times \overline{QC}[/tex]

[tex]\overline{QC} = 2 \times \overline{CZ}[/tex]

[tex]\overline{QC} = 2 \times 8 = 16[/tex]

Learn more here:

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Answer:

They distort differences between values.

Step-by-step explanation:

Non-zero axes distort differences between values, but they are not always misleading.

It depends on who is looking at them.

Consider the bar graphs below, showing the change in interest rates over time.

A naïve reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).

However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.

A professional who specializes in interest rates might find the information in the left-hand graph quite useful.

They distort differences between values.

We have given that, a graph

They distort differences between values,

Non-zero axes distort differences between values, but they are not always misleading.

It depends on who is looking at them.

Consider the bar graphs below, showing the change in interest rates over time.

A naïve reader might conclude that interest rates had risen sharply (the zero-axis shows that they have remained steady).

However, a professional who specializes in interest rates might find the information in the left-hand graph quite useful.

To learn more about the graph visit:

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Answer:

[tex]Y=(X-7)/2[/tex]

Step-by-step explanation:

we have

[tex]X=2t+3[/tex] -----> equation A

[tex]Y=t-2[/tex] -----> [tex]t=Y+2[/tex] -----> equation B

Substitute equation B in equation A

[tex]X=2(Y+2)+3[/tex]

[tex]X=2Y+4+3[/tex]

[tex]X=2Y+7[/tex]

solve for Y

[tex]2Y=X-7[/tex]

[tex]Y=(X-7)/2[/tex]

Answer:

B

Step-by-step explanation:

Answer:

The correct option is A.

Step-by-step explanation:

The area of a triangle is

[tex]A=\frac{1}{2}\times base\times height[/tex]

From the given figure it is clear that the base of the triangle STR is 6 ft and the height of the triangle 10 ft. So, the area of triangle STR is

[tex]A=\frac{1}{2}\times 6\times 10[/tex]

[tex]A=3\times 10[/tex]

[tex]A=30[/tex]

The area of triangle STR is 30 square ft. Therefore the correct option is A.

Answer:

Alex walks more miles

Step-by-step explanation:

Answer:

Jenna walks more miles per day

Step-by-step explanation:

i got this answer by doing 12 divided by 5 = 2.4 and 7 divided by 3 = 2.33333333333  and 2.4 is more that 2.33333333333  so Jenna walked futher,

i hope that this answer helped you, pls give me good votes if it did, because im new here and trying to get points.

Answer: $33

Step-by-step explanation: Divide 27/9 which is $3

-so you pay $3 for each pack

-then to find how much you need to pay for 11 packs you just multiply 11*3=33

So you work for 2 hours and each hour you get 7.50

So you do 2*7.50 = 15$

Then you do the windows

3 hours and every hour you earn 6.25

3*6.25=18.75$

Now you add them

15+18.75= 33.75$ but if you want an average then around 34$

the answer is 2yx^3/(2y^2)^3

Answer:

It extends the time of the collision

Step-by-step explanation:

The correct option is : It extends the time of the collision.

The padding helmets have cushions inside it that moves inwards when a ball hits the helmets.

When the collision occurs, the time will increase and less force will be exerted on helmet that is why the impact of the collision will be less.

Answer:

A. It extends the time of the collision.

Step-by-step explanation:

the picture

Step-by-step explanation:

[tex]\text{If}\ 10+\dfrac{6}{2}+3=10+3+3=16\\\\\text{If}\ \dfrac{10+6}{2+3}=\dfrac{16}{5}[/tex]

To simplify 10+6/2+3, we first perform the division operation (6 ÷ 2 = 3), and then carry out the addition operations in order (10 + 3 + 3), giving us a final result of 16.

To simplify 10+6/2+3, we have to follow the order of operations as guided by the mnemonic PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the given expression, there are no parenthesis, exponents, so we proceed by carrying out division and then addition.

Step 1: Perform the division operation 6 ÷ 2 = 3.

Step 2: Simplify the expression by performing the addition operations in the order from left to right. So, 10 + 3 (from division) + 3= 16.

Therefore, the simplified form of the original expression is 16.

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ANSWER

(1,-3)

EXPLANATION

The given equations are:

y = 5x - 8

y = 4x - 7

We equate the two equations to get:

5x - 8=4x - 7

Group similar terms:

5x - 4x=-7+8

Simplify bottom sides

x=1

Put x=-15 into the first equation:

y=5(1)-8

y=-3

(1,-3)

The solution is (1,-3)

ANSWER

See explanation

EXPLANATION

The point (3,-6) is the fourth quadrant.

In this quadrant only the cosine ratio and the secant ratio are positive.

The remaining four trigonometric ratios are negative.

The diagram is shown in the attachment.

We use the Pythagoras Theorem to find the hypotenuse, h.

[tex] {h}^{2} = {6}^{2} + {3}^{2} [/tex]

[tex] {h}^{2} = 36 + 9[/tex]

[tex] {h}^{2} = 45[/tex]

[tex]h = \sqrt{45} [/tex]

[tex]h = 3 \sqrt{5} [/tex]

[tex] \sin( \theta) = - \frac{opp}{hyp} [/tex]

[tex]\sin( \theta) = - \frac{6}{3 \sqrt{5} } [/tex]

[tex]\sin( \theta) = - \frac{2 \sqrt{5} }{ 5 } [/tex]

[tex]\sin( \theta) = - \frac{2}{ \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{adj}{hyp} [/tex]

[tex]\ cos(\theta) = \frac{3}{3 \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{1}{ \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{ \sqrt{5} }{5} [/tex]

[tex]\tan(\theta)= - \frac{opp}{hyp} [/tex]

[tex]\tan(\theta)= - \frac{6}{3} = - 2[/tex]

[tex]\csc(\theta)= - \frac{hyp}{opp} [/tex]

[tex]\csc(\theta)= - \frac{3 \sqrt{5} }{6} = - \frac{\sqrt{5} }{2} [/tex]

[tex] \sec( \theta) = \frac{hyp}{adj} [/tex]

[tex]\sec( \theta) = \frac{3 \sqrt{5} }{3} = \sqrt{5} [/tex]

[tex]\cot( \theta) = - \frac{adj}{opp} [/tex]

[tex]\cot( \theta) = - \frac{3}{6} = - \frac{1}{2}[/tex]

Answer:

x=1/2, x=-3

Step-by-step explanation:

2x^2+5x-3 = 0

(2x^2+6x)+(-x-3) = 0

2x(x+3)+-1(x+3) = 0

(2x-1)(x+3)=0

2x-1=0, x+3=0

x=1/2, x=-3

For this case we have by definition that:

[tex](f * g) (x) = f (x) * g (x)[/tex]

In this case we must find[tex](t * s) (x),[/tex] so:

([tex](t * s) (x) = t (x) * s (x) = (4x ^ 2-x + 3) * (x-7) =[/tex]

We must apply distributive property that states that:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

So:

[tex](4x ^ 2-x + 3) * (x-7) = 4x ^ 3-28x ^ 2-x ^ 2 + 7x + 3x-21 = 4x ^ 3-29x ^ 2 + 10x-21[/tex]

Answer:

[tex]4x^3-29x^2+10x-21[/tex]