if my friend and i went to get ice cream, I have $30 and each ice cream is $5. What equation would help me solve this?

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.  

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:

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:

[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]

Answer:

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

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

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.

[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:

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:

[tex]\large\boxed{3\div\dfrac{1}{5}}[/tex]

Step-by-step explanation:

Each 1 was divided into five equal parts. Each of these parts is 1/5. We calculate how many times 1/5 is in 3.

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]

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:

$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

Final answer:

The polynomial ₓ2y² has 1 term.

Explanation:

A polynomial is an algebraic expression consisting of terms that are variables raised to non-negative integer powers, multiplied by coefficients. The number of terms in a polynomial is determined by counting the number of distinct combinations of variables and exponents in the expression.

In the given polynomial, ₓ2y², there is only one term because there is only one combination of variables (x and y) raised to their respective exponents (2 and 2).

Therefore, the polynomial ₓ2y²has 1 term.

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:

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:

    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

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 ..

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:

What triangle below?

Step-by-step explanation:

Im confused sorry

Answer:

㏒b^bn = n

Step-by-step explanation:

Answer:

㏒b^bn = n

Step-by-step explanation:

[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:

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!!!

[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:

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.

Answer:

1. x=4 or x=10

2.  x=-10 or x=10

No equivalent

Step-by-step explanation:

1. |x-3|=7 and x-3=7

Absoulte rules.

x-3=-7 and x-3=7

Add 3 both sides.

x-3+3=-7+3

Simplify.

-7+3=-4

x=-4

x-3=7

Add by 3 both sides.

x-3+3=7+3=10

x=10

X=-4, and X=10 is the correct answer.

________________________________

2. |x|-3=7

Add by 3 both sides.

|x|-3+3=7+3

Simplify.

7+3=10

X=10

X=-10 and X=10 is the correct answer.

______________________________

The two equations |x-3|=7 and |x|-3=7, are solved differently. For |x-3|=7, the possible solutions are x=10 and x=-4. For |x|-3=7, the possible solutions are x=10 and x=-10.

The two equations you're looking at are: |x-3|=7 and |x|-3=7. They look very similar but they're solved differently because absolute value symbols affect all values inside them together.

For the first equation, |x-3|=7, we solve this by considering the two situations, x-3 = 7 and x-3 = -7. Solve each of these two equations separately, so you get x = 10 and x = -4.

For the second equation, |x|-3=7, firstly, we need to eliminate '-3' from the right-hand side by adding 3 to both sides, leading to |x| = 10. This is then broken down into the two possible situations as before: x = 10 and x = -10.

https://brainly.com/question/33804932

#SPJ2

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]

Answer:

y + 12 = 3(x - 2)

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are. Since both lines contain have to have similar rate of changes [slopes], we do not go any further.

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