Bailey brought a twin pack of gum for $2, this is 50 cents less than 2/3 the
cost of a triple pack of gum. What is the price of a triple pack of gum?

Let x represent a twin pack of gum

Let y represent a triple pack of gum

Answer:

Option D is correct answer.

Step-by-step explanation:

We are given the system of equations:

[tex]x+y=4\\x-y=-6[/tex]

Solving the system of equations to find values of x and y

Let:

[tex]x+y=4--eq(1)\\x-y=-6--eq(2)[/tex]

Adding both equations to find value of x

[tex]x+y=4\\x-y=-6\\------\\2x=-2\\x=\frac{-2}{2}\\x=-1[/tex]

So, we get value of x: x=-1

Now, putting value of x: x=-1 into equation 1 to find value of y

[tex]x+y=4\\Putx=-1\\-1+y=4\\y=4+1\\y=5[/tex]

So, we get value of y: y=5

The ordered pair will be: (-1,5)

So, Option D: The ordered pair(-1,5) is a a solution to the system of equations because it makes both equations true is correct choice.

Checking:

Put x=-1 and y=5 in equation 1

[tex]x+y=4\\-1+5=4\\4=4\:True[/tex]

Put x=-1 and y=5 in equation 2

[tex]x-y=-6-1-5=-6\\-6=-6\:\:\:True[/tex]

So, both equations are true.

Therefore, Option D is correct answer.

Given:

The base of 40-foot ladder is 8 feet from the wall.

To find:

How high is the ladder on the wall (round to the nearest foot).

Solution:

Ladder makes a right angle triangle with wall and ground.

We have,

Length of ladder (hypotenuse)= 40 foot

Base = 8 foot

We need to find the perpendicular to get the height of the ladder on the wall.

Let h be the height of the ladder on the wall.

According to the Pythagoras theorem,

[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]

[tex](40)^2=(8)^2+(h)^2[/tex]

[tex]1600=64+h^2[/tex]

[tex]1600-64=h^2[/tex]

[tex]1536=h^2[/tex]

Taking square root on both sides.

[tex]\pm \sqrt{1536}=h[/tex]

[tex]\pm 39.1918358=h[/tex]

Height cannot be negative. Round to the nearest foot.

[tex]h\approx 39[/tex]

Therefore, the height of the ladder on the wall is 39 foot.

Answer:

(4x2 - 2x) - (-5x2 - 8x)

= 4x2 - 2x + 5x2 + 8x.

= 4x2 + 5x2 - 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

Answer: 3x(3x + 2)

Step-by-step explanation:

Answer:

97

Step-by-step explanation:

you square 72 and 65 and add them together then take the square root of your answer aka 97 and thats the hypotenuse

Answer:

(0,-2)

Step-by-step explanation:

Answer:

-56=8(x-8)

-56=8x-64 +64

8=8x :8

1=x

Step-by-step explanation:

prove me wrong

Answer:

x=1

Step-by-step explanation:

You would do distributive property and multiply 8 by the x and -8

-56=8x-64

The add 64 on both sides

8=8x

divide 8

x=1

Answer:

AA similarity

Step-by-step explanation:

Your question is not well presented.

See attachment

Given

Triangles ABC and DBE

Required

Which postulate supports the similarities of ABC and DBE

At the first transformation (180 degrees rotation) both triangles maintain SSS and AAA relationships. i.e Side-Side-Side and Angle-Angle-Angle

This is so because rotations do not alter the side lengths; neither does it alter the angles.

When the second transformation (dilation) takes place, the lengths of both triangles ABC and DBE become different because dilation alters side lengths.

However, angle measurements remain unaltered.

Hence, AAA similarity answers the question

Answer:

x=2

Step-by-step explanation:

17x-8=11x+4

Add 8 to both sides:

17x=11x+12

Subtract 11 x from both sides:

6x=12

Divide both sides by 6:

x=2

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{2}[/tex] such that the two triangles are congruent as per the Side-Side-Side Congruence Postulate.

According to Side-Side-Side postulate, if the three sides of one the two triangles are congruent to each other then the two triangles are congruent.

Congruent triangles have the same shape as well as the same size.

[tex]\boldsymbol{\bigtriangleup MPQ\cong \bigtriangleup NPQ}[/tex]

This implies [tex]PM,PN[/tex] are same in length.

[tex]17x-8=11x+4[/tex]

       [tex]6x=12[/tex]

         [tex]x=2[/tex]

So, value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{2}[/tex].

Find out more information about Side-Side-Side postulate here:

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Answer:

-4 5/12

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4.41666666667

Answer:

14

Step-by-step explanation:

If he had 14 then he gave away 6, he'd have 8. 8 plus 4 is 12. He had 14 before giving any away.

Answer:

39

Step-by-step explanation:

-133/-7=19+15=39

check:39-15=19

19x(-7)=-133

Answer:

The equation of the straight line is  x - 2y +6 =0

Step-by-step explanation:

Explanation:-

Given a point ( 2, 4) and slope m =  [tex]\frac{1}{2}[/tex]

The equation of the straight line passing through the point and having slope 'm'

          y - y₁ = m ( x - x₁)

           y - 4 = [tex]\frac{1}{2}[/tex] ( x - 2)

          2( y -4) = ( x-2)

          2 y - 8 = x -2

          x - 2 y - 2 + 8 =0

          x - 2y + 6 =0

The equation of the straight line is  x - 2y +6 =0

The answer is:

y = 1/2x + 5

Work/explanation:

Since I have a point and the slope, I will write the equation in point slope form.

Point slope is

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

where m = slope and (x₁, y₁) is a point on the line

Plug in the data

[tex]\sf{y-4=\dfrac{1}{2}(x-2)}[/tex]

Now let's simplify to slope intercept

                    [tex]\large\begin{gathered}\sf{y-4=\dfrac{1}{2}x+1}\\\sf{y=\dfrac{1}{2}x+1+4}\\\sf{y=\dfrac{1}{2}x+5}\end{gathered}[/tex]

Answer:

[tex]m=-\frac{2}{5}[/tex]

Step-by-step explanation:

Answer: 55

Step-by-step explanation:

67

Answer:

(-2,0)

Step-by-step explanation:

When finding the x intercept, substitute 0 for Y. -20/10=-2.

I hope this helps

Answer:

The x-intercepts of that is (-2,0).

Answer: 3,750 miles

Step-by-step explanation:

Route takes him 125 miles each way so in a day he travels:

= 125 + 125

= 250 miles

He made 15 roundtrips so total miles is:

= 15 * 250

= 3,750 miles

Answer:

9.9

Step-by-step explanation:

Answer: (9x^2)^2 -1^2

Step-by-step explanation:

Jake rewrite the expression as,

⇒ (3x - 1) (3x + 1) (9x² + 1)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 81x⁴ - 1

And, Jake rewrites the expression as a difference of squares so he can factor it.

Now, We can rewrite the expression as;

⇒ 81x⁴ - 1

⇒ (9x²)² - 1²

⇒ (9x² - 1) (9x² + 1)

⇒ ((3x)² - 1²) (9x² + 1)

⇒ (3x - 1) (3x + 1) (9x² + 1)

Learn more about the mathematical expression visit:

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Answer:

650/100 X 3 = 19.5

19.50 X 4 = 78

$78

The required expression model is given as x + 8 / 6. Option B is correct.

Given that,
To determine the expression represents the calculation the sum of x and 8 is divided by 6

The equation model has defined as the model of the given situation in the form of an equation using variables and constants.

here,
According to the question,
The sum of x and 8 = x + 8
divided by 6
= x + 8 / 6

Thus, the required expression model is given as x + 8 / 6. Option B is correct.

Learn more about models here:
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Answer:

B. 13

Step-by-step explanation:

replace variables

5(5-3)+3

distribute

5(2)+3

multiply

10+3

add

13

Answer:

m (m + n) - n

= 5 (5+(-3)) - (-3)

= 5 (5-3) + 3

= 5 x 2 + 3

= 10+3

= 13

Answer:

Gas exchange takes place in the millions of alveolar in the lungs and the capillaries that envelop them. As shown below, inhaled oxygen moves from the alveolar to the blood in the capillaries, and carbon dioxide moves from the blood in the capillaries to the air in the alveolar.

Step-by-step explanation:

Gas exchange takes place in the millions of alveolar in the lungs and the capillaries that envelop them. As shown below, inhaled oxygen moves from the alveolar to the blood in the capillaries, and carbon dioxide moves from the blood in the capillaries to the air in the alveolar.

Answer:

hope this helps ! <33

Step-by-step explanation:

Gas exchange takes place in the millions of alveoli in the lungs and the capillaries that envelop them. Inhaled oxygen moves from the alveoli to the blood in the capillaries, and carbon dioxide moves from the blood in the capillaries to the air in the alveoli.

Answer:

ll

Step-by-step explanation:

ll

Answer:

20.65%

Step-by-step explanation:

[tex] \frac{19}{92} \\ \\ = \frac{19 \times 100}{92} \% \\ \\ = \frac{1900}{92} \% \\ \\ = 20.6521739 \%\\ \\ = 20.65\%[/tex]

Answer:

(168,12)

Step-by-step explanation:

Substitute x = 10y+48 in the first equation.

[tex]10y + 48 + y = 180 \\ 11y = 180 - 48 \\ 11y = 132 \\ y = \frac{132}{11} \\ y = 12[/tex]

We have got the y-value. Our next goal is to find the x-value by substituting y-value in any given equations.

For me, I will be substituting y = 12 in the first equation.

[tex]x + 12 = 180 \\ x = 180 - 12 \\ x = 168[/tex]

Answer Check

Substitute both x-value and y-value in both equations.

[tex]168 + 12 = 180 \\ 180 = 180[/tex]

Our first equation is true for both values.

[tex]168 = 10(12) + 48 \\ 168 = 120 + 48 \\ 168 = 168[/tex]

Our second equation is true for both values.

Thus, the answer is (168, 12)

Answer:

Step-by-step explanation:

Here you go mate

step 1

x^2+5x-14=0  equation/Question

step 2

x^2+5x-14=0  factor by setting them equal to zero

(x-2)(x+7)=0

answer

x=2 or x=-7

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Fixed costs= $7,900

Unitary cost per sandwich= $1.7

Selling price per unit= $7.75

To calculate the break-even point in units and dollars, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 7,900 / (7.75 - 1.7)

Break-even point in units= 1,306 sandwiches

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 7,900 / (6.05 / 7.75)

Break-even point (dollars)= $10,120