Dan Stocked up on batteries. He Brought 10 packages of AA and AAA batteries for a total of 72 batteries. The AA batteries are sold in packages of 6, and the AAA batteries are sold in packages of 8. Write a system of equations that can be solved to find how many packages of each type of battery Dan bought. Remember to define your variables.

Answer:

x=0 , y=4

Step-by-step explanation:

3x - 3y = -12        - eq1

4x + 3y = 12        - eq 2

Add eq 1 and 2

3x - 3y + 4x +3y = -12 + 12

7x = 0

x = 0

By substituting the value of x in  eq 2

4x + 3y = 12

4(0) + 3y = 12

3y = 12

y = 12 / 3

y = 4

Answer:

(x,y)=(24,-28)

Step-by-step explanation:

1. Multiply both sides by -1

3x+3y=-12

-4x-3y-=-12

2. Elimnate one variable by adding the equations

-x=-24

3. Change the signs

x=24

4. Susbstitue the value of x in the equation 3x+3y=-12

3 x 24 + 3 y = -12

y=-28

5. Check the solution by plugging in the values.

(x,y)=(24,-28)

Answer:

solution,

[tex]a. \: x(x + 2) \\ \: \: = x \times x + 2 \times x \\ \: \: = {x}^{2} + 2x[/tex]

[tex]b . \: x(2x - 5) \\ \: = x \times 2x - x \times 5 \\ \: \: = 2 {x}^{2} - 5x[/tex]

[tex]c. \: 2x(3x + 4) \\ \: = 2x \times 3x + 2x \times 4 \\ \: \: = 6 {x}^{2} + 8x[/tex]

[tex]d. \: 6x(x - 2) \\ \: \: = 6x \times x - 6x \times 2 \\ \: \: = 6 {x}^{2} - 12x[/tex]

Hope this helps...

Good luck on your assignment..

Step-by-step explanation:

if each the bonus is shared equally each will get 420

if 40% is shared by managers each manager will get 560

if 7 sales persons share 60% each will get 360

therefore Peter salesperson will get 360

but he thinks he will get 336 because if 420 is 125% that is including his extra 25% then hundred percent of the 420 is 336 which is not what he will get there for Janet is correct

Answer:

the ratio would be 1:4

Step-by-step explanation:

ratio of those who has nuts:

1/5

ratio of those who dont:

1-1/5=4/5

one against another:

1/5 : 4/5 = 1:4 = with : without

Answer:

730 trains would be needed  to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required

Step-by-step explanation:

Number of carriages in 1 train = 15

Number of seats in 1 carriage = 32

Number of seats in 15 carriages =[tex]32 \times 15 =480[/tex]

So, Number of seats in 1 train = 480

Number of trains needed  to seat 350,000 passengers=[tex]\frac{350000}{480}=730[/tex]

Number of carriage in 1 train = 15

Number of carriage in 730 trains = [tex]15 \times 730=10950[/tex]

Number of seats in 1 carriage = 32

Number of seats in 10950 carriage =[tex]32 \times 10950=350400[/tex]

Hence 730 trains would be needed  to seat 350,000 passengers , 10950 carriages would be needed and 350400 seats would be required

Answer:

Step-by-step explanation:

g(x) = radical 25/9x would be clearer if written as g(x) = radical (25/9)x.  Note that radical (25/9) = (5/3).

The graph of g(x) = radical (25/9)x would have the same shape as that of g(x) = radical x EXCEPT that it would be stretched vertically by a factor of (5/3).

Answer: g(x) = radical 25/9x would be clearer if written as g(x) = radical (25/9)x. Note that radical (25/9) = (5/3).

The graph of g(x) = radical (25/9)x would have the same shape as that of g(x) = radical x EXCEPT that it would be stretched vertically by a factor of (5/3).

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

The surface area of the box

= x^2 + 4hx  where x = a side of the square base and h is the height.

So x^2 + 4hx = 8

The volume of the box

V = x^2h

From the first equation we solve for h

4hx = 8 - x^2

h = (8 - x^2) / 4x

Now we substitute for h in the formula for the volume:

V = x^2 * (8 - x^2) / 4x

V =  8x^2 - x^4 / 4x

V =  2x - 0.25x^3

Finding the derivative:

V' = 2 - 0.75x^2 =  0  for max/mimn values

x^2 = 2/ 0.75 = 2.667

x = 1.633.

So the  length and width of the base is 1.633 m and the height

= ( 8 - 2.667) / (4*1.633)

= 0.816 m

The maximum volume =  0.816 *  2.667 =  2.177 m^2.

The answers are correct to the nearest thousandth.

Answer:

Check it below

Step-by-step explanation:

According to GHG platform India, in the period between [2011-2015] there was a growth of emissions in tons of Carbon Dioxide. As it follows below.

The Energy sector is the segment that contributes the most with this, followed by the Agricultural and the Industries and the Waste.

Answer:

D

Step-by-step explanation:

Given

[tex]R_{y-axis}[/tex] ￮ [tex]R_{y=x}[/tex] : (2, 3 )

Then the order of reflections is from right to left, that is

Under a reflection in the line y = x

a point (x, y ) → (y, x ) , thus

(2, 3 ) → (3, 2 )

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , thus

(3, 2 ) → (- 3, 2 ) → D

Answer:

∠ ABE = 46°

Step-by-step explanation:

Since BE bisects ∠ ABC , then

∠ EBC = ∠ ABE, substitute values

4x - 6 = 2x + 20 ( subtract 2x from both sides )

2x - 6 = 20 ( add 6 to both sides )

2x = 26 ( divide both sides by 2 )

x = 13

Thus

∠ ABE = 2x + 20 = 2(13) + 20 = 26 + 20 = 46°

Answer:

16

Step-by-step explanation:

Apply PEMDAS:

Solve the exponent, multiply from left to right, and then subtract and add from left to right.

[tex]3-2^2+4*3+5\\\\3-4+4*3+5\\\\3-4+12+5\\\\-1+12+5\\\\11+5\\\\\boxed{16}[/tex]

Answer: 16

Step-by-step explanation:

The important thing to remember here is the Order of Operations

The Order of Operations states that first solve Parentheses, then Exponents, then Multiplication and Division, then Addition and Subtraction.

There are no parentheses.

Exponents: 3 - 4+4*3+5

Multiplication and Division: 3 - 4 + 12 + 5

Addition and Subtraction:

-1+12+5

11+5

16

Hope it helps <3

Answer:

≈ 10.7 ft

Step-by-step explanation:

We have 2 secants to a circle from an external point.

The product of the measure of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant.

let the internal part of the right secant be x , then

6(6 + x) = 4(4 + 12) = 4 × 16 = 64 ( divide both sides by 6 )

6 + x ≈ 10.7 ( subtract 6 from both sides )

x ≈ 4.7

length of pass = 6 + 4.7 = 10.7

Answer:

1st Graph

Step-by-step explanation:

Simply use a graphing calculator and plug in the systems of equations into the graph. We then choose the closest-resemblanced graph.

Answer:

Its the first graph

Step-by-step explanation:

got it right on the test

Answer:

[tex]t = 2.86 \: s[/tex]

The ball remains in the air for 2.86 seconds.

Step-by-step explanation:

A baseball is hit into the air, and its height above the ground is described by the function

[tex]H(t) = -16t^2 + 45t + 2[/tex]

Where H(t) represents the height of the ball t seconds after it is hit.

The ball remains in the air before it hits the ground.

When the ball hits the ground,

[tex]H(t) = 0[/tex]

So,

[tex]0 = -16t^2 + 45t + 2[/tex]

The equation may be solved using the quadratic formula.

[tex]$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

Where

[tex]a = -16 \\\\b = 45 \\\\c = 2 \\\\[/tex]

So,

[tex]t=\frac{-(45)\pm\sqrt{(45)^2-4(-16)(2)}}{2(-16)} \\\\t=\frac{-45\pm\sqrt{(2025 - (-128)}}{-32} \\\\t=\frac{-45\pm\sqrt{(2153}}{-32} \\\\t=\frac{-45\pm 46.4004}{-32} \\\\t=\frac{-45 + 46.4004}{-32} \: and \: t=\frac{-45 - 46.4004}{-32}\\\\t= -0.04 \: and \: t = 2.86 \\\\[/tex]

Since the time cannot be negative, discard the negative value and accept the positive value

[tex]t = 2.86 \: s[/tex]

Therefore, the ball remains in the air for 2.86 seconds.

Answer:

64

Step-by-step explanation:

let given points be

(x1,y1)=(-3,-3)

and(x2,y2)=(3,1)

equation of given line ,

(y-y1)= ((y2-y1)/(x2-x1))×(x-x1)

therefore, 2x-3y+3=0.........(i)

comparing (i ) with ax+by+c=0 we get

a=2

b= -3

c=3

then the line parallel to (i) is

ax+by+k=0 where k = -bc

that is, 2x-3y+9=0 is the required equation

Answer:

19. y = 2/3x - 10/3

20. y = -3/2x - 4

Step-by-step explanation:

First off, we need to find the equation of the line shown. There are two coordinates given. The slope of the line is (1 - -3) / (3 - -3) = 4 / 6 = 2/3. The line obviously intersects the y-axis at -1, so the equation of the line is y = 2/3x - 1.

19. If a line were to be parallel to the given line, the line would have to have a slope of 2/3. So, we have y = 2/3x + b.

To solve for b, all you need to do is substitute the coordinates given, (2, -2), and solve.

-2 = (2/3) * 2 + b

b + 4/3 = -2

b = -6/3 - 4/3

b = -10/3.

So, the equation of the line is y = 2/3x - 10/3.

20. If a line were to be perpendicular to the given line, the line would have a slope that is the negative reciprocal of the given line's slope. The slope would be -3/2. So, we have y = -3/2x + b.

To solve for b, once again, put in the given coordinates, (-4, 2), and solve.

2 = (-3/2) * (-4) + b

b + 6 = 2

b = -4

So, the equation of the line is y = -3/2x - 4.

Hope this helps!

Answer:

16

Step-by-step explanation:

64 = 4x

64/4 = 4x/4

16 = x

Answer:

X=8.8 and Y=1

Step-by-step explanation:

Answer:

Correct answer is

[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]

Step-by-step explanation:

Let us rephrase the given statement mathematically.

We are given the fractions as:

[tex]\dfrac{a-3}{7}[/tex]

to be divided by:

[tex]\dfrac{3-a}{21}[/tex]

To find:

[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]

Now, let us have a look at the division rule in fractions:

[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]

is equivalent to

[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]

In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]

Now solving the given fraction by applying above rules:

[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]

[tex]\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3[/tex]

So, correct answer is:

[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]

Answer:

d on edg

Step-by-step explanation:

taking test rn

Answer:

The function for the outside temperature is represented by [tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex], where t is measured in hours.

Step-by-step explanation:

Since outside temperature can be modelled as a sinusoidal function, the period is of 24 hours and amplitude of temperature and average temperature are, respectively:

Amplitude

[tex]A = \frac{100\º-70\º}{2}[/tex]

[tex]A = 15\º[/tex]

Mean temperature

[tex]\bar T = \frac{70\º+100\º}{2}[/tex]

[tex]\bar T = 85\º[/tex]

Given that average temperature occurs six hours after the lowest temperature is registered. The temperature function is expressed as:

[tex]T(t) = \bar T + A \cdot \sin \left[2\pi\cdot\frac{t-6\,h}{\tau} \right][/tex]

Where:

[tex]\bar T[/tex] - Mean temperature, measured in degrees.

[tex]A[/tex] - Amplitude, measured in degrees.

[tex]\tau[/tex] - Daily period, measured in hours.

[tex]t[/tex] - Time, measured in hours. (where t = 0 corresponds with 5 AM).

If [tex]\bar T = 85\º[/tex], [tex]A = 15\º[/tex] and [tex]\tau = 24\,h[/tex], the resulting function for the outside temperature is:

[tex]T(t) = 85\º + 15\º \cdot \sin \left[\frac{t-6\,h}{24\,h} \right][/tex]

Answer:

11

Step-by-step explanation:

3|−5| − 2|−2|

Absolute value means take the non-negative value

3 * 5 -2 * 2

15 - 4

11

Answer:

( x+1) (x+3) (x+4)

Answer:

(a)Exponential

(b)[tex]P(t)=4.70(1.0136)^t[/tex]

(c)The price of milk next year will be: $4.76

(d)5 years

Step-by-step explanation:

The price of a gallon of milk has been rising about 1.36% per year since 2000.

(a)Since the price grows by a percentage (or constant factor) each year, an exponential function would be best to model the scenario.

(b)The exponential growth model is given as:

[tex]P(t)=P_0(1+r)^t$ where:\\P_0$=Initial Price\\r=Growth factor\\t=time (in years, for this case)[/tex]

The independent variable in the function is t. This represents the number of years since 2000.

(c)

[tex]I$nitial Price, P_0=\$4.70\\r=1.36\%=0.0136\\P(t)=4.70(1+0.0136)^t\\\\P(t)=4.70(1.0136)^t[/tex]

Therefore, the price of milk next year will be:

[tex]P(1)=4.70(1.0136)^1=\$4.76[/tex]

(d)We want to determine how long it will take for the price to top $5.

P(t)=$5

[tex]5=4.70(1.0136)^t\\$Divide both sides by 4.7$\\(1.0136)^t=\frac{5}{4.7} \\$Change to logarithm form\\t=Log_{1.0136}\frac{5}{4.7}\\t=4.58[/tex]

Therefore, in exactly 4.58 years, the milk price would be $5. Therefore, by the 5th year, the milk price would top $5.

Answer:

9 cm

Step-by-step explanation:

c^2=81

Take the square root of both sides.

The square root of c^2 is c.

The square root of 81 is 9.

c=9

Answer:

C = 9 centimeters

Step-by-step explanation:

First, look at the area of a square, which formula is c^2 or in standard format - s^2. Thus, we can say, c^2 = 81. Then, we can simplify, and put c = √81. Since 81 is a perfect square, 9 *  9 = 81. Thus the answer is 9 centimeters.

Answer:

a . See attachment

b. because we will find the distance from the bottom of the ladder to the base of the building.

c. sin 60 = opposite side / hypotenuse

d.sin 60 = x / 10

e .  8.66 ft =x

f. see attachment

i. cos 60° = adjacent side / hypotenuse

Step-by-step explanation:

a . See attachment

b. because cos 60° = adjacent side / hypotenuse, the hypotenuse is equal to the length of the ladder (10), and the adjacent side that we will find is the distance from the bottom of the ladder to the base of the building. not the height that the ladder reaches .

c. sin 60 = opposite side / hypotenuse

Because we will find the opposite side which is the height that the ladder reaches.

d.sin 60 = x / 10

e .  

0.866025403 = x/10

10 (0.866025403) =x

8.66 ft =x

f. see attachment

i. cos 60° = adjacent side / hypotenuse

Because we will find the adjacent side which is the distance from the bottom of the ladder to the base of the building.

Answer:

Step-by-step explanation:

5*2=10, 10*2=20...

it is a geometric progression with ratio= 2

a11=a10*2=2560* 2=5120

Answer:

y = -4

Step-by-step explanation:

5.1y = –0.3y – 21.6

5.1y + 0.3y = -21.6

5.4y = -21.6

y = -4

Answer:

y=  -4

Step-by-step explanation:

Solve this equation with a variable term on both sides.

5.1y = –0.3y – 21.6

What is the solution?

y =  -4

Answer:

Probability of blue or red = 3/10

Step-by-step explanation:

4 are black 10 are blue, 3 are red, 6 are green , 6 are blue and red and 1 .

Total = 30

Probability of having a blue = 6/30

Probability of having a blue= 1/5

Probability of a red = 3/30

Probability of a red= 1/10

Probability of a blue or a red=

Probability of blue + probability of red

= 6/30 + 3/30

= 9/30

= 3/10