Situation 1: Two students, Theo and Lance, each have some chocolates. They know that
they have the same number of chocolates. Theo has four full bags of chocolates and five
loose chocolates. Lance has two full bags of chocolates and twenty-nine loose
chocolates.
Determine the number of chocolates in a bag. Determine the number of chocolates each
child has.

Answer:

D.) u^2 - u-6 = 0 where u = (x-4)

Step-by-step explanation:

Answer: D

Step-by-step explanation:

edge 23

Answer:

a- 5 x 5

b- 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

c- 9 x 9 x 9 x 9 x 9

Step-by-step explanation:

the index represents how many times the number is to be multiplied.

5² = 5 x 5 = 25

6⁸ = 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6 = 1679616

9⁵ = 9 x 9 x 9 x 9 x 9 = 59049

（＾▽＾）

Answer:

[tex]x \leqslant 2[/tex]

Step-by-step explanation:

The point is shaded which means its is equal to and since the arrow goes to the left it is less than. Therefore x is less than or equal to 2

Answer:

x = 5

Step-by-step explanation:

3/5x = 1/2x + 1/2

collect like terms =

3/5x - 1/2x = 1/2

6x - 5x/10 =

x/10 = 1/2

2x = 10

x = 5

Hey there! I'm happy to help!

Let's represent our number of quarters with q and our dimes with d. We know that each q has a value of 0.25, and each d has a value of 0.1. This means that 0.25q+0.1d=1.85. We also know that q+d=11 as there are 11 total coins.

Here is our system of equations.

0.25q+0.1d=1.85

q+d=11

We are asked to solve with elimination. To do this, we need combine the equations to cancel out a variable to solve for the other. We have 1d on the bottom. Let's multiply the entire top equation by -10 to get a -1d on the top so we can do this.

-2.5q-d=-18.5

q+d=11

We combine the equations.

-1.5q=-7.5

We divide both sides by -1.5

q=5

Since there are 11 coins in total, this means that there are 5 quarters and 6 dimes.

Have a wonderful day!

Answer:

hi......

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Answer:

The correct answer is x = -2.

Step-by-step explanation:

To solve this equation, we must remember that it is our end goal to get the variable x alone on one side of the equation.

To do this, our first step should be to add 12 to both sides of the equation to cancel the -12 on the right side.  This is modeled below:

-14 + 12 = x - 12 + 12

If we add together the like terms to simplify, we get:

-2 =x

This is our answer. To check that our answer is correct, we can plug in the value we obtained for x back into the original equation.

-14 = x - 12

-14 = -2 - 12

-14 = -14

Since plugging in our value for x yielded a true statement, we can conclude that our answer is correct.

Hope this helps!

[tex]\circ\tt\:(a+b)(a^2-ab+b^2)[/tex]

[tex]\circ\tt\:a(a^2-ab+b^2)+b(a^2-ab+b^2)[/tex]

[tex]\circ\tt\:(a^3-a^2b+ab^2)+(a^2b-ab^2+b^3)[/tex]

[tex]\circ\tt\:a^3+(a^2b-a^2b)+(ab^2-ab^2)+b^3[/tex]

[tex]\circ\tt\:a^3+0+0+b^3[/tex]

[tex]\bigstar\:\boxed{\bf{\pink{a^3+b^3} }}[/tex]

Answer:

6 times as great

Step-by-step explanation:

8*10 to the power of 5

8*10 to the power of -1

Answer:

10^6

Step-by-step explanation:

● 8×10^5

● 8 × 10^(-1)

Divide the the first number by the second one

● 8×10^5/ 8×10^(-1) = 10^(5-(-1)) = 10^6

So 8×10^5 is greater 10^6 times than 8×10^(-1)

Answer:  see proof below

Step-by-step explanation:

Use the Sum/Difference Identity: tan (A + B) = (tanA + tanB)/(*1 - tanA · tanB)

Scratchwork:

tan (50) = tan (40 + 10)

             [tex]= \dfrac{\tan 40+\tan 10}{1-\tan 40\cdot \tan 10}[/tex]

tan 50 (1 - tan 40 · tan 10) = tan 40 + tan 10

tan 50 - tan 50 · tan 40 · tan 10 = tan 40 + tan 10

tan 50 = tan 40 + tan 10 + tan 50 · tan 40 · tan 10

Use the Reciprocal Identity: cot A = 1/ tan --> cot A · tan A = 1

Proof LHS → RHS

LHS:                           tan 50    - tan 40

Substitute tan 50:     tan 40 + tan 10 + (tan 50 · tan 40) · tan 10     - tan 40

Simplify:                     tan 10 + (tan 50 · tan 40) · tan 10

Reciprocal Identity:   tan 10 + tan 10

Simplify:                    2 tan 10

LHS = RHS:  2 tan 10 = 2 tan 10    [tex]\checkmark[/tex]

Answer: for x=-2

y+6(-2)=11

y+(-12)=11

y=11+12

y=23

    for x=0

y+(6*0)=11

y=11

    for x=4

y+6(4)=11

y+24=11

y=11-24

y= -13

Step)-by-step explanation:

you just remplace x with his value and solve y

Answer:

B(-5,5).

Step-by-step explanation:

It is given that midpoint of AB is M (-6,1).  

Coordinates of A are (-7,-3 ).

We need to find the coordinates of point B.

Let coordinates of point B are (a,b).

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

Midpoint of AB is

[tex]Midpoint=\left(\dfrac{-7+a}{2},\dfrac{-3+b}{2}\right)[/tex]

[tex](-6,1)=\left(\dfrac{-7+a}{2},\dfrac{-3+b}{2}\right)[/tex]

On comparing both sides, we get

[tex]\dfrac{-7+a}{2}=-6[/tex]

[tex]-7+a=-12[/tex]

[tex]a=-12+7[/tex]

[tex]a=-5[/tex]

[tex]\dfrac{-3+b}{2}=1[/tex]

[tex]-3+b=2[/tex]

[tex]b=2+3[/tex]

[tex]b=5[/tex]

Therefore, the coordinates of B are (-5,5).

Answer: the perimeter is 26 feet squared. the area is 30 feet

perimeter is all sides added together:

10+10+3+3= 26

area is base times length

10×3=30

dont forget units

Answer:

m = n-1

Step-by-step explanation:

2^m + 2^m = 2^n

Add on the left

2( 2^m) = 2 ^ n

2^1 ( 2^m) = 2^n

We know that a^b* a^c = a^ (b+c)

2^(1+m) =  2^n

The bases are the same so the exponents are the same

1+m = n

Solving for m

1+m-1 = n-1

m = n-1

Given :

2^m + 2^m = 2ⁿ

→ 2(2^m) = 2ⁿ

→ 2¹ × 2^m = 2ⁿ

→ 2^(1 + m) = 2ⁿ

As bases are equal, exponents are equal too.

→ 1 + m = n

→ m = n - 1

Answer:

a₁ = 38

Step-by-step explanation:

Given AP, where:

=============

aₙ = a₁ + (n-1)d

8a₈ = 12a₁₂

Answer:

9) y>0 or y<−14 10) Each artwork sold for $34.4

Step-by-step explanation:

#9 is fairly easy, just plug in a calc and pull out ans.

#10 so he needs to make $300 + $44 in total to recover everything as he wants $300 more in profit. set up the equation:

$300 (Profit) + $44 (Initial) = 10 ( # of paintings) x (how much to be sold for

[tex]\sqrt{3}\approx1.3[/tex]

[tex]\sqrt{9}=3[/tex].

Put first on about 1 and a third and second on exactly 3.

Hope this helps.

Answer:

-8

Step-by-step explanation:

-12r+4=100

100-4=96

-12r=96

96/-12=-8

Answer:

B) -12.4 + 20.6s

Step-by-step explanation:

width = (3.1s - 1.6) cm

Length = (7.2s - 4.6) cm

Perimeter of rectangle = 2* (length +width)

                                      = 2 *(7.2s - 4.6 + 3.1s - 1.6)    {add like terms}

                                      = 2* (7.2s + 3.1s - 4.6 - 1.6)

                                      = 2*( 10.3s - 6.2)   {distributive property}

                                      = 2*10.3s - 2*6.2

                                      = 20.6s - 12.4

Complete question is;

How many 10 - digit numbers are there, such that the sum of the digits is divisible by 2?

Answer:

There are 4500000000 ten digit numbers whose sum is divisible by 2.

Step-by-step explanation:

Since we are dealing with 10 digit numbers, the first 10 digit number whose sum is divisible by 2 is; 1000000001.

While the last 10 digit number whose sum is divisible by 2 is 9999999999.

Now,to find how many 10 digit numbers whose sum are divisible by 2, we will simply divide the difference of both numbers by 2 and then add 1 to the answer. This is because subtracting the minimum from the maximum gives us the number of 10 digit numbers we have. Then dividing by 2 gives the number of ten digit numbers with sum divisible by 2 in between. Then adding 1 to the result to cover the number not included gives;

((9999999999 - 1000000001)/2) + 1 = 4500000000

Answer:

Step-by-step explanation:

Geometric sequences have a common ratio between terms.  TRUE

Geometric sequences are restricted to the domain of natural numbers.  FALSE

Geometric sequences can have a first term of 0.  FALSE.  If this were true, then every member the sequence would also be 0.

The correct statements are,

Geometric sequences have a common ratio between terms.

A geometric series is one which has a constant ratio between successive terms.

Learn more about the Geometric sequences here:

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Answer:

Step-by-step explanation:

$3.00      -       4 bagles  

     ÷2               ÷2

$1.50       -       2 bagles  

     ×3              ×3

$4.5        -       6 bagles  

Answer: 3/4  / 7/8

Step-by-step explanation:

= 3/4  * 8/7  = 24/28 = 6/7 gallons

This is the volume of juice  when the jar is full.

Answer:

6/7

Step-by-step explanation:

Answer:

the 25 -75 because the baby is closer to 25 but still has plenty of room

The car seat appropriate for a child 33-lb will be shown by the inequality 25 < Child seat < 75. The inequality for a child up to and including 26 lb will be written as Child ≤ 26.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that a family is comparing different car seats. One car seat is designed for a child up to and including 26 lb. Another car seat is designed for a child between 18 lb and 40 lb. A third car seat is designed for a child between 25 lb and 75 ​lb.

A car seat appropriate for a ​33-lb ​child will come under the seat which is designed for a child between 25 lb to 75 lb.

The inequality for a child up to and including 26 lb will come under a car seat is designed for a child up to and including 26 lb. The inequality can be written as Child ≤ 26.

Therefore, the car seat appropriate for a child 33-lb will be shown by the inequality 25 < Child seat < 75.

To know more about inequality follow

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Answer:

they received 2400 eggs.

Step-by-step explanation:

12 * 200 = 2400

The number of eggs did the store receive is 2400 eggs.

To find number of eggs.

science that deals with the addition, subtraction, multiplication, and division of numbers and properties and manipulation of numbers. An example of arithmetic is adding two and two together to make four.

Given that:

A dozen (commonly abbreviated doz or dz) is a grouping of twelve.

1 dozen= 12 eggs

1/2 dozen=6 eggs

So upon calculate the 200 dozen of egg, to multiply with  1 dozen of eggs,

200 dozen= 200*12=2400 eggs

So, the number of eggs did the store receive is 2400 eggs.

Learn more about arithmetic here:

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Answer:

Solution: y - 4 = 1 / 12(x + 4)² or Option B

Step-by-step explanation:

Since the directrix is vertical, use the equation of a parabola that opens up or down -

(x - h)² = 4p(y - k)

Remember that the vertex, (h, k) is halfway between the directrix and focus. Therefore we can find the  y  coordinate of the vertex using the formula y = y coordinate of focus + directrix / 2.The  x -coordinate will be the same as the  x  coordinate of the focus.

Vertex: (- 4, 7 + 1 / 2) = (- 4,4)

Now we can find the distance from the focus to the vertex. The distance  from the vertex to the directrix is  represented by | p |. We can subtract the  y  coordinate of the vertex from the  y -coordinate of the focus to find  p.

p = 7 - 4 = 3

Substitute the known values for these variables into the given equation (x - h)² = 4p(y - k) to get our solution.

(x + 4)² = 4(3)(y - 4),

(x + 4)² = 12(y - 4)

1 / 12(x + 4)² = y - 4

y - 4 = 1 / 12(x + 4)² ~ As you can see your solution is option b.

Answer:

2/5

Step-by-step explanation:

cross simplify the 4 and 2

the equation becomes:

2/5 • 1/1 = 2/5

Answer:

2/5

Step-by-step explanation:

you just cross multyply so 4x1 is 4 and 5x2 is 10 and you get 4/10 and then you simplify it by 2 and that will get you 2/5

Answer:

it would be -3x-6

Step-by-step explanation:

if you distribute right you will change the two and the positive change into a negative and the last one x is not by itself plus it only change to one

Answer:

the answer is 7.1

Step-by-step explanation:

the tenth is the first number after the decimal point.