what is the solution to the system

C= ?
D= ?

​

Answer:

x + y ≥ 35 and 15x + 8y ≥ 350

Step-by-step explanation:

Mitch is packing books into boxes.

Each box can hold either 15 small books or 8 large books.

Now, given that Mitch needs to pack at least 35 boxes and at least 350 books.

Now, if x is the number of small book-boxes and y is the number of large book-boxes,

Then, we can write from the above conditions that

x + y ≥ 35.......... (1) and

{Since total number of boxes must be at least 35}

15x + 8y ≥ 350 .......... (2)

{Since the total number of books must be at least 350 and each large book-boxes contain 8 large books and each small book-boxes contain 15 small books}

Therefore, the equations (1) and (2) are the required inequality equations that model the situation. (Answer)

Answer:

{x∈Z+ | x is an even, 2≤x≤12}

Step-by-step explanation:

∈ = elememt of

Z+ = +ve integer

even = even no.

≤ = smaller than or equal to

The set builder notation is  {x : x =  2n where n ∈ N and n < 6}.

A set is a group or collection of objects or numbers, considered as an entity unto itself.  

Now the given set is,

Let S = {2,4,6,8,10,12}

Now, Set-builder notation describe a set by saying what properties its members have.

It uses curly brackets called "braces".

The first part after the first curly bracket tells you what set of numbers x belongs to.  

The ∈ symbol means "is an element of".  

Now,  x = 2n where n ∈ N

and n < 6

Therefore, the required set builder notation is,

S = {x : x =  2n where n ∈ N and n < 6}

Thus, the set builder notation is  {x : x =  2n where n ∈ N and n < 6}

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Answer:

Brett is 62 years old,    Mark is 80 years old     and Carl is  70 years old

Step-by-step explanation:

First; we let Brett age to be  = x

let  Mark age to be = y

let Carl age to be = z

From the question;

since Brett is 18 years younger than Mark, then Brett age is ;

x =  y - 18

Also, since  Carl is 10 years older younger than Mark, then Carl age is:

z   =   y-10

Also, from the question says  the sum of the ages of Brett, Mark and Carl is 212

This means when you add all their ages together, you will have 212

so;         x   +   y  +  z    =   212

From the equation above, we can substitute x with y-18 and then substitute z with y-10

y-18   +   y     +     y-10     =  212

3y   -  28    =    212

add 28 to both-side of the equation

3y   - 28   + 28   =    212  +   28

3y    =  240

Divide both-side of the equation by 3

3y/3   =   240/3

y   =   80

But x = y -18   =   80 -18  =   62

Also;   z =  y - 10   =  80  -10  =   70

Since x represent Brett age, then Brett's is 62 years old

Also, y represent Mark's age, therefore Mark is 80 years old

Finally z represent Carl's age, therefore Carl is 70 years old.

Answer:

[tex]\displaystyle \boxed{3\frac{1}{4}}[/tex]

Step-by-step explanation:

7n - 8 = 3n + 5

- 7n - 5 - 7n - 5

____________

[tex]\displaystyle \frac{-13}{-4} = \frac{-4n}{-4} \\ \\ 3\frac{1}{4} = n[/tex]

I am joyous to assist you anytime.

The width of plot of land is 13/8 kilometers.

Step-by-step explanation:

Area of rectangular plot = 52/96 square kilometers

Length of plot = 4/12 kilometers

Width of plot = w

Area of rectangle = length * width

[tex]\frac{52}{96}=\frac{4}{12}*w\\[/tex]

Multiplying both sides by [tex]\frac{12}{4}\\[/tex]

[tex]\frac{52}{96}*\frac{12}{4}=\frac{12}{4}*\frac{4}{12}w\\\\\frac{624}{384}=w\\\\\frac{13}{8}=w\\\\w=\frac{13}{8}[/tex]

The width of plot of land is 13/8 kilometers.

Keywords: rectangle, area

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Answer:

Proved

Step-by-step explanation:

Figure two triangles which are congruent to each other has been attached

Proof :

1)BC= CD ( given )

2) AC= CE ( Given)

3) ∠ACB= ∠ECD (  vertically opposite to each other)

therefore, ΔABC≅ΔDCE ( By SSA postulate)

Now, CF and CG be medians on the sides Ab and DE of the Δ's ABC and DCE respectively

⇒CF= CG  because of CPCTC that is corresponding parts of congruent triangles are congruent.

Therefore,  congruent triangles have congruent corresponding medians.

5x + 3x + 7x = 180

15x = 180

x = 12

I = 5(12) = 60

M = 3(12) = 36

S = 7(12) = 84

Check: 60 + 36 + 84 = 180

Answer:

∠I=75° , ∠M=45° ,∠S=105°, ∠E=173.5°

Step-by-step explanation:

given ∠I=5X,∠M=3X,∠S=7X, ∠E=128.5+3X

IN TRIANGLE IMS

∠I+∠M+∠S=180°

5X+3X+7X=180°

12X=180°

X=15°

HENCE ∠I=5X=[tex]5\times15°[/tex]

            ∠I=75°

      ∠M=3X=[tex]3\times15°[/tex]

     ∠M=45°

∠S=7X=∠[tex]7\times15°[/tex]

∠s=105°

∠E=128.5+3X=128.5+45=173.5°

∠E=173.5°

a) The total amount the Bells will pay for their house is $187,488. b) The interest paid, including the 3 points, is $97,488. c) The exact amount applied to the principal in the first payment is unknown without additional information.

a) To determine the total amount the Bells will pay for their house, we need to calculate the total amount paid over 20 years. The monthly mortgage payment is $781.20, so the annual payment would be $781.20 x 12 = $9374.40. Therefore, over 20 years, the Bells will pay $9374.40 x 20 = $187,488.

b) The interest paid over the 20-year mortgage period can be calculated by subtracting the total mortgage amount from the total amount paid. The total mortgage amount is $90,000, so the interest paid is $187,488 - $90,000 = $97,488, including the 3 points.

c) The first payment on the mortgage is typically applied mostly to the interest. However, to determine the exact amount applied to the principal, we need more information about the breakdown of the monthly mortgage payment between interest and principal.

Answer:

x=841/68

Step-by-step explanation:

-68(x-11)=1+(-94)

-68(x-11)=-93

-68x+748=-93

-68x=-93-748

-68x=-841

68x=841

x=841/68

Final answer:

To solve this problem, set up an equation by representing the unknown number as x. Distribute -68 to the terms inside the parentheses and solve for x by isolating it on one side of the equation.

Explanation:

To find the answer to this problem, we can set up an equation. Let's let the unknown number be represented by x. The difference between a number and 11 can be written as (x - 11). The problem states that -68 times this difference is equal to the number one plus -94, which can be written as -68(x - 11) = -94 + 1.

To solve this equation, we can distribute -68 to the terms inside the parentheses: -68x + 748 = -93. Then, we can subtract 748 from both sides to get -68x = -841. Finally, we divide both sides by -68 to find that x = 12.38.

Therefore, the solution to this problem is x = 12.38.

Answer:

One solution since x=0

For this case we must find the solution set of the given inequalities:

Inequality 1:

[tex]3x + 10 <3[/tex]

Subtracting 10 from both sides of the inequality:

[tex]3x <3-10[/tex]

Different signs are subtracted and the major sign is placed.

[tex]3x <-7[/tex]

We divide between 3 on both sides of the inequality:

[tex]x <- \frac {7} {3}[/tex]

The solution is given by all values of x less than[tex]- \frac {7} {3}[/tex]

Inequality 2:

[tex]2x-5> 5[/tex]

Adding 5 to both sides of the inequality:

[tex]2x> 5 + 5\\2x> 10[/tex]

Dividing by 2 to both sides of the inequality:

[tex]x> \frac {10} {2}\\x> 5[/tex]

The solution is given by all values of x greater than 5.

Thus, the solution set is given by:

(-∞, [tex]- \frac {7} {3}[/tex]) U (5,∞)

ANswer:

(-∞, [tex]- \frac {7} {3}[/tex]) U (5,∞)

Answer:

The proof is written below.

Step-by-step explanation:

Given:

[tex]DF \cong EF\\FG\ \textrm {bisects}\ \angle DFE[/tex]

Prove :

[tex]\triangle DFG \cong \triangle EFG[/tex]

Proof:

[tex]DF \cong EF \ \textrm{Given}\\FG\ \textrm{bisects}\ \angle DFE\ \textrm{Given}\\[/tex]

[tex]\angle 1 \cong \angle 2[/tex] Definition of angle bisector

[tex]\overline{FG} \cong \overline{FG}\ \textrm{Reflexive Property}\\\triangle DFG \cong \triangle EFG\ \textrm {SAS Congruence}[/tex]

Answer:

5n-28

Step-by-step explanation:

28-6n+7(2n-8)-3n

28-6n+14n-56-3n

28+8n-56-3n

28-56+8n-3n

-28+5n

5n-28

There are 20 players are on the team.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We have to given that;

On the middle school baseball team, 8 players are sixth graders.

And, Of the players, 40% are sixth graders.

Now,

Let number of players on the team = x

So, We can formulate;

⇒ 40% of x = 8

⇒ 40/100 × x = 8

⇒ 40x = 800

⇒ x = 800/40

⇒  x= 20

Thus, Number of players on the team = 20

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Final answer:

There are 20 players on the middle school baseball team in total, calculated by dividing the number of sixth graders (8) by the percentage that represents sixth graders (40%).

Explanation:

Based on the information given, if 40% of the players on the middle school baseball team are sixth graders, and there are 8 sixth graders on the team, we can calculate the total number of players on the team. We know that 40% is equal to 0.40 when expressed as a decimal. Thus, the equation to find the total number of players (T) is 0.40 * T = 8.

To find T, divide both sides of the equation by 0.40:

T = 8 / 0.40

T = 20

Therefore, there are 20 players on the team in total.

Answer:

x = 1

Step-by-step explanation:

-2x - 16 = -14 - 4x

-2x + 4x = -14 + 16

2x = 2

x = 1

Answer:

Add all pounds lost during 3 months. 3+7+4= 14. 4 lbsx4 months =16. 16-14=2. 2 lbs must be lost during the 4 month to stay consistent with the 4 lbs weight loss per month.

Step-by-step explanation:

To maintain an average weight loss of 4 pounds per month, you must lose 2 pounds in the fourth month. This calculation is obtained by subtracting the total weight already lost (14 pounds in three months) from the target total weight loss (16 pounds in four months).

The question is asking how much weight you need to lose in the fourth month to maintain an average weight loss of 4 pounds per month, given that you've lost 3, 7 and 4 pounds in the first three months respectively.

First, let's calculate the total weight you've lost so far: 3 pounds + 7 pounds + 4 pounds = 14 pounds lost in the first three months.

Next, calculate how much weight you would need to lose in total over four months to maintain an average loss of 4 pounds per month: 4 months * 4 pounds per month = 16 pounds.

Now, subtract the total weight you've already lost from the target total weight to find out how much weight you need to lose in the fourth month: 16 pounds - 14 pounds = 2 pounds. Therefore, you need to lose 2 pounds in the fourth month to maintain an average monthly weight loss of 4 pounds.

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Answer: 25

Step-by-step explanation: This problem states that the sum of four consecutive whole numbers is 94 and it asks us to find the largest number.

Three consecutive whole numbers can be represented as followed.

X ⇒ first number

X + 1 ⇒ second number

X + 2 ⇒ third number

X + 3 ⇒ fourth number

Since the sum of our four consecutive whole numbers is 94, we can set up an equation to represent this.

X + X + 1 + X + 2 + X + 3 = 94

We can combine the x's on the left side of the equation and combine the numbers as well.

4x + 6 = 94

      -6    -6   ← subtract 6 from both sides of the equation

4x = 88

÷4    ÷4

X = 22

X ⇒ first number   = 22

X + 1 ⇒ second number   = 23

X + 2 ⇒ third number   = 24

X + 3 ⇒ fourth number   = 25

Therefore, the largest number would be 25.

Answer:

2.5 x 13.7 = 34.25

4.9 + 1.6 = 6.5

Step-by-step explanation:

Here we are multiplying 2 decimals we can just write it as

[tex]25 * 10^{-1} * 137 * 10^{-1}[/tex]

= [tex]25*137*10^{-2}[/tex]

= [tex]3425 *10^{-2}[/tex]

= 34.25

Here we are just performing simple addition

4.9 + 1.6

= [tex]49 *10^{-1} +16*10^{-1}[/tex]

= [tex](49+16)*10^{-1}[/tex]

=[tex]65 * 10^{-1}[/tex]

= 6.5

Answer:

$5

Step-by-step explanation:

10% = 10/100 = 1/10.

1/10 of 50 = 5

Answer:

8 pounds per tablespoon

Step-by-step explanation:

2 (3) = 6

48 (1/6) = 8

Answer:

8 pounds per tablespoon

Step-by-step explanation:

2 (3) = 6

Step-by-step explanation:

Answer:

8.80

Step-by-step explanation:

Final answer:

To round 8.795 to the nearest cent, look at the third decimal place. Since it's 5 or greater, round up the second decimal place to get 8.80.

Explanation:

When rounding 8.795 to the nearest cent, the focus is on the hundredth's place, since a cent is one hundredth of a dollar. You look at the digit in the thousandth's place to decide whether to round up or down. The digit in the thousandth's place is a 5, which means we follow the rule to round up since it is greater than 5. Thus, rounding 8.795 to the nearest cent gives us 8.80.

Answer:

36.00 ÷ 54 = 36 ÷ 54

Step-by-step explanation:

Decimal Form:

0.66666666...

Fraction Form:

2/3

Percent form:

66.6...%

I hope this helps!

Answer:

66%, 2/3 or 0.66666...7

Step-by-step explanation:

Dividing 36.00 by 54 is the same as "36 ÷ 54". Now to solve:

36 ÷ 54 = 0.66666...7

There are different ways to show this such as:

66%, 2/3 and 0.66666...7

Hope this helps,

♥A.W.E.S.W.A.N.♥

P.S. The "..." in 0.66666...7 just mean there are more 6s.

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Answer:

Step-by-step explanation:

This can be modelled with the variable x to represent the "groups"

3x + 2

Multiplifcation means groups of.

3x is 3 times x, which is 3 groups of x.

The question 'Three groups of a number plus two' translates to the algebraic expression 3x + 2 in mathematics. Here, x represents the unknown number.

The question 'Three groups of a number plus two' pertains to algebraic expressions and equations. When you interpret the question as a mathematical equation, it represents the formula 3x + 2, where 'x' is a variable representing an unknown number. In this formula, 'Three groups of a number' corresponds to the component '3x', and 'plus two' is the mathematical operation adding 2 to this number. This is the fundamental concept behind forming algebraic expressions and equations.

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The solution for C in terms of D and W is:

[tex]C = \frac{W+4D}{3}[/tex]

Step-by-step explanation:

Solving a formula for a given variable means to isolate the variable on one side of the equation

Given equation is:

[tex]W = 3C-4D[/tex]

We have to solve for C in terms of W and D

Adding 4D on both sides

[tex]W+4D = 3C-4D+4D\\W+4D=3C[/tex]

Dividing both sides by 3

[tex]\frac{W+4D}{3}=\frac{3C}{3}\\C = \frac{W+4D}{3}[/tex]

So,

The solution for C in terms of D and W is:

[tex]C = \frac{W+4D}{3}[/tex]

Keywords: Formula, Variables

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Answer:

The equations that represent the situation are:

2y+x=5

5x-y=3

Answer:

2y+x=5

5x-y-3

Step-by-step explanation:

Two times of the larger number which is y is 2y added to the smaller number x is equal to 5 . Which is 2y+x=5

The difference of five times the smaller number and larger number is 5x-y

And the resulting answer is 3

ie..5x-y=3 , when the 3 crosses to the other side it becomes 5x-y-3=0

hence,the equation 5x-y-3

Answer:

A power of 10 is the number 10 multiplied by itself by the number of times indicated by the exponent.When the exponent is greater than o it is followed by zeros

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of the number with a power 10 is a multiplication of that number 10 times.

1024 can be a number with power 10

i.e [tex]2^{10}[/tex]

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A number with power 10.

This means,

The value of the number with a power 10 is a multiplication of that number 10 times.

i.e

[tex]2^{10}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

[tex]2^{10}[/tex] = 2³ x 2³ x 2³ x 2 = 8 x 8 x 8 x 2 = 1024

Similarly,

1024 can be a number with power 10

Thus,

The value of the number with a power 10 is a multiplication of that number 10 times.

1024 can be a number with power 10

i.e [tex]2^{10}[/tex]

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Answer:

The number of once is 9.1  

The number of hundreds is 8.9

Step-by-step explanation:

Given as :

The total of digits having ones and hundreds = 900

The sum of digits = 18

Let The number of ones digit = O

And The number of hundreds digit = H

So, According to question

H + O = 18             .........1

100 × H + 1 × O = 900          ........2

Solving the equation

( 100 × H - H ) + ( O - O ) = 900 - 18

Or, 99 H + 0 = 882

Or , 99 H = 882

∴   H = [tex]\frac{882}{99}[/tex]

I.e H = 8.9

Put the value of H in eq 1

So, O = 18 - H

I.e  O = 18 - 8.9

∴    O = 9.1

So, number of once = 9.1

number of hundreds = 8.9

Hence The number of once is 9.1  and The number of hundreds is 8.9

Answer

Final answer:

The number that fits the criteria of rounding to 900, having twice as many hundreds as ones, having all different digits, and the sum of its digits being 18, is 864.

Explanation:

The question involves finding a number that meets a set of criteria: it rounds to 900, has twice as many hundreds as ones, all its digits are different, and the sum of its digits equals 18. To solve the problem, we can break down the clues and use them to narrow down the possibilities.

Since the number rounds to 900, we know it must be in the range of 850 to 949. The clue that it has twice as many hundreds as ones implies that the number of hundreds is a digit that is double the digit in the ones place. And since all digits must be different, we are looking for a number that does not repeat any digit.

Given the criteria, let's assume the hundreds digit is '8' (since it's in the 800 series), and therefore the ones digit would be '4'. The only digit left to assign is the tens place, which cannot be the same as the other two and must ensure the sum of all three digits equals 18. The digit for the tens place should then be 18 - 8 - 4 = 6, making the number 864, which satisfies all conditions.

So, the number we are looking for is 864: it rounds to 900, has twice as many hundreds (8 hundreds) as ones (4 ones), all digits are different, and the sum of the digits (8+6+4) equals 18.

Final answer:

To determine which negative number is greater between -4.03 and -4.3, compare their standard forms with the same exponent, concluding that -4.03 is larger due to its higher coefficient.

Explanation:

To determine which number is larger between -4.03 and -4.3, we can compare them in standard form:

-4.03 = -4.03 × 100

-4.3 = -4.3 × 100

Since both numbers have the same power of 10 (exponent), we compare the coefficient: -4.03 is larger than -4.3 because 0.03 is greater than 0. Therefore, -4.03 is larger than -4.3.