Mary owned n sheep and Sam had exactly 4 times as many sheep as Mary. Mary buys 17 extra sheep and Sam sells 8 of his sheep. Sam still has more sheep than Mary. Form an inequality, in terms of n. Solve the inequality to find the least value of n. You must show all your working.

Answers

Answer 1

Answer:

The least value of n is, 9.

Step-by-step explanation:

Let n be the number of sheep in Integer.

Mary(M) owned the number of sheep is n i.e, M = n sheep

Sam(S) had exactly four times as many sheep as Mary , i.e, S = 4 n sheep

As per the given condition Mary buys 17 extra sheep

Now, Mary has total number of sheep, M = n +17 sheep

And Sam sells 8 of his sheep that means he has now,

[tex]S = 4n -8[/tex]

But, Sam still has more sheep than Mary i.e,  [tex]4n-8 > n+17[/tex]

Solve an inequality: [tex]4n-8 > n+17[/tex]

Add 8 both sides we get;

[tex]4n-8+8>n+17+8[/tex]

Simplify:

[tex]4n>n+25[/tex]

Now, subtract n from both the side, we get;

[tex]4n -n>n+25-n[/tex]

Simplify:

[tex]3n>25[/tex] or [tex]n>\frac{25}{3}=8.33333333[/tex]

Since n is the number of sheep in integer,

then the least value of n is, 9.  




Related Questions

Could someone give me step by step instructions PLEASE! Thanks so much!!

Answers

x=2

(2X-8.6)/2=-2.3

multiply both sides by 2 to gte rid of the denominator

2x-8.6= -4.6

add 8.6 to both sides

2x=4

x=2

Isolate the x. Note the equal sign. What you do to one side, you do to the other.

First, multiply 2 to both sides

(2x - 8.6)/2(2) = -2.3(2)

2x - 8.6 = -4.6

Isolate the x. First, add 8.6 to both sides

2x - 8.6 (+8.6) = -4.6 (+8.6)

2x = -4.6 + 8.6

2x = 4

Next, to isolate the x, divide 2 from both sides

2x/2 = 4/2

x = 4/2

x = 2

2 is your answer for x

~Rise Above the Ordinary

Which expression is equivalent to m-n?

Answers

Answer:

D

Step-by-step explanation:

The equivalent expression of the expression m - n will be m + (-n). Then the correct option is D.

What is an equivalent expression?

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ m - n

The equivalent expression of the expression m - n will be written as,

⇒ m - n

⇒ m + (-n)

The equivalent expression of the expression m - n will be m + (-n). Then the correct option is D.

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write an expression that uses partial products to multiply 8 x 64. Can your expression be written another way? Explain

Answers

we are asked to write an expression that uses partial products to multiply 8 and 64. In this case, we can break 8 into 2 x4 and 64 into 8x8. In this case, multiplying these factors equal to 512. Any factors will do actually since it will yield the same product.

Write an equation of the line in point slope form that passes through the two given points (8,-8) slope 3

Answers

equation: y - k=m(x-h)
M: slope
given point: (h,k)
plug in
y- (-3)=3(x-8)
Final answer:

The equation of the line in point slope form that passes through the two given points is y + 8 = 3x - 24.

Explanation:

The equation of the line in point slope form that passes through the two given points (8,-8) and slope 3 can be found using the formula y - y1 = m(x - x1), where (x1, y1) represents one of the given points and m represents the slope. Plugging in the values, we get y - (-8) = 3(x - 8). Simplifying this equation gives us y + 8 = 3x - 24. This is the equation of the line in point slope form.

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50+5y-20=14y-12-2y y=

Answers

Hey there!

Equation given :

50 + 5y - 20 = 14y - 12 - 2y

Combining like terms :

30 + 5y = 12y - 12

Adding 12 on both sides :

42 + 5y = 12y

Subtracting 5y on both sides :

7y = 42

Dividing by 7 on both sides :

y = 6

The value of y is 6.

Hope my answer helps!!

miranda has 19 pieces of candy. she wants to give an equsl number of pieces to her 6 friends. how many pieces of candy will each friend get? write the answer as a mixed number.

Answers

19/6 or 3 1/6 or 3.17

6 * 3 + 1 = 19


the answer is

[tex]3 \frac{1}{6}[/tex]

PLZ HElP!!! Simplify 10 – 3x – 13 + 5x 3 – 3x 1 2x – 3 3 – 2x

Answers

the answer to the first part is 2x-3

1. Find the length of a rectangular lot with a perimeter of 124 feet if the length is two more than twice the width.

2. Find the length of a rectangular lot with a perimeter of 50 feet if the length is five more than the width.

Answers

ANSWER TO QUESTION 1


Let the width be
[tex]w[/tex]
units.



Twice the width will be

[tex]2w[/tex]

Two more than twice the width will be

[tex]2w + 2[/tex]



We were told that the length is 2 more than twice the width. This means that,

[tex]l = 2w + 2[/tex]


This implies that,

[tex]w = \frac{l - 2}{2} - - eqn(1)[/tex]


The formula for finding the perimeter of a rectangle is given by:


[tex]perimeter = 2w + 2l - - eqn(2)[/tex]




We substitute 124 for the perimeter and equation (1) into equation (2)



[tex]124 = 2( \frac{l - 2}{2} ) + 2l[/tex]


This implies that,

[tex]124 = l - 2 + 2l[/tex]

[tex]\Rightarrow 124 + 2 = l + 2l[/tex]



[tex]\Rightarrow 126 = 3l[/tex]




We divide both sides by 3 to obtain,


[tex]l = 42[/tex]

Therefore the length is 42 feet.





ANSWER TO QUESTION 2


Let the width be
[tex]w[/tex]


units.


Five more than the width will be


[tex]w + 5[/tex]


We were told that the length is 5 more than the width. This means that,


[tex]l = w + 5[/tex]


We make w the subject to obtain,


[tex]w = l - 5 - - eqn(1)[/tex]



The perimeter is given by,

[tex]perimeter = 2w + 2l - - eqn(2)[/tex]

We substitute 50 for the perimeter and equation (1) into equation (2)


[tex]50 = 2(l - 5) + 2l[/tex]

Dividing through by 2 gives,


[tex]25 = l - 5 + l[/tex]



[tex]\Rightarrow 25 + 5 = l + l[/tex]



[tex]\Rightarrow 30 = 2l[/tex]


We divide both sides by 2 to get,

[tex]l = 15[/tex]


Therefore the length is 15 feet.

the length of a rectangle is 3 times the width. the area is 27 square centimeters. What is the length?

Answers

Hello.

The answer is: 24

length=3*width, this can be written as 3w

area=27 sq cm

Formula for the area of a rectangle=27 (area)= 3w (length) * w (width)

27=3w^2

then divide both sides by 3: 9=w^2

take the square root of both sides to get: w=3

Now that we know what the width is, we can substitute that and find the length: 3w= 3*3=24

have a nice day

20,21,22,23 are the ones I need help on if you can help I’ll mark you as super smart !!!

Answers

Answer:

20) 10x - 10 = 120

10x = 130

x = 13

21) 6x + 10 + 8x + 2 = 180

14x + 12 = 180

14x = 168

x = 12

22) 5x + 5x + 6 + 94 = 180

10x + 100 = 180

10x = 80

x = 8

23) 2x + 3 + 4x + 1 = 124

6x + 4 = 124

6x = 120

x = 20

Which statement is true about the end behavior of the graphed function? The graph and choices are attached.

Answers

The correct answer is A) as the x values go to positive infinity, then the graph goes to negative infinity.

We can tell this by looking at the graph values as x goes up. You'll notice, as we get higher and higher, the graph disappears down. This means it is heading towards negative infinity for the rest of the graph.

Answer:

The statement  which is true about the end behavior of the graphed function is:

As the x-value goes to positive infinity , the function's value go to minus infinity.       Step-by-step explanation:

We know that the end behavior of the function is the value where it approaches when x tends to plus infinity and minus infinity.

 From the graph of the function we see that the graph first decreases continuously and then it increases and again it decreases to minus infinity.

Also,

when x → -∞ we see that  f(x) → ∞

and when  x → ∞ then f(x) → -∞

As the function has opposite behavior in both the directions this means that the function is odd.

At x=0 the value of function is: -2

Which two square roots are sed to esimate √42?
(a) √25 and √36
(b) √36 and √49
(c) √49 and √64
(d) √25 and √64

Answers

The answer is c . I hope I helped


a shipping company delivered 38728 letters and 41584 packages. write and solve an equation to find how many items the company delivered.

Answers

38,728 + 41,584 = 80,312

The company delivered 80,312 items.

While preparing for a party, Luis spent 25 minutes blowing up 10 balloons. Write an equation to express how many minutes it took him to blow up one balloon.

Answers

m= 2.5x is the equation you want to use, hope this helped! <3


Answer:

The correct answer is x10= 25

Step-by-step explanation:

First we must analyze the information we have:

We know that Luis spent 25 minutes blowing up 10 balloons.

What we want to find out is how many minutes it took to blow up one.

So, if for 25 minutes -------- it blew up 10 balloons

         for x minutes -------------- blew up 1 ballon.

If we cross the terms the equation would be as follows:

x.10 = 25.1

And we just have to solve it:

x = 25/10

x = 2.5

The correct answer is that it took 2.5 minutes to blow up a balloon.

Mr. Piper is driving Roddy and Scott home from school. They both want to ride in the front seat. How can he make a fair decision about who rides in the front seat?Select all of the correct answers.
A.Put each person's name on a separate piece of paper in a bag. Randomly draw the winning name.
B.Flip a coin twice. If both tosses are heads, Roddy wins. If one is heads and one is tails, Scott wins.
C.Roll a number cube. If it lands on 1 or 2, Roddy wins. If it lands on any other number, Scott wins.
D.Roll a number cube. If it lands on an even number, Roddy wins. If it lands on an odd number, Scott wins.

Answers

Answer:

A.Put each person's name on a separate piece of paper in a bag. Randomly draw the winning name; and D.Roll a number cube. If it lands on an even number, Roddy wins. If it lands on an odd number, Scott wins.

Step-by-step explanation:

In order for it to be a fair decision, both boys have to have an equal chance of being selected.

For choice A, drawing their names from a bag, both names are equally likely to be chosen; that makes this fair.

For choice B, there is 1 way to get both heads when flipping a coin.  There are 2 ways to get heads and tails when flipping a coin.  This gives Scott a greater chance, so this is not fair.

For choice C, there are 2 ways to get a 1 or a 2.  There are 4 ways to get anything else.  This gives Scott a greater chance, so this is not fair.

For choice D, there are 3 even numbers and 3 odd numbers.  Both boys have an equal chance, so this is fair.

Answer:

it a and d on any where

Step-by-step explanation:

-4/7(-3/5)(-7/3) whats the answere

Answers

The answer is -0.8 welcome

Exact Form: −4/5

Decimal Form:−0.8

Well what I really need help in is to know how to do expanded form . Thx!

Answers

100000+10000+4000+6 This is written in expanded from please give brainlest

Please select the most simplified form of the equation. 6n + 40 =2n



Question 1 options:

n= -6


n = -10


n = 23


n = 5

Answers

n = - 10

6n + 40 = 2n ( subtract 2n from both sides of the equation )

4n + 40 = 0 ( subtract 40 from both sides )

4n = - 40 ( divide both sides by 4 )

n = [tex]\frac{-40}{4}[/tex] = - 10



Which of the following represents a function?

(3, 4), (-3, 2), (3, 8), (5, 5)

(2, 3), (4, 3), (-2, -3), (-4, -3)

(-1, 2), (-2, 1), (-1, -2), (-2, -1)

(5, 1), (5, 2), (5, 3), (5, 4)

Answers

Is there a none option? if not then it has to be B.
the second one because it pass the vertical line test

Charlie, Dan, and Ellie each made a paper chain. Charlie's was 9 1/2 feet long Dan's was 6 1/3 feet long, and Ellie's was feet long. When put together, how 8 1/3 long were the three chains?

Answers

24 1/6 but you should check the spelling your questions

Assuming Ellies was 8 /13 feet long

9 1/2 + 6 1/3 + 8 1/3 =

getting a common denominator of 6

9 3/6 + 6 2/6 + 8 2/6

23 7/6

24 1/6 feet


ANSWER FAST PLEASE Which is a reasonable first step that can be used to solve the equation 4x+3(x+2)=5(2x-3)

Answers

Distribute 3 to x + 2 and distribute 5 to 2x - 3

How does buying items in bulk usually help a consumer?

A.
The consumer gets better quality.
B.
The consumer pays less per item.
C.
There are fewer items to store.

Answers

B) The consumer pays less per item.

If a bag of chips cost .15, but if 20 bags cost $2, you are saving $1.

Hope I helped!

Good Luck!

Answer:

B.) The consumer pays less per item

Step-by-step explanation:

If you buy items in bulk, you will pay a higher total price but a lower price per item. For instance, buying a package of four rolls of paper towels will usually be cheaper than buying one roll four times.

what is the product for 24 and 32

Answers

Hi! I'm Jenny and I'm a mathematician! I'd love to help you with this problem! :)

Lets get started...

"What is the product for 24 and 32?"

Lets first clarify what the terms are for the results of MDAS in PEMDAS.

Multiplication: Product

Division: Quotient

Addition: Sum

Subtraction: Difference or result

We know that product is the result of multiplying.

So 24 x 32 is...

768

Message from ExperimentsDIYS:

Our team aims to please and if you have any question regarding your topic, we are here to help! We know that your education is very important. <3

Answer:

768

Step-by-step explanation:

24 times 32 = 768, just ask Siri

which number is equivalent to 0.3

1/3

33/100

5/6

2/3

Help plz asap!!!

Answers

None of them are equivalent to 0.3, unless it's 0.3 with a bar over the 3, in which case the answer is 1/3.

Solution:

Convert all the numbers to decimal form;

1/3 = 0.3 (where 3 is recurring)

33/100 = 0.33

5/6 = 0.83 (where 3 is recurring)

2/3 = 0.6 (where 6 is recurring)

The correct choice is  1/3 since its the only choice that don't give a limitation on rounding up the decimal value to 1 decimal place.

given the replacement set {0,1,2,3,4} solve 4x - 5 = 11

Answers

4x - 5 = 11
4x = 11 + 5 = 16
4x = 16
Divide by 4 from both sides
X = 4

A rental car agency charges $240 per week plus $0.25 per mile to rent a car. The charge for a minivan is $180 per week plus $0.40 per mile. After how many miles is the total charge for each vehicle the same?

Answers

Rental car agency charge:

Let's assume number of miles in as week as x miles

and total rent as R(x)

A rental car agency charges $240 per week plus $0.25 per mile to rent a car

so, we get equation as

[tex]R(x)=240+0.25x[/tex]

Minivan charge:

Let's assume number of miles in as week as 'x' hours

and total charge of minivan as M(x)

The charge for a minivan is $180 per week plus $0.40 per mile

so, we get

[tex]M(x)=180+0.40x[/tex]

now, we can set them equal

and then we can solve for x

[tex]240+0.25x=180+0.40x[/tex]

Subtract both sides by 0.25x

[tex]240+0.25x-0.25x=180+0.40x-0.25x[/tex]

[tex]240=180+0.15x[/tex]

Subtract both sides by 180

[tex]240-180=180+0.15x-180[/tex]

[tex]60=0.15x[/tex]

divide both sides by 0.15

and we get

[tex]x=400 miles/tex]............Answer


Final answer:

The total charge for each vehicle, a car and a minivan, is the same when 400 miles are driven.

Explanation:

The subject you're dealing with here is algebra, specifically, finding the point where two linear functions intersect which shows when the cost of renting the two different vehicles will be the same.

Let's use the formula for the cost of each vehicle, where C is the total cost, W is the flat weekly charge, M is the price per mile, and X is the number of miles driven:

For the car: C = $240W + $0.25M X

For the minivan: C = $180W + $0.40M X

Set these two equations equal to each other to solve for X, the number of miles driven when the two costs are equal:

$240W + $0.25M X = $180W + $0.40M X

Subtracting $180W from both sides and $0.25M X from both sides, you get:

$60W = $0.15M X

Finally, divide by $0.15M to solve for X:

X = $60W/$0.15M = 400 miles

Therefore, the total charge for each vehicle is the same when 400 miles are driven.

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HELP!!!!! The measure of the angle’s supplement is 20 degrees more than three times that of its complement. Find the measure of the angle described. The measure of the angle is?

Answers

By solving a linear equation, conclude that the measure of our angle is 55 degrees.

How to find the measure of the angle described?

We know that two angles A and B are supplementary if their measures add up to 180°, then:

A + B  = 180°

And two angles are complementary if their measures add up to 90°.

A + B = 90°

Now, let's define A as our angle, B as the supplement, and C as the complement, then we can write:

A + B = 180°

A + C = 90°

We know that B is 20° more than 3 times the complement, then we can write:

B = 20° + 3*C

Usuing the two equations above we can rewrite:

B = 180° - A

C = 90° - A

Replacing that above, we get:

(180° - A) = 20° + 3*( 90° - A)

We need to solve this linear equation for A.

180° - A = 20° + 270° - 3*A

3*A - A = 20° + 270° - 180°

2*A = 110°

A = 110°/2 = 55°

We conclude that the measure of our angle is 55 degrees.

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given that g(x)=x^2-3x-6, find (gog)(-3)

Answers

(gog)(-3) basically means g(g(-3)).

g(-3) = (-3)^2 - 3(-3) - 6

g(-3) = 12

g(12) = 102

So the answer is 102.

The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number. Find the two numbers.

Answers

Answer:


Step-by-step explanation:

Let [tex] x[/tex] be the greater number and [tex] y [/tex] be the smaller number. We know that their difference is 15, so we have

[tex] x-y=15 [/tex]

Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have

[tex] 2x+8 = 3y-4 \iff 2x-3y = -12 [/tex]

So, we have the follwing system:

[tex] \begin{cases} x-y=15\\2x-3y = -12\end{cases} [/tex]

From the first equation, we can derive [tex] x = y+15 [/tex], and substitute this expression in the second equation to get

[tex] 2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42 [/tex]

Substitute this value for y in the first equation to get

[tex] x-42=15 \iff x=15+42 \iff x = 57 [/tex]

Firstly, we need to write down the information given in the form of algebraic equations. We can represent our two unknown numbers, the greater and the lesser, as x and y respectively.

From the given information, we can form two equations. The first equation is from "the difference between the two numbers is 15", which gives us x - y = 15, where x is the larger number and y is the smaller one.

Also, we know that "If 8 is added to twice the greater number, the result is 4 less than 3 times the lesser number", this gives us the second equation: 2*x + 8 = 3*y - 4.

We now have a system of two equations that we can solve simultaneously:

1) x - y = 15
2) 2*x + 8 = 3*y - 4

To make it easier, let's multiply the first equation by 2, which gives us 2*x - 2*y = 30.

Now subtract the second equation (2*x + 8 = 3*y - 4) from the first (2*x - 2*y = 30), it yields: -2*y - 3*y = 30 - (-4 - 8).

This simplifies to -5y = 30 + 4 + 8, or -5*y = 42.

To get the value of y, divide by -5, therefore y = -42 / -5 = 42.

Now to find x, we can substitute y = 42 in the first equation (x - y = 15), so we get x = 42 + 15 = 57.

Hence, the greater number is 57 and the lesser number is 42.

There is a triangle and the first side is 3m , The second side is 4 - m , and the third side is 2m - 1. What expression would represent the perimeter of the triangle?

Answers

perimeter = 4m + 3

the perimeter is the sum of the 3 sides of the triangle, thus

perimeter = 3m + 4 - m + 2m - 1 = 4m + 3


Answer: 4m + 3


Step-by-step explanation:

This is because the perimeter of a triangle is the same as adding all of its sides.

3m+(4-m)+(2m-1)

Group like terms:

(3m-m+2m) + (4-1)

Then combine like terms to get your final answer of:

4m + 3


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