Mathematics High School

You and a friend are looking for an apartment. There are two final choices. Apartment A has a $1000 security deposit and costs $1200 each month. Apartment B has a $1500 and costs $1175 each month. How many months, m, will it take for the costs to be the same?

Answers

Answer 1
1000+1200m=1500+1175m
1200m=500+1175m
25m=500
m=20 months
Answer 2

The required months are x = 0.60 months where at the cost become same.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the total cost be y and the month be x
Apartment A has a $1000 security deposit and costs $1200 each month.
y = 1200x +1000 - - - - - (1)
Apartment B has $1500 and costs $1175 each month.
y = 1175x + 1500
From equation 1
1200x + 1000 = 1175x + 1500

1200x - 1175x = 500
825x = 500
x = 500 / 825
x = 0.60 months,
y = 1200*0.60 + 1000
y = 1,720

Thus, the required months are x = 0.60 months where the cost becomes the same.

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Related Questions

you pay $14.82 for 1.5 pound of ham. you buy 2.25 pounds of roast beef for $12.40 per pound. How much less does ham cost per pound than roast beef?

Answers

a pound of ham is 9.88$ and a pound of beef 5.51$ answer ham doesn't cost less roast beef is 4.37$ cheaper a LB.

Which phrase best describes a rock? A. a chemical arranged in a lattice B. a gabbro of minerals C. a mixture of crystals D. a fire-formed crystal

Answers

A gabbro of minerals.

How is volume calculated given mass and density?

Sum of mass and density
Mass divided by density
Mass multiplied by density
Difference of mass and density

Answers

Answer:

B.

Step-by-step explanation:

when trying to calculate the volume when being given the M or the mass, and the D or density, hears is the calculations needed for that: P=M/V, which also means volume is the mass divided by the volume, or density. Hence, the answer would be mass divided by density. hope this helps!!! (also, please give me brainliest.)

Volume is calculated given mass and density is Mass divided by density.

What is volume?

Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic meter and liter) or by various imperial units (such as the gallon, quart, cubic inch).

Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied.

Density is defined as a measure of how compact the mass in a substance or object is.

Since, density of a substance is measure as the ratio of its mass to its volume,

Density =  Mass/Volume

or, Density x volume =  mass

or, Volume =  Mass/Density

Hence,Volume is calculated given mass and density is Mass divided by density.

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A man rides a bicycle a distance of 48 miles in a certain amount of time. If the man increased his speed by 2 miles per hour, he reaches his destination four hours earlier. Find his usual speed. Show Work!

Answers

recall your d = rt, distance = rate * time.

so, in his usual speed, say is hmm "r" mph, so in his usual "r" speed, he rolls on for the 48 miles and it takes him "t" hours to get there.

now, if he increases his speed by 2 mph, then his new speed is "r + 2", and he arrives there 4 hours earlier, so if he took "t" hours going at "r" speed, then when he's going faster at "r + 2", he only takes "t - 4" hours, for the same 48 miles.

[tex]\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ \textit{usual speed}&48&r&t\\ \textit{faster speed}&48&r+2&t-4 \end{array} \\\\\\ \begin{cases} 48=rt\implies \frac{48}{r}=\boxed{t}\\ 48=(r+2)(t-4)\\ ----------\\ 48=(r+2)\left( \boxed{\frac{48}{r}}-4 \right) \end{cases} \\\\\\ 48=(r+2)\left( \cfrac{48-4r}{r} \right)\implies 48r=(r+2)(48-4r) [/tex]

[tex]\bf 48r=48r-4r^2+96-8r\implies 0=-4r^2+96-8r \\\\\\ 4r^2+8r-96=0\implies r^2+2r-24=0 \\\\\\ (r+6)(r-4)=0\implies r= \begin{cases} -6\\ \boxed{4} \end{cases}[/tex]

it cannot be a negative value, since is just a forward speed rate, so can't be -6.

-6 ,4 but speed can't go negative so the answer would be 4.

The standard error of the mean is calculated using which two quantities:

Answers

If a random variable has a standard deviation of σ and a sample of size n is collected for the variable, then the mean has a standard error given by σ/√n. So the standard error of the mean is calculated using the two quantities: standard deviation σ and the sample size n. 

Sweet T purchased a new pair of pants to wear to the battle of the bands on sale at 40 % off . He saved $20 . What was the regular price of the jeans ?

Answers

Hey there!

The answer is $50 because $20 is 40%, so times that by 2 which you get $20 and 80%. Then you divide 20 by 2 then you get 10 which is 20% so you add 10 and you get $50 which is 100%

15 POINTS NEED ANSWER ASAP!! WILL GIVE BRAINLIEST TO FIRST ANSWER

Which mass is greatest? a. 179,000 mg c. 75 g b. 0.043 kg d. 23,481 cg

Answers

179,000 mg = 0.179 kg
75 g = 0.075 kg
23,481 cg = 0.23481 kg
and 0.043 kg 

so 23,481 cg has greatest mass

answer
d. 23,481 cg

What is 65.6 divided by 8

Answers

The correct answer is 8.2
The answer is 8.2  i hope it helped and good luck

The container that holds the water for the football team is 7/10 full. after pouring out 3 gallons of water, it is 1/2 full. how many gallons can the container hold?

Answers

Hello!

So you figure that 7/10-5/10=2/10 that leave you with 1/5 left over. So if you take that into effect, all you have to do it multiply those 3 gallons by 5. Which gives you 15. So, your answer would be 15 gallons. 

I hope this helped!

I am, yours most sincerely
SuperHelperThingy

need help.... what is half of 1 3/4 IN A FRACTION plzzzzz

Answers

well 1 3/4 as improper fraction is 7/4 so 7/4 / 1/2
7/4 x 2/1 is 14/4 or 3 1/2
first add 1 (= 4/4) to 3/4 which equals 7/4, now to get half of 7/4 you make it easier by changing it to 14/8 (= 7/4) 

now half of 14/8 is easy

An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour. Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt. 0.75(x + y) = 120 x − y = 120 0.75(x − y)= 120 x + y = 120 120(x + y) = 0.75 120(x − y) = 1 120(x − y) = 0.75 120(x + y) = 1 Mark this and return

Answers

n aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.
Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? 
---
With wind DATA:
distance = 120 miles ; time = (3/4)hr ; rate = 120/(3/4) = 160 mph
----
Against wind DATA:
distance = 120 miles ; time = 1 hr ; rate = 120 mph
-----

Equation::
Let p be speed of the plane in still air
Let w be speed of the wind
==================================
With wind:: p + w = 160 mph
Against wind:: p - w = 120 mph
================================

Answer:

System of equation: 0.75(x+y)=120 and x-y=120

A is correct

Step-by-step explanation:

An aircraft travels with the wind for 120 miles in 0.75 of an hour.

The return trip is flown against the wind and takes exactly 1 hour.

Let speed of aircraft be x mph and speed of wind y mph

Formula:

[tex]speed=\dfrac{Distance}{Time}[/tex]

Case 1: When aircraft along with wind

Speed = x+y

Time = 0.75

Distance = 120

[tex]x+y=\dfrac{120}{0.75}[/tex]

[tex]0.75(x+y)=120[/tex]

0.75(x+y)=120

Case 2: When aircraft against with wind

Speed = x-y

Time = 1

Distance = 120

[tex]x-y=\dfrac{120}{1}=120[/tex]

x-y=120

Hence, The system of equation are 0.75(x+y)=120 and x-y=120

PLEASE ANSWER ASAPPPPPPPPPPPPPPPPPP

Share the advantages and disadvantages of the different methods for solving quadratic equations that you have learned. Share special techniques that you have developed along the way. For example, explain to your classmates your technique for remembering the quadratic formula (song, rhyme, rhythm, etc.) to help others remember it as well.

Answers

Factoring

The factors of a quadratic equation will be (qx + r) and (sx+t). If the solutions are all integers, you may be able to quickly find q, r, s and t. The advantage of this method is that factoring can be very fast. The disadvantage is that factoring may not work; for instance, factoring will not find solutions that are not integers.

Completing the Square

Completing the square is a multistep process. The main idea is to convert the original equation into one of the form (x + a)^2 = b, where a and b are constants. The advantage of this method are that it always works and that completing the square gives some insight into how algebra works more generally. The disadvantage is that this method is complex.

Quadratic Formula

The quadratic formula is x = (-b +- (b*2 - 4ac)^.5))/2a. The advantages of this method are that the quadratic formula always works and is straightforward. The disadvantages are that the formula provides no insight and can become a rote technique.

Guessing

Sometimes, you can guess an approximate solution. Then, you can increase or decrease your guess, depending on whether the result from your first guess is too big or too small. The advantages of this method are that guessing can be very fast if you guess right, and can get an approximate answer quickly, if that is all you need. The disadvantage is that sometimes you won't be able to make a good guess .

Find the value of k
given that the line through (−1, k)
and (−7,−2)
is parallel to the line y = x+1
.

Answers

The slope of the line given is 1 because that is the coefficient in front of x. A slope is found by dividing the change in y by the change in x. Knowing this, we can set up an equation with the points given.

1 = (-2 - k)/(-7 +1)

Now we'll solve to find k.
Firstly we'll multiple both sides by (-7 + 1):

1(-7 + 1) = (-2 - k)/(-7 +1)(-7 + 1)
-7 = -2 - k

Now we'll add 2 to both sides:
-7 + 2 = -2 - k + 2
-5 = -k

Now to get k by itself we must divide by negative one on both sides: 
-5/(-1) = -k/(-1)
5 = k

Your answer is 5 = k
Final answer:

Given two lines are parallel, their slopes are equal. After calculating the slopes of the two lines and solving the equation, we find that the value of 'k' in the question is 4.

Explanation:

In the realm of Mathematics, when two lines are parallel, their slopes are equal. The line y = x + 1 has a slope of 1. To find the slope of the line through (−7,−2) and (−1, k), use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Here, (x1,y1) is (−7,−2) and (x2,y2) is (−1, k). Hence, the equation for slope would look like this: m = (k - (-2)) / (-1 - (-7)).

As the slopes are equal, we can form an equation 1 = (k + 2) / 6. Solving this equation will give us the value of k. By multiplying both sides by 6, we obtain 6 = k + 2. Consequently, subtracting 2 from both sides, we get k = 4.

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33 is 75% of what number?

Answers

33 is 75% of what number...

33 = 0.75x
33 / 0.75 = x
44 = x <== so 33 is 75% of 44

Find the product (x-y) (3x-4y)

Answers

(x - y)(3x - 4y)

= x(3x - 4y) - y(3x - 4y)

= 3x^2 - 4xy - 3xy + 4y^2

= 3x^2 - 7xy + 4y^2
(x-y) (3x-4y)
x(3x-4y)-y(3x-4y)
3x²-4xy-3xy+4y²
3x²-7xy+4y²
or
3x²+4y²-7xy

Question 21 the ratio of men to women working for a company is 2 to 3 . if there are 140 employees total, how many women work for the company?

Answers

Let x = value the ratio was reduced by
So the equation is 2x + 3x = 140
                              5x = 140
                              x = 28
Men to Women is 2 to 3 so number of women = 3(28) = 84

Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water. This rate is constant

Answers

the ratio should be 2 /17 

The rate of using water per minute will be 8.5 gallons per minute.

What is the rate of flow?

The rate of flow of water is defined as the amount of water or any liquid flowing in a unit of time. If the gallons of water are flowing in some minutes the rate will be measured in the gallons of water.

Given that Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water.

The rate of flow of water will be calculated as:-

Rate of flow = Volume of water / Time

Rate of flow = 17 / 2

Rate of flow = 8.5 gallons per minute

Therefore, the rate of using water per minute will be 8.5 gallons per minute.

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Write an expression that is equivalent to 3/5 (3y+15)
3/5y +9, 3/5y+15, 9/5y+9, 9/5y + 15?

Answers

Given the expression

[tex] \frac{3}{5} (3y+15)[/tex]

The expression that is equivalent to the given expression is given by:

[tex]\frac{3}{5} (3y+15)= \frac{9}{5} y+ \frac{3}{5} (15)= \frac{9}{5} y+9[/tex]

(-11/2x+3)-2(-11/4x-5/2)=expression in simplest form needed!!

Answers

(-11/2x+3)-2(-11/4x-5/2)
= -11/2x + 3 + 11/2x + 5
= 8

answer
8

The given expression in its simplest form is 8.

The given expression is (-11x/2+3)-2(-11x/4-5/2).

We need to write the given expression in the simplest form.

What is an expression in its simplest form?

A simplified expression is one in which each base is written only once, there are no negative exponents and no parentheses. Simplifying an expression makes it easier to solve complex problems, and using the rules for exponents makes simplifying expressions easier.

Now, the given expression can be simplified as follows:

(-11x/2+3)-2(-11x/4-5/2)

=-11x/2+3+22x/4+10/2

=-11x/2+22x/4+3+5

=-22x/4+22x/4+8

=8

Therefore, the given expression in its simplest form is 8.

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Samuel recorded the number of different types of pets his friends have in the table shown below: Cats 5 Dogs 3 Rabbits 1 Guinea Pigs 3

Answers

4 different pets is the an

Answer:

Samuel's friends have a total of 12 pets.

Explanation:

To find the total number of pets Samuel's friends have, we simply add up the number of each type of pet:

Number of Cats: 5

Number of Dogs: 3

Number of Rabbits: 1

Number of Guinea Pigs: 3

Total number of pets = 5 (cats) + 3 (dogs) + 1 (rabbits) + 3 (guinea pigs) = 12

So, Samuel's friends have a total of 12 pets.

The area of a garden is 12.9 square feet.  Each square foot of the garden needs to have 2.6 pounds of soil.How many pounds of soil are needed for the garden?

Answers

2.6 pound of soil for each square foot,
so,for 12.9 square
2.6x12.9=33.54 pound of soils

Solve the inequality
-8x - 10 > 7x + 20

A.) x < - 30
B.) x > - 2
C.) x > - 30
D.) x < - 2

Answers

Final answer:

To solve the inequality -8x - 10 > 7x + 20, combine like terms, isolate the variable term, and solve for x. The correct answer is D) x < -2.

Explanation:

We need to solve the inequality -8x - 10 > 7x + 20.

First, let's combine like terms by adding 8x to both sides. This gives us -10 > 15x + 20. Next, subtract 20 from both sides to isolate the variable term. This gives us -30 > 15x. Finally, divide both sides by 15 to solve for x. This gives us x < -2.

Therefore, option D.) x < -2 is the correct answer.

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A computer is programmed to scan the digits of the counting numbers. For example, if it scans 
1 2 3 4 5 6 7 8 9 10 11 12 13 
then it scanned 17 digits altogether. If the computer begins it's task and scans the first 1392 digits starting with 1, what is the last counting number scanned?

Answers

Number of 1-digit numbers scanned (i.e. 1 - 9) = 9 digits

Number of 2-digits numbers scanned (i.e. 10 - 99) = 2 x 90 = 180 digits

Let the number of 3-digits numbers scanned be x (i.e. 100 - y), then 3 x (y - 99) = (1392 - 180 - 9)
3y - 297 = 1203
3y = 1203 + 297 = 1500
y = 1500 / 3 = 500

Therefore, the last counting number scanned is 500.

We _____ when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

Answers

Subtract because it has to deal with the many signs

We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

What is a mean?

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

The average deviation is calculated by taking the absolute value of the deviations from the mean, summing them, and then dividing by the total number of observations.

This gives us a measure of the average distance between each observation and the mean.

The formula for the average deviation is:

average deviation = Σ |x - mean| / n

where x is an observation, mean is the mean of the observations, and n is the total number of observations.

By taking the absolute value of the deviations, we ensure that negative and positive deviations do not cancel each other out when we sum them.

Thus,

We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

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Can someone please please help me.

Answers

Cd || gh #2 is given look at the bottom of the paper
Check out the attached image for the answers all on one sheet.

------------------------------------------------------------------------------

Label each row 1, 2, ..., all the way up to row 7. I'll refer to each statement and reason by the row number. For example, in row 2 we have "statement 2" and "reason 2". Statement 2 is already filled in for us while Reason 2 is blank. 

Statement 1 has "CD perpendicular to AE". This is given to us to be true as shown in the "given" portion at the very top of the problem (just under the diagram).

What's also given to us is the fact that "line segment CD is parallel to line segment GH". So we'll write "given" for reason 2.

------------------------------------------------------------------------------

Next up is reason 3, which is "definition of perpendicular". Why is this? Because the statement "angle ABD is a right angle" means angle ABD is 90 degrees. The term "perpendicular" means two lines or line segments or rays cross/meet at a 90 degree angle. 

Now onto reason 5. Note how angle ABD and angle GEF are alternate exterior angles. They are outside of the train tracks (CD and GH) and lay on alternate sides of the line FA. Since CD is parallel to GH (see line 2), this means the alternate exterior angles are congruent. For reason 5, we'll put "alternate exterior angles theorem"

------------------------------------------------------------------------------

Statement 7 is the the thing we want to prove. For any proof, the last statement is ALWAYS what you want to prove. If there's anything after this statement then we still have work to do and the proof isn't done. This is the last stop so to speak. So we simply write exactly what we want to prove (next to the "prove:" portion just below the diagram)

Reason 7 is "definition of perpendicular" because GEF is a right angle so GH is perpendicular to line FA. Like with reason 3, a 90 degree angle forms. 

------------------------------------------------------------------------------

Once again, check out the attached image to see all of the answers in the right spots.

Strawberry chews cost $0.03 more than lollipops. Sarah pays $0.54 for 2 strawberry chews and 4 lollipops. What is the price of a strawberry chew?

Answers

We will use this system of equations to solve this:

l = lollipop
s = strawberry chew

[tex] \left \{ {{4l + 2s = 0.54} \atop {s = l + 0.03}} \right. [/tex]

So first of all, let me explain these equations.

4l + 2s = 0.54 means that 4 lollipops and 2 strawberry chews cost $0.54
s = l + 0.03 means a lollipop plus 0.03 equals the cost of a strawberry chew.

Now, let's solve for s.

4l + 2s = 0.54
Subtract 4l from boths sides.
2s = 0.54 - 4l
Divide by 2 on both sides.
s = -2l + 0.27

Substitute.

-2l + 0.27 = l + 0.03
Subtract l from both sides.
-3l + 0.27 = 0.03
Subtract 0.27 from both sides.
-3l = -0.24
Divide by -3 on both sides.
l = .08

.08 + .03 = .11

A strawberry chew costs $0.11

A line with a slope of 2 passes through (3,9). Which choice is an equation of this line?

Answers

the equation is y=2x+3

Answer:

y - 9 = 22(x - 3)

Step-by-step explanation:

How do I work out 5x+2+3x

Answers

5x + 2 + 3x

add same types of numbers

5x + 3x + 2

8x + 2

find x

8x + 2 = 0
8x + 2 (-2) = 0 (-2)
8x = -2
8x/8 = -2/8

x = -1/4

hope this helps
5x + 3x = 8x

8x + 2

FINAL ANSWER: 8x + 2

You would add 5x and 3x because they are like terms. The 2 is just a regular number, it doesn’t have a variable along with it.

Write an equivalent expression using the multiplicative identity property

Answers

A possible answer could be 1x9= 9 which is itself.

For an expression equivalent to, let's say, -8, you could do: -2 + -6.

Extra points! Write the equation for the vertical line that contains point E(10, –3).

A) y=(3/10)x-3
B) x=10
C) Other (please write the equation)

Answers

Your answer would be B, x = 10. This is because that equation would produce a vertical line (up and down) that crosses every Y value at 10 on the X axis. If you're still confused, this is what the graph would look like.
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