Mathematics High School

Dewayne is comparing two checking accounts. One has a monthly fee of $7 and a per-check fee of $0.30, and the other has a monthly fee of $4 and a per-check fee of $0.40. What is the minimum number of checks Dewayne needs to write for the first bank to be a better option?

Answers

Answer 1

7 +0.30x = 4 +0.40x

subtract 4 from each side

3+0.30x = 0.40x

subtract 0.3x from each side

3 = 0.10x

divide both sides by 0.10

3 /0.10 = 30

30 checks would make both accounts equal

so he would need to write 31 checks for the first one to be better.

Answer 2

Answer:30

Step-by-step explanation:

it’s right

Related Questions

A map is drawn to scale such that 1/8 inch represents 65 feet. if the shortest route from the dorm to the grocery store measures 23 ¼ inches on the map, how many miles is it to the grocery store? round to the nearest tenth.

Answers

The answer is miles. I'll use decimals in my explanation.
23.25 divided by 0.2 equals 116.25
116.25 multiplied by 65 equals 7556.25
7556.25 divided by 5280 equals 1.43110795455
Rounded to the nearest tenth that's 1.4
Hope it helped.

Solve algebraically for x

Answers

3x + 1 = (x-1)^2
3x + 1 = x^2 - 2x + 1
0 = x^2 -5x
0 = x(x-5)
x = 0,5

Hope this helps!

Determined whether the graphs of each pair of equations are parallel, perpendicular or neither

Answers

One way to look at it would be to solve for y - if what x is multiplied by is the same for both sides, they're parallel. If one is the negative reciprocal (e.g. for 5/6 the reciprocal is 6/5 and the negative reciprocal is therefore -6/5) of another, they're perpendicular and if they're neither they're neither.Solving for y in x+5y=4, we can subtract x from both sides to get 5y=-x+4. Next, we can divide both sides by 5 to get -x/5+4=y. Since -x/5=(-1/5)(x) and -1/5 is not the negative reciprocal of 5/6 as established earlier, they are neither

Matching 1. protects against loss from automobile accidents of insured malpractice 2. protects against loss to insured's home and furnishings automobile 3. protects against loss from fire on insured's property liability 4. protects against loss from injury to others on insured's property fire 5. protects against loss from lawsuits against insured life 6. protects against loss from death of insured homeowners

Answers

2  Homeowners'
6  Life
3  Fire
4  Liability
5  Malpractice
1  Automobile

1. protects against loss from automobile accidents of insured - Automobile insurance.

2. protects against loss to insured's home and furnishings - Homeowners insurance

3. protects against loss from fire on insured's property - Fire insurance

4. protects against loss from injury to others on insured's property - Liability insurance

5. protects against loss from lawsuits against insured - Malpractice insurance

6. protects against loss from death of insured - Life insurance

A restaurant earns $1240 on Friday and $921 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day

Answers

Alright, to average 1000 per day over 3 days, we have 1000*3=3000 dollars. Since we already have 2 days, we do 3000-1240-921=839 

Answer:

The restaurant needs to earn $839 on Sunday.

Step-by-step explanation:

Consider the provided information.

Let $x needs to earn on Sunday, to average $1000 per day .

It is given that the average earn should be $1000

[tex]Average=\frac{\text{Sum of observations}}{\text{Total number of observation}}[/tex]

[tex]Average= \frac{1240+921+x}{3}[/tex]

[tex]Average= \frac{2161+x}{3}[/tex]

The average should be $1000, so substitute 1000 for average and solve for x.

[tex]\frac{2161+x}{3} =1000\\\\ 2161+x=3000\\\\x=3000-2161\\\\x=839[/tex]

Thus, the restaurant needs to earn $839 on Sunday.

The required equation is [tex]\frac{1240+921+x}{3}=1000[/tex].

What makes an irrational number irrational?

Answers

If written as a decimal, a irrational number would have an infinite amount of digits (note that this does not make it a irrational number). In addition (this DOES make it a irrational number), it cannot be equal to one integer divided by another.

Answer:

Step-by-step explanation:

What is the period of the function y=5/2 cos x/4?

Answers

8pi

...............................

The next train will arrive in 32 minutes and 30 seconds.

In how many seconds will the next train arrive?

____Seconds

Answers

So the first thing you need to do is convert the 32 minutes into seconds. You do this by multiplying 32 by 60. So 32x60=1920. Then you need to add the 30 to the 1920 so the answer would be 1,950 seconds. 
Final answer:

You can convert time from minutes to seconds by multiplying the number of minutes by 60. Therefore, if the train is due in 32 minutes and 30 seconds, the train will arrive in 1950 seconds.

Explanation:

To answer your question, we need to understand that 1 minute is equal to 60 seconds.

So, if the train arrives in 32 minutes, then it will arrive in 32 minutes * 60 seconds per minute, which equal 1920 seconds. And we have additional 30 seconds. So, the total time the train will arrive in is 1920 + 30 = 1950 seconds.

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Martin is logging the number of strikes he bowls per hour. He has determined the function to be f(x) = 2x + 5, where x represents hours and f(x) represents the number of strikes he has bowled. Which of the following options describes the restrictions to the domain and range correctly?
Domain, nonnegative values; range, values greater than −2.5
Domain, nonnegative values; range, values greater than or equal to 5
Domain, nonnegative values; range, values less than −2.5
Domain, nonnegative values; range, values less than or equal to 5

Answers

domain (x values) are non-negative values
range (f(x) values are : values greater then or equal to 5

Answer:

B. Domain, nonnegative values; range, values greater than or equal to 5

Step-by-step explanation:

Basically, domain is the set of values that x can take and range is the set of values that the result of f(x) can be.

Since x is the time Martin spends bowling, it cannot be negative. The least he can bowl is zero hours, so x cannot be a negative number.

For the lowest x can be (zero), f(x) is calculated as:

f(x) = 2(0)+5 = 0+5 = 5

For higher values of x, the equation can only yield higher results because the 2 that is multiplying it is positive. Multiplying a two positive numbers (2 and x, which cannot be negative) will always give a positive number. In other words, f(x) is directly proportional to x because its coefficient 2 is positive, which means that when x grows, f(x) grows.

This means that f(x) can never be lower than 5.

The best description is, then, nonnegative values for the domain and values greater or equal to 5 for the range.

Help me plz? I have no clue how

Answers

Take 2 points
(3, 9) and (0, 3)
Slope = (Y2 -Y1) ÷ (X2 -X1)
Slope = (3-9) / (0-3)
Slope = -6 / -3
Slope = 2

The equation will have the form    y = mx + b
We can rearrange this to   b = y -mx
Let's take one of the points (3, 9) and the slope (m) and enter it into the formula:
b = -9 -2*3
b= -3
Now we enter all that data into b = y -mx
and get
y = 2x -3


Out of 32 students in the class 5 said they rode their bikes to school based on their results how many of the 800 students in the school rode their bikes toschool

Answers

The ratio is 5:32.
To make this equivalent we need to find the ratio between 800 and 32:

800/32
25
Now, multiply 5 and 25

25*5
125

Hope this helped!

Is an equation with an integer coefficient will always have an integer solution true or false?

Answers

An equation with an integer coefficient will always have an integer solution. Integers are whole numbers ( positive and negative and zero ). One example of equation:
4 x = 5  ( 4 is an integer coefficient )
x = 5 : 4 = 1.25 ( not an integer )
Answer:
This is false.

I REALLY NEED THIS ONE IT'S MY LAST ONE.
Verify the identity. Justify each step.



please help and show your work.

Answers

[tex]\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \qquad % cosecant csc(\theta)=\cfrac{1}{sin(\theta)} \qquad % secant sec(\theta)=\cfrac{1}{cos(\theta)}\\\\ -------------------------------\\\\ \cfrac{sec(\theta )}{csc(\theta )-cot(\theta )}-\cfrac{sec(\theta )}{csc(\theta )+cot(\theta )}=2csc(\theta )\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}-\frac{cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1}{sin(\theta )}+\frac{cos(\theta )}{sin(\theta )}}\implies \cfrac{\frac{1}{cos(\theta )}}{\frac{1-cos(\theta )}{sin(\theta )}}-\cfrac{\frac{1}{cos(\theta )}}{\frac{1+cos(\theta )}{sin(\theta )}} \\\\\\ \cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1-cos(\theta )}-\cfrac{1}{cos(\theta )}\cdot \cfrac{sin(\theta )}{1+cos(\theta )}[/tex]

[tex]\bf \cfrac{sin(\theta )}{cos(\theta )[1-cos(\theta )]}-\cfrac{sin(\theta )}{cos(\theta )[1+cos(\theta )]} \\\\\\ \cfrac{sin(\theta )[1+cos(\theta )]~-~sin(\theta )[1-cos(\theta )]}{cos(\theta )[1+cos(\theta )][1-cos(\theta )]} \\\\\\ \textit{notice that }[1+cos(\theta )][1-cos(\theta )]\textit{ is a difference of squares}[/tex]

[tex]\bf \cfrac{\underline{sin(\theta )}+sin(\theta )cos(\theta )\underline{-sin(\theta )}+sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]} \\\\\\ \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[1^2-cos^2(\theta )]}\\\\ -------------------------------\\\\ \textit{recall that }sin^2(\theta)+cos^2(\theta)=1\implies sin^2(\theta)=1-cos^2(\theta)\qquad thus\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{2sin(\theta )cos(\theta )}{cos(\theta )[sin^2(\theta )]}\implies \cfrac{2\underline{sin(\theta )cos(\theta )}}{\underline{cos(\theta )sin(\theta )} sin(\theta )}\implies \cfrac{2}{sin(\theta )} \\\\\\ 2\cdot \cfrac{1}{sin(\theta )}\implies 2\cdot csc(\theta )\implies 2csc(\theta )[/tex]

Simplify -|-5 + 2|.
a)-7
b)-3
c)3
d)7

Answers

- | -5 + 2 | = - 3....the reason it is -3 is because the first negative sign falls outside of the absolute value bars.

if it would have been | - (-5 + 2) | ur answer would have been 3 because the negative sign fell in ur absolute value bars.
Step 1. Simplify [tex]-5+2[/tex] to [tex]-3[/tex]

[tex]-|-3|[/tex]

Step 2. Simplify [tex]|-3|[/tex] to [tex]3[/tex]

[tex]-3[/tex]

Done! :)

The difference between Alan's and Bea's age is three years. The sum of their ages is twenty-seven years. How old are they if-
A. Alan is older than bea?
B. Bea is older than Alan?

Answers

Alright. Take x as Alan's age, and y as Bea's age. We can start writing equations; from the first sentence, we find that x - y = 3. From the second sentence, x + y = 27. Adding the two equations, gives 2x = 30. Thus, x is 15, and it follows, that y = 15 - 3, or 12. So for A, Alan is 15, and Bea is 12, and for B, Bea is 15, and Alan is 12.
a - b = 3
a + b = 27
--------------add
2a = 30
a = 30/2
a = 15 <=== alan is 15

a + b = 27
15  + b = 27
b = 27 - 15
b = 12 <=== bea is 12 

evaluate a/z+bw^2 for a=21 b=3 w=6 z=7

Answers

(21/7) = 3
(6)^2 = 36

3+3(36) = 111

Look at the following expression, then factor the sum of terms as a product of the GCF and a sum. 4x + 12 = 4(____ + 3) What term is missing from the solution

Answers

4 is factored out, so 4x+12 becomes 4(x+3), i.e., x is this missing term.

A baseball team has home games on thursdaythursday and saturdaysaturday. the two games together earn ​$4285.004285.00 for the team. thursdaythursday​'s game generates ​$295.00295.00 less than saturdaysaturday​'s game. how much money was taken in at each​ game?

Answers

1,995 for each game.
1,995+1,995=3,990
3,990+295=4,285.00

A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a _____ conjecture. transformation. tessellation. composition.

Answers

Answer:A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.

Step-by-step explanation:

A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes are called tiles, without overlaps or gaps.They can be generalized to higher dimensions and a variety of geometries.

Therefore, A repeating pattern of figures that completely covers a plane, without gaps or overlaps, is called a tessellation.

Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a + 3.75b = 2071.50, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how may adult tickets were sold?

adult tickets

Answers

168 adult tickets were sold

Answer: There are 168 adult tickets that were sold.

Step-by-step explanation:

Let the number of adult tickets were sold be 'a'.

Let the number of student tickets were sold be 'b'.

Since we have given that

The ticket sales for opening night totaled as

[tex]10.50a+3.75b=2071.50[/tex]

And the number of students attended  = 82

so, b = 82

So, we will put the value of b in the above equation:

[tex]10.50a+3.75\times 82=2071.50\\\\10.50a+307.5=2071.50\\\\0.50a=2071.50-307.5\\\\10.50a=1764\\\\a=\dfrac{1764}{10.50}\\\\a=168[/tex]

Hence, there are 168 adult tickets that were sold.

How to get the B by itself

Answers

(a + b + c)/3 = A

(a + b + c)/3 x 3 = A x 3

a + b + c = A(3)

 a- a + b + c - c = A(3) - a - c

b = A(3) - a - c

hope this helps


( i dont know if the A is suppose to be there or not sorry)

If the interest rate on a savings account is 0.018%, approximately how much money do you need to keep in this account for 1 year to earn enough interest to cover a single $9.99 Below-Minimum-Balance Fee?
$55,555
$55
$555
$5,555

Answers

In this question, the interest rate is 0.018% and you need to have $9.99 interest. That mean, you need to divide the target interest value with the interest rate. The calculation would be:

interest = bank account * interest rate
$9.99 = bank account * 0.018%
bank account = $9.99/ 0.018%   (don't forget the % mean 1/100)
bank account = $55.500

Assuming that the $9.99 value is $9.9999... then the answer would be $55.555

Simplify r^4st^7 / 5r^5st^3
Simplify 7x^3y^9z^4 /28x^8y^2
Simplify 3a^3b * 2a^2b^4 / a^10b^3c^2
Explain if you can thankyou!!

Answers

Cancel out common factors (subtract exponents of common bases) 
1) r^4st^7 / 5r^5st^3 = st^4 / 5r
2) 7x^3y^9z^4 /28x^8y^2 = y^7z^4 /4x^5
The last one you need to multiply the factors first (add exponents of common factors)
3) 3a^3b * 2a^2b^4 / a^10b^3c^2 = 6a^6b^5/a^10b^3c^2 = 6b^2/a^4c^2

Hope this helps, let me know if you need more explanation!

The sum of the page numbers on the facing pages of a book is 629. what are the page numbers

Answers

So basically, these numbers have to be consecutive because they're facing pages.

So you can just divide this by 2, and then add one to the second number.

629/2 = 314 R1

So the first page number is 314, and for the second one, just add one, and you get 315.

The number of pages of the book is 315.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the sum of the page numbers on the facing pages of a book is 629.

Basically, these numbers have to be consecutive because they're facing pages.

To calculate the number of the pages divide this by 2, and then add one to the second number.

N = 629/2 = 314

Therefore, the number of pages of the book is 315.

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Please help with both questions thank you.

Answers

1) The height of this tree is 3 because North + south = height. The width will be 7 because east + west = width. Plugging this in to the perimeter formula:

2(3) + 2(7)
6 + 14
20!



Select the graph that best represents the solution set for 5x+1≤11

Answers

[tex]5x+1 \le 11[/tex]


[tex]5x+1-1 \le 11-1[/tex] Subtract 1 from both sides


[tex]5x \le 10[/tex]


[tex]\frac{5x}{5} \le \frac{10}{5}[/tex] Divide both sides by 5 to isolate x


[tex]x \le 2[/tex]


To graph this, draw out a number line. Plot a closed circle at 2 on the number line. The closed circle indicates we include this value in the solution set. This is the endpoint. We shade to the left of the endpoint to represent all of the values smaller than 2. The endpoint is included because of the "or equal to" portion of the inequality sign. 

What is the algebraic expression for the following word phrase: the quotient of j and 8

A.j-8
B.j+8
C.j
-
8
D.8j

Answers

[tex] \frac{j}{8} [/tex]

This is the correct algebraic expression for the quotient of j and 8. Quotient is just a fancy term for the answer to a division problem.

Answer:

[tex]\frac{j}{8}[/tex]

Step-by-step explanation:

the quotient of j and 8

We need to write the given word phrase in algebraic expression

Algebraic expression contains terms with numbers and variables with operators in between.

In the given word phrase , 'j' is the variable

quotient occurs only on division . so we divide 'j' and 8

The expression for word phrase the quotient of j and 8 is

[tex]\frac{j}{8}[/tex]

Leon correctly found the slope and y-intercept of the line that passes through the points (9, –8) and (3, 4) as follows.

m = -8, -4 = -12
9-3 -6 =-2


y = -2x+b
-8=-2(9)+b
-8= -18+b
10=b

a)y=-2x+10
B) y=-2x+10
C) y= 10x-2
D)y=10x +2

Answers

Answer:

[tex]\displaystyle y = -2x + 10[/tex]

Step-by-step explanation:

The work is already done. This is EXACTLY how you find the parallel line, however, two answer choices are an EXACT REPLICA of each other. Perhaps there was a typographical error?

I am joyous to assist you anytime.

the correct answer is option

a)y=-2x+10.

How do you locate the slope?

pick factors on the line and decide their coordinates. determine the difference in y-coordinates of these two factors (upward thrust). determine the difference in x-coordinates for those two factors (run). Divide the difference in y-coordinates by means of the difference in x-coordinates (upward thrust/run or slope).

How do u find slope-intercept shape?

resolve for the slope (m). recollect, the slope is equal to the alternate in y divided with the aid of the change in x (upward push overrun).remedy for the y-fee of the y-intercept (b). replace m and b with their values inside the y=mx+b system.

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What is the measure of 1 (1 point) 45 60 120 125?

Answers

Answer:

120°

i finished the quiz and that what i got

and for the rest

1.b

2.d

3.a

4.c

and number 5 is the first answer that i wrote

Step-by-step explanation:

What is the abbreviation for SI unit of mass

Answers

I would go with either NIST or SIKG. I put SIKG because the abbreviation for mass is kg and you r look for the SI unit of mass and then the SI stands for International System of units. So when you put both SI And KG (kilograms=mass) it makes SIKG.


This is probably not right but I tried.

Good Luck!
Kilogram
Kg I think I did this last year sk
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