The sum of two numbers is 99. If three times the smaller number is subtracted from the larger number, the result is 19. Find the two numbers.

Answers

Answer 1
This is a system of equations. Writing the words in math we get: (we use s as the smaller number and l as the larger one)

l + s = 99
l - 3s = 19

We isolate l in the second equation to get l = 19+3s.  Now we substitute our value of l into the first equation and simplify.
l + s = 99
(19+3s) + s = 99
19 + 4s = 99
4s = 99 - 19
4s = 80
s = 20

Now we know the value for s, we substitute our value for s in the first equation and solve for l.

l + s = 99
l + 20 = 99
l = 99 - 20
l = 79


l = 79 and s = 20. These are our two numbers.

Related Questions

Ten subtracted from seven times a number is 25 what is the number ?

Answers

x represents the unknown number

7x-10=25
add 10 to both sides

7x=35
divide both sides by 7

x=5

The number is 5.

What number do you subtract from 3 to get 10?

Answers

3 - x = 10
-x = 10 - 3
-x = 7
x = -7 <===
3-10 ( count backwards or use calculator)

= -7

is it possible for a 5 digit number to be rounded to a 6 digit number

Answers

no because no matter what you round it to you will always be multiplying the 5 digit number by itself that many times
When we round a number the new rounded number is simpler but the value is kept close to what it was. The common method for rounding numbers is the following: we decide which is the last digit to keep and leave this digit the same the same if the next digit is less than 5 or increase it by 1 if the next digit is bigger than 5.
Because the next digit matter, it is not possible for a 5 digit number to be rounded to 6 digit number. 

Yearly homeowner property taxes are figured at a rate of $1.15 tax for every $100 of home value. Find the property taxes on a townhouse valued at $73,000.

Answers

$100's in the home value = 73,000 / 100
= 730

property taxes = 1.15 X 730
= $839.50
Final answer:

To calculate the property taxes on a townhouse valued at $73,000, divide the value by $100 to find the number of $100 increments, and then multiply this by the tax rate of $1.15.

Explanation:

To find the property taxes on a townhouse valued at $73,000, we need to calculate the tax amount based on the given tax rate. The tax rate is $1.15 for every $100 of home value.

First, we need to find how many $100 increments are there in the home value.

Divide $73,000 by $100:

$73,000 ÷ $100 = $730

Now, multiply the number of $100 increments by the tax rate:

$730 × $1.15 = $839.50

Therefore, the property taxes on a townhouse valued at $73,000 would be $839.50.

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A cross-country skier skied at a rate of 10.82 miles per hour. In 2.45 hours, the skier covered 2.6509 miles.

Is this correct? Explain why or why not.

Answers

Answer:

CHEATING

Step-by-step explanation:

becaus eI got it right on egde

The information given that the skier covered 2.6509 miles is wrong because the decimal was wrongly put.

Since the cross-country skier skied at a rate of 10.82 miles per hour, it should be noted that in 2.45 hours, we've to multiply 10.82 miles by 2.45 hours and this will be:

= 10.82 × 2.45

= 26.509 miles

From the information given, we are told that in 2.45 hours, the skier covered 2.6509 miles, this is incorrect as the miles covered is 26.509 miles.

Therefore, information given that the skier covered 2.6509 miles is wrong because the decimal was wrongly put.

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Hera spent $16 on dinner. Then she spent S6 on dessert and some more on a taxi ride. Including the taxi fare, she spent a total of $31. How much money did Hera spend on the taxi ride? 2. (a) What is the unknown information? (b) Let x represent the unknown information. Write an addition equation that models the problem. (c) Solve the equation. (d) Answer the question PLEASE HELP !!!

Answers

A) unknown information is how much she spent on the taxi ride

B) 31 = x +16+6

C ) 31= x +22

     x =31-22 = 9

   She spent $9 on the taxi

(A) How much money Hera spent on the taxi ride.

(B) 31 = x + 16 +6

(C) 16 + 6 = 22 31 - 22 = 9

(D) She spent $9 on the taxi.

(also sorry im uh 4 years late aldksjfladfoajsdflkj)

a line and a point are ________ coplanar.
a. always
b. sometimes
c. never

Answers

Answer:

A. always

Step-by-step explanation:

parallel lines are always going to be coplanar

Write a pair of numbers such that the value of the 7 in the first number is 1,000 times the value of the 7 in the second number, and the value of the 3 in the first number is 100 times the value of the 3 in the second number

Answers

437,000
400,307

In the second number, the 7 is moved 3 places to the right, and the 3 is moved 2 places to the right.


(The digit 4 is used here simply to make the numbers be the same overall length. It can be changed to any other digit (except 3 or 7) or removed. Digits that are not 3 or 7 can replace any of the zeros.)

How many pairs of whole numbers have a sum of 110

Answers

Let's focus on positive numbers only, to simplify things.
This omits zero (0) and all negative numbers.
1+109=110
2+108=110
continue this until you discover the pattern.  Then count the number of sums that equal 110.

If the probability of drawing an ace from a deck of cards is 0.077 and the probability of rolling a "2" using a fair die is 0.167, then the probability of drawing an ace and rolling a "2" is

Answers

the probability of drawing an ace and rolling a "2" is = 0.077 × 0.167

you just multiply and get the answer.

The probability of drawing an ace and rolling a "2" is 0.012859.


What is probability?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the probability of drawing an ace from a deck of cards is 0.077 and the probability of rolling a "2" using a fair die is 0.167.

The probability of drawing an ace and rolling a "2" is calculated as,

Probability = 0.077 × 0.167

Probability = 0.012959

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WILL GIVE THE BRAINLIEST ANSWER!!!

Select the postulate that is illustrated for the real numbers.

25 + 0 = 25

The commutative postulate for multiplication

Multiplication by one

The addition inverse postulate

Commutative postulate for addition

The distributive postulate

Additive identity

The multiplication inverse

Answers

The answer for this question would be F) Additive identity or the sixth option.

The answer is additive identity because you're adding a number plus 0 and the result is the number u added.
F) Additive identity or number 6 
hope that helps 

During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?

Answers

1 min = 4cups
60 min = 1hr
4×60 =240
1hr=240 cups
2hrs = 480 cups
1 gallon = 16 cups
480/16 = 30 gallons

The caterer should bring 30 gallons of tea
In 2 hours you would need 30 gallons of tea.
Explanation:
4cups/per minute x 1 gallon/16cups x 60minutes/1 hour = 240gallons/16hours
240gallons/16hours = 15gallons/1 hour
15gallons/1 hour x 2 = 30 gallons/2 hours

two stores sell the same refrigerator for the same original price. Store A advertises that the refrigerator is on sale for 15% off the original price. Store B advertises that it is reducing the refrigerator’s price by $150. When Stephanie compares the sale prices of the refrigerator in both stores, she concludes that the sale prices are equal.

Let p represent the refrigerator’s original price.

Which equation models this situation?

Answers

The answer is 0.85p = p – 150

since the refrigerator is 15% off

it is selling at 100%-15% = 85% of the original value

85% = 0.85

 so 0.85Pis one price

other store is selling at p-150

 so 0.85p = p-150

Caecillia can run 3 over 20 of a Marathon in 2 over 3 of an hour compute the unit rate

Answers

3/20 marathon in 2/3 hour

we want to find per 1 hour

(3/20marathon)/(2/3hour)
multiply it by (3/2)/(3/2)
(3/20marathon times (3/2)/(6/6hour)
(9/40marathon)/(1hour)
9/40marathon per hour

the tangent line to the curve y=x^3-6x^2-34x-9 has slope 2 at two points on the curve. find the two points

Answers

[tex]\bf y=x^3-6x^2-34x-9\implies \cfrac{dy}{dx}=3x^2-12x-34 \\\\\\ \stackrel{\textit{slope of 2}}{2}=3x^2-12x-34\implies 0=3x^2-12x-36 \\\\\\ 0=x^2-4x-12\implies 0=(x-6)(x+2)\implies x= \begin{cases} 6\\ -2 \end{cases}\\\\ -------------------------------\\\\ \stackrel{y}{f(6)}=(6)^3-6(6)^2-34(6)-9\implies f(6)=-213\\\\\\ (\stackrel{x}{6}~,~\stackrel{y}{-213}) \\\\\\ \stackrel{y}{f(-2)}=(-2)^3-6(-2)^2-34(-2)-9\implies f(-2)=27\\\\\\ (\stackrel{x}{-2}~,~\stackrel{y}{27})[/tex]
Final answer:

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2. The two points are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

Explanation:

To find the two points where the tangent line to the curve y=x^3-6x^2-34x-9 has a slope of 2, we need to find the derivative of the function and set it equal to 2.

First, we find the derivative of the function:

dy/dx = 3x^2 - 12x - 34

Next, we set the derivative equal to 2 and solve for x:

3x^2 - 12x - 34 = 2

3x^2 - 12x - 36 = 0

Using the quadratic formula, we find the solutions for x:

x = (-b ± √(b^2 - 4ac))/(2a)

Substituting the values a = 3, b = -12, and c = -36 into the quadratic formula, we get:

x = (-(-12) ± √((-12)^2 - 4(3)(-36)))/(2(3))

x = (12 ± √(144 + 432))/6

x = (12 ± √(576))/6

x = (12 ± 24)/6

x = 12/6 ± 24/6

x = 2 ± 4

So the two points where the slope of the tangent line is 2 on the curve are (2, f(2)) and (6, f(6)), where f(x) = x^3-6x^2-34x-9.

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I need to know how to solve this in order correctly and the answers well

Answers

use order of operations

8^2 = 64

4(64+4*4*8)

4(64+128)

4(192)

768

In a grocery store there are 4 self-checkout lines and 8 lines with cashiers. Find the ratio of the number of lines with cashiers to the number of self-checkout lines. Express the answer as a simplified fraction.

Answers

8:4 Is the ratio of the number of lines with cashiers to the number of self-checkout lines.

Answer:  The required simplified fraction is [tex]\dfrac{2}{1}.[/tex]

Step-by-step explanation:  We are given that in a grocery store there are 4 self-checkout lines and 8 lines with cashiers.

We are to find the ratio of the number of lines with cashiers to the number of self-checkout lines.

Let n represents the number of lines with cashier and m represents the number of self-checkout lines.

Then, we have

n = 8 and  m = 4.

Therefore, the required ratio of the number of lines with cashiers to the number of self-checkout lines is given by

[tex]\dfrac{n}{m}=\dfrac{8}{4}=\dfrac{2}{1}.[/tex]

Thus, the required simplified fraction is [tex]\dfrac{2}{1}.[/tex]

Suppose that a large mixing tank initially holds 700 gallons of water in which 50 pounds of salt have been dissolved. another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min. if the concentration of the solution entering is 4 lb/gal, determine a differential equation for the amount of salt a(t) in the tank at time t > 0. (use a for a(t).)

Answers

Final answer:

The differential equation for the amount of salt a(t) in the tank at time t > 0 is dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t).

Explanation:

To find the differential equation for the amount of salt a(t) in the tank at time t > 0, we need to consider the rate of change of the salt concentration in the tank.

Let A(t) represent the amount of salt in the tank at time t. The salt entering the tank each minute is given by the concentration (4 lb/gal) multiplied by the rate of inflow (3 gal/min), which is 12 lb/min.

The salt leaving the tank each minute is given by the concentration in the tank (A(t)/V(t)) multiplied by the rate of outflow (2 gal/min), which is 2A(t)/(35 + (3 - 2)t).

Therefore, the rate of change of the salt in the tank is given by the difference between the rate of inflow and the rate of outflow: dA(t)/dt = 12 - 2A(t)/(35 + (3 - 2)t). This is our differential equation for the amount of salt in the tank.

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The entrance of a cave is at an elevation of 14 meters. The lowest part of the cave is at an elevation of negative 86. Write an integer to represent the elevation of the entrance to the cave.

Answers

Answer: 14 Given ,entrance of cave having an elevation of 14 m.since 14 is an integer which represent elevation

there are 2 aircraft carriers , A&B, and carrier a is longer in length than carrier B. The total length of these 2 carriers is 4,198 ft, while the differences of their lengths is only 10ft. Find the length of each carrier

Answers

Sum and difference problem.

Longer carrier = (sum+difference)/2 = (4198+10)/2 = 2104 ft
Shorter carrier = (sum-difference)/2 = (4198-10)/2 = 2094 ft.

Final answer:

Carrier A is 2104 feet long and carrier B is 2094 feet.

Explanation:

This problem can be solved using simple algebra. Let's denote the length of carrier A as 'a' and the length of carrier B as 'b'. We know two things about these lengths from the question:

The sum of the lengths is 4198 feet, hence: a+b=4198Carrier A is longer by 10 feet, hence: a-b=10

Now, you can add these two equations together to eliminate 'b'. This will give: 2a=4208. Hence, by dividing by 2, you will find that a=2104. Now, substitute a=2104 back into the first equation: a+b=4198. This will give: 2104+b=4198, which simplifies to b=2094. So, the length of carrier A is 2104 feet and the length of carrier B is 2094 feet.

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Ratio of the number of students in art class to the number of students in gym class was 2:7, however art class is small, and gym class is large, students changed for the second semester. Now the students in art class to the number students in gym class is 5:4. If 75 students are in art class in second semester, how many were in art class and gym class first semester?

Answers

semester 1:

let the number of students in the art class be 2a, and the number of the students in the gym class be 7a. (check: the ratio is 2a:7a = 2:7)

so the total number of students is 9a.


semester 2:

the 9a students are go to the art class and gym class at a a ratio of 5: 4, 

so 5a students go to the art class, and 4a students go to the gym class.



75 students are in art class in second semester means that 5a=75

so a=75/5=15.


In the 1st semester the number of students was: 

art class: 2a=2*15=30

gym class: 7a=7*15=105

i need help plez and thanks

Answers

the answer is 80, there multiplying x2 for each number

How does writing 3.441 in expanded form show why the same digit can have different values?

Answers

When expanded it would be 3+0.4+0.04+0.001. There is two fours, but because it is written in expanded form you can see that one is four tenths and the other is four hundredths. Although they are the same digit, you can see that they are different values, the way you wrote it helping you with that.
Final answer:

Writing 3.441 in expanded form shows that each digit represents a different value depending on its place in the decimal number. This is determined by the power (exponent) of 10 corresponding to the decimal shift from the right side of the digit. This understanding is essential for scientific notation and handling large and small numbers.

Explanation:

Writing the number 3.441 in expanded form helps to clarify why the same digit can possess different values based on its position in the decimal number. To write 3.441 in expanded form we break it down into the addition of its respective place values, like this:

3.441 = 3 x 1 + 0.4 x 1/10 + 0.04 x 1/100 + 0.001 x 1/1000.

As we can see, each digit represents a different value based on its placement. This is determined by the power (exponent) of 10 which is equal to the number of places the decimal is shifted from the right side of the digit. This method is also applicable to scientific notation, transforming both very large and very small numbers into more manageable expressions for calculations.

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If the machine has a probability of failure of 0.01, what is the probability of more than 1 failure occurring in a batch of 20 envelopes?

Answers

The Answer is 0.0169
see attachment for full solution

She has given recently are different length one is 3 4/5 feet long and the other is 3 1/2 feet long how much would she have to cut so it will be the same length

Answers

Final answer:

To make the lengths the same, she would have to cut 0.3 feet from the longer piece.

Explanation:

To find the amount she would have to cut to make the two lengths the same, we need to subtract the smaller length from the larger length.

The first length is 3 4/5 feet, which can also be written as 3 + 4/5 = 3 + 0.8 = 3.8 feet.

The second length is 3 1/2 feet, which can also be written as 3 + 1/2 = 3 + 0.5 = 3.5 feet.

Subtracting the smaller length (3.5 feet) from the larger length (3.8 feet), we get:

3.8 feet - 3.5 feet = 0.3 feet.

So she would have to cut 0.3 feet from the longer piece to make the lengths the same.

A post card collector has 1,230 postcards if she displays them on pages that hold 6 cares each how many pages does she need ?

Answers

There are 1230 postcards
each page can hold 6 cards

so your equation is 

1230/6 =x 

where as x is the pages she needs 

x = 205

She needs 205 pages exactly

hope this helps

Sathish is going on a 200020002000-kilometer road trip with two friends. The car consumes 666 liters of gas for every 100100100 kilometers, and gas costs \$1.20$1.20dollar sign, 1, point, 20 per liter. If Sathish and his two friends want to split the cost evenly, how much should they each pay?

Answers

First calculate the total amount of liters consumed:

Volume gas consumed = (6 L / 100 km) * 2000 km = 120 L

 

Then calculate the total cost:

Cost = ($1.20 / L) * 120 L = $144

 

Since there are three of them, so each must pay:

Payment of each = $144 / 3 = $48 per person


Answer:

$48 per person

Simplify (3a^3 b^3)(4ab^2)^2

Answers

[tex]\bf (3a^3b^3)(4ab^2)^2\implies (3a^3b^3)(4^2a^2b^{2\cdot 2})\implies (3a^3b^3)(4^2a^2b^4) \\\\\\ 3a^3b^34^2a^2b^4\implies 3\cdot 4^2a^3a^2b^3b^4\implies 3\cdot 16a^{3+2}b^{3+4}\implies 48a^5b^7[/tex]

Evaluate the numerical expression
[18 Divided by (2 x 3)] x 4

Answers

P: parenthesis
E: exponents
MD: multiplication or division (whichever comes first left to right)
AS: addition or subtraction (whichever comes first left to right)

This is the order of operations. We will use this to solve the equation correctly.
We will start with the parenthesis. 2x3=6.
[18/6]x4
Next, we will do the rest of the parenthesis.
18/6=3.
This gets rid of the parenthesis (or brackets.) We will now do the rest of the problem, which is multiplying 3 and 4.
3x4=12.
12 is your final answer.

The apartments in Ericas apartment house are consecutively numbered on each floor. The sum of her and next door neighbor's number is 2409. What are the two numbers?

Answers

Let x be the number of Ericas's apartment, the number of her neighbor will be 
x+1, so

x+ x+1 = 2409

2x = 2408 and x = 1204 and her next door neighbor's is 1205



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