Two positive integers x and y
x - y = 4
x² + y = 68
Findx and y
SolutionAdd the two equations together.
... (x - y) + (x² + y) = (4) + (68)
... x² + x = 72
Rearrange to standard form and factor.
... x² + x - 72 = 0
... (x + 9)(x - 8) = 0
Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.
... x + 9 = 0 ⇒ x = -9
... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution
Then we can find y from
... 8 - y = 4
... y = 4 . . . . . . . add y-4 to the equation
The two positive integers are 8 and 4.
To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.
Explanation:The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.
Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.
Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.
Therefore, the two positive integers are 4 and 8.
From the ground, a hot-air balloon went up at a speed of 375 feet per minute for 5 minutes. It then went down at a speed of 225 feet per minute for 6 minutes. How far is the hot-air balloon above the ground?
it went up: 375 *5 = 1875 feet total
it went down: 225 *6 = 1350 feet total
1875-1350 = 525
it is 525 feet above the ground
alvin is 13 years older than elga. the sum of their ages is 107. what is elga's age
Rob Retiree gets a Social Security benefit of $800 per month. His wife receives a benefit equal to 50 percent of Rob's benefit. If they take an additional $300 per month from savings, what will their monthly income be?
What does the equation y = x2 represent as a curve in the set of real numbers2?
Actually the given equation y = x^2 represents a parabola in the set of real numbers. A parabola is defined to be a symmetrical open plane curve created by the intersection of a cone with a plane parallel to its side. Since the square is on the x, therefore the parabola is opening upwards.
Answer:
Parabola
The equation y = x^2 represents a parabola as a curve
The equation is given as:
y = x^2
The above equation has a degree of 2
Polynomials that have a degree of 2 are referred to as quadratic equations
The curve of a quadratic equations are called parabola
Hence, the equation y = x^2 represents a parabola as a curve
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What is the quotient of 7670 and 94
divide:
7670 / 94 = 81.59574468
round the answer as needed.
Solve 11kx + 13kx = 6 for x.
A. X= 1/4k
B. X= 4k
C. X= 4/k
D. X= k/4
Answer:
Option (a) is correct.
[tex]x=\frac{1}{4k}[/tex]
Step-by-step explanation:
Given: Equation 11kx + 13kx = 6
We have to solve for x and choose the correct option from the given options.
Consider the given equation 11kx + 13kx = 6
Taking kx common, we have,
kx (11+13) = 6
Simplify, we have,
24kx = 6
Divide both side by 24, we have,
[tex]kx=\frac{6}{24}[/tex]
Simplify, we have,
[tex]kx=\frac{1}{4}[/tex]
Divide both side by k, we have,
[tex]x=\frac{1}{4k}[/tex]
Thus, Option (a) is correct.
What's 39,230 rounded to the nearest ten thousabd
A retired woman has $60,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. If we let x be the amount the woman invests in the 15% bond, how much in dollars will she be able to invest in her CD?
You ate 2⁄3 of the pizza. How many twelfths is that?
Find the area of a triangle that has a base of 10 inches and a height of 7 inches.
A) 8.5 in2
B) 17 in2
C) 35 in2
D) 70 in2
Answer:
C ) 35 in2
Step-by-step explanation:
i did the test
Write word form for number 7.351
Answer:
seven point three five one thousandths
Step-by-step explanation:
Which letters from the table represent like terms? -2x 3 4x 1
Music may help people relax. John got two groups of people together. He took everybody's pulse of blood pressure. The one group to listen to soothing music while other group sat in silence. After the song was over, he measured everyone's pulse and blood pressure.
What is the independent variable?
What is the dependent variable?
What are the constants or control variables?
In John's experiment, the independent variable is the condition of the groups (listening to music or sitting in silence), the dependent variables are pulse and blood pressure, and the control variables could include room temperature, the timing, the duration of the experiment, and the use of consistent measurement devices.
Explanation:In this experiment conducted by John, the independent variable is the condition under which each group is placed—which is, one group listening to soothing music and the other group sitting in silence. This is the independent variable because it's the factor that John changes or manipulates during the experiment.
The dependent variables here would be the pulse and blood pressure of the individuals in both groups. These variables are considered dependent because their values may change based on the effect of the independent variable (i.e., the type of noise the group is subjected to).
The constants, or control variables, in this experiment could include the room temperature, the timing of the experiment, the duration for which the conditions are applied (the length of the song), and the same pulse and blood pressure checking device, among others. These are the factors that remain the same throughout the experiment to ensure that the results are only influenced by the independent variable and not by any other factors.
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what is twenty less than twelve percent of a number minus the sum of twice the number and negative fifteen
Find the domain of the graphed function?
Answer:
The correct answer to this question is C: x > 0
Step-by-step explanation:
wich one of these numbers is not like the others 21,15,6,16,27
Charles can type 675675675 words in 999 minutes.
How many words can Charles type in 131313 minutes?
A senior class is selling lanyards as a fundraiser. The profit for each lanyard is $0.75. Write and solve an inequality to determine the number of lanyards the class must sell to make a profit of at least $250.
One card is randomly selected from a deck of cards. find the odds against drawing a blackblack fivefive.
A number n is less than 6 units from 0. Write an absolute value inequality
The absolute value inequality which relates to the expression n is less than 6 units from 0 is |n|< 6
The absolute value which stand for 6 units From 0 can be expressed as :
|0 - 6| = 6 (absolute value of any number or expression is always positive)This means that, the number n is less than 6
Therefore, the expression can be written as :
|n| < 6. This means that the absolute value of n is less than 6.
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To write an absolute value inequality when a number n is less than 6 units from 0, use the notation |n| < 6.
Explanation:To write an absolute value inequality, we need to express the distance between the number n and 0 as less than 6 units. This can be done by using the absolute value notation: |n| < 6. In this inequality, the absolute value of n must be less than 6 units.
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potatoes are selling for $0.48 per pound. How much is 12lbs of potatoes?
multiply price per pound by pounds
0.48 * 12 = $5.76 total
To receive a grade A, the average of four 100-point exams must be 90 or better. If a student received scores of 89, 82, and 94 on the first three exams, what minimum score does he need on the fourth exam to earn an A?
Elleanna is planning to join a DVD club and is investigating the options for membership. Option 1 is $20 membership fee $1.25 rental change for each DVD rented. Option 2 has no rental fee and changes $2.50 for each DVD rented. How many DVDs would Elleanna have to rent in order for the total cost of Option 1 to be equal to option 2?
Elleanna has to rent in order for the total cost of Option 1 to be equal to option 2 will be 16.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Elleanna is planning to join a DVD club and is investigating the options for membership. Option 1 is a $20 membership fee and $1.25 rental charge for each DVD rented. Option 2 has no rental fee and charges $2.50 for each DVD rented.
Let 'x' be the number of DVDs and 'y' be the total cost. Then the equations are given as,
y = 1.25x + 20
y = 2.5x
If the total cost becomes equal, then the number of DVDs rented will be given as,
2.5 = 1.25x + 20
1.25x = 20
x = 16
Elleanna has to rent in order for the total cost of Option 1 to be equal to option 2 will be 16.
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pep club members are making spirit buttons. They make 490 spirit buttons in 3 1/2 hours. Find the number of button pep club makes per hour
Answer:
140 button pep club makes per hour.
Step-by-step explanation:
Given : Pep club members are making spirit buttons. They make 490 spirit buttons in [tex]3\frac{1}{2}[/tex] hours.
To find : The number of button pep club makes per hour ?
Solution :
In [tex]3\frac{1}{2}[/tex] hours they make 490 buttons.
i.e. In 3.5 hours they make 490 buttons.
So, In 1 hours they make [tex]\frac{490}{3.5}[/tex] buttons.
In 1 hours they make 140 buttons.
Therefore, 140 button pep club makes per hour.
Solve for v
8v-4v=8
Answer:2
The cost of renting a car is $35/wk plus $0.25/mi traveled during that week. An equation to represent the cost would be y = 35 + 0.25x, where x is the number of miles traveled. If your cost was $51.25, how many miles were you charged for traveling?
To find the number of miles traveled when the total cost is $51.25, subtract the base cost from the total and divide by the per-mile rate, resulting in 65 miles traveled.
Explanation:The question asks how many miles were traveled if the total cost for renting a car was $51.25. According to the equation y = 35 + 0.25x, where y represents the total cost and x represents the miles traveled, we first need to subtract the base cost of $35 from the total cost to find out how much is charged for the mileage.
Here is how you calculate it:
Subtract the weekly rental cost from the total cost: $51.25 - $35 = $16.25. Divide the remaining cost by the cost per mile: $16.25 / $0.25 = 65 miles.
Therefore, you were charged for traveling 65 miles.
A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000. So far, they have spent $824,000. Which compound inequality correctly expresses how much more the publisher can spend?
$155,850 ≥ x ≤ $415,850
$155,850 ≤ x ≥ $415,850
$155,850 ≥ x ≥ $415,850
$155,850 ≤ x ≤ $415,850
Answer:
[tex]155,850 \leq x \leq 415,850[/tex]
Step-by-step explanation:
A publisher estimates their costs of publishing a book is from $980,000 to $1,240,000.
Let x be the amount publisher can spend
So, [tex]980000\leq x \leq 1240000[/tex]
Now we are given that So far, they have spent $824,000
So, [tex](980000-824000)\leq x \leq (1240000-824000)[/tex]
[tex]156000\leq x \leq 416000[/tex]
So, Option D is true
Hence compound inequality correctly expresses how much more the publisher can spend is [tex]155,850 \leq x \leq 415,850[/tex]
A certain natural number is not divisible by 7 can
it be divisible by 14?
in which quadrant is (-2,1 ) located
Which is true? A 4.02 > 4.1 B 4.181 < 4.118 C 4.5 > 4.49 D 4.665 > 4.67
The statements, 4.02>4.1, 4.181<4.118 and 4.665>4.67 are true. Therefore, options A, B and D are the correct answers.
How to compare to decimals?Comparing decimals involves starting with the digits having the highest place value, just like when comparing other whole numbers. We begin the comparison by putting the provided decimal numbers in a place value table. We move on to the digits in the next place to the right if the digits on the biggest place value match. Up till the digits that are different are reached, we continue comparing digits.
A) 4.02>4.1
Here, the statement is true.
B) 4.181<4.118
The statement 4.181<4.118 is true.
C) 4.5>4.49
The statement 4.5>4.49 is not true.
D) 4.665>4.67
The statement 4.665>4.67 is true.
Therefore, options A, B and D are the correct answers.
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