One positive integer is 6 less than twice another. The sum of their squares is 468. Find the integer
Answers
The two integers are 12 and 18.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, one positive integer is 6 less than twice another.
Let positive integer be x and the other positive integer is 2x-6
x²+(2x-6)²=468
x²+4x²-24x+36=468
5x²-24x+36-468=0
5x²-60x+36x-432=0
5x(x-12)+36(x-12)=0
(x-12)(5x+36)=0
(x-12)=0
x=12
So, 2x-6=18
Therefore, the two integers are 12 and 18.
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Related Questions
write a real world example that could be solved by using the inequality 4x+8≥32.then solve the inequality
Answers
how much was she paid per hour?
[tex]4x + 8 \geqslant 32[/tex]
[tex]4x \geqslant 24[/tex]
[tex]x \geqslant 6[/tex]
Sally was paid at least 6 dollars /hour.
A real-world situation for the inequality 4x + 8 ≥ 32 could involve calculating the minimum hours required at a part-time job to earn $32. Subtracting 8 and dividing by 4, we find that at least 6 hours of work are needed.
Explanation:A real-world example that could be solved by using the inequality 4x + 8 ≥ 32 might involve a situation where you need to determine how many hours you must work at a part-time job to earn at least a certain amount of money. Suppose you earn $4 per hour and you have already earned $8. You want to know the minimum number of hours you must work to have at least $32 in total.
To solve the inequality 4x + 8 ≥ 32, you would first subtract 8 from both sides, which gives you 4x ≥ 24. Then, you would divide both sides by 4 to find the number of hours (x) you need to work. Therefore, x ≥ 6. This means you must work at least 6 hours to earn $32 or more.
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**Aleta deposited $450 into a savings account earning 3.75% simple interest. How much interest will she earn in 6 years? Explain.
Answers
ie: 'ans' is the total of the previous equation.
450+3.75%
ans+3.75%
ans+3.75%
ans+3.75%
ans+3.75%
ans+3.75%
ans = 561.23.
If a couple plans to have 9 children, what is the probability that there will be at least one girl? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one girl in 9 children?
Answers
Figure this question out first as though you don't get any females. They are all males. The total number of ways that you can distribute 9 children by gender is 2^9 = 512
There is only one way that you can get all males and that is M M M M M M M M M so the chances are 1 chance in 512 or 1/512
All males = 0.001953
So the chances of there being at least 1 female is
1 - 1/512 = 0.998
Which contrary to my opening remark is almost certainty.
state whether the relationship between x and y in y=4x-5 is proportional or not
Answers
A red balloon starts at 7.3 meters off the ground and rises at 2.6 meters per second. A blue balloon starts at 12.4 meters off the ground and rises at 1.5 meters per second. Write and solve an equation to determine when the balloons are at the same height.
Answers
Since the red balloon rises at 2.6 meters per second, we can represent this part of the equation as 2.6s. The balloon is already 7.3 meters off of the ground, so we just add the 7.3 to the 2.6s:
2.6s + 7.3
Since the blue balloon rises at 1.5 meters per second, we can represent this part of the equation as 1.5s. The balloon is already 12.4 meters off of the ground, so we just add the 12.4 to the 1.5:
1.5s + 12.4
To determine when both balloons are at the same height, we set the two equations equal to each other:
2.6s + 7.3 = 1.5s + 12.4
Then, we solve for s. First, the variables must be on the same side of the equation. We can do this by subtracting 1.5s from both sides of the equation:
1.1s + 7.3 = 12.4
Next, we must get s by itself. We work towards this by subtracting 7.3 from both sides of the equation:
1.1s = 5.1
Last, we divide both sides by 1.1. So s = 4.63.
This means that it will take 4.63 seconds for both balloons to reach the same height. If we want to know what height that is, we simply plug the 4.63 back into each equation:
2.6s + 7.3
= 2.6 (4.63) + 7.3
= 19.33
1.5s + 12.4
= 1.5 (4.63) + 12.4
= 19.33
After 4.63 seconds, the balloons will have reached the same height: 19.33 meters.
Final answer:
To find when two balloons are at the same height, set up two equations equal to each other with the starting heights and rates of ascent, and solve for the time. The two balloons will be at the same height approximately 4.636 seconds after they start rising.
Explanation:
To determine when two balloons will be at the same height, we can set up an equation based on their starting heights and their rates of ascent. We have a red balloon that starts at 7.3 meters off the ground and rises at 2.6 meters per second, and a blue balloon that starts at 12.4 meters off the ground and rises at 1.5 meters per second.
Let's let t represent the time in seconds after the balloons begin to ascend. The height of the red balloon at any time t can be expressed as:
Height_red = 7.3 + 2.6t
Similarly, the height of the blue balloon at any time t is:
Height_blue = 12.4 + 1.5t
To find out when the balloons are at the same height, we set the two equations equal to each other:
7.3 + 2.6t = 12.4 + 1.5t
Now, we solve for t by subtracting 1.5t from both sides:
2.6t - 1.5t = 12.4 - 7.3
1.1t = 5.1
Next, we divide both sides by 1.1 to isolate t:
t = 5.1 / 1.1
t ≈ 4.636 seconds
Thus, the balloons will be at the same height approximately 4.636 seconds after they begin to ascend.
HELP!!! 100 POINTS+ BRAINLIEST for correct answer
Mary leaves her house to take a walk. The graph shows the distance, d, in feet from her house that Mary is at any given time, t, in minutes. How many minutes has Mary walked when she reaches the farthest point from her house?
Answers
Here's the picture of the graph that goes with this question.
Your brother is 13 your age. Your sister is 6 years older than your brother. Your sister is 10 years old. Write and solve an equation to find your age a.
Answers
By setting up equations using the information about your siblings' ages, we find out that you are 12 years old.
To find your age, we can set up an equation based on the information given:
Your sister is 10 years old.
Your brother is 13 your age, meaning 1/3 of your age.
Your sister is 6 years older than your brother. Therefore, if your brother's age is b, your sister's age is b + 6.
Since your sister is 10, this allows us to write the equation for your brother's age as:
b + 6 = 10
Solving for b, we get:
b = 10 - 6 => 4
Now we know your brother is 4 years old, and since he is 13 your age, we can write another equation:
a ÷3 = 4
Multiplying both sides by 3 to solve for a:
a = 4 × 3 => 12
You are 12 years old.
Use the Law of Sines to find the missing angle of the triangle. Find m<b to the nearest tenth.
A) 110.0 degrees
B) 153.9 degrees
C) 26.1 degrees
D) 70.0 degrees
Answers
SinA/a=SinB/b=SinC/c
2. You don't need the fraction SinC/c, so you can eliminate it. Then:
SinA/a=SinB/b
A=40°
a=19
B=m∠b
b=13
3. When you substitute this values into SinA/a=SinB/b, you obtain:
SinA/a=SinB/b
Sin(40°)/19=SinB/13
SinB=13xSin(40°)/19
m∠b=SinB^-1(13xSin(40°)/19)
m∠b=26.1°
Therefore, the answer is: 26.1 degrees.
Answer: D) 70.0
Step-by-step explanation: :)
Solve the equation on the interval [0,2pi) 4sin^2x-3=0
Answers
4sin²x=3
sin²x=3/4
sinx=√3/2 or -√3/2
x=π/3, 2π/3, 4π/3, or 5π/3
The equation 4sin^2x-3=0 has a solution of x=π/3,2π/3,4π/3,5π/3.
What is equation?An equation is basically a relationship between two variables in equal to form. In an equation each variable must have a solution or value.
How to solve an equation?The equation given as 4sin²x-3=0
We have to first find the value of x in the equation itself which is 4sin²x=3
sin²x=3/4
sinx=√3/2 or -√3/2
x=π/3, 2π/3, 4π/3, or 5π/3.
Hence the solution for the equation 4[tex]sin^{2}x-3[/tex]=0 is x=π/3,2π/3,4π/3,5π/3.
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a company is shipping a motorcycle in a box with the dimensions of 4 2/3 feet by 3 3/4 feet by 8 ft the box also has packing material to help protect the motorcycle. what is the volume, in cubic feet, of the box?
Answers
[tex]4 \frac{2}{3} \times 3 \frac{3}{4} \times 8 = 140[/tex]
Hence, the volume of the box is 140 cubic feet.
(64+28+76)÷6 show how you can calculate the number of 3/4 cup servings
Answers
The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after 200 years.
Answers
Where:
[tex]N_{0} [/tex] is the initial sample
[tex]t[/tex] is the time in years
[tex]t_{1/2} [/tex] is the half life of the substance
[tex]N(t)[/tex] is the remainder quantity after [tex]t[/tex] years
From the problem we know that:
[tex]N_{0} =100[/tex]
[tex]t=200[/tex]
[tex]t_{1/2} =1600[/tex]
Lets replace those values in our equation to find [tex]N(t)[/tex]:
[tex]N(200) =100e^{( \frac{(-0.693)(200)}{1600}) } [/tex]
[tex]N(200)=100e^{( \frac{-138.6}{1600} )} [/tex]
[tex]N(200)=100e^{-0.086625} [/tex]
[tex]N(200)=91.7[/tex]
We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.
robert leaves his home to go to his office .he drives 6 km north and then 4km due east.approximatley what is the shortest distance from roberts home to his office,in kilometers
Answers
a²+b²=c²
6²+4²=c²
36+16=c²
52=c²
7.21=c
Answer=7.21km
substitution method for 7x-2y=1 & x-2y=1
Answers
7x - 2y = 1 (1)
x - 2y = 1 (2)
From equation (1), obtain
2y = 7x - 1 (3)
Substitute (3) into (2).
x - (7x - 1) = 1
-6x + 1 = 1
-6x = 0
x = 0
From (3), obtain
2y = 7*0 - 1 = -1
y = -1/2
Answer: (0, -1/2) or x=0, y= -1/2.
The balcony of an apartment is 4 feet by 7 feet. On a scale drawing of the apartment, the balcony is 0.8 inch by 1.4 inches, and the kitchen is 2.4 inches by 2.8 inches. What are the actual dimensions of the kitchen? Enter your answers in the boxes. The actual dimensions of the kitchen are feet by feet.
Answers
Thus, 2.4 inches * 5 = 12 feet and 2.8 inches * 5 = 14 feet
12 feet x 14 feet
Answer:
12 by 14
Step-by-step explanation:
took quiz
The coordinates of the vertices of parallelogram ABCD are A(-3,2) , B (-2,-1) , C ( 4,1) and D ( 3,4). The slopes of which line segments could be calculated to show that ABCD is a rectangle?
1) AB and DC
2) Ab and BC
3) AD and BC
4) AC and BD
When you say what answer you chose can you explain why that’s the answer please in depth?
Answers
I cannot draw the rectangle here. When you draw the line of x and y axis, plot the numbers, when you connect the dot, you will see the rectangle.I don't know how to draw it here, but that is the answer.
To show that a parallelogram is a rectangle, we need to show that ONE of the interior angles is a right angle.
Therefore we need to find the angle between two adjacent sides.
To find two adjacent sides in a parallelogram with vertices in counter-clockwise, we need two sides with a common vertex, for example,
AB+BC, or BC+CD, or CD+DA, or DA+AB.
Any two sides without a common vertex are opposite sides.
Mr kenrick made three deposits to his account to his bank account in this order 460,185, and 240 show how to use a commutative property to find the sum of the deposits mentally
Answers
We have then:
(460 + 185) + 240 = 240 + (460 + 185) = 885
Answer:
(460 + 185) + 240 = 240 + (460 + 185) = 885
(05.02)Find the measure of angle x in the figure below:
Two triangles are shown such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 55 degrees. The lower right angle is marked as 30 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees.
Answers
Answer:
x=95°Step-by-step explanation:
We are given that: Two triangles are such that one triangle is inverted and they share a common vertex. The lower triangle has two angles at the base. The lower left angle is marked as 55 degrees. The lower right angle is marked as 30 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees.
The figure of such a triangle is attached to the answer.
As we know that sum of all the angles of a triangle is equal to 180°.
⇒ 55°+30°+x=180°
⇒ 85°+x=180°
⇒ x=180°-85°
⇒ x=95°
Hence, the angle at the vertex is 95°.
The measure of angle x in the inverted triangle formed by two triangles sharing a common vertex is 95 degrees .
Two triangles sharing a common vertex. The angles given are as follows:
Measure of the lower left angle of the lower triangle = 55 degrees.
Measure of the lower right angle of the lower triangle = 30 degrees.
The angle at the vertex of the inverted triangle (at the top) can be found by subtracting the sum of the angles in the lower triangle from 180 degrees .
Since the sum of angles in a triangle is always 180 degrees.
Sum of angles in the lower triangle
= 55 degrees + 30 degrees
= 85 degrees.
Now, subtract the sum of angles in the lower triangle from 180 degrees to find the angle at the vertex of the inverted triangle (x degrees):
x degrees = 180 degrees - 85 degrees
= 95 degrees.
Therefore, the measure of angle x is 95 degrees.
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The transport layer handles the transmission error by requesting the damaged segments to be retransmitted. if the probability of a segment being damaged is p, what is the mean number of the transmissions required to send a segment? you can assume the acknowledgements are never lost for solving this question.
Answers
This distribution may be applied to the given situation, where the probability of success is p.
Let n=number of transmissions required (n ≥ 1)Then
P(n)=(1-p)^(n-1)*p (probability that n transmissions are required)
and the mean number of transmissions required
μ = 1/p
Final answer:
The mean number of transmissions required to send a segment successfully, given a damage probability of p, is calculated as 1/(1-p). This is derived from the geometrical distribution, representing the expected number of trials until the first success.
Explanation:
The question asks for the mean number of transmissions required to successfully send a segment given that the probability of a segment being damaged is p, and assuming acknowledgements are never lost. To solve this, we consider each transmission attempt as an independent trial with only two outcomes: success (with probability 1-p) or failure (with p). The problem thus resembles a geometrical distribution where the expected value (mean number of trials to get the first success) can be calculated as 1/(1-p). Therefore, if the probability of a segment being damaged is p, the mean number of transmissions required to send a segment successfully is 1/(1-p).
For example, if the probability of damage is 0.1 (p=0.1), then the mean number of transmissions would be 1/(1-0.1) = 1.1111, rounding up since you can't have a fraction of a transmission in reality.
adding and subtracting fractions with unlike denominators
Answers
Change the fractions to the common denominator.
Then you add or subtract the fractions.
Finally, you may need to reduce the fraction.
Example 1:
Add
1/5 + 1/3
The least common denominator is 15.
Both denominators must become 15.
1/5 + 1/3 = 3/3 * 1/5 + 5/5 * 1/3 = 3/15 + 5/15 = 8/15
Example 2:
Subtract
3/8 - 1/3
The least common denominator is 24.
3/3 * 3/8 - 8/8 * 1/3 = 9/24 - 8/24 = 1/24
Both in addition and subtraction, you only add or subtract the numerators. The denominator of the answer is the common denominator.
Example problem:
2/3 + 4/5 = ?
The L.C.D is equal to 15 (from multiplying the denominators 3 and 5 together).
Now you can make the first fraction (2/3) have a denominator of 15 by multiplying it by a ratio of 1 (5/5). For the second denominator (4/5) multiply it by a ratio of 1 as well (3/3). Now the fractions will be (2/3)(5/5) + (4/5)(3/3) = 10/15 + 12/15
Because the fractions have the same denominator now you can now add them together and then simplify the fraction to its simplest form.
10/15 + 12/15 = 22/15 (This fraction cannot be reduced further, it is the final answer)
Part A: The area of a square is (25x2 − 10x + 1) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (81x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answers
PART A:
As the expression given is the area of a square (and in a square the sides are all of equal length) when we factor (write as a product) this expression we should get two identical factors. If you remember how to distribute twice (teachers usually use the term F.O.I.L.) this question is asking you to go backwards...the expression is what you get when you "FOIL" so what were the two terms before?
25x^2 --> What can you multiply to get 25x^2? Since the terms have to be identical that's 5x. That is (5x)(5x) gives 25x^2.
Next we look at the last term (1) and think what can you multiply by itself to get 1? That's 1 as (1)(1)=1.
This means that the expression 25x^2 -10x + 1 = (5x+1)(5x+1) = (5x+1)^2.
The side of the square is 5x+1
PART B:
Here you are asked to factor [tex]81 x^{2} -9 y^{2} [/tex]. You might notice that [tex]81 x^{2}[/tex] is a perfect square. [tex]81 x^{2} =(9x)(9x)[/tex]. Similarly, [tex]9 y^{2} =(3y)(3y)[/tex]. We are dealing with the difference (notice the subtraction sign between the terms) of squares.
How do we factor the difference of squares? It is: (square root of first term + square root of second term)(square root of first term - square term of second). In symbols it is: [tex] a^{2} - b^{2} =(a+b)(a-b)[/tex].
In our case, we get [tex]81 x^{2} -9 y^{2} =(9x+3y)(9x-3y)[/tex].
If you forget or don't see that it is the difference of squares you can still figure it out by reasoning it out. What two terms give you the first when multiplied and what two terms give you the second?
Assume the method dosomething has been defined as follows: public static void dosomething (int[] values, int p1, int p2) { int temp = values[p1]; values[p1] = values[p2]; values[p2] = temp; } what does the method do?3
Answers
INPUT:
list of integers with name "values"
integer with name "p1"
integer with name "p2"
OUTPUT:
there is no output variable as in declaration of a method there is void
ANALYSIS:
"int temp = values[p1]"
this line creates variable "temp" which is integer. then this line goes to the list "values" and takes value that is at position "p1" and stores it into variable "temp"
"values[p1] = values[p2]"
this line goes to the list "values" and takes value that is at position "p2" and stores it into variable that is at position "p1"
"values[p2] = temp"
this line takes value of the variable "temp" and stores it into list values at position "p2"
Short explanation:
this code replaces values of the list at between positions p1 and p2
How to do this because I do not understand how to do it
Answers
-------------------------------------------
Work Shown:
Convert the time 7:45, which represents 7 min 45 sec, to seconds only
7:45 = (7 min) + (45 sec)
7:45 = (7*60 sec) + (45 sec)
7:45 = (420 sec) + (45 sec)
7:45 = (420+45) sec
7:45 = 465 sec
Do the same for 5:51
5:51 = (5 min) + (51 sec)
5:51 = (5*60 sec) + (51 sec)
5:51 = (300 sec) + (51 sec)
5:51 = (300+51) sec
5:51 = 351 sec
So the initial time is 465 seconds and it drops to 351 seconds
Subtract the values to find the amount dropped: 465-351 = 114
Divide that difference over the initial time: 114/465 = 0.24516
Move the decimal over 2 spots to the right to convert to a percentage: 0.24516 --> 24.516%
Then round to the nearest hundredth of a percent (2 decimal places) to go from 24.516% to 24.52% which is our final answer
So the reduction is roughly 24.52%
This means if you took 24.52% of the initial time and subtracted it off, then you'd get to about 351 seconds.
Answer:
24.52%
Step-by-step explanation:
What angle does this piece of pie form?
Answers
Round 3,989.23655 to the nearest tenth
Answers
Sam has bought a camera for $200 when it was on 20% off sale. What was the original price of the camera
Answers
x - .2x = 200 ← original price - discount amount = sale price
.8x = 200 ← 1x - 0.2x = .8x
x = 250 ← divided both sides by .8
The original price was $250
Answer250
Step-by-step explanation:
rhombus and a square have one and the same side of 6 cm. The area of the rhombus is 4/5 of the area of the square. Find the height of the rhombus.
Answers
1. area_rombus=a*h, where a=6 - the length of the side, h - height.
h=area_rombus/a.
2. area_sq=a², where a=6 - the length of the square.
area_sq=36, area_rombus=4/5 *36=28.8.
3. according to the item 1 h=area_rombus/a=28.8/6=4.8.
answer: 4.8
Answer:
4.8 cm
Step-by-step explanation:
Solve for Y
Y + 1.48 = 6.71
Answers
-1.48 -1.48
y=5.23
Isolate the Y by subtracting 1.48 to both sides
Y + 1.48 (-1.48) = 6.71 (-1.48)
Y = 6.71 - 1.48
Y = 5.23
5.23 is your answer
hope this helps
An employee has an annual salary of $51,300. They receive $2,830 in health insurance and $4,600 in paid time off per year. They drive their personal vehicle for work which costs them $600 per month, but the company reimburses them $0.54 per mile for the total work miles driven. If the employee drives 36,000 miles for work for the year, what will be their total employment compensation?
a.
$70,740
b.
$70,970
c.
$77,570
d.
$78,170
Answers
The total employment compensation of the employee is b. $70,970.
What are Arithmetic operations?Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.
Given that,
Annual salary of the employee = $51,300
Health insurance per year = $2,830
Paid time off per year = $4,600
Monthly expense for personal vehicle = $600
Yearly expense = 12 × $600 = $7200
Reimbursement for the vehicle = $0.54 per work mile
Reimbursement for vehicle for 36,000 miles for work for the year = $0.54 × 36,000 miles = $19,440
Total employment compensation = ($51,300 + $2,830 + $4,600 + $19,440) - $7200
= $70,970
Hence the employment compensation is $70,970.
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The floor plan of a home is dilated by a factor of 8 to create a new, larger floor plan. The area of the new floor plan is (8, 16, 32, 64, 256) times larger than the area of the original floor plan?
Answers
x-----------> Initial length x of the floor plan
y-----------> Initial length y of the floor plan
A1-----------> initial area of the floor plan
1) A1= x*y
2) the floor plan of a home is dilated by a factor of 8
then
x2=8x
y2=8y
the new area A2=x2*y2
A2=(8x)*(8y)=64*x*y--------> 64*A1
A2=64*A1
the answer is
The area of the new floor plan is 64 times larger than the area of the original floor plan
The area of the larger square is 16 times larger than the area of the smaller square.
Explanation:The area of the larger square is 16 times larger than the area of the smaller square.
To find the area of a square, you square the length of one side.
For example, if the smaller square has a side length of 4 inches, the area is 4 * 4 = 16 square inches. The larger square, with side length 8 inches, has an area of 8 * 8 = 64 square inches. Therefore, the area of the larger square is 64 / 16 = 4 times larger than the area of the smaller square.
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