One positive integer is 6 less than twice another. the sum of their squares is 569. find the integers.
Answers
Let y be the second integer
x=2y-6
x²+y²=596
(2y-6)²+y²=596
4y²-24y+36+y=569
4y²-23y+36-569=0
4y²-23y-533=0
y= -9.021 or 14.771
I have attached a graph below of the equation.
Since the integer has to be positive (mentioned in question), -9.021 cannot be a solution.
x=2y-6
x=2(14.771)-6
x=23.542
Hope I helped :)
Related Questions
What is the median for this set of numbers?
10, 9, 23 , 68, 70, 4, 12, 4
Answers
4, 4, 9, 10, 12, 23, 68, 70
Then, find the "middle" number in this list.
This case, there are two middle numbers: 10 and 12.
Take the average, or mean, of these two.
Your answer is 11.
4, 4, 9, 10, 12, 23, 68, 70
Cancel them out and you are left with 10 and 12.
Add 10 and 12 then divide by 2.
The median is 11.
I hope this helps love! :)
Bens date of birth is a prime number between 15 and 25. This number has 57 as a multiple.
Answers
How many perfect squares less than 100 have a tens digit of 6?
Answers
^^^^^^^^^^
Hank draws a line with a zero slope through the points (–2, 4) and (3, b). Which value of b could represent Hank’s second point? –3 –1 4 9
Answers
(-2,4)(3,4)
4-4. / 3- -2=. 0/5=0
So the answer is 4
Hope this helped
As per the slope of a line, the value of 'b' is 4.
What is the slope of a line passing through two points?The slope of a line(m) passing through two points (x₁, y₁) and (x₂, y₂)can be represented as:
m = (y₂ - y₁)/(x₂ - x₁)
Given, the slope of the line is (m) = 0.
Here the given points are (–2, 4) and (3, b).
Therefore, substituting the values, we get:
0 = (b - 4)/[(3 - (- 2)]
⇒ (b - 4)/5 = 0
⇒ b - 4 = 0
⇒ b = 4
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What is 0.182 rounded to the 2 decimal point?
(2dp)
Answers
hope it helps
Which ordered pairs are solutions to the inequality 2x+y>−4?
Select each correct answer.
(5, −12)
(−3, 0)
(−1, −1)
(0, 1)
(4, −12)
Answers
we will proceed to resolve each case to determine the solution
we have
[tex]2x+y>-4[/tex]
[tex]y>-2x-4[/tex]
we know that
If an ordered pair is the solution of the inequality, then it must satisfy the inequality.
case a) [tex](5,-12)[/tex]
Substitute the value of x and y in the inequality
[tex]-12>-2*5-4[/tex]
[tex]-12>-14[/tex] ------> is True
therefore
the ordered pair [tex](5,-12)[/tex] is a solution of the inequality
case b) [tex](-3,0)[/tex]
Substitute the value of x and y in the inequality
[tex]0>-2*-3-4[/tex]
[tex]0>2[/tex] ------> is False
therefore
the ordered pair [tex](-3,0)[/tex] is not a solution of the inequality
case c) [tex](-1,-1)[/tex]
Substitute the value of x and y in the inequality
[tex]-1>-2*-1-4[/tex]
[tex]-1>-2[/tex] ------> is True
therefore
the ordered pair[tex](-1,-1)[/tex] is a solution of the inequality
case d) [tex](0,1)[/tex]
Substitute the value of x and y in the inequality
[tex]1>-2*0-4[/tex]
[tex]1>-4[/tex] ------> is True
therefore
the ordered pair [tex](0,1)[/tex] is a solution of the inequality
case e) [tex](4,-12)[/tex]
Substitute the value of x and y in the inequality
[tex]-12>-2*4-4[/tex]
[tex]-12>-12[/tex] ------> is False
therefore
the ordered pair [tex](4,-12)[/tex] is not a solution of the inequality
Verify
using a graphing tool
see the attached figure
the solution is the shaded area above the line
The points A,C, and D lies on the shaded area, therefore the ordered pairs A,C, and D are solution of the inequality
Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work. 1/4X^3=-27/4
Answers
Answer:
x=3
Step-by-step explanation:
Mike and Kate plan to save money for their wedding over a 20 month period. They will need to save $8,000 to help pay for the wedding. They set aside the same amount each month. After a year they saved $4,000. Mike and Kate know they must adjust their plan in order to meet their goal, so they came up with the following options:
Option A: Stay with saving the same amount they've been saving each month but postpone the wedding 2 months.
Option B: Increase the amount of money they save each month by $80 from what they've been saving. Which of the following is a true statement?
a. Only option A will allow them to meet their goal.
b. Only option B will allow them to meet their goal.
c. Both options A and B will allow them to meet their goal.
d. Neither option A nor option B will allow them to meet their goal.
Answers
Answer: D (Neither option A nor option B will allow them to meet their goal.
Hope this helps!
Perry surveyed 60 students at her school and found that 0.45 of the students she surveyed said their favorite class is math. Another 35% of the students she surveyed reported that their favorite class is science. How many more students in the survey prefer math over science? 6 7 27 21
Answers
Explain how to multiply the complex #'s (3+2i)(4-i)
Answers
Multiply every term of the first binomial by every term of the second binomial.
Then combine like terms, and remember that i^2 = -1.
(3 + 2i)(4 - i) =
= 12 - 3i + 8i - 2i^2
= 12 + 5i + 2
= 14 + 5i
What is the conclusion of the following conditional a number is divisible by two if the number is even
Answers
HOPE THIS HELPED
Solve by quadratic formula
Answers
a = leading coefficient (highest power term)
b = term with just an x to the first power.
c = constant.
Plug in and solve! :)
find the sum. 12x2 + 9x2=
Answers
To calculate the sum of 12x² + 9x², add the coefficients (12 and 9) to get 21 and then multiply by x², resulting in a sum of 21x².
To find the sum of the expression 12x² + 9x², you simply add the like terms. Both terms have an x² component, so they can be combined.
Here's how you do it:
First, identify the coefficients of the x² terms, which are 12 and 9.
Next, add these two coefficients together: 12 + 9 = 21.
Finally, multiply the sum of the coefficients by x2 to get the final answer: 21x².
Therefore, the sum of 12x² + 9x² is 21x².
Describe the translation from AB TO AB
Answers
→A = (-5,1)
A' = (4,3)
so x moved from -5 to 4 which is an increase of 9
so x+9
y moved from 1 to 3 which is an increase of 2
so y+2
so answer should be:
(x,y) → (x+9,y+2)
The table represents the height of a ball thrown up from the roof of a building, h(t), in meters, t seconds after it is thrown upward. Which statements are true? Check all that apply.
Answers
Answer:
A. The ball is at the same height as the building between 8 and 10 seconds after it is thrown.
C. The ball reaches its maximum height about 4 seconds after it is thrown
Step-by-step explanation: • The ball is at the same height as the building between 8 and 10 seconds after it is thrown. TRUE - the height is zero somewhere in that interval, hence the ball is the same height from which it was thrown, the height of the roof of the building.
• The height of the ball decreases and then increases. FALSE - at t=2, the height is greater than at t=0.
• The ball reaches its maximum height about 4 seconds after it is thrown. TRUE - the largest number in the table corresponds to t=4.
• The ball hits the ground between 8 and 10 seconds after it is thrown. FALSE - see statement 1.
• The height of the building is 81.6 meters. FALSE - the maximum height above the building is 81.6 meters. Since the ball continues its travel to a distance 225.6 meters below the roof of the building, the building is at least that high.
If you multiply a number by 3 and then subtract 5 you will get 40 what is the number
Answers
The number will be 15.
Hope this helped.
To find the answer the question first write it out. 3*x-5=40. move the five over next to the 40 and cancel out -5. so the new equation looks like this. Then add 40+5 which is 45.Lastly you have the number 3 and the variable x. now you have to divide 3 by 45 to get your final answer 15. so x=15.
3*x=40+5
3*x=45
Hope this helps!!
A bottle of soft drink is two thirds full. Jack drinks one quarter of the remaining soft drink. How full is the bottle now
Answers
Charli,
First find what 1/4 of 2/3 is.
1/4 of 2/3 = 1/6
(That is 1/4 times 2/3 = 1/6)
So, the bottle was 2/3 full, it is now ...
2/3 - 1/6
=4/6 - 1/6
= 3/6 or 1/2 full.
We know that the bottle of soft drink has a remaining volume which is 2 / 3 of the original.
Since Jack drank 1 / 4 of the remaining volume, hence only 3 / 4 now finally remains, the total is:
(2 / 3) * (3 / 4) = 6 / 12 = 1 / 2
Hence the bottle is now one half full
A fish tank at an aquarium has a volume of 1,568 cubic feet and a depth of 8 feet. If the base of the tank is square, what is the length of each side of the tank?
Answers
volume = l x w x h
1568 /8 = 196
sqrt(196) = 14
each side is 14 feet
Answer with Step-by-step explanation:
A fish tank is in the shape of cuboid.
It's height is 8 feet
and volume=1568 cubic feet
we know that volume of cuboid=lbh
where l is the length, b is the width and h is the height
The base of the tank is square
i.e. l=b
Volume=l²h
⇒ 1568=l²×8
⇒ l²=196
⇒ l=14
Hence, The length of base of tank=14 feet
width of tank=14 feet
and height=8 feet
Point M is the midpoint of AB . AM= 3x+3, and AB=8x−6
What is the length of AM?
The answer is 21 but i don't know the steps to get it. HELP
Answers
or, 3x+3=(8x-6)/2
or, 6x+6=8x-6
or, 2x=12
Therefore,x=6
so,AM=3*6+3=21
The length of AM is:
21 units.
Step-by-step explanation:Point M is the midpoint of AB.
AM= 3x+3, and AB=8x−6
Since, the midpoint divides the line segment into two equal parts i.e. it bisects the line segment.
Hence, we have:
AM+MB=AB
Also, AM=MB
Hence, we have:
[tex]3x+3+3x+3=8x-6[/tex]
on combining the like terms in the left hand side of the equation we have:
[tex]3x+3x+3+3=8x-6\\\\6x+6=8x-6[/tex]
Now, on subtracting both side of the equation by 6x we have:
[tex]6=8x-6-6x\\\\6=8x-6x-6\\\\6=2x-6[/tex]
on adding 6 on both side of the equation we have:
[tex]6+6=2x\\\\12=2x\\\\2x=12\\\\x=\dfrac{12}{2}\\\\x=6[/tex]
Hence, we have:
[tex]AM=3\times 6+3\\\\AM=21\ \text{units}[/tex]
Given right triangle MNO, which represents the value of cos(M)?
a) ON/MN
b) MN/MO
c) ON/MO
d) MN/ON
Answers
The option that represents cos M is MN / MO
Using trigonometric ratios, we can find the ratio of sides of a right angle triangle.
Trigonometric ratios:sin x = opposite / hypotenusecos x = adjacent / hypotenusetan x = opposite / adjacentTherefore,
cos M = adjacent / hypotenuse
cos M = MN / 0M
Therefore, cos M = MN / MO
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Yearly attendance at a local movie theater is 56,000 and grows continuously at a rate of 4.2% each year. What is the approximate attendance at the movie theater in nine years?
Answers
The growth rate is 4.2% or 0.042 per year.
That is,
Year 0: 56,000
Year 1: 56,000*1.042
Year 2: 56,000*1.042²
and so on.
This is a geometric sequence with
a₁ = 56,000 and r = 1.042
The n-th term is
a(n) = a₁ rⁿ⁻¹
When n=9, obain
a₉ = 56,000*1.042⁸ = 77,826.9 ≈ 77,827
Answer: 77,827
The approximate attendance at the movie theater in nine years, with a continuous growth rate of 4.2%, is around 79,918.
Explanation:The question provided can be solved using the formula for continuous growth, A = P ert, where A is the final amount, P is the initial principal amount (56,000 in this case), r is the rate of growth (4.2% or 0.042 when expressed as a decimal), and t is time in years (9 years here).
To find the approximate attendance at the movie theater in nine years, we substitute our values into the formula: A = 56000 x e(0.042 x 9). After calculating this, we find that the approximate attendance at the movie theater after nine years is about 79,918.
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The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 153°, c = 10, b = 14
Answers
Answer:
The given triangle is possible.
Step-by-step explanation:
Given, the measurement of triangle ABC are,
∠ B = 153°, c = 10, b = 14,
By the law of sine,
[tex]\frac{sin C}{c}=\frac{sin B}{b}[/tex]
By cross multiplication,
[tex]sin C = \frac{c\times sin B}{b}[/tex]
By substituting the values,
[tex]sin C=\frac{10\times sin 153^{\circ}}{14}[/tex]
[tex]sin C=0.324278928386[/tex]
[tex]\implies \angle C=18.9218948147\approx 18.922^{\circ}[/tex]
Since, with help of sin law we found the measurement of the unknown angle of the triangle.
Hence, the given triangle is possible.
Answer:
C = 18.9°, A = 8.1°, a ≈ 4.3
Sam and chad are ticket-sellers at their class play. sam is selling student tickets for $2.00 each, and chad selling adult tickets for $5.50 each. if their total income for 24 tickets was $83.00, how many tickets did sam sell?
Answers
The number of tickets sold to students by Sam will be 14.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sam and Chad are ticket-sellers at their class play. Sam is selling student tickets for $2.00 each, and Chad selling adult tickets for $5.50 each. if their total income for 24 tickets was $83.00.
Let x be the number of tickets sold to students and y be the number of tickets sold to adults. Then the equation is given as,
x + y = 24 ...1
2x + 5.5y = 83 ...2
From equations 1 and 2, then we have
2(24 - y) + 5.5y = 83
48 - 2y + 5.5y = 83
3.5y = 35
y = 10
Then the value of x will be given as,
x + 10 = 24
x = 24 - 10
x = 14
The number of tickets sold to students by Sam will be 14.
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Let g(x) = 2x and h(x) = x2 + 4. Evaluate (h ∘ g)(−5).
A. 104
B. −246
C. 146
D. 250
Answers
Answer:
Option A is correct
The value of (h ∘ g)(−5) is, 104
Step-by-step explanation:
Given the functions:
g(x) = 2x
[tex]h(x) = x^2 + 4[/tex]
We have to find (h ∘ g)(−5).
[tex](h o g)(-5) = h(g(-5))[/tex] ....[1]
At x = -5
g(-5) = 2(-5) = -10
then
Substitute the g(-5) in [1] we have;
[tex](h o g)(-5) = h(-10)[/tex]
⇒[tex](h o g)(-5) = (-10)^2+4 = 100+4 = 104[/tex]
⇒[tex](h o g)(-5) = 104[/tex]
therefore, the value of (h ∘ g)(−5) is, 104
Mr. Lewis sees a red light ahead and applies the brakes on his car. The car travels 300.5 feet before coming to a stop. For each foot the car travels during this time, its speed changes by −0.2 miles per hour.
What is the total change in the car's speed during that time?
a) -36.15
b) -60.1
c) 60.10
d) 36.15
Answers
multiply 300.5 feet by -0.2 mph
300.5 * -0.2 = -60.1 change
Your friend weights 62 kg, how many grams is this?
Answers
Rectangle EFGH is translated according to the rule T -5,9(x,y). If the coordinates of the pre-image of point H are(-2,-3) what are the coordinates of H’
Answers
Answer: The co-ordinates of the image H' are (-7, 6).
Step-by-step explanation: Given that the rectangle EFGH is translated according to the following rule :
[tex]T_{-5,9}(x,y).[/tex]
We are to find the co-ordinates of the image H' if the co-ordinates of the pre-image H are (-2, -3).
We know that
[tex]T_{h,k}(x,y)=(x+h,y+k).[/tex]
For the given information, we have
(h, k) = (-5, 9) ⇒ h = -5 and k = 9.
Therefore, we get
[tex]T_{-5,9}(-2,-3)=(-2-5,-3+9)=(-7,6).[/tex]
Thus, the co-ordinates of the image H' are (-7, 6).
BRAINLIETS ND POINTSTO ANSWER THAT SHOWS ALL WORK YOU MIGHT NEED TO WORK OUT ON PAPER!!!
you are given the following equation:
+6=4/5(+3)
3a. Identify the slope of the equation.
3b. Identify the point used in the equation.
3c. Graph the equation.
Answers
the points used were (-3,-6) and (2,-2)
FOR 10 POINTS WILL MARK BRAINLIEST It costs $175 to rent a jet ski for 2 hours. It costs $300 to rent a jet ski for 2 hours. It costs 300$ to rent a jet ski for 4 hours. Write an equation that represents the cost y (in dollars) of renting a jet ski for x hours
Answers
The equation that represents the cost y (in dollars) of renting a jet ski for x hours is y = -87.50x + 525.
Explanation:The equation that represents the cost y (in dollars) of renting a jet ski for x hours can be found by analyzing the given information. Let's break it down step by step:
We are given that it costs $175 to rent a jet ski for 2 hours. This means the cost per hour is $175 / 2 = $87.50.We are also given that it costs $300 to rent a jet ski for 4 hours. This means the cost per hour is $300 / 4 = $75.Based on these two data points, we can see that as the number of hours increases, the cost per hour decreases. Therefore, we can infer that the cost of renting a jet ski is a linear function of the number of hours.Now, let's use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.In this case, we can use the point (2, 175) and the slope -87.50 to write the equation:
y - 175 = -87.50(x - 2)Simplifying the equation:
y - 175 = -87.50x + 175
y = -87.50x + 350 + 175
y = -87.50x + 525
Therefore, the equation that represents the cost y (in dollars) of renting a jet ski for x hours is y = -87.50x + 525.
Factor 64-x^15 in mathhhhgg
Answers
Answer:
Factor of [tex]64-x^{15}[/tex] is [tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
Step-by-step explanation:
We need to factor the expression [tex]64-x^{15}[/tex]
Re-write the given expression [tex]64-x^{15}[/tex] as;
[tex]4^{3}-(x^{5})^{3}[/tex]
Since, [tex]a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})[/tex]
so, here [tex]a = 4[/tex] and [tex]b = x^{5}[/tex]
[tex](4-x^{5})(4^{2}+4x^{5}+(x^{5})^{2})[/tex]
[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
Hence, factor of [tex]64-x^{15}[/tex] is
[tex](4-x^{5})(16+4x^{5}+x^{10})[/tex]
The value of factor of expression 64 - x¹⁵ is,
⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)
We have to given that;
To factor the expression,
⇒ 64 - x¹⁵
Now, We can simplify as;
⇒ 64 - x¹⁵
⇒ 4³ - (x⁵)³
⇒ (4 - x⁵) (4² + 4x⁵ + (x⁵)²)
⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)
Therefore, The value of factor of expression 64 - x¹⁵ is,
⇒ (4 - x⁵) (16 + 4x⁵ + x¹⁰)
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