The johnson twins were born twelve years after their older sister.This year,the product of the three siblings' ages is exactly 1244 more than the sum of their ages.How old are the twins?
Answers
(s - 12)(s - 12)(s). The sum of their ages would be s + (s - 12) + (s - 12). Since the product of their ages is 1244 more than the sum, we have the equation
(s - 12)(s - 12)(s) = s + (s - 12) + (s - 12) + 1244
Multiplying the first two factors on the left (First, Outer, Inner, Last) we have
(s² - 12s - 12s + 144)(s) = s + (s - 12) + (s - 12) + 1244
Combining like terms on both sides we have:
(s² - 24s + 144)(s) = 3s + 1220
Using the distributive property on the left we have
s³ - 24s² + 144s = 3s + 1220
We don't want a variable on both sides, so subtract 3s:
s³ - 24s² + 144s - 3s = 1220
Subtract 1220 from both sides to get our cubic equation to solve:
s³ - 24s² + 144s - 3s - 1220 = 0
Combine like terms:
s³ - 24s² + 141s - 1220 = 0
We want to consider the factors of 1220. After using a factor tree, we get the factors are 2*2*5*61. This gives us possible ages for the sister of 2, 4 (2*2), 4, 10 (2*5), 20 (2*2*5), 61, or older. We can eliminate 2, 4, and 5, since the twins are born and they are 12 years younger than her. This leaves 20, 61 or the older ages (which are improbable; the next age from 61 would be 61*2 = 122).
We will use synthetic division to try 20. Set up the problem with the coefficients of our equation (first image). We bring the 1 down. Now we multiply this 1 by the 20 we're dividing by and put it under the second coefficient (second image). We add these two together now (third image). Continue by multiplying again by 20, then adding, etc. (remaining images; I can't add more than 5, but you keep the pattern going). Since we get 0 at the end, that means that 20 did indeed divide into the problem and is the sister's age. Since the twins are 12 years younger, they are 20-12 = 8.
Related Questions
A power line extends from a light pole 43 meters to the ground and makes an angle of 30 degrees with the ground. To the nearest tenth of a meter, how tall is the light pole?
Answers
To solve this problem, you should first draw a picture. Then, you can determine which trig ratio that you will use. In this case, you are dealing with the opposite side from the angle and the hypotenuse.
Therefore, you can use the sin ratio.
Our equation will be:
sin30 = x/43
0.5 = x/43
21.5 = x
The light pole is 21.5 meters tall.
Good luck,
MrEQ
For each pair of shapes decide whether they are congruent similar or neither
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Choose the correct product of (3x + 8)2. 9x2 − 64 9x2 + 64 9x2 + 48x + 64 9x2 − 48x + 64
Answers
Answer: The correct answer is 9x^2 + 48^x + 64
Step-by-step explanation:
The correct answer is 9x^2 + 48^x + 64
The graph shows the distance, y, in miles, of a moving motorboat from an island for a certain amount of time, x, in hours.
What is the speed of the motorboat?
A) 225 miles per hour
B) 25 miles per hour
C) 75 miles per hour
D) 50 miles per hour
Answers
Answer:
Option D.,50 miles per hour
Step-by-step explanation:
The graph shows the distance covered by motor boat at = y, ( in miles )
The certain amount of time on = x ( in hours )
The slope of the given line will represent the speed of the motorboat.
The given line passes through two points ( 0, 25 ) and ( 4, 225 )
Therefore, slope of the line = [tex]\frac{y-y'}{x-x'}[/tex]
= [tex]\frac{225-25}{4-0}[/tex]
= [tex]\frac{200}{4}[/tex]
= 50
The speed of the motorboat is 50 miles per hour.
on a city map, the scale is 5 cm = 12 km,if a street is 12.5 cm long on the map what is the actual length of the street?
Answers
A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700. Before receiving this statement, John saw he was charged a total of $48.10. Write and solve an equation to determine how many minutes he must have used during the month. Write an equation without decimals.
Answers
x=the number of minutes extra uses
y= total
40+0.45x=48.10
0.45x=48.10-40
0.45x=8.10
0.45/0.45=8.10/0.45
x=18
There are 18 minutes John must have used during the month.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A cell phone company has a basic monthly plan of 40$ plus $0.45 for any minutes uses over 700.
Before receiving this statement, John saw he was charged a total of $48.10.
Let the time he must have used during the month = x
So, We can formulate the equation as;
⇒ $48.10 = $40 + $0.45 x
Solve for x as;
⇒ 48.10 - 40 = 0.45x
⇒ 8.10 = 0.45x
⇒ x = 8.10 / 0.45
⇒ x = 18
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There are y children in an orphanage and they shared $x among themselves. If each of them got $7 there were $4 left.If there were $5 more,each would get $8.
(a) Write the pair of simultaneous linear equation connecting x and y.
(b) Hence, find
(i) x
(ii) y
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.. 8y = x +5
b) Subtract the first equation from the second.
.. (8y) -(7y +4) = (x +5) -(x)
.. y -4 = 5
.. y = 9
.. 7*9 +4 = x = 67
bi) x = 67
bii) y = 9
simplify 3/8+1/6 help
Answers
We can solve this problem by cross them
[tex] \frac{3}{8} + \frac{1}{6} = ? \\ \\ 8 + 1 = ? \\ \\ 6 + 3 = ? \\ \\ \frac{9}{24} + \frac{4}{24} [/tex]
Answer: [tex] \frac{13}{24} [/tex]
Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Explain how the suffix -less affects the meaning of the spelling words expressionless and fearless. (explain plz) FAST !!!
Answers
PLEASE HELP ME! IM GETTING TIMED!!
A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
MAKE SURE TO SHOW YOUR WORK?
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Volume of cylinder=pi*r^2*h
V=pi*6^2*14
V=1582.56
Volume of cone=pi*r^2*h/3
V=pi*6^2*6/3
V=226.08
1582.56+226.08=1808.64 or 1808.6 cubic inches
Malinda’s pair of ski boots and skis have a mass of 6 kilograms. What is the mass of one ski boot and one ski
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What is the value of the 6 in 34.967
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that's my answer
Hope this helps, send me a message if you have any other questions at all, kiddo =)
HELP 11190 POINTS
The dot plot shows the number of visitors. Determine the median of the data set.
A) 56
B) 61
C) 62
D) 68
Answers
Solution:
we are given with a dot plot where we can see that the number of visitors.
we have been asked to find the median of the data set.
From the data plot , we can write the data set as below
56,56,56,56,58,58,60,62,62,62,63,65,65,68,68.
Here the data set is already arranged in the ascending order.
Now if the number of data points in the data set is odd then middle number is the median.
If the number of data points in the data set is even then the sum of middle two divided by 2 gives the median.
Here the number of data points in the data set is odd.
So the median is 8th value from any side.
Hence the median of the given data set is 62.
A builder could get 6 sheets of sheetrock for 3$. If he bought 60 sheets , how much money would he have spent
Answers
Godfrey just got a new credit card that offers both an introductory APR and a standard APR. If the standard APR is 11.2%, which of the following rates would most likely be the introductory APR?
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Let
x------------------- > introductory APR
y------------------- > standard APR
we have that
x < y
the only rate that is lower than the standard is the option A) 1.2%
the answer is 1.2 %
Answer: 1.2-apex
...............
Coco buys a very large rectangular chocolate bar and decides that each day, she
will cut the largest possible square off of the bar and eat it. When the remaining
part of the chocolate bar is a square, she will eat all that is left. The table shows
the area, in square centimeters, of the square Coco eats on each day. If Coco
finishes the chocolate bar on Day 6, what was the length of the longer side of the
chocolate bar when Coco bought it?
Table is included need answer ASAP.
Answers
Answer: 39
Step-by-step explanation:
On each of the six days Coco ate a square piece of chocolate with side length 15 cm, 15 cm, 9 cm, respectively. Then find the slope versus. 15*15+9*1=236. Then you have to do 236-200=36. Later 36+3, since there were three numbers to get 39.
A theater can seat 720 people. The number of rows is 6 less than the number of seats in each row. How many rows of seats are there?
Answers
Jarrod helped his teachers pack textbooks into boxes for the summer. He packed 8 boxes of science textbooks with 16 books per box. He also packed math textbooks with 12 books per box.
If x represents the total number of boxes he packed, which of the following equations can be used to find the total number of books that Jarrod packed into boxes?
A.
y = 128x + 12
B.
y = 12(x - 8) + 128
C.
y = 12x + 128
D.
y = 128(x - 8) + 12
Answers
Final answer:
The correct equation to represent the total number of books Jarrod packed is B. y = 12(x - 8) + 128, which acknowledges he packed 8 boxes of science books and the remaining boxes were for math books.
Explanation:
Jarrod packed 8 boxes of science textbooks with 16 books per box, which totals to 8 × 16 = 128 books.
For the math textbooks, if x represents the total number of boxes packed, then Jarrod would have packed (x - 8) boxes of math textbooks since he already packed 8 boxes of science textbooks.
Each math textbook box contains 12 books, so the number of math books packed is 12 × (x - 8). The total number of books that Jarrod packed is the sum of both science and math books, which is given by 128 + 12 × (x - 8).
The correct equation that represents this word problem is B. y = 12(x - 8) + 128, where y is the total number of books packed and x is the total number of boxes packed.
What value of x would make rq tangent to Circle P at point Q?
Answers
9² + 12² = (x+9)²
We use x+9 because the unknown segment x would combine with the radius, 9, to give that side of the triangle (the hypotenuse).
81 + 144 = (x+9)(x+9) ---- remember that squared means multiplied by itself
225 = (x+9)(x+9)
Multiply the right hand side:
225 = x² + 9x + 9x + 81
225 = x² + 18x + 81
Subtract 225 from both sides:
225 - 225 = x² + 18x + 81 - 225
0 = x² + 18x - 144
Use the Quadratic Formula to solve:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\x=\frac{-18 \pm \sqrt{18^2-4(1)(-144)}}{2(1)} \\ \\x=\frac{-18 \pm \sqrt{324--576}}{2} \\ \\x=\frac{-18 \pm \sqrt{324+576}}{2} = \frac{-18 \pm \sqrt{900}}{2}[/tex]
This gives us
[tex]x=\frac{-18 \pm 30}{2} = \frac{-18+30}{2} \text{ or } \frac{-18-30}{2}[/tex]
Since -18 - 30 = -48, and a negative number doesn't make sense in this situation, we have
x = (-18+30)/2 = 12/2 = 6.
The value of x cannot be negative, hence the value of x would make rq tangent to Circle P at point Q is 6
From the given circle geometry, since the line PQ is perpendicular to QR, hence the triangle PQR is a right-angle triangle.Given the following from the geometry;
Adjacent side = QR = 12Opposite side = PQ = 9Hypotenuse side = PR = 9 + xUsing the pythagoras theorem;
[tex]c^2=a^2+b^2\\(9+x)^2=9^2+12^2\\81+18x+x^2=81+144\\x^2+18x+81-225=0\\x^2+18x-144=0\\[/tex]
Factorize the result to have;
[tex]x^2+24x-6x-144=0\\x(x+24)-6(x+24)=0\\(x-6)(x+24) =0\\x=6 \ and \ -24\\[/tex]
Since the value of x cannot be negative, hence the value of x would make rq tangent to Circle P at point Q is 6
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Karim sent a chain email to 10 of his friends. The number of people who got the email increases by a factor of 1.4 every week. Write an expression that best represents the
number of people who got the email after three weeks.
Answers
Final answer:
The number of people who got the email after three weeks can be calculated using the formula: F = 10 * (1.4)^t, where F represents the number of people, 10 represents the initial number of friends, 1.4 represents the factor of increase, and t represents the number of weeks. After substituting t = 3, we find that approximately 27 people will have received the email after three weeks.
Explanation:
To represent the number of people who got the email after three weeks, we can use the formula:
F = 10 * (1.4)^t
Where:
F represents the number of people who got the email10 represents the initial number of friends Karim sent the email to1.4 represents the factor by which the number of people increases each weekt represents the number of weeksSubstituting t = 3 into the formula, we can calculate the number of people who got the email after three weeks.
F = 10 * (1.4)^3 = 10 * 2.744 = 27.44
Therefore, after three weeks, approximately 27 people will have received the email.
The correct expression is:
(B) [tex]\(10 \cdot 1.4^6\)[/tex]
Sure, let's break it down step by step:
1. Initial number of people who received the email: Karim sent the email to 10 friends, so initially, [tex]\(10\)[/tex] people received it.
2. Factor by which the number of recipients increases each week: The number of recipients increases by a factor of [tex]\(1.4\)[/tex] each week.
3. Number of people who received the email after 1 week: To find this, we multiply the initial number of recipients by the factor for 1 week, which is [tex]\(10 \times 1.4 = 14\).[/tex]
4. Number of people who received the email after 2 weeks: Now, we take the number of recipients after 1 week (14) and multiply it by the factor for another week, [tex]\(1.4\)[/tex], giving us [tex]\(14 \times 1.4 = 19.6\)[/tex]. Since we can't have a fraction of a person, we round this up to the nearest whole number, which is [tex]\(20\).[/tex]
5. Repeating this process for 6 weeks: We continue this process for each additional week until we reach the 6th week.
6. General formula for the number of recipients after [tex]\(n\)[/tex] weeks: After [tex]\(n\)[/tex] weeks, the number of recipients can be calculated using the formula:
[tex]\[10 \times 1.4^n\][/tex]
So after 6 weeks, the expression becomes:
[tex]\[10 \times 1.4^6\][/tex]
7. Final Answer: The correct choice is (B) [tex]\(10 \times 1.4^6\).[/tex]
The correct question is:
Karim sent a chain email to 10 of his friends. The number of people who got the on: il increases by a factor of 1.4 every week.
Which expression gives the number of people who got the email after 6 weeks?
Choose 1 Anwer:
(A) [tex]$(10 \cdot 1.4)^6$[/tex]
(5) [tex]$10 \cdot 1.4^6$[/tex]
(c) [tex]$10+1.4 \cdot 6$[/tex]
(D) [tex]$(10+1.4) \cdot 6$[/tex]
Write the equation of a line that is perpendicular to y=-0.3x+6 and that passes through the point (3,-8)
Answers
we know that
if two lines are perpendicular
then
the product of their slopes is equal to minus one
so
[tex]m1*m2=-1\\m2=-1/m1[/tex]
in this problem the slope of the given line is
[tex]m1=-0.3=-\frac{3}{10}[/tex]
the value of m2 is
[tex]m2=-1/(-3/10)=\frac{10}{3}[/tex]
with the point [tex](3,-8)[/tex] and the slope m2 find the equation of the line
the equation of the line in the form point-slope is
[tex]y-y1=m*(x-x1)[/tex]
substitute the values
[tex]y+8=\frac{10}{3}*(x-3)[/tex]
[tex]y=\frac{10}{3}x-10-8[/tex]
[tex]y=\frac{10}{3}x-18[/tex]
therefore
the answer is
[tex]y=\frac{10}{3}x-18[/tex]
The following table represents the sample space of rolling two number cubes.
1 2 3 4 5 6
1 1-1 1-2 1-3 1-4 1-5 1-6
2 2-1 2-2 2-3 2-4 2-5 2-6
3 3-1 3-2 3-3 3-4 3-5 3-6
4 4-1 4-2 4-3 4-4 4-5 4-6
5 5-1 5-2 5-3 5-4 5-5 5-6
6 6-1 6-2 6-3 6-4 6-5 6-6
How many favorable outcomes are there for the event "rolling exactly one even number"?
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If eight people sat at a round dinner table and each person had to shake everyone else’s hand once how many handshakes will take place
Answers
7 +6+5 +4 + 3 + 2 + 1 = 28
This problem is like the shaking hands problem having to do with what happens at the end of a hockey team. The winners sometimes stay on the ice and the first player goes down the line and "High Fives" all the other members of the team.
He's done so he goes to the dressing room. No more high 5s for him.
Next the second player does the same thing. Then he leaves the ice and so on down the to the last two players when one high fives the other.
Done.
Your problem is exactly the same.
The formula as you probably know is Sum = (n + 1)*n/2
What would my final balance be if I put $650 in the bank for 60 months with an interest rate of 6%?
Answers
If interest is compounded annually, 650*1.06^5 ≈ 869.85 . . . . dollars.
If interest is compounded quarterly, 650*1.015^20 ≈ 875.46 . . dollars.
If interest is compounded monthly, 650*1.005^60 ≈ 876.75 . . .dollars.
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What is the length of GE? Explain how you determined the length or show your work.
Answers
Lisa goes to school 7 hours per day, works 3 hours per day, and sleeps for 8 hours per day. What is the ratio of hours Lisa works to hours Lisa sleeps?
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3 : 8
The ratio of hours Lisa works to hours Lisa sleep is 3: 8.
what is the ratio?
The comparison of two quantities is known as a ratio. which could be easily determined by dividing one value by other which also indicates the percentage.
Given Lisa works 7 hours per day, works 3 hours per day, and sleeps for 8 hours per day. Therefore, the ratio of hours Lisa works to hours Lisa sleeps is the work hour of Lisa divided by hours of sleep per day.
Hence, the required ratio is 3: 8.
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2(-20)+3[5/4(20)]+4(50)
Answers
-40 +3*25 +200 = 35 +200 = 235
George is putting trim around his rectangular deck, including the gate. He will need 48 feet of trim to do the entire deck. If the deck is 14 feet long, how wide is the deck?
Answers
We need to convert the given information to meaningful mathematical equation.
Statement: "George is putting trim around his rectangular deck, including the gate. He will need 48 feet of trim to do the entire deck.", it means
[tex] Perimeter \; of\; the\; rectangle=48\; feet [/tex]
Assuming ' L ' as length of the rectangle & ' W ' as the width of the rectangle, the perimeter of rectangle is given by the below formula.
[tex] Perimeter \; of\; the\; rectangle\; =\; 2(L+W) [/tex]
We know "the deck is 14 feet long", which means...
[tex] L=14 \; feet [/tex]
Substituting 14 for L and 48 for Perimeter of rectangle in the formula above, we can set up and equation in terms of W.
[tex] 2(L+W)=Perimeter \; of\; the\; rectangle\\ 2(14+W)=48\\ Divide \; 2\; on\; both\; sides, \; we\; get...\\ \\ \frac{2(14+W)}{2}=\frac{48}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ 14+W=24\\ Subtracting\; 14\; on\; both\; sides\\ \\ 14+W-14=24-14\\ Combine\; like\; terms\\ \\ W=10 [/tex]
Conclusion:
The width of the deck is 10 Feet
what is 13 divide to 83.2
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A container is 25ft × 50ft.If you have to draw using the scale 1 inch:5ft,what are the dimensions of the container that you will draw?
Answers
[tex]\frac{1 \text{in}}{5 \text{ft}}= \frac{x \text{in}}{25 \text {ft}}[/tex]
Cross multiply:
[tex]5*x=1*25 \\ 5x=25[/tex]
Divide both sides by 5:
[tex]\frac{5x}{5}= \frac{25}{5} \\ x=5[/tex]
The scale model that matches the 25 ft side of the container will be 5 inches.
The second proportion:
[tex]\frac{1 \text{in}}{5 \text{ft}} = \frac{x \text{in}}{50 \text{ft}}[/tex]
Cross multiply:
[tex]5*x=1*50 \\5x = 50[/tex]
Divide both sides by 5:
[tex]\frac{5x}{5}= \frac{50}{5} \\x = 10[/tex]
The part of the scale model that matches the 50 ft side of the container will be 10 inches.