To solve this, we need to turn this word problem into a system of linear equations. To do this, let's use x to stand for Mr. Fontana's age, and y to stand for his son's age.
The first sentence states that eight years ago, Mr. Fontana was six times as old as his son.
eight years ago = x - 8
Fontana was six times as old as his son = 6(y - 8). Remember, we need subtract 8 from his son's age, which is why I wrote it as 6(y - 8), and his father was 6 times his son's age 8 years ago, which is why I multiplied 6 by y - 8.
Now, putting this all together gives us our first equation:
x - 8 = 6(y - 8)
We can now rewrite this equation in standard form:
x - 8 = 6y - 48 ----->
x - 6y = -48 + 8 ----->
x - 6y = -40 <----- this is our first linear equation
To find our second, we need to turn the second sentence into an equation. It says that in 12 years, Mr. Fontana will be twice as old as his son:
x + 12 = 2(y + 12)
Now, we need to rewrite this equation in standard form:
x + 12 = 2y + 24 ----->
x - 2y = 24 - 12 ----->
x - 2y = 12 <----- this is our second linear equation. We now have our system of equations:
x - 6y = -40
x - 2y = 12
Now we can find the father's age (x) and his son's age (y). First, multiply the second equation by -1, giving us:
x - 6y = -40
-x + 2y = -12
Now we can add both equations together:
x - x - 6y + 2y = -40 + -12 ----->
-4y = -52
Solve for y, by dividing both sides of the equation by -4, giving us:
y = 13
So, now we know the son's age: 13
To find the father's age, replace y in either the first equation or the second equation, with 13. Let's use the first equation:
x - 6(13) = -40 ----->
x - 78 = -40 ----->
x = 78 - 40 ----->
x = 38
Therefore, Mr. Fontana is 38 years old and his son is 13 years old.
The vertice of triangle ABC are A(8,4), B(6,3) and C(5-5). Find the angle between the side AB and BC.
Answer:
Step-by-step explanation:
Use law of cosines
c² = a² + b² - 2abcosθ
cosθ = (c² - a² - b²) / -2ab
c = length of AC = √(8 - 5)² + (4 - (-5))² = √90
b = length of AB = √(8 - 6)² + (4 - 3)² = √5
a = length of BC = √(6 - 5)² + (3 - (-5))² = √65
cosθ = (√90² - √65² - √5²) / -2√65√5
cosθ = 20 / -36.05551...
cosθ = - 0.5547001
θ = 123.69°
-4(-2u+3)-u=3(u-7)-5
where you simplify your answer as much as possible
Answer:
-7/2
Step-by-step explanation:
-4(-2u+3)-u=3(u-7)-5
8u-12-u=3u-21-5
8u-u-12=3u-26
7u-12=3u-26
7u-3u-12=-26
4u-12=-26
4u=-26+12
4u=-14
u=-14/4
simplify
u=-7/2
Answer:
u = - 3.5
Step-by-step explanation:
Before solving this you have to know that,
(-) × (-) = (+)
(-) × (+) = (-)
(+) × (+) = (+)
Let us solve now.
[tex]-4(-2u+3)-u=3(u-7)-5[/tex]
[tex]8u-12-u=3u-21-5[/tex]
[tex]7u-12=3u-26[/tex]
[tex]7u-3u=12-26[/tex]
[tex]4u=-14[/tex]
[tex]\frac{4u}{4} = \frac{-14}{4}[/tex]
[tex]u=-3.5[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Describe the location of the polnt having the following coordinates. abscissa and ordinate have the same sign
Quadrant II or Quadrant IV
Quadrant II or Quadrant III
Quadrant or Quadrant IV
Quadrant I or Quadrant III
Answer:
i think its D
Step-by-step explanation:
hope this helps!
CAN YOU GUYS HELP PLEASE, I HAVE A LIMIT ON THIS!!!!
Answer:
the 2nd choice
Step-by-step explanation:
hope this helps
may i get braineist pls
Answer:
A. or y=-1/3x-3
Step-by-step explanation:
3,311L how many millilters
Answer:
3311 mililiters
Step-by-step explanation:
1 L = 1 liter = 1000 mililiters
3.311L = 3.311 liters = 3.311*1000 = 3311 mililiters
Anita plans to give her husband 3 shirts for his birthday. She narrows the search to 3 shirts from a selection of 17 shirts at Dillon's Store or 3 from a selection of 20 shirts at The Men's Shop. In how many ways can she select the shirts
Using the combination formula, it is found that she can select the shirts in 775,200 ways.
The order in which the shirt are chosen is not important, hence, the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem:
3 shirts from a set of 17.Then, 3 shirts from a set of 20.They are independent, hence, to find the total, we multiply both combinations.[tex]T = C_{17,3} \times C_{20,3} = \frac{17!}{3!14!} \times \frac{20!}{3!17!} = 680 \times 1140 = 775200[/tex]
She can select the shirts in 775,200 ways.
To learn more about the combination formula, you can check https://brainly.com/question/25821700
How many pennies dose Michael please help please I need your help please please please please help
Answer: He has 91, to figure this out count everything in top row which is 13 and then count everything in left row only which is 7 and 13 x 7 is 91
Step-by-step explanation:
Hope everyone has a happy holiday for whatever you celebrate :)
Answer:
Happy holidays to everyone!
Step-by-step explanation:
Solve the system of two linear equations below graphically y= -x + 1 y= -1/3+ 3
Answer:
Step-by-step explanation:
48a^21 b^5
——————-
16a^21 b^4
Answer:
3b
Step-by-step explanation:
A sports store has jerseys representing the seven Canadian NHL teams and the eight Canadian CFL teams. Five of these jerseys have to be chosen for display in a store window. The store owner decides to choose three NHL and two CFL jerseys. These jerseys will be arranged in a row in the store window.
The number of displays that can be made by choosing the jerseys and then arranging them in the window is
A. 4900
B. 11 760
C. 117600
D. 1411 200
The answer key says the right Answer is (C), I just don't know how to get there.
Answer:
possible arrangements
CCNNN
CNCNN
CNNCN
CNNNC
NCCNN
NCNCN
NCNNC
NNCCN
NNCNC
NNNCC
Ten ways to arrange the window
for any one of these there are
NHL
7 ways to fill the first position
6 ways to fill the second
5 ways to fill the third
7•6•5 = 210 ways to select the NHL jerseys
CFL
8 ways to fill the first position
7 ways to fill the second
8•7 = 56 ways to select the CFL jerseys
210•56 = 11760 ways to select a set of 5 jerseys
11760•10 = 117 600 possible ways to arrange the window
What is the range of the following function, if the domain is {1,3,12}?
f(x) = x - 3
How can a person best reduce the risk of sustaining permanent injuries?
Wear protective clothing while sleeping at home.
Secure a seat belt only when riding in the front seat.
Wear a cracked bicycle helmet while riding a bicycle.
Put away guns in a lockbox that is secure and in a discrete location.
Answer:
Put away guns in a lockbox that is secure and in a discrete location.
Have a good day <3
2/5 of 40 I need help
Answer:
32. A.
Step-by-step explanation: because i did 4/5 of 40 and got 32.
LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Finding missing sides- similar triangles Algebraic practice )
Answer:
x=9
Step-by-step explanation:
since the triangles are similar, the sides are all in proportion. This means that:
[tex] \frac{uw}{eg} = \frac{uv}{fg} [/tex]
Now we can just sub in the sides:
[tex] \frac{91}{13} = \frac{56}{x - 1} [/tex]
simplify the first fraction
[tex] \frac{7}{1} = \frac{56}{x - 1} [/tex]
Now we can cross multiply
56=7(x-1)
56=7x-7
63=7x
Therefore:
×=9
Choose the number that makes the statement true: -5>?
a. 9
b. -9
C. -3
d. 3
Answer: This is B.) -9
Step-by-step explanation:
Step-by-step explanation:
All of those numbers are greater than -5 except for B.
Find the perimeter of a semicircle with a radius of 9 in.
Please explain and be accurate.
Answer:
9π + 18
Step-by-step explanation:
The circumference of a circle is pi times diameter, so 9 x 2 = 18 inches, which is the diameter. That will be the flat side of the semicircle. Then the circumference of the whole circle will be 18π. To find the curved side of the semi-circle, divide this by 2, so you get 9π. Therefore the answer is 9π + 18. The rough answer to 3 decimal places is 46.274
I NEED HELP WITH #5 and #4
What is the value of f(x) = -3-x when x = -7?
A-10
) B -4
4
D 10
Answer:
#5. C 4
#4. J 0.3 meters
Step-by-step explanation:
No. 5
f(-7) = -3-(-7)
f(-7) = 4
C
No. 4
s = sqrt(0.09)
s = 0.3 meters
Solve the inequality for x.
9x - 7 < 7x - 25
Answer:
x<-9
Step-by-step explanation:
subtract the 7x from the right side to bring it over to the left side to get:
2x-7<-25
then add the 7 from the left side to bring it over to the right side to get:
2x<-18 and then divide both sides by 2 to get the final inequality to be:
x<-9
Therefore, the solved inequality is x < -9.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
The average price of an item is $42 with a standard deviation of $3
Find a 98% confidence interval about the mean (one decimal place).
Is a value of X=48 unusually high or is it normal? Choose correct explanation!
The mean price goes between $ 41.16 and $ 42.84, so a value of $ 48 is unusually high.
Since the average price of an item is $ 42 with a standard deviation of $ 3, to find a 98% confidence interval about the mean, and determine if a value of X = 48 is unusually high or if it is normal, the following calculations should be done:
(((42 - 3) + (42 + 3)) / 2) x 0.98 = X ((39 + 45) / 2) x 0.98 = X 42 x 0.98 = X 41.16 = X
(((42 - 3) + (42 + 3)) / 2) x 1.02 = X ((39 + 45) / 2) x 1.02 = X 42 x 1.02 = X 42.84 = X
Therefore, as the mean price goes between $ 41.16 and $ 42.84, a value of $ 48 is unusually high.
Learn more about maths in https://brainly.com/question/25908442
Explain this picture
Answer:
It's A bar graph but I got to see the question to be for sure but its a bar graph and it helps you measure rates of things from numbers , months , years etc .
Step-by-step explanation:
Please help me!!!!!!!!!
Answer:
y=25x+1150
Step-by-step explanation:
1425-1275=150
150/6=25 so 25 dollars per month
1275-5(25)
1275-125=1150
y=25x+1150
PLEASE HELP!!!
List 5 fractions that are equal to 3/4!
Answer:
9/12
6/8
30/40
27/36
15/20
Step-by-step explanation:
Mr. Irwin Sold adult tickets
Answer:
i dont know how to do it231
Step-by-step explanation:
1123234
Equivalent ratios
6:3 X:12 18:x
(SAT Prep) Find the value of x
Answer:
x = 36
Step-by-step explanation:
3x+2x=180
5x=180
x=36
Answer:
x=36 degrees
Step-by-step explanation:
a prisms base has a perimeter of 12cm and a height of 2 cm. the area of the base was 5cm. what is the surface area of the prism.
[tex]\text{Surface Area of Prism} = (2 \times \text{Base Area}) + (\text{Base perimeter} \times \text{height})\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=(2 \times 5)+(12\times 2)\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=10+24\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=34~~ \text{cm}^2[/tex]
some help, I need some answers
Step-by-step explanation:
here
10^2=8^2+X^2
X^2=100-64
X=√36
X=6
Zanele Situ is a disabled Olympic gold-medallist javelin champion. She threw the javelin a distance of 16,22 m in London at 2012 Olympics. She threw the javelin to a distance of 17,90 m in Rio at 2016 Olympics. By what percentage did the distance increase?
Answer:
10,4%
Step-by-step explanation:
The percentage change is found from ...
(amount of change)/(original amount) × 100%
(17,90 -16,22)/(16,22) × 100% = 1,68/16,22 × 100% ≈ 10,358% ≈ 10,4%
Gravity is a force that acts upon a ball after it is thrown?
A. True
B. False
True or false, depending on the specifics. True, because the gravity makes it go to the ground. False, because gravity is always working, so you don't need to throw the ball. However since it doesn't say that it only happens when you throw it. The answer should be true.