The sum of the digits of a positive 2-digit number is 12. The units digit is 3 times the tens digit. Find the number
Answers
Answer:
44
Step-by-step explanation:
Answer:
93
Step-by-step explanation:
Let’s call the tens digit x and the unit digit y. From the question we know that x + y = 12 and that x = y^2, giving us the following system of equations:
x + y = 12
x - y^2 = 0
Let’s multiply the second one by -1, to get rid of one of the unknowns in the system.
x + y = 12
-x + y^2 = 0
By adding together the two, we get y^2 + y = 12. As that is a quadratic equation, let’s make it of the form Ay^2 + By + C = 0, so subtracting 12 from each side gives as y^2 + y - 12 = 0. Then let’s solve the quadratic equation to find out the two values of y we get out of it, one of which is legal in the above system of equations.
y = (-B +/- sqrt(B^2–4AC))/2A
This time, both A and B are 1, while C is -12. By entering them in the above formula, we get the inner part of the square root to be 49, and thus the square root to give 7. So solving y = (-1 +/- 7)/2 gives two alternatives, either y = -4 (impossible, as it has to be a digit, ie has to be between 0 and 9 inclusive) or y = 3.
Then let’s return to the system of equations, and as both digits appear without any modifiers in the first one, let’s use it to find x with. So x + 3 = 12, x = 12 - 3, x = 9.
As x is the tens digit and y the unit digit per how the variables were chosen, we can with confidence say that the number is 93.
Related Questions
Pedro ordered a 6 footlong sub sandwich and plans to share it with his friends. If each portion is divided evenly in 3/5 of a foot, how many friends will Pedro share his sandwich with?
Answers
Answer:
10
Step-by-step explanation:
You would divide 6 feet by 3/5 of a foot would would be .6 so 6/.6 would be 10Tim’s age is nine more than his sister, Jill. Twice his age added to twice Jill’s age is 330.
Answers
Answer:
jill age is 78 and tim's age is 87
Step-by-step explanation:
let jill age be x then, tim's age is 9+x
by the question,
2(9+x) + 2x = 330
or,18 + 2x + 2x = 330
or,4x = 330-18
or, x = 312÷4
x = 78
9+x= 9+78=87
I PROMISE TO MARK BRAINLIESTTTTT
Answers
Answer:
D!
Step-by-step explanation:
Express in the form 1: n.
Give n as a decimal.
8 : 6
please help
Answers
Answer:
n = 0.75
1 : 0.75
Step-by-step explanation:
To get from 8 to 1, you have to divide by 8. You do that to the number 6.
6/8 = 3/4 = 75/100.
Therefore, n = 0.75.
A tree casts a shadow that is 7 feet long. A person nearby casts a shadow that is 3.5 feet long. The person is
5 feet tall. What is the height of the tree?
Answers
In quadrilateral PQRS, the exterior angle at Q measures 155 and PS = QR. What measure of ∠PSR would confirm that PQRS is a parallelogram?
Answers
Answer:
The measure confirming that PQRS would be 25
Step-by-step explanation:
It's easier if you draw it down.
1. We need to make this shape a parallelogram and the way we will do that is by making angle Q and angle S the same, because in parallelograms those opposite angles are required to be the same.
\
155 \
P \ -------------------------\ Q
\ 25 \
\ \ so that's your shape
S \______________\ R
2.We were given that the exterior angle of Q measures 155, and since exterior and interior angles combined make 180, then we can assume that the interior angle of Q is 25.
3. As mentioned before, in a parallelogram, opposite angles are the same and therefore PSR (which is just asking for the middle letter, S) is equal to 25 because Q is also 25.
Can I get some help with this is the Last question
Answers
Answer:
x = 11
Step-by-step explanation:
Here, we want to get the value of x
Let’s start by looking at the point U
Now, we can see angles on a straight line at that point
Mathematically, angles on a straight line are supplementary
What this mean is that they add up to 180
Now, the value of the angle that falls into the triangle on that straight line will be;
180-(11x + 12)
Now, we have all the angles of the triangle
Mathematically, the sum of all is 180 as the a sum of the angles of a triangle is 180
5x + 10 + 58 + 180-(11x+2 )= 180
5x + 10 + 58 -11x-2 = 0
-6x+ 66 = 0
6x = 66
x = 66/6
x = 11
PLS someone help me find the slope it’s my last question
Answers
slope is 1
slope formula: y2-y1/x2-x1
4-3/0-(-1)
A line passes through the points (8, 8) and (4, 0). What is its equation in slope-intercept form?
Answers
Explanation: (8,8) 8-4 and 8-0
- (4,0)- 4 8
- you take the 8 as the numerator and 4 and the denominator and then divide 8 by 4 to=2 which is your slope
- you pick 1 set of points (I chose (8,8) to finish the problem)
8(y-intercept)= 2(slope) • 8(x-intercept) +b
8= 16+b
-16 -16 (subtract 16 from both sides)
-8 (8-16) =b {b=-8)
-now you put together your equation,
which leaves you with { y=2(x) - 8}
^ ^
your slope your B value
Your middle school is having a carnival. Admission into the carnival is $8, and each game inside the carnival costs $0.50.
Part A: Which inequality represents the possible number of games, g, that can be played with $20?
A. 8g+0.50≤20
B. 8g+0.50≥20
C. 0.50g+8≤20
D. 0.50g+8≥20
Answers
can you please help me and explain how to do both of these problems, I don't understand
Answers
In a class of 40 students, 26 are girls and 14 are boys. What is the ratio of girls to the total number of students?
Answers
Answer:
13:20
Step-by-step explanation:
no. of girls=26
total no. of students =40
ratio of girls to total no. of students=26:40
which means, the ratio is 13:20
HELP!!!! BRAINIEST ANSWER + POINTS!!! PLEASE BE SERIOUS (I NEED ALL 5 POINTS + EXPLANATION)
Answers
Answer:
slope=3
y-intercept=-1
Step-by-step explanation:
Mark wants to continue using whole liters of paint and thinks he can create a mixture of green paint the is 38 liters. Evaluate Mark's thinking using mathematical reasoning.
The ratio from blue to yellow paint is 2:3
I need helpppppp ASAP
Answers
Answer: It's not possible to create 38 liters of green paint with whole liters of blue and yellow paint.
======================================================
Explanation:
The ratio of blue to yellow is 2:3. We have 2 parts blue and 3 parts yellow.
Multiply both parts by x to get 2x:3x
We have 2x parts of blue paint, and 3x parts of yellow paint.
x is some positive whole number.
In total, we have 2x+3x = 5x liters of paint. Set this equal to 38 and solve for x to get
5x = 38
x = 38/5
x = 7.6
We don't get a whole number, which contradicts how we set up x earlier. This must mean that Mark must use a fractional liters, instead of whole liters.
-------------------------
Here's another way to look at it:
Lets say he uses 2 liters of blue and 3 liters of yellow. This mixes to 2+3 = 5 liters of green.
Now let's say he uses 4 liters of blue and 6 of yellow. I multiplied both parts by 2. This mixes to 4+6 = 10 liters of green.
We continue this process to get the following
6 liters of blue + 9 liters of yellow = 15 liters of green8 liters of blue + 12 liters of yellow = 20 liters of green10 liters of blue + 15 liters of yellow = 25 liters of green12 liters of blue + 18 liters of yellow = 30 liters of green14 liters of blue + 21 liters of yellow = 35 liters of green16 liters of blue + 24 liters of yellow = 40 liters of greenAs you can see, we don't land on 38 liters of green. We can get to 35 liters or 40 liters, but not 38. Each of the amounts of green are a multiple of 5.
This is confirmation that Mark will have to use some fractional amount of liters of blue and yellow paint.
5 Rectangles and 2/5 of the Rectangles Will Be Purple How Many Purple Rectangles Will She Need To Make 3 Scarfs?
Answers
Answer: 6
Step-by-step explanation:
Here's the complete question:
Olivia is making scarves. each scarf will have 5 rectangles, and 2/5 of the rectangles will be purple. how many purple rectangles does she need for 3 scarves.
Since each scarf have 5 rectangles, and 2/5 of the rectangles will be purple. The number of purple needed for each scarf will be:
= 2/5 × 5 = 2 purple
Therefore, the number of purple rectangles she need for 3 scarfs will be:
= 2 × 3
= 6
Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $2 per miletowed. Write a function expressing Linda's towing cost, C, in terms of miles towed, x. Find thecost of having a car towed 14 miles.
Answers
The cost of having a car towed 14 miles is $103.
To express Linda's towing cost, C, in terms of miles towed, x, we can use the given information that Little Town Auto charges a flat fee of $75 plus $2 per mile towed.
The function for the towing cost, C, can be written as:
C(x) = 75 + 2x
Where x represents the number of miles towed.
To find the cost of having a car towed 14 miles, we substitute x = 14 into the function:
C(14) = 75 + 2(14)
C(14) = 75 + 28
C(14) = 103
Therefore, the cost of having a car towed 14 miles is $103.
To know more about cost click here :
https://brainly.com/question/31665993
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32. Which graph represents yas a function of x?
Answers
Answer:
second one
Step-by-step explanation:
i am pretty sure
what is the fraction of 2 1/4
Answers
Answer:
9/4
Step-by-step explanation:
2 1/4 = 9/4 From mixed fraction to an improper fraction: "the numerator of the improper fraction" = "denominator" xx "the whole number" + "the numerator of the mixed fraction" The denominator remains as it is. So 2 1/4 = (4 xx 2 + 1)/4 = 9/4
Answer:
9/4
Step-by-step explanation:
Multiply the denominator which is 4 by the whole number which is 2.
4 x 2 = 8
Next add the numerator to the 8.
8 + 1 = 9
The 9 is now the numerator and keep the original denominator.
9/4
HELPPPPPPPPPPPPPPPPPPPPPPPP
Which of the following expressions is a common factor when the expressions x2 – 9 and x2 – 5x + 6 are factored?
A.
x + 3
B.
x2
C.
x – 3
D.
x – 2
Answers
Find the product.
-0.3(4.1) =
Answers
Answer:
-1.23
Step-by-step explanation:
-0.3 x 4.1 = -1.23.
A negative number times a positive number equals a negative number.
This is correct right?
Answers
Answer:
Yes, it is not a diameter
Step-by-step explanation:
It's going through the circle (sphere) which makes it a diameter
I and D are not going straight through the middle
I need some help I rlly appreciate it!!!!
Answers
54 is the quotient of 11 and a number
Answers
Answer:
594
Step-by-step explanation:
54 * 11 = 594
54 Is the quotient of 11 and 594 because 594 divided by 11 is 54.
(sorry if this is incorrect, i may had misinterpreted the question)
Answer:
11/54Step-by-step explanation:
54 is the quotient of 11 and a number
Let the number be x
11/x = 54x = 11/54The number is 11/54
250 adults were randomly selected in a grocery store they were asked how they feel about the stores coupon policy 180 were satisfied with the current policy based on the results of the sample 940 adult shop in the Store that day about how many would be expected to be happy with the current coupon policy
Answers
Answer:
870
Step-by-step explanation:
250-180=70
940-70=870
Answer:
The answer to this question is 677
HELP PLEASEE PLEASEE HELP ): ?
Answers
Answer:
They pass through origin
Step-by-step explanation:
Hope maka help
A body falls from rest with an acceleration of 10m/s square. what is the velocity after 5s?How far has it fallen by them.
Answers
Answer:
The velocity after 5s s is 20
I WILL GIVE YOU BRAINLY PLSS
Evaluate m( m + n) – n, use m = 5 and n = -3
A. 7
B. 13
C. 43
D. 37
PLSS SHOW YOUR WORK PLSS
Answers
Answer:
B. 13
Step-by-step explanation:
[tex]m(m + n) - n[/tex]
[tex]m = 5 \\ n = - 3[/tex]
Substitute m = 5 and n = - 3 in the expression.
[tex]5(5 + ( - 3)) - ( - 3) \\ 5(5 - 3) + 3 \\ 5(2) + 3 \\ 10 + 3 \\ 13[/tex]
Remind that negative multiply negative must equal positive.
Distribute 5
25+(-15)-(-3)
The minus (-3) turns into a positive so you get +3 and you add it all together and get 13 :)
The sum of the digits of a given two digits the new numbers is 5 .if the digits are reversed, the new number is reduced by 27 . find the given number
Answers
Answer:. The numbers are 41 and 14
Step-by-step explanation: X and Y represent the digits. In the Tens place, the digit has 10× its base value. Therefore we can set up equations to model the information given:
10x+y = 10y + x +27
X + Y = 5
y =5-x rewritten to substitute for y
10x + 5-x = 10(5-x)+x +27
Distribute and then combine like terms:
9x +5 = 50 - 9x +27
Add 9x to both sides; subtract 5 from both sides.
9x +9x = 50+27-5
18x = 72 Combine like terms. Then divide both sides to solve for x.
x = 4
4+y=5 Substitute 4 for x; solve for y.
y=1
Substitute values of x and Y into the original equation and check.
40 +1 = 10 +4 + 27
41 = 14+ 27
True! 41=41
The numbers are 41 and 14.
What is 0.82 as a fraction in simplest form?
(I also need the work if not its ok!)
Answers
Answer:
f 41/50
Step-by-step explanation:
10. Keith has 7.8 ounces of tuna salad. If
he makes 3 sandwiches with an equal
amount of tuna on each, how much tuna
does he put on each one?
Answers
Answer:2.6 ounces per sandwich
Step-by-step explanation: 7.8/3= 2.6