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
Help? Show work!
Triangle PQR ≅ Triangle XYZ
PQ = 3a + 4 and XY = 5a – 12. Find a and PQ.
Answers
Given:
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ=3a+4[/tex]
[tex]XY=5a-12[/tex]
To find:
The value of a and PQ.
Solution:
We have,
[tex]\Delta PQR\cong \Delta XYZ[/tex]
[tex]PQ\cong XY[/tex] (CPCTC)
So,
[tex]PQ=XY[/tex]
[tex]3a+4=5a-12[/tex]
Isolating variable terms, we get
[tex]3a-5a=-4-12[/tex]
[tex]-2a=-16[/tex]
Divide both sides by -2.
[tex]a=\dfrac{-16}{-2}[/tex]
[tex]a=8[/tex]
Now,
[tex]PQ=3a+4[/tex]
[tex]PQ=3(8)+4[/tex]
[tex]PQ=24+4[/tex]
[tex]PQ=28[/tex]
Therefore, the value of a is 8 and the value of PQ is 28.
If UW = 9x -9, what is UW in units?
Answers
3,000 is 1/10 of?-
300
300,000
3,000
30,000
Answers
Answer:
30,000
Step-by-step explanation:
3,000 times 10 is 30,000, therefore 30,000/10=3,000
Answer:
Step-by-step explanation:
3000 of 1/10
3000*0.1=300
The weight of a mandarin orange is about 6 ounces. A basket that weighs 4 ounces will hold m mandarin oranges, the total weight is 70 ounces. Which equation represents the basket of oranges?
4 + 6m = 70
6 + 4m = 70
70 + 4m = 6
70 + 6m = 4
.
Answers
Answer:
4 + 6m = 70
Step-by-step explanation:
4 is the basket
6m is the total weight of mandarins
70 is total weight
Answer
A is the answer
Indicate whether the measures 3.1, 4.8, and 10.2 can be the side lengths of a triangle. If they can, classify the triangle.
Answers
The measures 3.1, 4.8, and 10.2 cannot be the side lengths of a triangle.
What is triangle inequality?"It states that the sum of any two sides must be greater than the third side."
For given question,
we have been given the measures 3.1, 4.8, and 10.2
We need to check whether given measures can be the side lengths of a triangle.
First we check whether the given measures obey triangle inequality or not.
3.1 + 4.8 = 7.9
7.9 < 10.2
This means, the measures 3.1, 4.8, and 10.2 do not obey triangle inequality
Therefore, the measures 3.1, 4.8, and 10.2 cannot be the side lengths of a triangle.
Learn more about the triangle inequality here:
https://brainly.com/question/1163433
#SPJ2
Simplify the following by combining like terms:
1y - 8xy + 7x - 5y + 4xy + 9x
Answers
Answer:
-4y-4xy+16x
Step-by-step explanation:
Hope this helps!! If you need it step by step I'll comment it in the comments.
what is an equation of the line that passes through the point (-6,-1) and is perpendicular to the line 6x-y=7? (has to be in y=mx+b form)
Answers
Answer:
y = [tex]-\frac{1}{6}[/tex] x - 2
Step-by-step explanation:
Slopes of perpendicular lines are opposite reciprocals.
If AB ⊥ CD , then [tex]m_{AB}[/tex] [tex]m_{CD}[/tex] = - 1
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
~~~~~~~~~~~
6x - y = 7 ⇔ y = 6x - 7
Slope of given line is 6
Slope of a perpendicular line is [tex]-\frac{1}{6}[/tex]
( - 6, - 1 )
y + 1 = [tex]-\frac{1}{6}[/tex] (x + 6)
y = [tex]-\frac{1}{6}[/tex] x - 2
answer pleaseesesese
Answers
Answer:
a
Step-by-step explanation:
its a bc a is the only one that is the answer
Evaluate -x + 8 for x = 5.
Answers
Answer:
3 is the answer
Step-by-step explanation:
-(5)+8
-5+8=3
you just change x for 5 and go from there
In this problem, you have to use substitution!
-x + 8, when x = 5
1) Substitute the value of 'x' with '5'
-x + 8
= -5 + 8
2) Reverse the expression to make it easier to solve [optional]
-5 + 8
= 8 - 5
3) Solve!
8 - 5
= 3
Your answer is 3
I hope this helps!
- sincerelynini
Question 10
10 pts
Miguel wants to repair his home. He places a 17-foot ladder against the side of the house 8feet
from the base of the house. What is the height of Miguel's home, x, from the ground to the top of
the ladder at the roof, to the nearest tenth of a foot?
Answers
Answer: 15
HELPPPP
Predict the number of sales in month 5.
The store sold fewer blue jeans
after the
new pants became popular.
Enter the correct answer.
7904
3952
1976
988
?
Answers
Explanation: the sales are being cut in half every month
Yw. ;)
Evaluate \dfrac p4 +pq
4
p+pqstart fraction, p, divided by, 4, end fraction, plus, p, q when p=8p=8p, equals, 8 and q=6q=6q, equals, 6.
Answers
Answer:
4
Step-by-step explanation:
Answer:
its 50
Step-by-step explanation:
Solve the following word problem using two variables. Show each step of your work.
John is five years older than Maya. The sum of their ages is 27. Find both ages.
Answers
Answer:
John is 16 and Maya is 11
Step-by-step explanation:
x=Maya's age
x+5=John's age
x+x+5=27
2x+5=27
-5 -5
2x=22
/2 /2
x=11
x+5=
11+5= 16
Solve each equation for x. Provide the Justifications for each step.
6-2x=10
Answers
can someone pls answer this question for my sis she's in the 4th grade and i don't remember how to solve this
17/15 - 4/5
TYSM( btw worth twelve points )
Answers
Answer:
i think its 13/45
Step-by-step explanation:
158, 155,152,...
Find the 34th term.
Answers
Answer:
56
Step-by-step explanation:
158 - ( 3 * 34) = 56
The perimeter of a rectangle is 70cm. if its length is decreased by 5cm and its width is increased by 5cm, its area will increase by 50 cm^2. Find the length and the width of the original rectangle.
Answers
Answer:
l=25, w=10
Step-by-step explanation:
2(25)+2(10)=70
25*10=250
25-5=20
10+5=15
20*15=300
Answer:
width = 10
lenghth = 25
Step-by-step explanation:
What is the square root of 100?
Answers
Answer:
the square root of 100 is 10
10x10=100
Answer:
the square root of 100 is 10
Step-by-step explanation:
hi please help me , if u dont mind
Answers
Answer:
C or B
Step-by-step explanation:
Answer: i believe it would be B
Step-by-step explanation: Basically the graph points keep moving up.
In triangle DEF, CG = (x + 5) units and DG = (3x - 2) units.
Triangle D E F has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments D C, E B, F A.
[Figure may not be drawn to sacle]
What is DG?
12 units
17 units
34 units
51 units
Answers
A centroid is the intersection point of the medians of a triangle. The required length of DG is 2.4 unit.
What is a triangle?A triangle is a two dimensional shape bounded by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.
Given that,
There is a triangle ΔDEF.
The centroid of the given triangle is G.
The medians of the triangle are DC, EB and FA.
CG = (x + 5)
DG = (3x - 2)
Here, CG and DG are parts of the median DC.
Since, centroid of a triangle divides its each medians into the ratio of 2 : 1
in the direction from the vertex to the midpoint of the opposite side.
The following expression can be written for the given problem,
DG/CG = 1/2
=> (3x - 2)/ (x + 5) = 1/2
=> 2(3x - 2) = x + 5
=> 6x - x = 5 + 4
=> x = 9/5
=> x = 1.8
Thus, DG = (3x - 2)
= 3 × 1.8 - 2
= 2.4
Hence, the length of DG is given as 2.4 unit.
To know more about triangle click on,
https://brainly.com/question/2773823
#SPJ1
Answer:
34 units
Step-by-step explanation:
The first time i took the pretest i guessed 17 units and it was incorrect, so when i had to go through with the lesson and take the quiz i guessed 34 units and it was correct.
Molly shot 20 baskets in 4 minutes. Nico shot 42 baskets in 6 minutes.
How many more baskets did Nico shoot per minute? (If you answer this one, you will 15 points and I can answer one of urs too!)
Answers
nico shot 42 basket in 6 minutes
per minute =42÷6
7
nico shot 7 basket per minute
.
Answer:
2
Step-by-step explanation:
Molly 60.4=240 20:4=5
Nico 60.6=360 42:6=7
7-5=2
Evaluate -31-8+31−31−8+31minus, 31, minus, 8, plus, 31.
Answers
Answer:
-24
Step-by-step explanation:
-8 -31 -8 + 31 - 31 -8 + 31
-8 -8 - 31 - 8 - 31
-8 -8 -8
-24
whats the equation for the perpendicular bisector of the line segment whose endpoints are (-5,3) and (3,7)?
Answers
Answer:
The equation of perpendicular bisector of the line segment passing through (-5,3) and (3,7) is: [tex]y = -2x+3[/tex]
Step-by-step explanation:
Given points are:
(-5,3) and (3,7)
The perpendicular bisector of line segment formed by given points will pass through the mid-point of the line segment.
First of all we have to find the slope and mid-point of given line
Here
(x1,y1) = (-5,3)
(x2,y2) = (3,7)
The slope will be:
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{7-3}{3+5}\\m = \frac{4}{8}\\m = \frac{1}{2}[/tex]
The mid-point will be:
[tex](x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\ = (\frac{-5+3}{2},\frac{3+7}{2})\\= (\frac{-2}{2},\frac{10}{2})\\=(-1,5)[/tex]
Let m1 be the slope of the perpendicular bisector
Then using, "Product of slopes of perpendicular lines is -1"
[tex]m.m_1 = -1\\\frac{1}{2}.m_1 = -1\\m_1 = -1*2\\m_1 = -2[/tex]
We have to find the equation of a line with slope -2 and passing through (-1,5)
The slope-intercept form is given by:
[tex]y = mx+b\\y = -2x+b[/tex]
Putting the point (-1,5) in the equation
[tex]5 = -2(-1)+b\\5 = 2+b\\b = 5-2\\b = 3[/tex]
The final equation is:
[tex]y = -2x+3[/tex]
Hence,
The equation of perpendicular bisector of the line segment passing through (-5,3) and (3,7) is: [tex]y = -2x+3[/tex]
could someone please help me with this
Answers
Answer:
E is the correct choice
Step-by-step explanation:
i hope this helps
a bed of a pickup truck measures 4 ft by 8 ft to the nearest inch what is the length of the longest thin metal bar that will lie flat in the bed
Answers
Answer:
11 ft 3 in
Step-by-step explanation:
The bed of a pickup truck measures 4 feet by 8 feet. To the nearest inch, what is the length of the longest thin metal bar that will lie flat in the bed? 11 ft 3 in.
Answer:
Step-by-step explanation:
the diagonal is the longest so use Pythagoras
c^2 =a^2 + b^2
c^2=4^2+8^2
c^2=16+64
c =[tex]\sqrt{80}[/tex]
c = 8.944 ft
Simplify. 11 3/4 - 8 1/2 A. 3 1/4 B. 3 1/3 C. 4 1/4
Answers
Answer:
A
Step-by-step explanation:
11 3/4 - 8 1/2 = 3 1/4
Tell which number is greater.
17%, 4/25
Answers
ILL GIVE BRAINLIEST
An angle measures 100° less than the measure of its supplementary angle. What is the measure of each angle? _° and _°
Answers
Answer:
Step-by-step explanation:
the sum of supplementary angles equal to 180
let x=angle
180-x= the other angle
180-x=x-100
2x=280
x=140
the other angle is 40
kiersten is 6ft tall. She is standing in front of a tree and notices her shadow. If her shadow is 9 feet away from her and the shadow of the tree is 84 feet away from the tree, how tall is the tree?
Answers
If kiersten is 6ft tall. She is standing in front of a tree and notices her shadow and her shadow is 9 feet away from her. The height of the tree is 56 feet.
How to find the height?Given data:
kiersten height = 6ft tall
Shadow = 9 feet away
Shadow of tree = 84 feet
The equation that will be use to find the height is 6/9= x/84
Let x represent the tree's height
So, let solve for x
6/9= x/84
Cross multiply:
9x = 6(84)
9x = 504
Divide both side by 9x
x= 504/9
x = 56 feet
Therefore we can conclude that the height of the tree is 56 feet.
Learn more about height here:https://brainly.com/question/1739912
#SPJ1
the value of the 7 in 0.076 is 1/10 the value of the 7 in 2.79
Answers
Answer:
true
Step-by-step explanation:
the second 7 is in the tenth place and the first 7 is in the hundredth place, which is 1/10 the tenth place
I agree...................