Answer:
-7/5
Step-by-step explanation:
What are 5 fractions equivalent to 7/8?
Answer:
14/16
24/32
48/64
96/128
192/256
Step-by-step explanation:
Take 7 multiply it by 2, then take 8 and multiply it by 2
When you get your answer (14/16) multiply that by two
Keep going until you have 5 numbers
Answer:
14/16
21/24
28/32
35/40
42/48
Step-by-step explanation:
1. 7/8
7x2=14
8x2=16
14/16
2. 7/8
7x3=21
8x3=24
21/24
3. 7/8
7x4=28
8x4=32
28/32
4. 7/8
7x5=35
8x5=40
35/40
5. 7/8
7x6=42
8x6=48
42/48
What is the common ratio between successive terms in the sequence?
2.-4.8.-16, 32, -64,...
0-2
-6
6
2
Answer: -2
Step-by-step explanation:
You multiply the number before in the sequence by -2 to get the number that follows.
2*-2 = -4
-4*-2 = 8
And so on...
write a polynomial equation for each set of roots 5 and 7
Answer:
x²-2x-35
Step-by-step explanation:
(x-7)(x+5)
x²+5x-7x-35
x²-2x-35
1. 1.5 ÷ 1.2
2. 3.42 ÷ 0.6
3. 11.77 ÷ 1.1
4. 18.16 ÷ 0.4
5. 140.21 ÷ 1.4
Answer:
1. 25
2. 5.7
3. 10.7
4. 204
5. 100.5
Step-by-step explanation:
calculator
Enter the slope of the line through the points (4, 15) and (4, 12). *
Answer:
-3/0 is the slope....or just -3.
Step-by-step explanation:
slope method = m= y2 - y1/ x2 - xm = 12 - 15/ 4 - 4 = -3/0 or just -3 simplified.
Did the scale factor of 0.75 enlarge reduce or stay the same?
Answer:
[tex]\huge\boxed{\sf Reduces}[/tex]
Step-by-step explanation:
Since the scale factor of 0.75 is less than 1, So the dilated image is a reduced image.
Thus the scale factor of 0.75 reduces the dilated image.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Answer:
-it reduces-
Step-by-step explanation:
good luck:)
Which expression has a value different from the others?
A. -108 + 105
B. 9.9 + (12.9)
C. -7 2/9 - ( -4 2/9)
D. 637 - 641
Answer:
I think B
Step-by-step explanation:
A. -108+105
-3
B. 9.9+(12.9)
22.8
C. -7 2/9 -(-4 2/9)
-3
D. 637 - 641
-4
Is the last one written wrong because if that one is 637-640 or 638-641 than it would equal -3. Then the answer would be B.
A road sign indicates a school bus stop is 0.3km. How far is that in metres?
Answer:
The answer is 300.
Step-by-step explanation:
A kilometer is 1000 meters, therefore 0.3 km x 1000 = 300 meters
why is side BD equal to side CE
Answer:
At each vertex at least 3 faces meet (maybe more).
Step-by-step explanation:
What is the value of the expression 8³?
A. 24
B. 83
C. 512
D. 6,561
Answer:
its c and thats on purrrr
Step-by-step explanation:
It’s not b!!!! Help me please
Answer:
D maybe? im not sure
Step-by-step explanation:
What are the domain and range of the function x^2-2x^2-4?
[tex] {x}^{2} - 2 {x}^{2} - 4 \\ - {x}^{2} - 4[/tex]
The Quadratic Function has the domain as the set of all real numbers.
For the range, start from minimum value to maximum value.
But because the parabola is downward as a < 0. Thus, there are no minimum value but the maximum value instead.
Therefore the range is y <= -4
Please help me fastttt!!!!
Answer:
-4
Step-by-step explanation:
2^2 =4
PMDAS
-36 / 4 +5
-9+5
-4
What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at 4, negative 2, B double prime at 4, negative 1, C double prime at 1, negative 1, D double prime at 1, negative 2. Reflected over the x‒axis and reflected over the y-axis Reflected over the y-axis and rotated 180° Reflected over the x‒axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise
Answer:
Reflection over the y-axis and rotation of 180°
Step-by-step explanation:
We have,
Rectangle ABCD with co-ordinates A(-4,2), B(-4,1), C(-1,1) and D(-1,2).
It is transformed to a new rectangle A'B'C'D' with co-ordinates A'(-4,-2), B'(-4,-1), C'(-1,-1) and D'(-1,-2).
The graph of both the triangles is shown below.
we see that,
The rectangle ABCD is reflected about y-axis and then rotated 180° to obtain A'B'C'D'.
Reflected about y-axis Rotation of 180°
A= (-4,2) (4,2) A'= (-4,-2)
B= (-4,1) (4,1) B'= (-4,-1)
C= (-1,1) (1,1) C'= (-1,-1)
D= (-1,2) (1,2) D'= (-1,-2)
Hence, the second rectangle is formed by: Reflection over the y-axis and rotation of 180°.
Answer:
b- reflect over y- axis and rotate 180 degrees
Step-by-step explanation:
Reflected about y-axis Rotation of 180°
A= (-4,2) (4,2) A'= (-4,-2)
B= (-4,1) (4,1) B'= (-4,-1)
C= (-1,1) (1,1) C'= (-1,-1)
D= (-1,2) (1,2) D'= (-1,-2)
Mark bought gifts for his friends, and each gift cost $9. Let y represent the total cost and x represent the number of gifts. Write an equation to
represent the proportional relationship between the total cost and the number of gifts he bought. (4 points)
Оа
y = 8x
Oь
1
y = 8
Oc
y = 9x
Od
1
10
ya
Answer:
9x=y
Step-by-step explanation:
9 times x will equal the number of gifts (y). so the answer is Oc= y=9x
Part B
Line m has a slope of -3. Another line n is parallel to line m. What is the slope of line n?
Slope of linen is
Answer:
Step-by-step explanation:
the slope of line n is also -3 as it is parallel to m
The answer is A
Help please!! There are two pictures. This is timed. I’ll give brainliest also!
Answer:
X=-5 y=31
X=-1 , y=7
X=0 , y=1
X=1 y=-5
Step-by-step explanation:
Answer:
x = -5, y = 31
x = -1 , y = 7
x = 0, y = 1
x = 1, y = -5
Step-by-step explanation:
y = -6x + 1
1. y = -6 ( -5 ) + 1
y = 31
2. y = -6 ( -1 ) + 1
y = 7
3. y = -6 ( 0 ) + 1
y = 1
4. y = -6 ( 1 ) + 1
y = -5
Which is true about the product of 3/8 and 7/2?
Answer:
Nothing ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎ฏ๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎๎
Step-by-step explanation:
Answer:
Do you have the options? Or..
According to the 2014 national population projections published by the U.S. Census Bureau, the U.S. population is projected to be 334.4 million in 2020 with an estimated growth rate of 0.79% per year. Assuming the growth rate remains constant, find the projected population in 2050.
Answer:
423,437,744
Step-by-step explanation:
Given that :
Projected population in 2020 = 334.4 million
Estimated growth rate (r) = 0.79%
Projected population in 2050 ;
Using the exponential growth function :
Estimated value = initial value(1 + growth rate)^time
Initial value = i
Time = 2020 - 2014 = 6 years
334.4 = i(1 + 0.0079)^6
334.4 = i(1.0079)^6
334.4 = i2.43087455521E−13
i = 3.189786E8
Initial population = 318. 978 million
Estimated Population in 2050:
2050 - 2014 = 36
Projected population = 3.189786E8(1.0079)^36
Projected population = 3.189786E8*1.3274801
= 423437743.82586
= 423437744 million
I need answer as quick
Answer:
C
Step-by-step explanation:
(x+7)(x+1)(x+4)=
x^3+12x^2+39x+28 or C
Answer:
C
Step-by-step explanation:
Given
(x + 7)(x + 1)(x + 4) ← expand the second/ third factors using FOIL
= (x + 7)(x² + 5x + 4)
= x(x² + 5x + 4) + 7(x² + 5x + 4) ← distribute both parenthesis
= x³ + 5x² + 4x + 7x² + 35x + 28 ← collect like terms
= x³ + 12x² + 39x + 28 → C
What is the value of A in the equation shown?
Answer:
is this algebra 1
Step-by-step explanation:
Answer:
The answer is 1
Step-by-step explanation:
you isolate the variable by dividing each side
Write a cubic function whose graph is shown
Answer:
what grade
Step-by-step explanation:
If 7x-3x+17-x+1=108, what is the value of 4x+x?
Answer:
150
Step-by-step explanation:
1. combine like terms
7x-3x-1x=3x
17+1=18
2. subtract
108-18=90
3. divide
90/3=30
which means x=30
4. plug it in
4X30+30=150
consider polynomial function f f(x)=(x-1)^2(x+3)^3(x+1)
use the equation to complete each statement about this function
The zero located and x=1 has a multiplicity of __ and the zero located at x=-3 has a multiplicity of __. The graph of the function will touch, but not cross, the x-axis at the x-value of __.
Answer:
x1=-3, x2=-1,x3=1
Step-by-step explanation:
not sure if this helps but it did for me
The blanks will have values 2, 3, and 1 respectively.
What is zero of a function?
Zero of a function is defined as the roots of the function for which the value of the function will be 0 at those points.
If p is the zero of the function f(x)=0 then f(p)=0.
We have,
f(x) = (x-1)² (x+3)³ (x+1)
Now,
The zero is located at x=1 and has a multiplicity of 2.
Because the number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity.
So,
Now,
The zero is located at x = - 3 and has a multiplicity of 3.
And,
The graph of the function will touch, but not cross, the x - axis at the x - value of 1.
Learn more about zero and multiplicity here:
https://brainly.com/question/14059007
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(2x−6)+4(x−3)
Find the sum.
Answer:
6x - 18 or 6*(x - 3)
Step-by-step explanation:
Pull out like factors: 6x - 18 = 6 • (x - 3)
Hope this helps! Please mark as brainlest.
Thanks!
If a household appliance has a wattage of 7,043 and is in use for 9 hours, how much CO2 was produced? Round to 1 decimal.
Answer: = 62.8 pounds of CO₂
Step-by-step explanation:
1 kilowatt per hour produces 0.99 pounds of C02.
The total wattage in hours used was;
= 7,043 * 9 hours
= 63,387 watts
In kilowatts;
= 63,387/1000
= 63.387 kilowatts
CO2 produced;
= 63.387 * 0.99
= 62.75313
= 62.8 pounds of CO2
42 kids bought popcorn at the movie. This was 60% of the kids who attended the movie.
How would you summarize the process to find the number of kids who attended the
movie?
Answer:
Total number of children = 70
Step-by-step explanation:
Given:
Number of kids buy popcorn = 42
Percent of kids buy popcorn = 60% = 0.6
Find:
Total number of children
Computation:
Total number of children = Number of kids buy popcorn / Percent of kids buy popcorn
Total number of children = 42 / 0.6
Total number of children = 70
choose all the polygons
Answer:
A, B, E, F
Step-by-step explanation:
A polygon is ANY shape formed with only straight lines.
WILL GET BRAINLIEST AND POINTS PLS HELP
Answer:
D. -6
Step-by-step explanation:
frist elimnate the postive numbers because it is impossible if it was a positve number.
Then you have two numbers left, all you have to do is multiply each one by either 3 or -5.
so -10.3 is too big and -6 is just right
x = -6
The sum of the tens digit and the hundreds digit of a number is three times the units digit. 1/5 of the sum of all three digits is 1 less than the units digit. Find all three-digit numbers that satisfy these conditions.
Answer: The numbers are:
965
875
785
695
Step-by-step explanation:
We have a 3 digit number that can be written as:
a*100 + b*10 + c
Where a, b, and c are single-digit numbers.
a is the hundreds
b is the tens
c is the unit.
We know that:
"The sum of the tens digit and the hundreds digit of a number is three times the units digit."
a + b = 3*c
" 1/5 of the sum of all three digits is 1 less than the units digit."
(a + b + c)/5 = c - 1
Then we have the two conditions:
a + b = 3*c
(a + b + c)/5 = c - 1
From the first one, we can write:
(a + b)/3 = c
Replacing that in the other equation we get:
(a + b + a/3 + b/3)/5 = a/3 + b/3 - 1
(4/3)*(a + b)/5 = (a/3 + b/3) - 1
(4/15)*(a + b) = (a + b)/3 - 1
(4/15)*(a + b) - (a + b)/3 = - 1
-(1/15)*(a + b) = -1
a = 15 - b
Then we can give different values for b, and find the values of a and c, where a and c must be positive.
b = 9
a = 15 - 9 = 6
Then:
c = (9 + 6)/3 = 5
(notice that a + b = 15, then c will be always equal to 5, reggardless of the values of b and a).
This number will be:
695.
if b = 8, then:
a = 15 - 8 = 7
and c = 5, same as before.
the number is 785.
If b = 7, then:
a = 15 - 7 = 8
The number is 875
if b = 6, then:
a = 15 - 6 = 9
The number is:
965