Answer:
The original number is 572.
Step-by-step explanation:
Let the 3 digit number by xyz.
Where x is the hundreds digit, y is the tens digit and z is the units digit.
Hence, the digit is (100x + 10y + z).
From the question, the tens digit equals to the sum of the hundreds digit and the units digit.
That is,
y = x + z ...... (1)
Also, from the question, the hundreds digit of this number is 3 more than the units digit.
That is,
x = z + 3 ...... (2)
Also, from the question, If the digits were reserved, the new number is 11 less than half of the original number
If the digit were reversed, that is xyz becomes zyx. Then, the new number is (100z + 10y + x).
the new number is 11 less than half of the original number
That is,
(100z + 10y + x) + 11 = 1/2(100x + 10y + z)
This becomes
200z + 20y + 2x + 22 = 100x + 10y + z
200z - z +20y -10y +2x - 100x = -22
199z + 10y -98x = -22 ...... (3)
Solving the equations simultaneously,
Put the value of x in equation (2) into equation (1)
x = z + 3 ...... (2)
y = x + z ...... (1)
That is,
y = (z+3) + z
y = 2z + 3 ...... (4)
Put the value of y in equation (4) into equation (3)
199z + 10y -98x = -22
199z + 10(2z +3) -98x = -22
199z + 20z + 30 -98x = -22
219z -98x = -22-30
219z -98x = -52 ...... (6)
Put the value of x in equation (2) into equation (6)
219z -98(z+3) = -52
219z -98z -294 = -52
121z = -52 + 294
121z= 242
z = 242/121
∴ z = 2
Put the value of z into equation (2)
x = z + 3
x = 2 + 3
∴ x = 5
Put the values of z and x into equation (1)
y = x + z
y = 5 + 2
∴ y = 7
Hence, x = 5, y = 7 and z = 2.
Recall that the original number is 100x + 10y + z.
100x + 10y + z = 100(5) + 10(7) +2 = 500 + 70 + 2 = 572
Hence, the original number is 572.
Please help me I really don't know
The function 1.5x + 0.5y = 12 represents the number of hardcover books x and softcover books y you can buy at a used book sale.
a. solve the equation
b. make an input-output table to find ordered pairs for the function.
c. plot the ordered pairs in a coordinate plane.
Answer:
Step-by-step explanation:
Let's solve for x.
1.5x+0.5y=12
Step 1: Add -0.5y to both sides.
1.5x+0.5y+−0.5y=12+−0.5y
1.5x=−0.5y+12
Step 2: Divide both sides by 1.5.
1.5x
1.5
=
−0.5y+12
1.5
x=−0.333333y+8
Answer:
x=−0.333333y+8
Enter an equation to describe the linear relationship.
The temperature, y, of a pot of water is 45 °F. The temperature increases by 25 °F per minute,x , when being heated.
The equation is y=
At a firefighters' pancake breakfast, the firefighters served 345 people and raised $1395. As adult's ticket to the pancake breakfast was $5 and the cost of a child's ticket was $3. What was the number of child and adult tickets sold?
Answer:
Number of adult tickets = 180
Number of child tickets = 165
Step-by-step explanation:
Given:
Total number of ticket = 345
Total amount = $1,395
Cost of adult ticket = $5
Cost of child ticket = $3
Find:
Number of child and adult tickets
Computation:
Assume;
Number of child tickets = a
Number of adult tickets = b
So,
a + b = 345...........eq 1
3a + 5b = 1,395...........eq2
3 x in eq 1
3a + 3b = 1,035.........eq3
eq2 - eq3
2b = 360
b = 180
Number of adult tickets = 180
a + b = 345
a = 165
Number of child tickets = 165
What is the coefficients of x4 in the expansion of (1+x)4(1+2x)3.
By the binomial theorem,
(1 + x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴
(1 + 2x)³ = 1 + 6x + 12x² + 8x³
In the expansion of (1 + x)⁴ (1 + 2x)³, we get an x⁴ when multiplying
• x⁴ and 1 to get x⁴;
• 4x³ and 6x to get 24x⁴;
• 6x² and 12x² to get 72x⁴; and
• 4x and 8x³ to get 32x⁴.
Add these up:
x⁴ + 24x⁴ + 72x⁴ + 32x⁴ = 129x⁴
Problem Francine uses 2 3 3 2 start fraction, 2, divided by, 3, end fraction cup of pineapple juice for every 1 3 3 1 start fraction, 1, divided by, 3, end fraction cup of orange juice to make a smoothie.
Answer:
Pineapple juice = 2 cups
Step-by-step explanation:
Francine uses 2/3 cup of pineapple juice for every 1/3 cup of orange juice to make a smoothie , how many cups of pineapple juice does Francine use for 1 cup of orange juice
Pineapple juice : Orange juice
2/3 cup : 1/3 cup
how many cups of pineapple juice does Francine use for 1 cup of orange juice
Let x = cups of pineapple juice
Pineapple juice : Orange juice
x cup : 1 cup
Equate the ratios
2/3 cup : 1/3 cup = x cup : 1 cup
2/3 ÷ 1/3 = x / 1
2/3 × 3/1 = x / 1
6/3 = x / 1
Cross product
6 * 1 = 3 * x
6 = 3x
x = 6/3
x = 2
Pineapple juice = 2 cups
Can exponents be integers
Answer:
NO
Step-by-step explanation:
Exponents are expressed as numbers or variables in superscript above a base number. When the exponent is equal to or greater than 2, it directs how many times the base number is to be multiplied. The numbers 1 and 0 are special exponents, and negative integers as exponents stand for reciprocal values.
Answer:
It matters of what the whole number in front is.
Step-by-step explanation:
For example: 6 to the power of 2 = 36
if the first number is a decimal: 1.6 to the power of 2.56
Its NOT an exponent if the starting number is a decimal usually.
solving a compound inequality. check all that apply.
Answer:
The solutions are:
-28.25, -14.5, -2.25
Step-by-step explanation:
Given compound inequality is:
[tex]-17.5\leq \frac{2x+4}{3} <17.5[/tex]
The compound inequalities are broken down into two inequalities to find the solution
The two inequalities will be:
[tex]\frac{2x+4}{3} \geq -17.5[/tex] AND [tex]\frac{2x+4}{3}<{17.5}[/tex]
Solving both inequalities one by one
[tex]\frac{2x+4}{3} \geq -17.5\\2x+4 \geq -52.5\\2x \geq -52.5-4\\2x \geq -56.5\\\frac{2x}{2} \geq \frac{-56.5}{2}\\x \geq -28.25\\\frac{2x+4}{3} < 17.5\\2x+4 < 52.5\\2x < 52.5-4\\2x \geq 48.5\\\frac{2x}{2} \geq \frac{48.5}{2}\\x < 24.25[/tex]
The solution is:
-28.25 ≤ x < 24.25
We have to see which options lie in the solution range.
The solutions are:
-28.25, -14.5, -2.25
PLEASE HELP WITH THE 2
Answer:
ok good luck jsjsksksksksks
Answer:
y=32
Step-by-step explanation:
45+z+y=180
z=103 by the exterior angle theorem
45+103+y=180
148+y=180
y=32
In a family of 11, what is the probability that there will be more boys than girls
Answer:
P(all female)= 1/2 x 1/2 x 1/2 = 1/8
P(all male ) = 1/2 x 1/2 x 1/2 = 1/8
P(all one gender) = P(all female) + P(all male) = 1/8 + 1/8 = 1/4
What is the probability that a three-child family is two girls and one boy?
Each possible birth order has P=1/8. That is, P(G,G,B)=P(G,B,G)=P(B,G,G)=1/8.
So, P(2G,1B)= 3/8 and P(1G,2B)= 3/8.
This allows us to write the overall gender probability distribution for families of three children as follows:
1/8 will be three girls
3/8 will be two girls and one boy
3/8 will be one girl and two boys
1/8 will be three boys
Adding it all up, we have 1/8 + 3/8 + 3/8 + 1/8 = 1 (100%)
Step-by-step explanation:
Braniliest
What is the value of of x when 3x = 54?
A) x = 18
B) x = 51
C) x = 57
D) x = 162
A) x = 18
3x = 54
=> x = 54/3
=> x = 18
Answer:
A) x= 18
Step-by-step explanation:
I took the test on USA TEST PREP. Also cause ima smarty pants.
hey i hope ur having a good day can you answer these?
thank you
question one
180 - 6 = 174 ( c )
because angles on a straight line are 180 !
question two
AB = 6 units
AC = 8 units
( i just counted the boxes )
BC = square root ( 36 + 64 ) = 10
( pythagorus’ theorum )
6 + 8 + 10 = 24 units ( b )
im late but :(
Answer:
1. C
2. B
Step-by-step explanation:
hope this helped <33
bye hope ur day is good :)
A group of 8 children and 10 adults ate going to a movie. Child tickets cost $2 and adults tickets cost $4. How much will the movie tickets cost in all ?
Answer:
56$
Step-by-step explanation:
8*2=16
10*4=40
16+40=56
If x is 5, then 6x=??
Answer:
30
Step-by-step explanation:
since x=5, and it's 6x, it'd be the same as 5x6, or 6(5).
Answer:
I think it should equal 30
Step-by-step explanation:
If x is 5 it would be 6(5) so you multiply 6 and 5 which equals 30
(sorry if i'm wrong)
Mr. Alvarez is buying every boy on his son's football team a new football. The footballs are sold in packages of 4. There are a total of 15 boys on the football team.
Part A:
In order for every boy to receive a football, how many packages of footballs does Mr. Alvarez need to buy?
Part B:
Using your findings in Part A, if every package costs $20.97, how much will Mr. Alvarez spend on footballs? PLEASEE HELP
Answer:
A)4 packs of footballs
B)$83.88
Step-by-step explanation:
If every boy needs a football then he is unable to buy just 3 cause then he would only have 12 footballs
3*4=12
So he would need 4 packs of footballs
B) because he needs 4 packs he multiplies 4 by 20.97 a pack.
4*20.97=83.88
2. A maintenance crew is paving a road in 7-hour shifts. After
10 shifts, 1.25 miles of road have been paved. After 45 shifts,
5.625 miles of road have been paved. At what rate is the
maintenance crew paving the road in miles per shift?
What is the independent quantity?
What is the dependent quantity?
How many miles are paved per shift worked?
miles/shift
Answer:
The answer is the first one
Step-by-step explanation:
please show work
a car travels 100 miles in 2 hours (with a constant speed). how much time will it take traveling 275 miles
Answer:
5.5 hours (If rounded, then 6)
Step-by-step explanation:
If you divide 100 by 2, it would be 50. So then you would have to divide 275 by 50, which will get you your time. Which is 5.5 hours.
does the oval graph represent a function why or why not?
Answer:
No
Step-by-step explanation:
Because using the vertical line test, the function is passed through twice.
Maria has a job picking apples. She can pick 52 apples per hour. How many apples can she pick in 45 minutes.
Answer:
39
Step-by-step explanation:
1) In 2000, there were approximately 109 million cell phone users in the United States. The number of cell
phone users grew to approximately 189 million after one year.
a) Write an exponential model that represents the number of cell phone users in the United States, where t
represents the number of years after 2000.
[2]
[1]
b) What is the percent rate of change?
[1]
c) What would be the number of cell phone users in 2015?
[3]
2) Which statement applies to the graph of f(x)=e* below.
Answer:
the answer is 298
Step-by-step explanation:
help!!!!!! asap please!
Answer:
ITS ONE
Step-by-step explanation:
WHEN YOU MULTIPLY 1X1 YOU GET ONE
A system of two linear equations has infinite solutions. What does this tell you about the graph of the system?
А) The system graphs as parallel lines.
B) The system graphs as one line
C) The system graphs as perpendicular ones.
D) The system graphs as intersecting lines
Answer:
B) The system graphs as one line.
Step-by-step explanation:
The solutions of systems are basically the points where the two lines of the linear equations meet, or intersect.
So, picture it like this: if a system of linear equations has INFINITE (never-ending) solutions, then it must mean that the two lines intersect at EVERY single one of their points. And if they intersect at every one of their points, then that must mean that they are the same line, even if the equations are written differently.
Hope this helps!
A truck is working to carry a batch of goods including sand and
stone but it can only carry 20 tons at most. The carriage
charges of each ton of sand and stone are 10 and 15 dollars
respectively. Its owner wants to earn at least 250 dollars. Write
a system of inequalities to express this situation. What is the
least possible number of tons of stone the owner needs to
carry to meet his own goal?
tons
Enter the answer
Check it
Answer:
Y=10
Step-by-step explanation:
No
Which is it? A,B,C or D
Which of the following is not a function?
A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 2, 3. Column 2 is labeled y with entries 3, 4, 5, 9.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 1, 2, 3. Column 2 is labeled y with entries 0, 3, 4, 7.
y = 3x² – 6x + 4
{(3, 4), (6, 5),
(7, 9), (9, 15)}
Answer:
A on edge. -
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 1, 2, 3. Column 2 is labeled y with entries 0, 3, 4, 7.
y = 3x² – 6x + 4
{(3, 4), (6, 5),
(7, 9), (9, 15)}
Step-by-step explanation:
got it right
Answer:
it is A on edge the guy before me is wrong
Step-by-step explanation:
Anna sells candy apples at her yard sale. She wants to earn more than $40. She sells the apples for $2 and has earned $26. How many apples does she need to sell to reach her goal?
Answer:
7 apples
Step-by-step explanation:
40 - 26 = 14
14 / 2 = 7
The price of mangoes in a grocery store is 3 for $5. How much will 5
mangoes cost? Round the answer to the nearest hundredth.
Answer:
8 and one thirds
Step-by-step explanation:
5 times 5 is equal to 25 and 25 divided by 3 is 8.3333
Answer:
$8.33
Step-by-step explanation:
So, to figure out how much one mango costs, I did $5 divided by 3, which gave me 1.66.
I then multiplied that by 5 to see how much 5 mangos cost, and I got $8.33
Help me solve these two find the value of x please help
Hi there!
[tex]\large\boxed{\text{x = 12, x = 5}}[/tex]
Problem 1:
The angles pictured are vertical angles, so each will be equivalent. Therefore:
(5x + 5)° = 65°
Subtract 5 from both sides:
5x = 60
Divide both sides by 5:
x = 12°.
Problem 2:
The two angles are supplementary, so they add up to 180°. Therefore:
180° = (9x)° + (12x + 75)°
180 = 9x + 12x + 75
Combine like terms:
180 = 21x + 75
Subtract 75 from both sides:
105 = 21x
Divide both sides by 21:
x = 5°.
Calculate the area of the rectangle.
Answer:
12
Step-by-step explanation:
You count all of the blue squares
Given line p is parallel to line q, measure of angle 3 = 5x - 3 and measure of angle 8 = 4x - 6, find x.
Answer:
None
Step-by-step explanation:
There is not enough information to be given a correct answer
expand and simplify completely (log). PLEASEE HELP ASAP!!! I WILL GIVE BRAINLIEST!! thank you so much!!!!
Answer:
c. [tex]2 log3(y)+1+log3(x)[/tex]
Step-by-step explanation:
When expanding and simplifying, we can see that the answer is [tex]1+log3(x) + 2log3(y)[/tex], which matches Answer Choice C.Answer:
( C ) 1+log3x+2log3y
Step-by-step explanation: