the standard addition algorithm below is being used to add three two-digit numbers 4z + 27 + x 5 equals y 14. If x, y, and z each represent a different digit from 0 to 9 what is the value of (x)(y)(z)?
Answers
[tex]z+7+5=4 \\ z+12=4[/tex]
From this we can conclude that total sum of these three numbers is 14. Number 1 we carry to next step. So we have:
[tex]z+12=14 \\ z=2[/tex]
For the tens positions of all numbers we have:
[tex]4+2+x+1=1 \\ 7+x=1[/tex]
The extra number 1 on left side comes from the carry from last step. Similar to ones position we know that total sum is 11.
[tex]7+x=11 \\ x=4[/tex]
Now we insert x and z to find out y:
[tex]42+27+45=y14 \\ 114=y14 \\ y=1[/tex]
Now we need to find out the product of these three numbers:
[tex]x*y*z=4*1*2=8[/tex]
Related Questions
What is an atom? GIVING BRAINLIEST 30 POINTS PLEASE HELP
Question 1 options:
an indivisible particle
one of the three particles that make up all matter
an element without an electrical charge
the basic particle that makes up matter
Question 2 (1 point) Question 2 Unsaved
What is a neutron?
Question 2 options:
a subatomic particle with no electric charge, found in the electron cloud
a subatomic particle with no electric charge, found in the nucleus of an atom
a subatomic particle with no electric charge, found in the neutron cloud
a subatomic particle with either a positive or negative electric charge, found in the nucleus of an atom
Question 3 (1 point) Question 3 Unsaved
What is a proton?
Question 3 options:
a subatomic particle with a -1 negative electric charge, found in the proton cloud
a subatomic particle with a +1 positive electric charge, found in the nucleus of an atom
a subatomic particle with a -1 negative electric charge, found in the nucleus of an atom
a subatomic particle with a +1 positive electric charge, found in the proton cloud
Question 4 (1 point) Question 4 Unsaved
What is an electron?
Question 4 options:
a subatomic particle with a +1 positive electric charge, found in the electron cloud
a subatomic particle with a -1 negative electric charge, found in the nucleus of the atom
a subatomic particle with a +1 positive electric charge, found anywhere in an atom
a subatomic particle with a -1 negative electric charge, found in the electron cloud
Question 5 (1 point) Question 5 Unsaved
What is an electron cloud?
Question 5 options:
the area surrounded by the nucleus of an atom, where electrons and neutrons can be found
the area that surrounds the nucleus of an atom, where electrons can be found
the area that surrounds the nucleus of an atom, where electrons and neutrons can be found
the area surrounded by the nucleus of an atom, where electrons can be found
Question 6 (1 point) Question 6 Unsaved
What is an ion?
Question 6 options:
an atom with either more or fewer electrons than protons, giving the atom either a positive or negative charge
an atom with either more or fewer neutrons than protons, giving the atom a different atomic mass
an atom with either more or fewer electrons than protons, giving the atom a significantly different atomic mass
an atom with either more or fewer neutrons than protons, giving the atom either a positive or negative charge
Question 7 (1 point) Question 7 Unsaved
What are isotopes?
Question 7 options:
atoms of the same element that have different atomic masses because they have different numbers of protons
atoms of the same element that have different atomic masses because they have different number of electrons
atoms of the same element that have different electric charges because they have different numbers of neutrons
atoms of the same element that have different atomic masses because they have different numbers of neutrons
Question 8 (1 point) Question 8 Unsaved
Which statement is FALSE?
Question 8 options:
An ion can be either positively or negatively charged
Isotopes are caused by different numbers of neutrons in the electron cloud
Question 9 (1 point) Question 9 Unsaved
Look at the timeline below. What is missing from the timeline?
Question 9 options:
1913 CE: Bohr proposed that electrons can change their orbit with a change of energy. He calls the orbits valence shells.
Question 10 (1 point) Question 10 Unsaved
What is the overall charge of an atom’s nucleus?
Question 10 options:
positive
neutral
negative
It depends on how many protons are in the nucleus.
It depends on how many neutrons are in the nucleus.
Question 11 (1 point) Question 11 Unsaved
Where is most of the mass in an atom?
Question 11 options:
electrons
nucleus
electron cloud
protons
neutrons
Answers
2. Option 2
3. Option 2
4. Option 4 (not completely sure)
5. Option 2
6. Option 1 (not completely sure)
7. Option 4
8. Isotopes are caused by different numbers of neutrons in the electron cloud
9. Not sure of the question
10. Positive charge
11. nucleus
Answer:
1. Option 4
2. Option 2
3. Option 2
4. Option 4 (not completely sure)
5. Option 2
6. Option 1 (not completely sure)
7. Option 4
8. Isotopes are caused by different numbers of neutrons in the electron cloud
9. Not sure of the question
10. Positive charge
11. nucleus
Step-by-step explanation:
Give the guy above me brainliest.
A triangle has side lengths of 14 cm, 48 cm, and 55 cm.
Answers
Trey graphs the equations y = –x2 + 2x + 3 and y = x2 – 2x + 3 to solve the equation –x2 + 2x + 3 = x2 – 2x + 3. His graph is shown below.
mc011-1.jpg
What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
Answers
The solution of the equation [tex]-x^2+2x+3=x^2-2x+3[/tex] are the x-coordinates of common points on the graphs of the function [tex]y=-x^2+2x+3[/tex] and [tex]y=x^2-2x+3.[/tex]
As you can see from the attached diagram these graphs intersect at points (0,3) and (2,3), then the solutions of the previous equation are x=0 and x=2.
Answer: x=0, x=2.
If 5/9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank ?
Answers
If 5/9 of a tank can be filled in 2 minutes, it would take 3.6 minutes to fill the whole tank by setting up a proportion and solving for the time.
Explanation:If 5/9 of a tank can be filled in 2 minutes, then to find the time it takes to fill the whole tank, we can set up a proportion. Since time is directly proportional to the amount of the tank filled, we have the following relationship:
Fraction of tank filled / Time to fill that fraction = 1 (whole tank) / x minutes
So, 5/9 of the tank is to 2 minutes as 1 whole tank is to x minutes:
(5/9) / 2 = 1 / x
Cross-multiplying gives us:
5x = 18
Dividing both sides by 5:
x = 18/5
x = 3.6 minutes
Therefore, it would take 3.6 minutes to fill the whole tank.
Final answer:
To find out how long it takes to fill the entire tank, set up the proportion of (5/9) of the tank in 2 minutes to (9/9) of the tank in x minutes, which gives x = 3.6 minutes for the whole tank to be filled.
Explanation:
If 5/9 of a tank can be filled in 2 minutes, we can set up a direct proportion to find out how long it would take to fill the entire tank. We are trying to find the time required to fill 9/9 (or the whole tank) if 5/9 takes 2 minutes. To solve this, we calculate:
Set up the proportion where the fraction of the tank filled is directly proportional to the time taken: (5/9) / 2 = (9/9) / x minutes.
Now we solve for x, which represents the total time to fill the tank: x = (2 minutes * 9/9) / (5/9).
Simplify the right side: x = 2 minutes * (9/5).
Calculate the value of x: x = 3.6 minutes.
Therefore, it will take 3.6 minutes to fill the entire tank.
Sandra used benchmark fractions to describe some insects she collected she said the ladybug is about 1/4 inch long and the cricket is about 2/3 inch long which insect is longer
Answers
The length of cricket is longer than ladybug.
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
We have to given that;
Sandra used benchmark fractions to describe some insects she collected she said the ladybug is about 1/4 inch long and the cricket is about 2/3 inch long.
Here, The length of ladybug = 1/4 inch
And, The length of cricket = 2/3 inch
Now, By comparing we get;
⇒ 1/4 and 2/3
⇒ 3/12 and 8/12
⇒ 3/12 < 8/12
Hence, The length of cricket is longer than ladybug.
Learn more about the fraction visit:
https://brainly.com/question/5454147
#SPJ5
What is the name of the line of reflection for the pair of figures?
Answers
The name for the line of reflection of the two figures is called the "line of symmetry". It's the line that marks a point where you can fold a figure evenly.
Hope this helps!
Hope this helps!
if 10/4 = 14/x what is x?
Answers
Explanation:
1) set the proportion:
10 14
----- = -----
4 x
2) clear the unknown, x
10x = 14(4)
=> 10x = 56
=> x = 56 / 10
=> x = 5.6
The sum of two numbers is 67. The smaller number is 21 less than the larger number. What are the numbers?
Answers
bigger number = x
smaller number = x - 21
The sum of the two numbers is 67.
x + x - 21 = 67
2x - 21 = 67
2x = 67 + 21
2x = 88
x = 44
x = 44
x - 21 = 44 - 21 = 23
The larger number is 44 and the smaller one is 23
The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The sum of the two numbers is 67. The smaller number is 21 less than the larger number.
Let the two numbers be 'x' and 'y' and x > y. Then the equations are given as,
x + y = 67 ...1
x = y + 21 ...2
From equations 1 and 2, then we have
y + 21 + y = 67
2y = 46
y = 23
Then the value of 'x' is given as,
x = 23 + 21
x = 44
The equations are x + y = 67 and x = y + 21. Then the two numbers are 44 and 23.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ2
The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal
BD if you know that the perimeter of triangle ABD is 8 cm.
how do you solve it??? thanks
Answers
the perimeter of ABD is 8, therefore, BD=ABD-(AB+AD)=8-5=3
3cm is the answer.
mark's soup recipe makes 6 servings and uses 4 carrots and 2 potatoes. Drag carrots and potatoes into the box to show how many Mark needs for 15 servings.
Answers
Answer:
10 carrots and 5 potatoes
Step-by-step explanation:
If 6 servings uses 4 carrots and 2 potatoes we can determine how many carrots and potatoes must be used per serving.
Lets look at the carrots:
[tex]=4/6=0.67[/tex]
Therefore for 15 servings:
[tex]=0.67×15=10.05≈10[/tex]
Lets look at potatoes:
[tex]=2/6=0.33[/tex]
Therefore for 15 servings:
[tex]=0.33×15=4.95≈[/tex]
at halloween 3/10 of the candy robin receivd was chocolate. what percent of candy was chocolate,
PLEASE HELP ME!!!!!!!
Answers
3/10=0.3
0.3 *100=30% was chocolate
Lan pays a semiannual premium of $700 for automobile insurance, a monthly premium of $145 for health insurance, and an annual premium of $450 for life insurance.
the monthly expense is $
Answers
Answer:
$300
Step-by-step explanation:
1.automobile insurance : $700 semiannual premium
Annual premium = $700×2=$1400
2.
Health insurance :$145 per month
Annual premium= $145×12=$1740
3. Life insurance: $450 annual
Total annual premium
$1400+$1740+$450=$3590
Hence his monthly expenses on premium =
[tex]\frac{3590}{12}[/tex]
=$299.16
=$300 Approximately
The diagonals of a rhombus are 12 in. and 16 in. long. The length of a side of the rhombus is 10 in. What is the height of the rhombus? Explain how you found your answer.
Answers
.. A = (1/2)*d₁*d₂
.. A = (1/2)*(12 in)*(16 in)
.. A = 96 in²
If b is the base and h is the height, the area is given by
.. A = b*h
We know the values of A and b, so
.. 96 in² = (10 in)*h
.. (96 in²)/(10 in) = h = 9.6 in
The height is 9.6 in.
find the area of an equilateral triangle (regular 3-gon) with the given measurement 9-inch A=sq. in.
Answers
[tex]\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \begin{cases} s=length~of\\ \qquad a~side\\ -------\\ s=9 \end{cases}\implies A=\cfrac{9^2\sqrt{3}}{4}\implies A=\cfrac{81\sqrt{3}}{4}[/tex]
Verify the identity. Show your work. (1 + tan^2u)(1 - sin^2u) = 1
Answers
What are the solutions to the equation √ ̅5x + 1 = x + 1?
Answers
0 is your solution
√5(0) + 1 = (0) + 1
0 + 1 = 0 + 1 (True)
No other number works, because it will not equal
hope this helps
Find the midpoint of side EF. Figure EFGH is shown. E is at negative 2, 3. F is at 1, 6. G is at 4, 3. H is at 1, 0. (−1, 4) (−0.75, 4.25) (−0.5, 4.5) (−0.25, 4.75)
Answers
[x1+x2/2 , y1+y2/2]
[-2+1/2 , 3+6/2]
[-1/2 , 9/2]
[-0.5 , 4.5]
The midpoint is [0.5 , 4.5]
Hence, the mid-point of side EF is located at:
(-0.5,4.5)
Step-by-step explanation:We know that the coordinates of a mid-point C(e,f) of a line segment AB with vertices A(a,b) and B(c,d) is given by:
[tex]e=\dfrac{a+c}{2},\ f=\dfrac{b+d}{2}[/tex]
Here we have to find the mid-point of side EF.
E(-2,3) i.e. (a,b)=(2,3)
and F(1,6) i.e. (c,d)=(1,6)
Hence, the coordinate of midpoint of EF is:
[tex]e=\dfrac{-2+1}{2}\ ,\ f=\dfrac{3+6}{2}\\\\\\e=\dfrac{-1}{2}\ ,\ f=\dfrac{9}{2}\\\\\\e=-0.5\ ,\ f=4.5[/tex]
Hence, the mid-point of side EF is:
(-0.5,4.5)
Solve for x. x − 4 1/6 = 9 1/3 A) −131 2 B) −51 6 C) 131 2 D) 51 6
Answers
Nancy has nine books and she has read 8 total books Sally has two times more books the Nancy how many books does Sally have
Answers
Sally has 18 books, as she has two times more books than Nancy, who has 9 books. The equation used is Sally's books = 2 × Nancy's books. Therefore, 2 × 9 = 18.
To determine how many books Sally has, we need to understand that she has two times more books than Nancy. Nancy has a total of 9 books.
The equation we use here is:
Sally's books = 2 × Nancy's booksGiven Nancy's books = 9:
Sally's books = 2 × 9 = 18Therefore, Sally has 18 books.
How do you find the perimeter of a tennis court with an area of 7,200?
Answers
The prices of six different types of cell phones, in dollars are 49, 189, 79, 250,125,85. how many data points are closer ti the center than the mean absolute deviation?
Answers
A student who was ineligible for financial aid needed to borrow 775,000 for tuition,books,and living expenses. Some money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each interest rate if the annual interest owed was 67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%.
8%:
9%:
10%:
Answers
Since we are only looking at one year, and we assume the interest is compounded no more than annually, we can use the formula for simple interest:
I = prt
Let p be the amount borrowed at 10%. Then 4p, or 4 times the amount borrowed at 10%, is borrowed at 8% interest. The remaining amount, (775000-4p-p) or (775000-5p) is borrowed at 9%. The amount of interest for each portion of the loan is given by:
I=p(0.1)(1)
I=4p(0.08)(1)
I=(775000-5p)(0.09)(1)
Adding these together for the total amount of interest, $67,500, we have:
67500=p(0.1)(1)+4p(0.08)(1)+(775000-5p)(0.09)(1)
Simplifying the right hand side we have:
67500=0.1p+0.32p+69750-0.45p
Combining like terms gives us:
67500= -0.03p+69750
Subtract 69750 from both sides:
67500-69750= -0.03p+69750-69750
-2250= -0.03p
Divide both sides by -0.03:
-2250/-0.03 = -0.03p/-0.03
75000 = p
So $75000 is the amount borrowed at 10%; 4(75000)=$300,000 borrowed at 8%; and 775000-75000-30000= $400,000 borrowed at 9%.
which ratio is porportional to 18/21? A.2/3 B. 30/35 C. 36/48 D.1/3
Answers
You have:
a) 18/21=2/3
18x3/21x2
36≠42 (2/3 is not proportinal to 18/21).
b)18/21=30/35
18x35/21x30
630=630 (30/35 is proportional to 18/21)
c)18/21=36/48
18x48/21x36
864≠756 (36/48 is not proportinal to 18/21)
d)18/21=1/3
18x3/21x1
54≠21 ( 1/3 is not proportinal to 18/21)
Therefore, you can conclude that the correct option is: B.30/35
Bob traveled 90 miles which was 250/3 % of his trip. How many miles did he still have to travel?
Answers
Answer:
18
Step-by-step explanation:
[tex]90[/tex] ÷ [tex]\frac{250}{3} = 1.08[/tex]
This is 1% of the trip
[tex]1.08[/tex] · [tex]100 = 108[/tex]
This is the amount of the whole trip
[tex]108 - 90 = 18[/tex]
So the answer is he has to 18 more miles to travel.
Using synthetic division, find (x4 − 2) ÷ (x + 1).
Answers
Answer:
Step-by-step explanation:
We have given:
x^4-2/x+1
Put x+1 = 0
x= 0-1
x= -1
-1 | 1 0 0 0 -2
| -1 1 -1 1
_______________
1 -1 1 -1 -1
Thus it makes the expression:
x^3-x^2+x-1 - 1/x+1
You can further confirm this expression by solving the expression:
(x4 − 2) ÷ (x + 1).
x^4 - 1 -1/x+1
x^4-1/x+1 - 1/x+1
(x^2-1) (x^2+1)/x+1 - 1/x+1
(x-1)(x+1) (x^2+1)/x+1 - 1/x+1
x+1 n the numerator will be cancelled out by x+1 in the denominator.
(x-1) (x^2+1) - 1/x+1
Multiply (x^2+1) by x-1
x(x^2+1) -1(x^2+1) - 1/x+1
x^3+x-x^2-1 - 1/x+1
x^3-x^2+x-1 - 1/x+1 ....
120 meals to 52 meals
Answers
x% of 120 meals is 52 mealsx% * 120 = 52x/100 * 120 = 52x = 52 * 100 / 120x = 43.3%
100% - 43.3% = 56.7%
The percent of change is 56.7%.
one bag of toy animals weigh12 ounces. what is the total weight, in ounces, of the bags of toy animals in one crate
Answers
Pepper Jackie has 12 picks. 1 out of every 4 picks is orange . The rest are green. How many picks are orange?
Answers
the sum of two integers is 9 and the sum of their squares is 53. Find the integers.
Answers
y = 9 - x
x^2 + y^2 = 53
x^2 + (9 - x)^2 = 53 Remove the brackets.
x^2 + 81 - 18x + x^2 = 53 Collect the like terms on the left.
2x^2 - 18x + 81 = 53 Subtract 53 from both sides.
2x^2 - 18x + 81 - 53 = 0
2x^2 - 18x + 28 = 0 This factors, but you can see it much easier if you pull out 2 as a common factor.
2(x^2 - 9x + 14) = 0
2(x - 2)(x - 7) =0 You could divide by 2 on both sides. But you can also leave it.
x - 2 = 0
x = 2
x - 7 = 0
x = 7
If x = 2 then y = 7
If x = 7 then y = 2
A set of scores ranges from a high of x = 96 to a low of x = 11. if these scores were placed in a grouped frequency distribution table, what is the best value for the interval width?
Answers
The range of the data is = Maximum- Minimum = 96 - 11 = 85
10 classes will be most suited for this data.
The class width for each data can be calculated as:
Class Width = Range / Number of Classes = 85/10 = 8.5
Class width is always rounded to nearest next integer. So the class width will be 9 in this case.
So, the best value of class width or interval width for the given data will be 9.
The best value for the interval width is 17
The highest and the lowest data elements are given as:
x = 96
x = 11
Start by calculating the range
Range = High - Low
So, we have:
Range = 96 - 11
Range = 85
The interval width depends on the number of classes.
Assume that the number of classes is 5,
Then the width is calculated as:
Width = Range / Class
So, we have:
Width = 85/5
Width = 17
Hence, the number of interval width is 17
Read more about interval width at:
https://brainly.com/question/16631975