The original number is 64
Step-by-step explanation:
The given is:
The sum of the digits of a two-digit number is 10When the digits are reversed the new number is 18 less than the original numberWe need to find the original number
Assume that the unit digit of the number is x and the ten digit is y
∵ The unite digit of the number is x
∵ The ten digit of the number is y
∵ The sum of the two digits is 10
- Add x and y, then equate the sum by 10
∴ x + y = 10 ⇒ (1)
∵ The value of the number is x + 10y
- Reverse the digits means y will be the unit digit and x will
be the ten digit
∴ The new number is y + 10x
∵ The new number is 18 less than the original number
- That means their difference is 18, (the original number minus
the new number = 18)
∴ (x + 10y) - (y + 10x) = 18
- Simplify the left hand side
∴ x + 10y - y - 10x = 18
- Add the like terms in the left hand side
∴ -9x + 9y = 18
- Divide both sides by 9
∴ -x + y = 2 ⇒ (2)
Now we have a system of equation to solve it
Add equation (1) and (2) to eliminate x
∴ 2y = 12
- Divide both sides by 2
∴ y = 6
- Substitute the value of y in equation (1) to find x
∵ x + 6 = 10
- Subtract 6 from both sides
∴ x = 4
∵ The original number is x + 10y
∵ x = 4 and y = 6
∴ The original number = 4 + 10(6) = 4 + 60 = 64
The original number is 64
To check the answer reverse the digits of the number
∵ The new number is y + 10x
∴ The new number = 6 + 10(4) = 6 + 40 = 46
∵ The original number is 64
∵ The new number is 46
∵ 64 - 46 = 18
∴ The new number is less than the original number by 18
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Answer:
The original number is 64.
Name two number that are not integers but that are opposite. Explain how you know
Answer:
Decimals, fractions and mixed units are not integers.
Step-by-step explanation:
Final answer:
Opposite non-integer numbers are pairs like 1/2 and -1/2 or 3.5 and -3.5. These pairs are not integers due to their fractional parts, yet they add up to zero, confirming they are opposites.
Explanation:
When we refer to numbers that are not integers but are opposites, we are seeking pairs of numbers whose sum is zero. Integers are whole numbers such as -1, 0, and 1, which do not include fractions or decimals. On the other hand, rational numbers are ratios of integers like 2/1 or 3/4, and these can be non-integers.
Consider the rational numbers 1/2 and -1/2; these are opposite numbers because they add up to zero. Similarly, another pair could be 3.5 (which is the same as 7/2) and -3.5 (or -7/2). These numbers are not integers because they have fractional parts, yet they are opposites because their sum is zero.
In both cases, these pairs demonstrate the mathematical property that when a number is added to its opposite, the result is always zero, which is a fundamental aspect of additive inverses. This is how we can verify that 1/2 and -1/2, as well as 3.5 and -3.5, are non-integer opposites.
Jeff finds some bugs .he finds 10 fewer grasshopper than cricket.he finds 5 fewer cricketsthan lady bug.if Jeff finds 5 grasshoppers how many ladybugs does Jeff find?how many crickets does he find? Write two equations to solve the problem
Answer:
15 crickets; 20 ladybugs
C = G + 10
L= C+5
Step-by-step explanation:
Crickets = C
Ladybugs = L
Grasshoppers = G
We know he found 5 grasshoppers, so:
C = G + 10 --> because he found 10 more crickets than grasshoppers
if we plug in 5 for G (grasshoppers), we can solve for C (crickets):
C= 5+10
15 Crickets
Now that we know he found 15 crickets we can make our second equation:
L= C+5 --> because he found 5 more ladybugs than crickets
if we plug in 15 C (crickets), we can solve for L (ladybugs):
L= 15+5
20 Ladybugs
If Jeff found 5 grasshoppers, the given information leads to two equations showing that he found 15 crickets and 20 ladybugs.
Explanation:Based on the information given, you can form two equations according to the number of insects Jeff found.
If Jeff found 5 grasshoppers, you can substitute 5 for G in the first equation, which will give you the number of crickets: 5 = C - 10, gives C = 15.
Then, you can substitute C = 15 into the second equation to find the number of ladybugs: 15 = L - 5, gives L = 20.
So, Jeff found 15 crickets and 20 ladybugs.
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2X plus 5 minus X plus 3X plus X -2
Answer:
=5x+3
Step-by-step explanation:
The first three steps in determining the solution set of the system of equations, y = x2 - 2x + 8 and y = 2x + 11, algebraically
are shown in the table.
Step
Step 1
Step 2
Step 3
Equation
-X° -2x+8 - 2x+11
0 - x² + 4x+3
0-(x + 1)(x+3)
Which represents the solution(s) of this system of equations?
(-3,-1)
(-3,5)
(-3,5) and (-1,9)
(1, 13) and (3, 20)
Answer:
(-3,5) and (-1,9)
Step-by-step explanation:
x+1 = 0 ; x + 3=0
x = -1 ; x = -3
y = 2*-1 +11 ; y = 2*-3 +11
y = -2+11 = 9 ; y = -6 +11 =5
Answer: (-3,5) and (-1,9)
Step-by-step explanation:I ain’t gonna lie stole this mans answer but for trust reasons
solve -15=3/7b ''''''''''''''''''''''''''''''''
Answer:
Therefore,
[tex]b=-35[/tex]
Step-by-step explanation:
Solve:
[tex]-15=\dfrac{3}{7}b[/tex]
To Find:
b = ?
Solution:
[tex]-15=\dfrac{3}{7}b[/tex] ..............Given
Step 1 .Multiply Both the side by 7 we get
[tex]-15\times 7=7\times \dfrac{3}{7}b\\\\-105=3b[/tex]
Step 2. Divide Both the side by 3 we get
[tex]\dfrac{-105}{3}=\dfrac{3b}{3}\\\\-35=b\\b=-35[/tex]
Therefore,
[tex]b=-35[/tex]
Which expression is equivalent to (−2)x + (−6)x?
A) −8x
B) −4x
C) 4x
D) 8x
sasha cuts four idenetical circles from a square piece of black poster board as shown what is the left over board use 3.14 for pi
Answer:
therefore the left over board is 0.216[tex]a^{2}[/tex] where 'a' is length of a side of the black poster board.
Step-by-step explanation:
i) Sasha cuts 4 identical circles from a square piece of black poster.
ii) let each side of the square piece be a.
iii) let us divide the square piece into four equal square parts from which the four identical circles will be cut
iv) therefore the side of each smaller square will be [tex]\frac{a}{2}[/tex].
v) therefore the diameter of each identical circle will be [tex]\frac{a}{2}[/tex]
vi) therefore the radius if each of the four identical circles will be [tex]\frac{1}{2} \times \frac{a}{2} = \frac{a}{4}[/tex]
vii) the area of each of the four identical circles will be = [tex]\pi \times (\frac{a}{4} )^{2} = 3.14 \times (\frac{a}{4}) ^{2} = \frac{3.14a^{2}}{16} = 0.196a^{2}[/tex]
vii) the area of each of the four smaller squares = [tex]\frac{a}{2} \times \frac{a}{2} = \frac{a^{2} }{4} = 0.25a^{2}[/tex]
viii) therefore the area left over from each of the four smaller squares
= 0.25[tex]a^{2}[/tex] - [tex]0.196a^{2}[/tex] = 0.054[tex]a^{2}[/tex]
ix) therefore the left over board is given by 4 [tex]\times[/tex] 0.054[tex]a^{2}[/tex] = 0.216[tex]a^{2}[/tex] where a is length of a side of the black poster board.
Aliyah and her friends are going on a road trip that is 32 3/4 miles long. They have already driven 12 1/2 miles. How much farther do they have to drive? Answer in decimal form
Answer:
They have to drive [tex]20\frac{1}{4}[/tex] miles more
Step-by-step explanation:
Given:
Total Distance of the road trip = [tex]32 \frac{3}{4}[/tex] miles
Distance travelled already = [tex]12 \frac{1}{2}[/tex] miles.
To Find:
How much farther do they have to drive = ?
Solution:
The distance they have to travel farther = Total distance - distance travelled
The distance they have to travel farther = [tex]32 \frac{3}{4} - 12 \frac{1}{2}[/tex]
=>[tex]\frac{128 + 3}{4} - \frac{24 +1}{2}[/tex]
=>[tex]\frac{131}{4} - \frac{25}{2}[/tex]
=>[tex]\frac{131- 50}{4}[/tex]
=>[tex]\frac{81}{4}[/tex]
=>[tex]20\frac{1}{4}[/tex]
| 12) 5124.
What is 12 divided by 5124
0.0023419203747073 but i think you mean 5124 by 12 and that is 427
does this represent a function why or why not
Answer:
the answer is B.
Step-by-step explanation:
According to the x and y axis, it shouild be B.
Answer:
I cannot see the screenshot
Step-by-step explanation:
What is the missing length?
10.2 cm
a
area=51 cm2
Answer:
a = 10 cm
Step-by-step explanation:
Area of triangle, A = 51 cm²
base, b = 10.2 cm
Let height of triangle be a cm
Formula:-
[tex]A=\dfrac{1}{2}\times a\times b[/tex]
[tex]51=\dfrac{1}{2}\times a\times 10.2[/tex]
[tex]a=\dfrac{51\times 2}{10.2}[/tex]
[tex]a=10[/tex]
hence, the missing length is 10 cm
7 cm)
8 cm
11 cm
What is the area of this composite figure?
Answer:
88
Step-by-step explanation:
first multiply 7×8 #2 take that answer then multiply by 11
Answer:
616
Step-by-step explanation:
What is x exponent 2 + 3x - 4 = 6X
Answer:
x=-2/3
Step-by-step explanation:
2+3x-4=6x
2-4=6x-3x
-2=3x
x=-2/3
three times a first number minus a second number equals negative forty The first number plus twice the second number equals negative forty
Consider the Piece-Wise graph described by the following equation:
Determine the coordinates of the point on the graph where x=3.
(3, 1)
(3, 3)
(3, 5)
(3, 13)
Answer:
Hey, Dalilah. I hope I'm not too late, but the answer is (3,5).
Step-by-step explanation:
You have to use the equation that includes the x value of 3.
4x+1 only includes x values that are less than 3.
2x-1 includes x values that are greater than or equal to 3.
I plugged 3 into both of these equations (4x+1; x < 3 & 2x-1; x ≥ 3) in order to see which equation would've been true.
4(3)+1 = 13; 13 < 3 [False] 13 isn't less than 3 -- and 2(3)-1 = 5; 5 ≥ 3 [True] 5 is greater than or equal to 3.
Since the equation 2(3)-1; 5≥3 is true, you should use this equation. I used Demos in order to graph Y=2(3)-1. At the bottom of that I put x=3, and it showed me (3,5).
I'll post the pictures for proof and better clarification if this is confusing, love.
f(x)=3x−7−−−−−√3f(x)=2
(100 points)
Simplify.
√310
√30/10
√3/10
√3/5
√15/5
Which expression is equal to √5/11 ?
√5/11
√55/11
25/11
5√11/11
Answer:
30/10 and 5/11
Step-by-step explanation:
An angle measures 18 more than the angle of its complementary what is the measure of each angle
Answer:
71
Step-by-step explanation:
Complementary angles have measures that add to 90°.
ABC and CBD are complementary angles.
Since the angles are complementary, their measures must add to 90°. Set up an equation and solve for n.
n + 18° = 90°
n + 18° − 18° = 90° − 18°
n = 72°
The measure of the complementary angle is 72°.
What are the values of x and y in the matrix subtraction below?
Answer:
Option x=-15 and y=15 is correct
Therefore the values are x=-15 and y=15
Step-by-step explanation:
Let A and B be the given matrices
Let [tex]A=\left|\begin{array}{ccc}-20&4&9\\16&0&-6\end{array}\right|[/tex]
and [tex]B=\left|\begin{array}{ccc}-5&-6&0\\1&7&11\end{array}\right|[/tex]
To find the subtraction of the matrix A and B
[tex]A-B=\left|\begin{array}{ccc}-20&4&9\\16&0&-6\end{array}\right|-\left|\begin{array}{ccc}-5&-6&0\\1&7&11\end{array}\right|[/tex]
[tex]=\left|\begin{array}{ccc}-20+5&4+6&9-0\\16-&0-7&-6-11\end{array}\right|[/tex]
[tex]=\left|\begin{array}{ccc}-15&10&9\\15&-7&-17\end{array}\right|[/tex]
Therefore [tex]A-B=\left|\begin{array}{ccc}-15&10&9\\15&-7&-17\end{array}\right|[/tex]
Therefore compare [tex]A-B=\left|\begin{array}{ccc}-15&10&9\\15&-7&-17\end{array}\right|[/tex]=[tex]\left|\begin{array}{ccc}x&10&9\\y&-7&-17\end{array}\right|[/tex]
We get x=-15 and y=15
Therefore the values are x=-15 and y=15
Option x=-15 and y=15 is correct
Answer:
A
Step-by-step explanation:
E2020
Subtract (-x - 2) - (4x + 3)
Answer:
-5x-5
Step-by-step explanation:
Because when you distribute your - into 4x + 3 then you are going to have. big equation like -x-2-4x-3. And then when you simplify it its going to be -5x-5.
Answer:
-x-2-4x-3 (distribute the negative)
-5x-5
Mark brainliest!!
2 divided 62.2
What is the answer
The answer would be 31.1
Answer:
31.1
Step-by-step explanation:
Times 62.2 by ten to make it a whole number, which is 622. Now it looks easier! 622/2=311. But don't forget to divide it by ten again!
6.50 is 25% of what number?
Answer:
26
Step-by-step explanation:
25% is 1/4 so 6.50+6.5+6.50+6.50= 26
Answer: 26
Step-by-step explanation: Reading through the problem we have "6.50 is" that's 6.50 =, "25%" 25/100, "of" times, "what number" x.
I changed 25% to 25/100 because "percent" means over 100.
Reducing the 25/100 to 1/4, we have 6.50 = [tex]\frac{1x}{4}[/tex].
Multiplying both sides by 4 to get rid of the fraction, we have 26 = x.
So 6.50 is 25% of 26.
LAST 2 MATH QUESTIONS FOR TODAY and if since it's two questions, I'm giving 15 pts.
Answer:
JK and CB.
JL and AB.
Step-by-step explanation:
Corresponding sides.
A shoreline is eroding at rate of 2 5/18 feet each year at this rate,how many feet will the shoreline erode in 8 years
The shoreline will erode approximately 22 7/9 feet in 8 years.
Explanation:To find the total erosion over 8 years, we can use the given rate of erosion per year. The rate is 2 5/18 feet each year, and to calculate the total erosion over 8 years, we can multiply this rate by the number of years.
[tex]\[ \text{Rate of erosion per year} = 2 \frac{5}{18} \text{ feet} \][/tex]
[tex]\[ \text{Total erosion over 8 years} = \text{Rate of erosion per year} \times \text{Number of years} \][/tex]
[tex]\[ \text{Total erosion} = 2 \frac{5}{18} \times 8 \][/tex]
To perform this calculation, first convert the mixed number into an improper fraction:
[tex]\[ \text{Total erosion} = \frac{41}{18} \times 8 \][/tex]
Multiply the numerators and denominators:
[tex]\[ \text{Total erosion} = \frac{328}{18} \][/tex]
Now, simplify the fraction:
[tex]\[ \text{Total erosion} = 18 \frac{2}{18} \][/tex]
Thus, the shoreline will erode approximately[tex]\(18 \frac{2}{18}\) feet in 8 years, which simplifies to \(18 \frac{1}{9}\) or \(22 \frac{7}{9}\) feet.[/tex]
x + 3 + x - 8 + x = 55
Answer:
x = 20
Step-by-step explanation:
Combine like terms
3x-5=55
Add the 4 on both sides
3x-5=55
+5 +5
3x=60
Divide both sides by 3
x = 20
a developer wants to develop 5 acres of land. Each lot in the develope is to be 1/12 of an acre. How many lots will the land developer have in the 5 acres?
Final answer:
The land developer can create 60 lots of 1/12 acre each from a 5-acre parcel of land.
Explanation:
The student's question asks how many lots of 1/12 acre each can be created from a 5-acre parcel of land. To find the answer, divide the total acres available (5 acres) by the size of each lot (1/12 acre). Using division for fractions, we invert the divisor and multiply:
5 ÷ (1/12) = 5 × (12/1) = 60
Therefore, the land developer will be able to create 60 lots from the 5 acres.
Evaluate A^2 for A = -3.
Answer:
for A = -3
A² = A×A = (-3) × (-3) Two minus negate each other
= 3 ×3
= 9
:)
If the first difference of a sequence is the arithmetic sequence 2, 4, 6, 8, 10,...Find the first six terms of the original sequence in each of the following cases?
Step-by-step explanation:
The first differences being [tex]2, 4, 6, 8, 10,...[/tex] means
2 is the difference between the 1st and 2nd terms4 is the difference between the 2nd and 3rd terms6 is the difference between the 3rd and 4th terms8 is the difference between the 4th and 5th terms10 is the difference between the 5th and 6th termsSo,
If
The first term of the sequence is 2.
then
The second term of the sequence is [tex]2 + 2 = 4[/tex]
The Third term of the sequence is [tex]4 + 4 = 8[/tex]
The Fourth term of the sequence is [tex]8 + 6 = 14[/tex]
The Fifth term of the sequence is [tex]14 + 8 = 22[/tex]
The Sixth term of the sequence is [tex]22 + 10 = 32[/tex]
Keywords: sequence, arithmetic sequence
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Prince is 6n years old. jordan is (3n + 10) years older than prince
a) find jordans age
b) find the total age of prince and jordan
c) kimberly is 9 yrs younger than prince. find kimberlys age
d) find the total age of three people
e) if n = 4 find the total age of the 3 people
Answer:
a) 9n + 10 years.
b) 13n + 10 years.
c) 6n - 9 years
d) 19n + 1 years.
e) 77 years.
Step-by-step explanation:
a) Prince is 6n years old. Jordan's age is (3n + 10) years more than Prince.
So, Jordan's age is (6n + 3n + 10) = 9n + 10 years.
b) The total age of Prince and Jordan will be (6n + 9n + 10) = 13n + 10 years.
c) Kimberly's age is 9 years less than Prince.
So, the age of Kimberly will be 6n - 9 years.
d) The total age of the three people will be (6n - 9 + 13n + 10) = 19n + 1 years.
e) If n = 4, then total age of three people will be 19(4) + 1 = 77 years. (Answer)
How can I solve 764+135 faster using a different strategy?
The Answer is a calculator is best way to get an answer quickly
Step-by-step explanation:
Answer add the tens place first then after you get that number you add the hundreds place and after you get that answer you add the thousands place and then after you get that answer you have you answer!!