Given:
x, y and z are integers.
To prove:
If [tex]3x-y+5z[/tex] is even, then at least one of x, y or z is even.
Solution:
We know that,
Product of two odd integers is always odd. ...(i)
Difference of two odd integers is always even. ...(ii)
Sum of an even integer and an odd integer is odd. ...(iii)
Let as assume x, y and z all are odd, then [tex]3x-y+5z[/tex] is even.
[tex]3x[/tex] is always odd. [Using (i)]
[tex]5z[/tex] is always odd. [Using (i)]
[tex]3x-y[/tex] is always even. [Using (ii)]
[tex](3x-y)+5z[/tex] is always odd. [Using (iii)]
[tex]3x-y+5z[/tex] is always odd.
So, out assumption is incorrect.
Thus, at least one of x, y or z is even.
Hence proved.
9. Determine which of the following sequences is a geometric sequence. Check all that apply.
3,9, 27, 81, ...
100, 90, 80, 70, ...
5, 10, 20, 40, ...
2, 10, 18, 26,...
625, 125, 25, 5, ...
-2, 6, -18, 54, ...
Step-by-step explanation:
first geometric sequence
3^1, 3^2 ,3^3, 3^4,......
3, 9, 27, 81.......
second
5^1, 5^2, 5^3, 5^4,........
5, 25, 125, 625,........
third
2, 10, 18, 26,.....
which has the difference of 8
fourth
100, 90, 80, 70,......
19 dozen cookies to individual cookies
Answer:
228 individual cookies.
Step-by-step explanation:
To convert 19 dozen cookies to individual cookies, we first have to identify that:
[tex]dozen=12[/tex]
If a dozen is equal to 12, to solve, we simply must multiply the amount of dozens, which is 19, by a dozen, which is 12:
[tex]19*12=[/tex]
[tex]228[/tex]
Therefore, there are 228 individual cookies.
-
We can check our work by dividing the individual number of cookies, 228, by dividing buy the amount of dozens, 19, and a dozen, 12:
[tex]228[/tex] ÷ [tex]19=12[/tex]
[tex]228[/tex] ÷ [tex]12=19[/tex]
As you can see, our quotients are the two figures we started with, and when multiplied together, give us 228 individual cookies; therefore, our solution is correct!
Which of the numbers given below is an irrational number ?
0
2.14
2.14367.....................
Answer:
2.14367............. is a irrational number.Write the equation of the line through the points (1, 3), (3, 3)
Answer:
y = 3
Step-by-step explanation:
P ( 1 , 3) and Q ( 3 , 3 )
The straight line is parallel to the x-axis since the two points have the same y.
The intercept with the y-axis is 3.
The slope-point equation for a line is:
y = m*x + b (1)
m is the slope and b is the intercept with the y-axis
To calculate the slope
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = 3 - 3 / 3 - 1 m = 0 / 2 m = 0
therefore, equatio (1) becomes
y = 0*x + 3
y = 3
John's Mathematics exam mark this year is increased by 5% to 84. Find his Mathematics exam mark
last year.
Answer:
80%
Step-by-step explanation:
Let's call the past exam mark m,
m*105%=84
m*105/100=84
m=84/(105/100)
m=80
Hope this helps!
Answer:
80
Step-by-step explanation:
new value = 84
old value = n
can use percent change formula: (new value - old value) / old value = 5/100
[tex]\frac{84-n}{n}[/tex] = [tex]\frac{5}{100}[/tex]
cross-multiply (you can simplify 5/100 to be 1/20 first): 20(84 - n) = n
1680 - 20n = n
1680 = 21n
n = 80
Quick!! pls help lol!!
Answer:
I think 53
Step-by-step explanation:
If the biggest line is 100 the do 100-47=53
Sorry if I’m wrong
whoever comments first gets brainliest and whoeverelse answers gets 50 points cause why not 2=2=3=4=5=6=7=8=9=0+12345-7=9(so it doesn't get taken down)
Answer:
Yo whats up
Step-by-step explanation:
I win and im the brainlest.
(I’ll give brainliest)
Answer:
letter choice A and C
Step-by-step explanation:
jshdhd
I dont know why it says im in high school im in middle school. But anyways can someone please explain how to get percentage.
Answer:
Step-by-step explanation:
To change a decimal into a percent you multiply by 100.
If there is a fraction that you need to convert into a percent. Completely divide the fraction. 4/5 = 0.8 then multiply by 100 you get 80%. This means that 4 is 80% of 5
Answer:
how to get a percentage from a decimal is when you take the decimal point and move it twice to the left
Step-by-step explanation:
for example
.07 = 7%
does that make sense?
Find the value of X. round to the nearest tenth
There is no equation, what is the equation?
Answer:
what is the equation
Step-by-step explanation:
If the simple interest on $7,000 for 9 years is 3,780, then what is the interest rate?
Answer:
6%
Step-by-step explanation:
Interest = Principal × Rate × Time/100
$3780 = $7000(9)(rate)/100
63000rate = 378000
rate= 378000/63000
rate = 6% per annum (Answer)
3-2|x+4|+3=1 the answer for this
Answer:
x={-3/2,-13/2}
Step-by-step explanation:
3-2|x+4|+3=1
-2|x+4|+6=1
-2|x+4|=-5
|x+4|=5/2
x+4=5/2
x+4=-5/2
x=5/2-4
x=-3/2
x=-5/2-4
x=-13/2
What is RU?
A.20
B.30
C.12
D.15
Answer:
a
Step-by-step explanation:
The segment RT is a perpendicular bisector and means Δ RSU is isosceles, then the 2 legs are congruent, that is
RS = RU , substitute values
8x = 6x + 5 ( subtract 6x from both sides )
2x = 5 ( divide both sides by 2 )
x = 2.5
Thus
RU = 6x + 5 = 6(2.5) + 5 = 15 + 5 = 20 → a
TJ rented a truck to move to a apartment the regular price of a Truck Rental is $200 TJ has a 50% off coupon he wants to know the sale tax of the truck rental
Answer:
$100
Step-by-step explanation:
From the question, we are given the following
Rental price of the truck
percentage off coupon = 50%
Required
Sale tax of the truck rental
Sale tax of the truck rental = 50% of the truck price
Sale tax of the truck rental = 50% of $200
Sale tax of the truck rental = 50/100 * 200
Sale tax of the truck rental = 0.5 * 200
Sale tax of the truck rental = $100
Hence the sale tax of the truck rental is $100
Which percent is equivalent to 2.5?
2.5%
25%
250%
2,500%
Answer:
250%
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
Select the correct answer.
Which statement is true about this equation?
3(-y + 7) = 3(y + 5) + 6
A
The equation has one solution, y= 0.
OB.
The equation has one solution, y=-1.
C.
The equation has no solution.
D.
The equation has infinitely many solutions.
Reset
Answer:
THE ANSWER IS A. I GOT IT RIGHT ON EDMENTUM.
Step-by-step explanation:
A
The equation has one solution, y= 0
2 numbers are in ratio 2 is to 4 if their sun is 147 then what i the largest number?
Answer:
The larger number is 98
Step-by-step explanation:
Let the numbers be a and b
a/b= 2/4
4a = 2b ------- 1
a + b = 147 -----2
a= 147 - b -------3
Substitute equation 3 into 1
4(147 -b) = 2b
588 - 4b = 2b
588= 2b + 4b
588 = 6b
b= 588/6
b= 98
Substituting b= 98 into 1
4a = 2(98)
4a = 196
a= 49
The larger number is 98
X = [ ? ]
PLEASE HELP
Step-by-step explanation:
60° + 60° + x + x = 180°. (Sum of angles in a triangle = 180°)
Therefore 2x = 60° and x = 30°.
Answer:
Step-by-step explanation:
2x + 60 = (180 - 60)
x = (180-120)/2
x = 30
Please help me! I don’t know what to do!!! 15 pts!!
Answer:
is (A).
Step-by-step explanation:
The answer is (A).
Which expression is equivalent-3(6x+7)+4(7x+2)
Answer: are there choices?
Step-by-step explanation:
I am just confused on how to do this question. A 37-inch TV is 37-inches diagonally across the screen. Which of these dimensions best describes a 37-inch TV? A. 15 x 34 B. 16.5 x 32 C. 17 x 28 D. 17 x 32
Given that,
A TV is 27 inch diagonally across the screen.
To find,
The dimensions that best describes a 37 inch TV.
Solution,
Let a and b are length and width of the TV. Let c be the diagonal. Using Pythagoras theorem,
[tex]c=\sqrt{a^2+b^2}[/tex]
If dimensions are 15 x 34,
[tex]c=\sqrt{15^{2}+34^{2}}\\\\=37.16\ inch[/tex]
If dimensions are 16.5 x 32,
[tex]c=\sqrt{16.5^{2}+32^{2}}\\\\=36.003\ inch[/tex]
If dimensions are 17 x 28,
[tex]c=\sqrt{17^{2}+28^{2}}\\\\=32.756\ inch[/tex]
If dimensions are 17 x 32,
[tex]c=\sqrt{17^{2}+32^{2}}\\\\=36.23\ inch[/tex]
It is clear that if dimensions are 15 x 34, the diagonal is 37 inches. Hence, the correct option is (a).
PUZZLE: six wolves catch six lambs in six minutes. How many wolves will be needed to catch sixty lambs in sixty minutes?
no, the answer is not sixty!!
can someone please help me, will give brainliest
Answer:
(d) 1 mile = 10 blocks
Step-by-step explanation:
The ballpark is 8 blocks west and 15 blocks north of Jeff's home. The Pythagorean theorem tells us the straight-line distance is ...
d² = 8² +15² = 64 +225 = 289
d = √289 = 17 . . . blocks
The problem tells us this represents 1.7 miles, so the proportion is ...
blocks/miles = 17 blocks/(1.7 miles) = 10 blocks/mile
The map scale is 1 mile = 10 blocks.
PLZZZZZZZZZ HELP!!!
Select the correct answer.
In 14 days, the daily high temperature in Cedar Hills dropped by 16.8 degrees Fahrenheit. What is the average daily rate of change in the high temperature in degrees Fahrenheit?
A.
+2.2
B.
+1.2
C.
+1.1
D.
-1.2
E.
-2.2
the answer choice is B.
3x+7y=17
3x-6y=4
solve this by elimination method plzzzzzzzzzzzzz helppppppppppppp meeeeeeeeeee
Answer:
[tex](\frac{10}{3}, 1)[/tex]
Step-by-step explanation:
1) In order to solve a system of equations with the elimination method, you need to add or subtract the two equations and "eliminate" variables by canceling out terms. This leaves you with an equation with only one variable to solve. Then, once you solve that equation, you can substitute the answer you got into one of the system's equations to find either the x or y value.
This problem already has one 3x in each equation, so let's focus on canceling that term out, eliminating the x variable. To set up this situation, we need one 3x to be negative, so let's multiply the terms in 3x-6y = 4 by -1, which gets us to -3x + 6y = -4. Now let's "cancel out" those x variables by adding them together. (This work is shown in the first picture.)
Remember to add the other terms. This leaves us with the equation 13y = 13. By isolating y, we can find its value, which leaves us with y = 1.
2) Next, let's substitute 1 for y in one of the two equations. In this case, I used 3x + 7y = 17. Then, isolate x to find its value:
[tex]3x + 7 (1) = 17\\3x + 7 = 17 \\3x = 10 \\x = \frac{10}{3}[/tex]
Therefore, the answer would be [tex](\frac{10}{3} , 1)[/tex].
y is inversely proportional to the square of x.
A table of values for x and y is shown.
Х| 1 2 3 4
Y| 4 1 4/9 1/4
a) Express y in terms of x.
b) Work out the positive value of x when y = 25
Answer:
[tex]a) \: y = \frac{4}{ {x}^{2} }[/tex]
[tex]b) \: x = \frac{2}{5} [/tex]
Step-by-step explanation:
Please see the attached pictures for the full solution.
what is the domain and range
Answer:
0,1,2,3 is the domain
-2,1,2,4 is the range
Find the nth term of this quadratic sequence
4,9, 16, 25, 36,
Answer:
[tex]a_{n}[/tex] = (n + 1)²
Step-by-step explanation:
The terms are square numbers with each term shifted to the right by 1
That is 1, 4, 9, 16, 25, 36, .....
Thus to obtain 4 in the first position, then
n = 1 → (1 + 1)² = 2² = 4
To obtain any term add 1 to its position in the sequence, that is
[tex]a_{n}[/tex] = (n + 1)²
Help ASAP plz
3. Solve by graphing. (y=mx + b)
y=-x+10
x+y=10
What is the solution and also solve using algebra
Answer: Im sorry im bad at mafs
Step-by-step explanation:
TRAVEL It is about 350 miles from Ruidoso, New Mexico, to Abilene, Texas. Haruko has already driven 75 miles and made it to Roswell, New Mexico. She hopes to finish the rest of her trip, including stops, in 5 hours. Write an equation to find the average speed Haruko needs to drive to finish the rest of her trip in 5 hours.
Answer:
55 mph
Step-by-step explanation:
Given that:
Total miles of journey = 350 miles
Miles already driven = 75 miles
To cover the rest of the journey in 5 hours, the average speed of travel. Will be:
Recall:
Speed = (Distance left to cover ÷ budgeted travel time)
Distance left to cover : (total miles - distance already driven)
Average speed required = (350 - 75) / 5
= 275 / 5
= 55 mph