Answer and Step-by-step explanation:
(a) Given that x and y is even, we want to prove that xy is also even.
For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.
(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:
Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.
(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.
find the difference.
(4−5y)−2(3.5y−8)
Answer:
-12y + 20
Step-by-step explanation:
First, you simplify each term:
apply the distributive property:
4 - 5y - 2 (3.5y) - 2 x -8
Multiply 3.5 by -2:
4 - 5y - 2 (3.5y) - 2 x -8
Multiply -2 by -8:
4 - 5y - 7y +16
Next, we simplify by adding terms:
Add 4 + 16:
-5y - 7y + 20
Subtract 7y from 5y:
-12y + 20
Hence the simplified form is -12y + 20
Answer:
-4·(3y-5)
Step-by-step explanation:
Help! Marking Brainliest (Check Screenshot) Please show work, thank you.
Step-by-step explanation:
Area of Square picture = 20.25 in²
Side lengths of Square picture
= √(20.25 in²) = 4.5 in.
Therefore the dimensions of the picture
is 4.5in by 4.5in.
Josiah and his children went into a grocery store and he bought $15 worth of peaches and mangos. Each peach costs $0.50 and each mango costs $1.50. He bought 2 more mangos than peaches. Graphically solve a system of equations in order to determine the number of peaches, x,x, and the number of mangos, y,y, that Josiah bought.
Here is a rectangle.
9 cm
7 cm
Work out the perimeter of the rectangle.
Answer:
P=32cm
Step-by-step explanation:
Answer: 32
Step-by-step explanation: 9+9 =18
7+7= 14
14+18=32
a piggy bank has $6.95 and contains only nickles and dimes. If there are a total of 91 coins, how many nickles are there
Answer:
There are 43 nickels in the piggy bank.
Step-by-step explanation:
Given that:
Number of coins = 91
Worth of coins = $6.95 = 6.95*100 = 695 cents
Let,
x be the number of nickles
y be the number of dimes
According to given statement;
x+y=91 Eqn 1
5x+10y=695 Eqn 2
Multiplying Eqn 1 by 5
5x+5y = 455 Eqn 3
Subtracting Eqn 3 from Eqn 2
(5x+10y)-(5x+5y)=695-455
5x+10y-5x-5y=240
5y = 240
[tex]\frac{5y}{5}=\frac{240}{5}[/tex]
y = 48
Putting y=48 in Eqn 1
x+48=91
x=91-48
x= 43
Hence,
There are 43 nickels in the piggy bank.
rob has 7.8 ounces of tuna salad. If she makes three sandwiches with an equal amount of tuna on each, how much tuna does she put on each one?
Answer:
2.6 tuna
Step-by-step explanation:
Amount of tuna salad rob has = 7.8ounces
Amount of sanndwiches made = 3sandwiches
If she had equal amount of tuna on each sandwiches
Amount of tuna in each = Total amount of tuna/Amount of sandwiches
Amount of tuna in each = 7.8/3
Amount of tuna in each = 2.6 tuna
Hence she put 2.6 tuna in each sandwiches
Two boats leave the same place at the same time. The first boat heads due north at 10 kilometers per hour. The second boat heads due west at 16 kilometers per hour. After 2.5 hours, how fast is the distance between the boats increasing
Answer:
18.87 km/hr
Step-by-step explanation:
First boat is heading North with a speed of 10 km/hr.
Second boat is heading West with a speed of 16 km/hr.
Time for which they move = 2.5 hours
To find:
The speed at which the distance is increasing between the two boats.
Solution:
Let the situation be represented by the attached diagram.
Their initial position is represented by point O from where they move towards point A and point B respectively.
[tex]Distance = Speed \times Time[/tex]
[tex]Distance\ OA = 10 \times 2.5 = 25\ km[/tex]
[tex]Distance\ OB = 16 \times 2.5 = 40\ km[/tex]
We can use Pythagorean Theorem to find the distance AB.
AB is the hypotenuse of the right angled [tex]\triangle AOB[/tex].
According to Pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^2 = 25^2 + 40^2\\\Rightarrow AB^2 = 2225^2\\\Rightarrow AB^2 \approx 47.17\ km[/tex]
The speed at which distance is increasing between the two boats is given as:
[tex]\dfrac{47.17}{2.5} \approx 18.87\ km/hr[/tex]
In Miami, Florida, there is an 80% probability of extreme high winds on a specific day. How was this probability most likely determined
Answer:
80%
Step-by-step explanation:
Since this is an 80% chance we can say that on these days with same conditions, the probability of extreme high winds is 80% of the time in Miami.
Megan picked 15 blueberries on Monday, 35 on Tuesday, and 55 on Wednesday. Based on the pattern, how many blueberries will she pick on Thursday?
The concept of hope is nothing more than giving up. A word that holds no true meaning.
Answer:
lol fr
Step-by-step explanation:
Answer:
Big pp
Step-by-step explanation:
HELP ONLY ANSWER IF YOU ARE TODALLY SURE I WILL GIVE BRAINLEST TO WHOEVER IS RIGHT WORTH 18 POINTS DON'T JUST ANSWER BUT READ IT THEN ASWESR
Which equation can be used to calculate the area of the shaded triangle in the figure below?
A rectangle is shown with a width of 6 ft and a length of 16 ft. There is a diagonal line through the rectangle, and the bottom half is shaded in grey.
1. 2(16 × 6) = 192 square feet
2. 2(16 + 6) = 44 square feet
3. 1 over 2.(16 × 6) = 48 square feet
4. 1 over 2.(6 + 16) = 11 square feet
A mix of 32 quarters and dimes totals $6.35. Find the system of equations that would help you answer the question and then find how many quarters (x) and dimes (y) you would have?
Answer:
21 quarters and 11 dimes = 32 coins
Step-by-step explanation:
x + y = 32
0.25x + 0.10y = 6.35 [take the first equation and make it equal to x]
x = 32 - y [now take this equation and plug it in the above]
0.25 (32-y) + 0.10y = 6.35
8 - 0.25y + 0.10y = 6.35
8 - 0.15y = 6.35 [subtract 8 from both sides]
-0.15y = -1.65 [divide by -0.15 to isolate y]
y = 11 so there are 11 dimes
plug it into the first equation: x + 11 = 32; x = 21 so there are 21 quarters
write an equation in point slope form for the line through the given point with the given slope (-4, -3); m=8
Answer:
An equation in point-slope form for the line will be:
[tex]y - (-3) = 8 (x - (-4))[/tex]
Please check the attached line graph also.
Step-by-step explanation:
Given
The point (-4, -3)
The slope m = 8
To determine
Write an equation in point slope form for the line.
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where
m is the slope of the line(x₁, y₁) is the pointIn our case,
(x₁, y₁) = (-4, -3)The slope m = 8substituting the values m = 8 and the point (-4, -3)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y - (-3) = 8 (x - (-4))[/tex]
Therefore, an equation in point-slope form for the line will be:
[tex]y - (-3) = 8 (x - (-4))[/tex]
Please check the attached line graph also.
Valeria's Cupcakes recently sold 3 pumpkin cupcakes and 9 other cupcakes. Considering this data, how many of the next 8 cupcakes sold would you expect to be pumpkin cupcakes?
Answer: 24 Pumpkin cupcakes.
Step-by-step explanation:
We know that:
They recently sold 6 Pumpkin cupcakes and 8 other cupcakes.
Then we can model this with the ratio 6:8
This means that for each 6 Pumpkin cupcakes sold, they also sell 8 of another type of cupcakes.
With this information, if they sell 56
If $600 was placed in a savings account with an interest rate of 0.5%,
find the total amount in the account after 8 years and 3 months (8.25
years)?
I got it wrong so oof
can u pls help me with this question
Answer:
0.12$ , I'm probably wrong lolol
plz answer my question
Whenever Jean sees the white streaks left in the sky by an airplane, she excitedly tells her kids it's Buzz Lightyear. One day, her son asked her how fast Buzz could fly. Jean, knowing that Buzz is really an airplane, told him about 500 miles per hour. How many feet per second can Buzz travel? Show your work, friends.
Answer:
The Buzz can travel 733.33 feet per second.
Step-by-step explanation:
An hour has 60 minutes, each of which has 60 seconds. So one hour has 60*60 = 3600 seconds.
The airplane can fly 500 miles per hour. Each mile has 5280 feet. So the plane can fly 500*5280 = 2640000 feet in one hour.
Per second, we have:
[tex]\frac{2640000}{3600} = 733.33[/tex]
The Buzz can travel 733.33 feet per second.
what percent is a is b? pls help i need it right away
Answer:
what ???????????????????? repost this question
be quick! i will mark the correct one brainliest :)
((11-7)+(14/7)^2)=
A. 4
B. 2
C. 5
D. 8
What is an equivalent ratio for 7:9
What is the answer to this ? PLEASE HELP I HAVE 3 minutes
Answer:
(2, 4)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of EqualityAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x
x = -y + 6
Step 2: Solve for y
Substitution
Substitute in x: y = 2(-y + 6)Distribute 2: y = -2y + 12Isolate y terms: 3y = 12Isolate y: y = 4Step 3: Solve for x
Define equation: x = -y + 6Substitute in y: x = -4 + 6Add: x = 2HELP ASAP GIVING BRAINLIST
Step-by-step explanation:
An open circle means that it isn't equal to the number so the sign would either be < or >
The number that the circle is on is -1 so x is either < or > to -1
x is anything to the left to -1 so the inequality would be x< -1
I hope this helps!!!
There are 54 bookshelves in the library
and 3,240 books total.
How many books does
each shelf hold?
Answer:
60
Step-by-step explanation:
Assuming that all 54 shelves hold the same number of books its just a matter of dividing them (or sharing them equally) on each shelf.
3240 / 54 = 60
Each shelf holds 60 books.
The scholastic assessment test is standardized to be normally distributed with a mean μ=500 and a standard deviation σ=100. What percentage of SAT scores falls
a. between 500 and 600
b. between 400 and 600
c. between 500 and 700
d. between 300 and 700
e. above 600
f. below 300
Answer:
68.27%.
Step-by-step explanation:
Here we have [tex]\mu=500,\sigma=100[/tex]
Let X shows the SAT score. z-score for X=400 is
[tex]z=\frac{X-\mu}{\sigma}=\frac{400-500}{100}= -1[/tex]
z-score for X=600 is
[tex]z=\frac{X-\mu}{\sigma}=\frac{600-500}{100}=1[/tex]
So the proportion of SAT scores falls between 400 and 600 is
[tex]P(400<X<600)=P(-1<z<1)=0.6827[/tex]
hence, required percentage is 68.27%.
one can use the same method to find the% for all other cases as
well.
If Fran were to paint her living room alone, it would take 6 hours. Her sister Denise
could do the job in 8 hours. How long would it take them working together? If needed,
submit your answer as a fraction reduced to lowest terms.
Please show steps !! my last test for the semester!! 20 points PLEASE!!!
Answer:
r1 =6
r2 =8
t = ?
[(1/r1) * t] + [(1/r2)*t] = 1
t/6 + t/8 = 1
multiply by common denominator... 24
24 (t/6 + t/8 = 1)
4t + 3t =24
7t = 24
t = 24/7 = 3.4hrs
A scuba diver ascends 5 3/4 feet to the top of a boat platform. The diver then descends 20 1/8 feet by jumping off the boat. Write and evaluate on subtraction expression to show what lever under sea level the scuba currently is
What is a point-slope equation of the line with slope -12 that goes through the point (5, 3)?
A. y- 3 = -12(x - 5)
B. y + 3 = 12(x + 5)
C. y + 3 =-12(x + 5)
D.y-3 = 12(x - 5)
Answer:
A. y- 3 = -12(x - 5)
Step-by-step explanation:
a group of hikers is progressing steadily along up uphill trail. the graph shows their elevation