Addition, subtraction, multiplication.
Addition: The addition of two integers produces another integer.
Subtraction: The subtraction of two integers produces another integer.
Multiplication: The product of two integers is an integer.
Division between two integers can produce a rational number that is not in the set of integers e.g. 1/3
This only includes the four basic arithmetic operations, you can include exponentiation and the modulo operation if you want to for the same reasons as above.
Answer:
Step-by-step explanation:
Looking at the right angle triangle that contains x and y, we would apply trigonometric ratio to determine x an y. Taking 60 degrees as the reference angle,
Hypotenuse = y
Adjacent side = x
Opposite side = 36
Therefore,
Sin # = opposite side / hypotenuse
Sin 60 = 36/y
y = 36/Sin60 = 36/0.8660 = 41.57
Cos # = adjacent side/hypotenuse
Cos 60 = x/41.57
x = 41.57Cos 60 = 41.57 × 0.5 = 20.785
Sin45 = z/36
z = 36Sin45 = 36 × 0.7071 = 25.4556
Answer:
x = - 4, x = 6
Step-by-step explanation:
To find the x- intercepts let y = 0 , that is
- 3(x + 4)(x - 6) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 6 = 0 ⇒ x = 6
Answer:
1. Yes
∆RST ~ ∆WSX
by SAS
2. Yes
∆ABC ~ ∆PQR
by SSS
3. Yes
∆STU ~ ∆JPM
by SAS
4. Yes
∆DJK ~ ∆PZR
by SAS
5. Yes
∆RTU ~ ∆STL
by SAS
5. Yes
∆JKL ~ ∆XYW
by SAS
6. No
7. Yes
∆BEF ~ ∆NML
by SAS
8. Yes
∆GHI ~ ∆QRS
by SSS
9. x=22
10. x=12
Step-by-step explanation:
1. RS/WS=ST/SX and m<RST=m<WSX
2. AB/PQ=8/6=4/3
BC/QR=AC/PR=12/9=4/3
AB/PQ=BC/QR=AC/PR
3. ST/JP=10/15=2/3
SU/JM=14/21=2/3
ST/JP=2/3=SU/JM
and m<TSU=70°=m<PJM
4. DK/PR=8/4=2
JK/ZR=18/9=2
DK/PR=2=JK/ZR
and m<DKJ=65°=m<PRZ
5. RT/ST=UT/LT
and m<RTU=m<STL
6. KL/YW=20/18=10/9
JL/XW=36/24=3/2
KL/YW=10/9≠3/2=JL/XW
7. BF/NL=24/16=3/2
BE/NM=39/26=3/2
BF/NL=3/2=BE/NM
and m<EBF=m<MNL
8. GH/QR=32/20=8/5
HI/RS=40/25=8/5
GI/QS=24/15=8/5
GH/QR=HI/RS=GI/QS=8/5
9. x/33=18/27
Simplifying the fraction on the right side of the equation:
x/33=2/3
Solving for x: Multiplying both sides of the equation by 33:
33(x/33)=33(2/3)
x=11(2)
x=22
10. x/16=9/12
Simplifying the fraction on the right side of the equation:
x/16=3/4
Solving for x: Multiplying both sides of the equation by 16:
16(x/16)=16(3/4)
x=4(3)
x=12
Answer:
7) a= 20
8) m= 5
9)n = 5
10) b = 8
Step-by-step explanation:
7) 18+2=-2+2+a
>> 20 = a >> a = 20
18 + 2 = 20 so that isolates the variable leaving a = 20
8) -7+12 = m -12+12
>>> 5 = m >> m = 5
-7 + 12 = 5 so that again isolates the variable leaving m = 5
9) <u>-8(7</u> + <u>7n</u>) = -336
>> -56+56 + -56n = -336+56
>>> -56n/-56 = -280/-56
>>>> n = 5
use distributive property, cancel out necessary numbers, isolate the variable. leaving n = 5.
10) -140 = <u>-7(-4 </u>+ <u>3b)</u>
>> -140 = 28 - 21b >> -140-28 = -21b +28-28 ( flipped the numbers)
>>> -168/-21 = -21b /-21
>>>> 8 = b >> b =8
Hope it helps!
