Answer:
i) 28 - 30i
ii) 36 + 28i
Step-by-step explanation:
i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i
z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i
2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i
ii) w = -1 + 5i and z = 4 - 8i
w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40
⇒collect like terms
w × z = -4 + 28i - 40
∵ 
∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i
Answer:
C. (2, 1)
Step-by-step explanation:
-3y = x-5
x+ 5y = 7
Subtract x from both sides in the first equation. Write the second equation below it.
-x - 3y = -5
x + 5y = 7
Add the two equations above.
2y = 2
Divide both sides by 2.
y = 1
Substitute y with 1 in the second original equation and solve for x.
x + 5(1) = 7
x + 5 = 7
Subtract 5 from both sides.
x = 2
Answer: C. (2, 1)
Answer:
a) The unit rate for calories per cup is 100 calories per cup
b) 200 calories in 2 cups of cereal.
Step-by-step explanation:
A box of cereal states that there are 75 calories in a three fourths 3/4-cup serving.
a) What is the unit rate for calories per cup?
This is calculated as:
3/4 cup = 75 calories
1 cup = x
Cross Multiply
3/4x = 75 calories × 1
x = 75 calories /3/4 cup
x = 75 ÷ 3/4
x = 75 × 4/3
x = 100 calories per cup
The unit rate for calories per cup is 100 calories per cup
b) How many calories are there in 2 cups of the cereal?
From the above question
3/4 cup = 75 calories
2 cups = x
Cross Multiply
3/4x = 75× 2
x = 150 ÷ 3/4
x = 150 × 4/3
x = 200 calories
There are 200 calories in 2 cups of cereal.
Subtract 1111 from both sides
5{e}^{{4}^{x}}=22-115e4x=22−11
Simplify 22-1122−11 to 1111
5{e}^{{4}^{x}}=115e4x=11
Divide both sides by 55
{e}^{{4}^{x}}=\frac{11}{5}e4x=511
Use Definition of Natural Logarithm: {e}^{y}=xey=x if and only if \ln{x}=ylnx=y
{4}^{x}=\ln{\frac{11}{5}}4x=ln511
: {b}^{a}=xba=x if and only if log_b(x)=alogb(x)=a
x=\log_{4}{\ln{\frac{11}{5}}}x=log4ln511
Use Change of Base Rule: \log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}logbx=logablogax
x=\frac{\log{\ln{\frac{11}{5}}}}{\log{4}}x=log4logln511
Use Power Rule: \log_{b}{{x}^{c}}=c\log_{b}{x}logbxc=clogbx
\log{4}log4 -> \log{{2}^{2}}log22 -> 2\log{2}2log2
x=\frac{\log{\ln{\frac{11}{5}}}}{2\log{2}}x=2log2
Answer= −0.171
The answer is TT=T because why will it be a true or false
