Solve using DISTANCE = RATE X TIMEMike left home on his bicycle at 10:00 A.M., traveling at 50 m/h. At noon, he arrived at his destination. How many miles did he drive?

Answers

Answer 1
Answer: The rate is speed which 50m/h. so he left the home at 10:00 and arrived at noon which 12:00pm so the difference is 2 hours which means he took 2 hours to get there.
to find the distance. 
D=RxT = 50 x 2 = 100mile
Answer 2
Answer: Distance = Rate * Time

The rate he is going at is 50 mph
The time it took is 10 am to 12 pm. That is 2 hours.

Distance = 50 mph * 2 hr

Distance = 100 miles

Mike drove 100 miles.

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Find the inverse of each function1) g (x)= 3+(x-1)^3
4) f (x)=x^3+2
5) f (n)= 5 square root of (-n+1/2)

Answers

to find the inverse
1. replace f(x) or g(x) or f(n) with y
2. switch places of x and y
3. solve for y
4. replace y with f⁻¹(x) or g⁻¹(x) or f⁻¹(n)



1.
g(x)=3+(x-1)^3
replace
y=3+(x-1)^3
switch
x=3+(y-1)^3
solve
x=3+(y-1)^3
subtract 3
x-3=(y-1)^3
cube root both sides
\sqrt[3]{x-3}=y-1
add 1
\sqrt[3]{x-3}+1=y
switch y with g⁻¹(x)
g⁻¹(x)=\sqrt[3]{x-3}+1





4. f(x)=x^3+2
replace with y
y=x^3+2
switch x and y
x=y^3+2
solve for y
x=y^3+2
subtract 2
x-2=y^3
cube roo both sides
\sqrt[3]{x-2}=y
replace with f⁻¹(x)
f⁻¹(x)=\sqrt[3]{x-2}



5.
f(n)=5√(-n+1/2)
replace
y=5√(-n+1/2)
switch n and y
n=5√(-y+1/2)
solve for y
n=5√(-y+1/2)
divide both sides by 5
n/5=n=√(-y+1/2)
square both sides
(n^2)/(25)=-y+1/2
subtract 1/2 from both sides
(n^2)/(25)-(1)/(2)=-y
multiply both sides by -1
-(n^2)/(25)+(1)/(2)=y
replace with f⁻¹(n)
f⁻¹(n)=-(n^2)/(25)+(1)/(2)



1.  g⁻¹(x)=\sqrt[3]{x-3}+1
4.  f⁻¹(x)=\sqrt[3]{x-2}
5.  f⁻¹(n)=-(n^2)/(25)+(1)/(2)











Please help I've been stuck on this question for a while now. How do I solve (1/2)^4 (1/2)^-2? It has to do with Multiplying and Dividing Expressions with Exponents. Please show work so I may figure it out on my own.

Answers

The value of the expression is 0.25

Explanation:

The expression is $\left((1)/(2)\right)^(4)\left((1)/(2)\right)^(-2)$

Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.

Thus, we have,

$\left((1)/(2)\right)^(4)\left((1)/(2)\right)^(-2)=\left((1)/(2)\right)^(4-2)$

Adding the exponents, we have,

$\left((1)/(2)\right)^(4)\left((1)/(2)\right)^(-2)=\left((1)/(2)\right)^(2)$

Applying exponent rule, $\left((a)/(b)\right)^(c)=(a^(c))/(b^(c))$, we have,

$\left((1)/(2)\right)^(2)=(1^(2))/(2^(2))$

Simplifying, we get,

(1)/(4)

Dividing, we have,

0.25

Thus, the value of the expression is 0.25

Juanita is 13 years older than her cousin. The sum of their ages is no less than 103 years. Enter an inequality that can be used to represent this situation in the first box, where x represents Juanita's cousin's age. Enter the youngest age Juanita's cousin can be in the second box.

Answers

y = x + 13
y + x ≥ 103
x + 13 + x ≥ 103
Inequality is:
2 x + 13 ≥ 103
2 x ≥ 103 - 13
2 x ≥ 90
x ≥ 90 : 2
x ≥ 45
The youngest age Juanita`s cousin can be is 45.

Answer:

45

Step-by-step explanation:

Mr young has 30 times as many pencils as jack. The whole class has 200 times as many pencils as jack. If jack has 2pencils, how many pencils does mr young have ? And the whole school have?

Answers

well you would do 30*2= 60
and that would be your answer

A medical clerk noticed that 7635 patients were admitted to the hospital  in a one-year period. 4/15  of them had heart or lung diseases. How many patients with heart or lung diseases were admitted to the hospital during the year?

Answers

7635*4/15
=2036 patients

adam used the three fraction s to make a circle graph and colored each a different color. what fraction of the graph is not colored?

Answers

1/3 is your answer......
If there were no division of circle before, the answer is 0