A car is going 50 miles per hour. A rate that describes this would have units of

Marc was born on his grandmother’s 56th birthday. In how many years will Marcs grandmother be 5 times as Marc will be then?

sergey [27]

Answer:

In 14 years Marc's grandmother will be 5 times as Marc will be then

Step-by-step explanation:

1. Information given to us to solve the problem:

Marc's age today = 0

Marc's grandmother age today = 56

2. In how many years will Marc's grandmother be 5 times as Marc will be then?

x = Number of years when Marc's grandmother age will be 5 times as Marc will be then

Let's solve for x, this way:

5 times Marc age in x years = Marc's grandmother age in x years

5 (0 + x) = 56 + x

5x = 56 + x

5x - x = 56 (Subtracting x at both sides)

4x = 56

x = 56/4

x = 14

Let's prove that x = 14 is correct:

5 (0 + 14) = 56 + 14

70 = 70

We proved that x = 14 is correct

In 14 years Marc's grandmother will be 5 times as Marc will be then

6 0

3 years ago

The length of a rectangle is 4 m longer than its width. if the perimeter of the rectangle is 36 m , find its area.

ycow [4]

Answer: The area of the rectangle is: " 77 m² " .

__________________________________________________________
Note: The formula for the area, "A" of a rectangle:

→ A = L * w ;

in which:
A = "area (of rectangle)" ; [in units of "m² " ; that is: "square meters" ] ;

L = length = "(4 + w)" {in units of "meters (m)" } ;

w = width {in units of "meters (m)" } ;
_______________________________________________________

So; " A = L * w " ;

Substitute the known expression for the "length, L" ; & rewrite the formula for the given area of OUR area for the rectangle in OUR GIVEN PROBLEM:

 → A = (4 + w) * w '' ;
______________________________________________________

Note the formula for the perimeter, "P" ;

→ P = 2L + 2w ;

↔ 2L + 2w = P

→ 2L + 2w = 36 m ;
_____________________________________________________
We want to find the "area" , "A" :
_____________________________________________________
Using the formula for the "perimeter, "P" (of the rectangle) ; & given that the perimeter is: "36" (meters) ;

→ 2L + 2w = 36 ;

→ Let us plug in the values for "Length (L)" & "width (w)" ;

→ 2(w + 4) + 2w = 36 ;

So; (2*w) + (2*4) + 2w = 36 ; Solve for "w" ;

→ 2w + 8 + 2w = 36 ;

 → Combine the "like terms" :

+ 2w + 2w = 4w ;

→ And rewrite:

4w + 8 = 36 ;

Now, subtract "8" from EACH SIDE of the equation:

4w + 8 − 8 = 36 − 8 ;

to get:

4w = 28 ;

Now, divide EACH SIDE of the equation by "4" ;
to isolate "w" on EACH SIDE of the equation ; & to solve for "w" ;

4w / 4 = 28 / 4 ;

→ w = 7 ; → The "width" of the rectangle is: " 7 m " .

Now, we can find the "length" of the rectangle:

The length, "L" , of the rectangle = 4 + w = 4 + 7 = 11 .

→ L = 11 . → The "length" of the rectangle is: " 11 m " .
___________________________________________________

Now, we can find the area, "A", of the rectangle.

A = L * w = 11 m * 7 m = " 77 m² " .

→ The area of the rectangle is: " 77 m² " .
__________________________________________________

To check our answer:
__________________________________________________

→ " P = 2L + 2w " ;

Given that "P = 36 m" ;

Plug in "36 m" (for "P") ; into the equation ;

and plug in our calculated values for
 "length, L" (which is "11 m") ; & "width, w" (which is "7 m") ;

to see if the equation holds true ; that is, to see if both sides of the equation are equal ;
_______________________________________________________

→ 36 m = ? 2L + 2w ?? ;

→ 36 m = ? 2(11 m) + 2(7 m) ?? ;

→ 36 m = ? 22 m + 14 m ?? ;

→ 36 m = ? 36 m ? Yes!
__________________________________________________

3 0

3 years ago

Can someone help me with this Exponential Growth and Decay word problem? I have been able to get the rest of them done but this

Vinvika [58]

Answer:

A) 61.68

Step-by-step explanation:

This is an exponential decay of 0.875. The way to know that is to get that is $\frac{right}{left} \\$ (Pick a random number and divide by the number to the left of it) From there, there is a 12 hour difference from 7 am to 7pm! Divide 306.25/0.875 and divide it by 0.875 by the answer of that each time 12 times. The exact answer is 61.68402914

4 0

4 years ago

Read 2 more answers

Can someone help me and explain step by step

Shkiper50 [21]

Answer: 5) r = 5, 8th term = -78,125

6) r = 5, 8th term = -312,500

7) r = 5, {1, 5, 25, 125, 625}

8) r = 5, {-4, -20, -100, -500, -2500}

Step-by-step explanation:

The explicit formula of a geometric sequence is: $a_n=a_1\cdot r^{n-1}$ , where;

n is the number of the term
a₁ is the first term
r is the common ratio

$5)\ a_n=-5^{n-1}\\.\qquad =-1\cdot 5^{n-1}\quad \rightarrow \quad a_1=-1\ and\ r=5\\\\a_8=-5^{8-1}\\.\quad =-5^7\\.\quad =-78,125\\\\\\6)\ a_n=-4\cdot 5^{n-1}\quad \rightarrow \quad a_1=-4\ and\ r=5\\\\a_8=-4\cdot 5^{8-1}\\.\quad =-4\cdot 78,125\\.\quad =-312,500$

$7)\ a_1=1\ and\ r=5\\.\quad a_2=1\cdot 5=\boxed{5}\\.\quad a_3=5\cdot 5=\boxed{25}\\.\quad a_4=25\cdot 5=\boxed{125}\\.\quad a_5=125\cdot 5=\boxed{625}\\\\\\\\8)\ a_1=-4\ and\ r=5\\.\quad a_2=-4\cdot 5=\boxed{-20}\\.\quad a_3=-20\cdot 5=\boxed{-100}\\.\quad a_4=-100\cdot 5=\boxed{-500}\\.\quad a_5=-500\cdot 5=\boxed{-2500}\\\\\\$

8 0

3 years ago

Can you multiply by 4 in a geometric sequence?

Free_Kalibri [48]

Yes, because in a geometric sequence, we multiply or divide to get to the next term.

I hope it helps!

$*RosalindCordelia*$

5 0

3 years ago

Read 2 more answers