80Divided by 3 plz help

Two numbers are in the ratio 3:8. The larger number is 96, find the sum of the numbers

zloy xaker [14]

Answer:

The sum of the numbers is 132

Step-by-step explanation:

First find the smallest number

3/8=x/96
2(96)=8x
288=8x
x=36

Thus, you found the smallest number

then there sum given as 96+36=132

6 0

2 years ago

Simplify

frosja888 [35]

Just do this :
-1 + 30 - 5y
29 - 5y
or -5y + 29
the answer is C

6 0

3 years ago

Tamara and Jason work at a widget factory. Tamara arrived at work before Jason and began making widgets. Tamara had already made

Mrac [35]

Answer:

See explanation!

Step-by-step explanation:

The remaining question reads:

Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.

Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?

Part C: How many widgets will Tamara and Jason have produced?

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To solve this problem we can construct an linear algebraic expression for each person, principally denoted as:

$y=ax+c$

where

$y$ :is our dependent variable (which is a function of $x$ )

$x$ :is our independent variable

$a$ :is the slope

$c$ :is the y-intercept constant value (if any present)

Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.

Tamara

Has already made 20 widgets and produces at a rate of 8 widgets per hour thus here $c=20$ and $a=8$ , so Tamara's equation reads:

$y_{T}=8x+20$

Jason

Has not produced any widgets yet and produces at a rate of 12 widgets per hour thus here $c=0$ and $a=12$ , so Jason's equation reads:

$y_{J}=12x$

So the system of equations will be

$y_{T}=8x+20\\y_{J}=12x$

Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?

Since we want to find the amount of time (i.e. the value of $x$ ) it takes for both of them to produce the same number of widgets we can just equate the two equations ans solve for $x$ as follow:

$y_{T}=y_{J}\\8x+20=12x\\8x-12x=-20\\-4x=-20\\x=\frac{-20}{-4}\\ x=5$

So it takes them 5 hours to produce the same amount of widgets.

Part C: How many widgets will Tamara and Jason have produced?

Now we can simply plug in the value of $x=5$ in any of the two equations (i.e. either for Tamara or Jason) to find the number of widgets produced.

$y_{T}=8(5)+20=40+20=60$

So in a time-space of 5 hours Each will have produced 60 widgets and in total will be 60+60 = 120 widgets.

6 0

3 years ago

If f(x) is discontinuous, determine the reason.

inn [45]

The function is

$f(x) = \begin{cases} x^2-4 &\mbox{if } x\ \textless \ 1, \\ 
x+4 & \mbox{if } x\ \textgreater \ 1. \end{cases}$ .

To the left of 1 the function is a quadratic polynomial, to the right, it is a linear polynomial. Polynomial functions are always continuous, so the only candidate point for discontinuity is x=1.

The left limit is calculated with 1 substituted in $x^2+4$ , which gives 5.

The right limit, is computed using the rule for the right part of 1, that is x+4.

Thus, the right limit is 1+4=5.

So, both left and right limits are equal. Now if f(1) is 5, then the function is continuous at 1.

But the function is not defined for x=1, that is x=1 is not in the domain of the function. Thus, we have a "whole" (a discontinuity) in the graph of the function.

The reason is now clear:

Answer: f(1) is not defined

5 0

4 years ago

impeded by the current the outing club took 4 hours and 24 minutes to paddle 11 km up the exeter river to their campsite last we

lilavasa [31]

Answer: if there had been no current, the rate would have been 4 km/hr.

The rate of the current is 1.5km/hr

Step-by-step explanation:

Let x represent the speed of the boat in still water.

Let y represent the speed of the current.

Impeded by the current the outing club took 4 hours and 24 minutes(4 + 24/60 = 4.4 hours) to paddle 11 km up the exeter river to their campsite last weekend. This means that the total speed with which they travelled is (x - y) km/h

Distance = speed × time. Therefore

11 = 4.4(x - y)

Dividing through by 4.4, it becomes

2.5 = x - y - - - - - - - - - - -1

The next day the same current was with them and it took only 2 hours to make the return trip to campus. This means that the total speed with which they travelled is (x + y) km/h. The distance travelled is

11 = 2(x + y)

Dividing through by 2, it becomes

5.5 = x + y - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

8 = 2x

x = 8/2 = 4

Substituting x = 4 into equation 1, it becomes

2.5 = 4 - y

y = 4 - 2.5

y = 1.5

3 0

3 years ago