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kkurt [141]
2 years ago
7

Micah and Linda are 230 feet apart when they start walking toward one another. Linda walks twice as fast as Micah so whenever Mi

cah travels x feet, Linda travels 2 x feet. Let x represent the number of feet Micah has traveled since he started walking toward Linda. Write an expression in terms of x to represent the total number of feet Micah and Linda have walked toward one another.
Mathematics
1 answer:
BigorU [14]2 years ago
7 0

Answer:

D(x) = 3x

Step-by-step explanation:

Micah travels at a rate of 'x' feet over a specific period.

Linda travels at a rate of '2x' feet over that same period.

Since they are walking in opposite directions, the total distance they have walked towards one another (D) can be determined by adding both distances:

D(x) = x+2x\\D(x) = 3x

The expression that describes the number of feet they have walked toward one another is D(x) = 3x.

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2 years ago
What is the equation of the line with a slope of 3/4 that goes through the point (4, 1) in slope-intercept form?
Svetach [21]

Answer:

y=\frac{3}{4}x+-2

Step-by-step explanation:

We do not have enough information for slope intercept form. But we can use the point-slope formula to find the information. The formula is y -y_{1} =m(x -x_{1}) where we substitute a point (x,y) for (x_{1},y_{1}).  

We have m=3/4 and (4, 1). We input m and x_{1} =4\\y_{1}=1.

y-1=\frac{3}{4} (x-4)

We now simplify the parenthesis and solve for y.

y-1=\frac{3}{4} (x-4)\\y-1=\frac{3}{4}x+\frac{3}{4} (-4)

We convert -4 into a fraction with 1 as the denominator.

y-1=\frac{3}{4}x+\frac{3}{4} (\frac{-4}{1} )\\y-1=\frac{3}{4}x+\frac{-12}{4}\\y-1=\frac{3}{4}x+-3

We add 1 to both sides to isolate y,

y-1+1=\frac{3}{4}x+-3+1\\y=\frac{3}{4}x+-2

This is slope intercept form. The line as slope 3/4 and y-intercept (0,2) or b=2.

4 0
3 years ago
Help i’m confused i don’t know what to do
VMariaS [17]

Answer:

-84i - 12i

Step-by-step explanation:

The distributive property is: a(b+c) = ab + ac

In this case, we have -6i(-14i+2)

-6i = a

-14i = b

2 = c

-6i(-14i+2) = -6i(-14i) + -6i(2)

= 84i^2 - 12i

= -84 - 12i

7 0
2 years ago
Read 2 more answers
In a single growing season at the smith family orchard, the average yield per apple tree is 150 apples when the number of trees
Mariana [72]

Answer:

100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

Step-by-step explanation:

<u>Functions </u>

Expressing some quantities in terms of other(s) comes in handy to understand the behavior of the situations often modeled by those functions.

Our problem tells us about the smith family orchard, where the average yield per apple tree is 150 apples when the number of trees per acre is 100 (or less). But the average yield per tree decreases when more than 100 trees are planted. The rate of decrease is 1 for each additional tree is planted

Let's call x the number of trees planted per acre in a single growing season. We have two conditions when modeling:  when x is less than 100, the average yield per apple tree (Ay) is (fixed) 150.

Ay(x)=150\ ,\ x\leqslant 100

When x is more than 100:

Ay(x)=150-x\ ,\ 100< x\leqslant 150

The upper limit is 150 because it would mean the Average yield is zero and no apples are to be harvested

Part 1

We are asked what happens if the number of trees per acre was doubled, but we don't know what the original number was. Let's make it x=60

If x=60, then we must use the first function, and

Ay(60)=150

The yield per acre will be 150*60=9000 apples

If we doubled x to 120, we would have to use the second function

Ay(120)=150-x=30

The yield per acre will be 30*120=3600 apples

Note that doubling the number of trees would make the production decrease

If we started with x=30, then  

Ay(30)=150, and we would have 150*30=4500 apples per acre

We already know that for x=60 (the double of 30), our production will be 9000 apples per acre

This shows us that in some cases, increasing the number of trees is beneficial and in other cases, it is not

Part 2

The total yield is computed as

Y(x)=x.Ay(x)

This function will be different depending on the value of x

Y(x)=150x\ ,\ x\leqslant 100

Y(x)=150x-x^2\ ,\ 100< x\leqslant 150

To find the maximum total yield we take the first derivative

Y'(x)=150\ ,\ x\leqslant 100

Y'(x)=150-2x\ ,\ 100< x\leqslant 150

The first expression has no variable, so the total yield must be evaluated in the endpoints

Y(0)=0

Y(100)=15000

Now, the second expression contains variable, it will be set to 0 to find the critical point

150-2x=0

x=75

x is outside of the boundaries, we cannot find the maximum in this interval

Answer: 100 trees should be planted per acre to maximize the total yield (15000 apples per acre)

7 0
3 years ago
Julia went to the movies and bought one jumbo popcorn and two chocolate chip cookies for $5.00. Marvin went to the same movie an
hichkok12 [17]
X=price of one jumbo popcorn
y=price of one chocolate chip cookies

$5.00=$5.00(100 cts / $)=500 cts
$6.00=$6.00(100 cts / $)=600 cts

We suggest this system of equations:

x+2y=500
x+4y=600

we solve this system of equations by reduction method.

-(x+2y=500)
  x+4y=600
----------------------
      2y=100    ⇒ y=100/2=50

x+2y=500
x+2(50)=500
x+100=500
x=500-100
x=400

solution: one chocolate chip cookie cost 50 cts.
4 0
3 years ago
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