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horrorfan
1 month ago
10

Given f(x) and g(x) = f(x) + k, look at the graph below and determine the value of k. k = ______ Graph of two lines. f of x equa

ls 1 over 3 x plus 2 and g of x equals 1 over 3 x plus 5
Mathematics
1 answer:
lawyer [12.5K]1 month ago
7 0

Solution:

We know, g(x) = f(x) + k --------(1)

It is given that f(x) = \frac{1}{3}(x+2)

and g(x) = \frac{1}{3}(x+5)

Substituting f(x) and g(x) into equation (1):

→ \frac{1}{3}(x+5) = \frac{1}{3}(x+2) + k

→ \frac{1}{3}[x+5-x-2] = k

→ k = \frac{1}{3} \times 3=1

Thus, the value of k is 1.

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Pia uses 6 cups of sugar to make 8 pies. At that rate, how much sugar will it take to make 12 pies?
zzz [12365]

Answer: 9 cups

Step-by-step explanation: If 6 cups make 8 pies, then 3 cups will yield 4 pies. Hence, 9 cups would suffice for 12 pies


5 0
29 days ago
Read 2 more answers
Anumeha is mowing lawns for a summer job. For every mowing job, she charges an initial fee of $ 10 $10dollar sign, 10 plus a con
Zina [12379]

Answer:

F(t) = 10 + 5(t)

Step-by-step explanation:

The complete question is as follows;

Anumeha is mowing lawns for a summer job. For each lawn she mows, she charges a $10 starting fee plus an hourly rate. For example, her fee for a 5-hour job is $35. Let f(t) denote Anumeha's fee for a job f (in dollars) based on how many hours (t) were needed to finish it. Write the formula for this function.

Solution

We aim to establish the formula F(t) representing the fee Anumeha charges per job.

Key to formulating this function is understanding the constant charge she applies per job.

We know she earns $35 for mowing for 5 hours.

Therefore, the constant fee can be deduced as follows;

Since it’s a $10 starting fee along with an hourly rate;

35 = 10 + 5(x)

where x refers to the hourly rate

35 = 10 + 5x

5x = 35-10

5x = 25

x = 25/5

x = $5

This indicates that she charges a constant fee of $5 per hour

Thus, we can now write the equation.

F(t) = 10 + 5(t)

where t represents the number of hours spent on each job

6 0
1 month ago
Rob borrows $15.00 from his father, and then he borrows $3.00 more. Drag numbers to write an equation using negative integers to
PIT_PIT [12445]

Answer:

Rob's total debt to his father is calculated as: -$15 - $3 = -$18

Step-by-step explanation:

Initially, Rob borrows $15.

Then, he borrows an additional $3.

Expressing this with negative integers gives us

-15 - 3 = -18

4 0
1 month ago
Read 2 more answers
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that th
Zina [12379]

Answer:

Step-by-step reasoning:

(a)

To have an accepted bid, it needs to exceed $10,000. Let bid x be a continuous random variable uniformly distributed between

$10,000 and $15,000

The range for accepted bidding is [ {\rm{\$ 10,000, \$ 15,000}], with b = $15000 and a = $10000.

The provided bidding range is [$10,000,$12,000]. The probability is determined as follows,

\begin{array}{c}\\P\left( {X{\rm{ < 12,000}}} \right){\rm{ = }}1 - P\left( {X > 12000} \right)\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{12000}^{15000}\\\end{array}

=1- \frac{[15000-12000]}{5000}\\\\=1-0.6\\\\=0.4

(b)  The accepted bidding range is [$10,000,$15,000], where b = $15,000 and a =$10,000. The given bidding range is [$10,000,$14,000].

\begin{array}{c}\\P\left( {X{\rm{ < 14,000}}} \right){\rm{ = }}1 - P\left( {X > 14000} \right)\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{14000}^{15000}\\\end{array} P(X14000)

=1- \frac{[15000-14000]}{5000}\\\\=1-0.2\\\\=0.8

(c)

The optimal amount to bid for maximizing the probability of acquiring the property is calculated as,  

The accepted bidding range is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The provided bidding range is [$10,000,$15,000].

\begin{array}{c}\\f\left( {X = {\rm{15,000}}} \right){\rm{ = }}\frac{{{\rm{15000}} - {\rm{10000}}}}{{{\rm{15000}} - {\rm{10000}}}}\\\\{\rm{ = }}\frac{{{\rm{5000}}}}{{{\rm{5000}}}}\\\\{\rm{ = 1}}\\\end{array}

(d)  If you know someone willing to pay you $16,000 for the property, would you still consider bidding less than the amount mentioned in part (c)? Why or why not?

5 0
28 days ago
∠rst and ∠vst are a linear pair, m∠rst = 3x 7, and m∠vst = 9x 17. what are the measures of m∠rst and m∠vst?a.46, 134b.26, 154c.5
babunello [11817]
M∠ rst + m∠ vst = 180°
3 x + 7° + 9 x + 17° = 180°
12 x + 24° = 180°
12 x = 180° - 24°
12 x = 156°
x = 156°: 12
x = 13°
m ∠ rst = 3 · 13° + 7° = 39° + 7° = 46°
m ∠ vst = 180° - 46° = 134°
Answer:
A ) 46° and 134°
6 0
20 days ago
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