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Paladinen [302]
3 years ago
12

A pencil at a stationery store costs $1, and a pen costs $1.50. Stefan spent $7 at the store. He bought a total of 6 items. Whic

h system of equations can be used to find the number of pencils (x) and pens (y) he bought?
Mathematics
2 answers:
Elena-2011 [213]3 years ago
7 0
Let pencil represent x
pen represent y
Next, we have this two equation:
x+1.5y=7
x+y=6
Then, I will use substitution to find the value of x and y:
x+1.5y=7
-
x+y=6
=
0.5y=1
y=2 pens
x+y=6
x+2=6
Subtract 2 for both side
x+2-2=6-2
x=4 pencils
Check:
x+y=6 items
4+2=6 items Right

x+1.5y=7
4+1.5(2)=$7
$4+$3=$7
$7=$7
As a result, there are 4 pencils , and 2 pens. Hope it help!
Nina [5.8K]3 years ago
4 0
Y= # of pencils 
z= # of pens
1y + 1.50z = 7
Total # of pencils and pens combined equals 6 
4 pencils = $4
2 pens = $3 
$4 + $3 = $7 
4 pencils + 2 pens = 6 items total
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Solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!​
Misha Larkins [42]

Answer:

[0.25, 2]

Step-by-step explanation:

We have

4t² ≤ 9t-2

subtract 9t-2 from both sides to make this a quadratic

4t²-9t+2 ≤ 0

To solve this, we can solve for 4t²-9t+2=0 and do some guess and check to find which values result in the function being less than 0.

4t²-9t+2=0

We can see that -8 and -1 add up to -9, the coefficient of t, and 4 (the coefficient of t²) and 2 multiply to 8, which is also equal to -8 * -1. Therefore, we can write this as

4t²-8t-t+2=0

4t(t-2)-1(t-2)=0

(4t-1)(t-2)=0

Our zeros are thus t=2 and t = 1/4. Using these zeros, we can set up three zones: t < 1/4, 1/4<t<2, and t>2. We can take one random value from each of these zones and see if it fits the criteria of

4t²-9t+2 ≤ 0

For t<1/4, we can plug in 0. 4(0)²-9(0) + 2 = 2 >0 , so this is not correct

For 1/4<t<2, we can plug 1 in. 4(1)²-9(1) +2 = -3 <0, so this is correct

For t > 2, we can plug 5 in. 4(5)²-9(5) + 2 = 57 > 0, so this is not correct.

Therefore, for 4t^2 ≤ 9t-2 , which can also be written as 4t²-9t+2 ≤ 0, when t is between 1/4 and 2, the inequality is correct. Furthermore, as the sides are equal when t= 1/4 and t=2, this can be written as [0.25, 2]

8 0
3 years ago
A thermometer is taken from a room where the temperature is 20°C to the outdoors, where the temperature is 3°C. After one minute
IrinaVladis [17]

Answer:

A. T=7.12°C; B. t=3.32min

Step-by-step explanation:

In order to find the answer we can use the Newton's law of cooling:

y(t)=y0e^{kt} where:

y0=initial temperature - room temperature

k=coefficients

t=time

Because the outdoors temperature is 3°C, the initial temperature is 20°C, and because the thermometer reads 11°C after 1min we have:

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A. Temperature after an extra minute.

y(2)=17e^{-0.4353*2}

y(2)=7.12 so the answer is 7.12°C

B. Time in order to read 4°C

4=17e^{-0.4353*t}

ln(4/17)/(-0.4353)=t}

3.32min=t

6 0
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