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3 years ago

Solve the simultaneous equations 3x + 2y = 30 3x - y = 21

Mathematics

1 answer:

Mrac [35]3 years ago

3 0

Answer:

x = 8 , y = 3

Step-by-step explanation:

3x + 2y = 30

3x - y = 21 -> y = 3x - 21

3x + 2 (3x - 21) = 30

3x + 6x - 42 = 30

3x + 6x = 30 + 42

9x = 72

x = 72/9 = 8

y = 3*8 - 21 = 24 - 21 = 3

∴ x = 8 & y = 3

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The picture shows the number of colored shirts sold this week at Joan’s Clothing Shop. Joan assumes this trend will continue. Sh

lisov135 [29]

Answer:

She should order 96 orange shirts

Step-by-step explanation:

The picture is shown below.

From the picture below Joan sold 10 blue shirts, 3 gray shirts , 5 orange shirts and 8 green shirts out of the colored Shirts. The ratio of the colored shirt sold are 10 : 3 : 5 : 8 . The total shirt sold that week is 10 + 3 + 5 + 8 = 26 colored shirts.

If she assumes the trend is going to continue the number of orange she should order can be calculated below.

Let us find the ratio of orange shirt sold to the total colored shirt sold.

orange shirt sold / total colored shirt sold = 5/26

This means every group of 26 colored shirts sold will have 5 orange shirt . So they told us she requested a total of 500 colored shirts . Following the same trend, how many group of 26 colored shirt are in 500.

5/26 = x/ 500

cross multiply

2500 = 26x

divide both sides by 26

x = 2500/26

x = 96.15

x = 96 orange shirts

She should order 96 orange shirts

6 0

3 years ago

Read 2 more answers

What are the values of x and y

Murljashka [212]

E 10 12

x=18*5)14. x=40/4. x=10. y=(15*4)/5 y=60/5 y=12.

resposta : 10 e 12

4 0

2 years ago

A gas is said to be compressed adiabatically if there is no gain or loss of heat. When such a gas is diatomic (has two atoms per

Tems11 [23]

Answer:

The pressure is changing at $\frac{dP}{dt}=3.68$

Step-by-step explanation:

Suppose we have two quantities, which are connected to each other and both changing with time. A related rate problem is a problem in which we know the rate of change of one of the quantities and want to find the rate of change of the other quantity.

We know that the volume is decreasing at the rate of $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ and we want to find at what rate is the pressure changing.

The equation that model this situation is

$PV^{1.4}=k$

Differentiate both sides with respect to time t.

$\frac{d}{dt}(PV^{1.4})= \frac{d}{dt}k\\$

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:

$\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)$

Apply this rule to our expression we get

$V^{1.4}\cdot \frac{dP}{dt}+1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}=0$

Solve for $\frac{dP}{dt}$

$V^{1.4}\cdot \frac{dP}{dt}=-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}\\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot V^{0.4} \cdot \frac{dV}{dt}}{V^{1.4}} \\\\\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}$

when P = 23 kg/cm2, V = 35 cm3, and $\frac{dV}{dt}=-4 \:{\frac{cm^3}{min}}$ this becomes

$\frac{dP}{dt}=\frac{-1.4\cdot P \cdot \frac{dV}{dt}}{V}}\\\\\frac{dP}{dt}=\frac{-1.4\cdot 23 \cdot -4}{35}}\\\\\frac{dP}{dt}=3.68$

The pressure is changing at $\frac{dP}{dt}=3.68$ .

7 0

3 years ago

calvin and susie baked some cookies in the ratio of 3 : 7. calvin baked 60 fewer cookies than susie. how many cookies did they b

kow [346]

Answer:

Step-by-step explanation:

Ratio of cakes baked by Calvin and Susie = 3 : 7

Cakes baked by Calvin = 3x

Cakes baked by Susie = 7x

Cakes baked by Calvin = Cakes baked by Susie - 60

3x = 7x - 60

7x - 60 = 3x

7x = 3x + 60

7x - 3x = 60

4x = 60

x = 60/4

x = 15

Cakes baked by Calvin = 3*15 = 45

Cakes baked by Susie = 7 *15 = 105

Total cakes baked = 45 + 105 = 150

They both baked 150 cakes altogether.

8 0

2 years ago

Evaluate 2^5/2^2 i need some help lol

seraphim [82]

2^5/2^2 = 2^(5-2)
= 2^3
= 8

8 0

3 years ago

Read 2 more answers