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3 years ago

Find the solution of this system of equations 4x + y = 3 4x - y = -5

Mathematics

2 answers:

Blababa [14]3 years ago

6 0

-1/4 is the answer.

laiz [17]3 years ago

4 0

Answer:

y = 7/2

x = -1/8

Step-by-step explanation:

4x + y = 3-----------eqn 1

4x - y = -5----------eqn 2

Let's pick eqn 1

4x + y = 3

Let's make y the subject of the formula

y = 3 -4x

Since y = 3 - 4x, substitute the value of y into eqn 2

4x - ( 3 - 4x) = -5

Using the - to open the bracket

4x - 3 + 4x = -5

16x - 3 = -5

16x = -5 + 3

16x = -2

Divide through by 16 to get the value of x

16x/ 16 = -2/16

x = -1/8

Since we've gotten the value for x, find y using eqn 1

4x + y = 3

4(-1/8) + y = 3

-4/8 + y = 3

y = 3 + 4/8

LCM is 8

y = 24 + 4 / 8

y = 28/8 ( using 4 to divide)

y = 7/2

x = -1/8

y = 7/2

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A conservative estimate of the number of stars in the universe is 6 x 10^22. The average human can see about 3,000 stars at nigh

Ilia_Sergeevich [38]

$2 \times 10^{19}$ times more stars are there in universe compared to human eye can see

<h3><u>Solution:</u></h3>

Given that, conservative estimate of the number of stars in the universe is $6 \times 10^{22}$

The average human can see about 3,000 stars at night with only their eyes

To find: Number of times more stars are there in the universe, compared to the stars a human can see

Let "x" be the number of times more stars are there in the universe, compared to the stars a human can see

Then from given statement,

$\text{Stars in universe} = x \times \text{ number of stars human can see}$

<em><u>Substituting given values we get,</u></em>

$6 \times 10^{22} = x \times 3000\\\\x = \frac{6 \times 10^{22}}{3000}\\\\x = \frac{6 \times 10^{22}}{3 \times 10^3}\\\\x = 2 \times 10^{22-3}\\\\x = 2 \times 10^{19}$

Thus $2 \times 10^{19}$ times more stars are there in universe compared to human eye can see

5 0

3 years ago

Element X is a radioactive isotope such that its mass decreases by 26% every day. If an experiment starts out with 810 grams of

ioda

Answer:

The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.

The function to represent the mass of the sample after t days is $A(t) = 810(0.74)^t$

Step-by-step explanation:

Exponential equation of decay:

The exponential equation for the amount of a substance is given by:

$A(t) = A(0)(1-r)^t$

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Hourly rate of change:

Decreases 26% by day. A day has 24 hours. This means that $A(24) = (1-0.26)A(0) = 0.74A(0)$ ; We use this to find r.

$A(t) = A(0)(1-r)^t$

$0.74A(0) = A(0)(1-r)^{24}$

$(1-r)^{24} = 0.74$

$\sqrt[24]{(1-r)^{24}} = \sqrt[24]{0.74}$

$1 - r = (0.74)^{\frac{1}{24}}$

$1 - r = 0.9875$

$r = 1 - 0.9875 = 0.0125$

The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.

Starts out with 810 grams of Element X

This means that $A(0) = 810$

Element X is a radioactive isotope such that its mass decreases by 26% every day.

This means that we use, for this equation, r = 0.26.

The equation is:

$A(t) = A(0)(1-r)^t$

$A(t) = 810(1 - 0.26)^t$

$A(t) = 810(0.74)^t$

The function to represent the mass of the sample after t days is $A(t) = 810(0.74)^t$

5 0

3 years ago

Point T has coordinates (-7, -3). If it's reflected across the line x = 2, what will be the coordinates of its image? A (7, -3)

anastassius [24]

B is the answer
just like the picture
( T' is not exact. it just shows the reflection)

8 0

3 years ago

Gavyn, Pip and Mark share £102 in a ratio 1:2:3. How much money does each person get?

rosijanka [135]

Answer:

see explanation

Step-by-step explanation:

sum the parts of the ratio , 1 + 2 + 3 = 6 parts

divide the amount by 6 to find the value of one part of the ratio

£102 ÷ 6 = £17 ← value of 1 part of the ratio , then

2 parts = 2 × £17 = £34

3 parts = 3 × £17 = £51

Gavyn gets £17

Pip gets £34

Mark gets £51

5 0

2 years ago

Read 2 more answers

Four students each contribute $12 to buy a pizza, salad, and large soda. How much would each student pay if two more students al

geniusboy [140]

Answer:

Step-by-step explanation:

4 students contribute 12$ Each.

So, total amount becomes 12 x 4 = 48$

If two more students contribute it makes a total of 6 students.
so we now divide the 48$ by 6
48/6=8$

8 0

2 years ago