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Nadya [2.5K]
3 years ago
8

- 8th Grade Math - Solve the system of equations: 2x - 4y = 10, x = 2y + 5

Mathematics
1 answer:
4vir4ik [10]3 years ago
4 0

Answer:

All real numbers

Step-by-step explanation:

Since x=2y+5, and 2x-4y=10, substitute 2y+5 for x into 2x-4y=10

2(2y+5)-4y=10

Use distributive prop.

4y+10-4y=10

10=10

Since both sides of the equation are always equivalent,

All real numbers work, since the two equations are the same line.

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Question : A square game board is divided into smaller squares, each with sides one-ninth the length of the sides of the board.
bagirrra123 [75]

Answer:

Therefore the game board is divided into 81 smaller squares.

Step-by-step explanation:

Given that, there is a square game.

Consider x be length of one side the square.

The volume of the square is = side ×side

                                               =x² square units

Since the length of side of smaller square is one-ninth of the game board.

Then one side length of the smaller square is \frac19x units.

The area of a smaller square is =(\frac19x)\times (\frac19x)

                                                    =\frac{1}{81}x^2

Let a number of square is formed from the game board.

a ×The area of one smaller square= The area of game board.

According to the problem,

a\times (\frac{1}{81}x^2)=x^2

\Rightarrow a =\frac{x^2\times 81}{x^2}

\Rightarrow a= 81

Therefore the game board is divided into 81 smaller squares.

4 0
3 years ago
Name the opposite of 7
zysi [14]

The opposite of 7 on a number line would be -7 because if you look at 0 as a mirror, then the opposite of 7 is -7.

8 0
3 years ago
PLEASE HELP I NEED HELP 10 POINTS
mestny [16]

Answer:

A kite with a 100 foot-long string is caught in a tree. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 30 feet from the bottom of the tree. Find the measure of the angle between the kite string and the ground.

17°

27°

63°

73°Step-by-step explanation:

8 0
3 years ago
Employees from A and company B receive annual bonuses. What information would you need to test the claim that the difference in
lyudmila [28]

Answer:

1. The required information are

The average annual bonuses, \bar {x}_1 received by employees from company A

The average annual bonuses, \bar {x}_2 received by employees from company B

The standard deviation, σ₁, of the average annual bonuses for employees from company A

The standard deviation, σ₂, of the average annual bonuses for employees from company A

The number of employees in company A, n₁

The number of employees in company B, n₂

2. The null hypothesis is H₀: \bar {x}_1 - \bar {x}_2 ≤ 100

The alternative hypothesis is Hₐ: \bar {x}_1 - \bar {x}_2 > 100

Step-by-step explanation:

1. The required information are

The average annual bonuses, \bar {x}_1 received by employees from company A

The average annual bonuses, \bar {x}_2 received by employees from company B

The standard deviation, σ₁, of the average annual bonuses for employees from company A

The standard deviation, σ₂, of the average annual bonuses for employees from company A

The number of employees in company A, n₁

The number of employees in company B, n₂

2. The null hypothesis is H₀: \bar {x}_1 - \bar {x}_2 ≤ 100

The alternative hypothesis is Hₐ: \bar {x}_1 - \bar {x}_2 > 100

The z value for the hypothesis testing of the difference between two means is given as follows;

z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\frac{\sigma_{1}^{2} }{n_{1}}-\frac{\sigma _{2}^{2}}{n_{2}}}}

At 0.5 level of significance, the critical z_\alpha = ± 0

The rejection region is z > z_\alpha and z < -z_\alpha

Therefore, the value of z obtained from the relation above more than or less than 0, we reject the null hypothesis, and we fail to reject the alternative hypothesis.

7 0
3 years ago
Use the pi key on a scientific or graphing calculator to compute the percent of error of the approximation of pi, 3.14, to the v
Kitty [74]
Percent error is calculated as \frac{approximation-theoretical}{theoretical}*100.
The approximation in this case is 3.14, and the theoretical or actual value is pi.

Using the formula, the percent error will be:
\frac{3.14- \pi }{ \pi }*100 = -0.0507%

4 0
3 years ago
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