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3 years ago

How many solutions does the system of equations below have? y = −6x + 9 y = 9/8x − 3

Mathematics

1 answer:

torisob [31]3 years ago

4 0

Answer:

1 solution

Step-by-step explanation:

A system of two equations can be classified as follows:

1) If the slopes are the same but the y-intercepts are different, the system has no solution.

2) If the slopes are different, the system has one solution.

3) If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions

Hope this helps you

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A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine w

Alenkinab [10]

Answer:

The diagonals of the polygon ABCD bisect each other

Step-by-step explanation:

The given vertices of the polygon are;

A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1)

Given that the vertices of the polygon in clockwise order from the top left corner are ABCD, we have the diagonals as AC and DB

By the midpoint formula, we have;

$(x_m , \ y_m) = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )$

Where;

$(x_m , \ y_m)$ = The midpoint coordinates

Therefore, the midpoint of diagonal AC = $\left (\dfrac{1 + (-1)}{2} , \ \dfrac{4 + (-4)}{2} \right ) = (0, 0)$

The midpoint of diagonal DB = $\left (\dfrac{(-4) +4}{2} , \ \dfrac{1 + (-1)}{2} \right ) = (0, 0)$

Therefore, given that the coordinates of the location of the midpoint of the diagonals AC and DB is the same, the diagonals bisect each other

Each diagonal passes through the midpoint of the other diagonal.

3 0

3 years ago

Can anyone pls help me I really need help pls help me I will mark them as brainiest pls!!! Can u do it in a paper and then send

Tom [10]

Answer:

see them bellow

Step-by-step explanation:

6 0

4 years ago

I need your help guys !!!!!!!!

Ber [7]

$\bold{\huge{\blue{\underline{ Solution}}}}$

$\bold{\underline{ We \: have \:given \: that, }}$

Distance between the house and tower is 35 m
The height of the tower is 60 m
The height of the house is 25 m

$\bold{\underline{ Now}}$

Height of the house is 25m

$\bold{\underline{ So, }}$

$\sf{ CE = 25m }$

Therefore,

$\sf{ AB = AD - CE }$

$\sf{ AB = 60 - 25 }$

$\sf{ AB = 35 m }$

Now, In Right angled ABC

$\bold{tan Φ =}{\bold{\frac{ AB}{BC}}}$

$\bold{tan Φ =}{\bold{\frac{ 35}{35}}}$

$\bold{ tan Φ = 1 }$

$\bold{ tan Φ = 45 °}$

$\sf{\red{Hence, \: The \:angle \:of \:depression\: is \:45°}}$

7 0

2 years ago

A company advertises that its cans of caviar each contain 100 g of their product. A consumer advocacy group doubts this claim, a

Blizzard [7]

Answer:

The value of the test statistic is -3.14.

Step-by-step explanation:

Test statistic:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the expected value, $\sigma$ is the standard deviation and n is the size of the sample.

A company advertises that its cans of caviar each contain 100 g of their product.

This means that $\mu = 100$

They calculate a sample mean weight of 99 g and a sample standard deviation of 0.9 g. Sample of 8 cans.

This means that $X = 99, \sigma = 0.9, n = 8$

So the test statistic will be given by:

$t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{99 - 100}{\frac{0.9}{\sqrt{8}}}$

$t = -3.14$

The value of the test statistic is -3.14.

8 0

3 years ago

What is the 4 math methods

erastovalidia [21]

The Four basic Mathematical Operations are:
•Addition
•Subtraction
•Multiplication
•Division

5 0

3 years ago