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2 years ago

What is the equation of a line (in standard form) that passes through point A(1,-4) and has a slope of 3/4?

Mathematics

1 answer:

Anna35 [415]2 years ago

8 0

Answer:

3x-4y=19

Step-by-step explanation:

Hi there!

We want to write the equation of the line in standard form that passes through the point (1, -4) and has the slope of 3/4

Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0, and a cannot be negative

First, in order to find ax+by=c, we'll need to get slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

Since we already know the slope (3/4), we can substitute it into the formula for y=mx+b.

y=3/4x+b

Now we need to solve for b

Since the equation passes through the point (1, -4), we can use it to solve for b

Substitute 1 as x and -4 as y.

-4=3/4(1)+b

Multiply

-4=3/4+b

Subtract 3/4 from both sides

-19/4=b

Now substitute -19/4 as b into the equation

y=3/4x-19/4

Now we have the equation in slope-intercept form, but remember, we want it in standard form

Since x and y are on the same side in standard form, subtract 3/4x from both sides

-3/4x+y=-19/4

Remember that a cannot be negative, and the coefficients are integers (they cannot be fractions)

So in order to clear the fractions and change the sign of the equation, multiply both sides by -4

-4(-3/4x+y)=-4(-19/4)

Multiply

3x-4y=19

Hope this helps!

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Answer:

The expected value of the game to the player is -$0.2105 and the expected loss if played the game 1000 times is -$210.5.

Step-by-step explanation:

Consider the provided information.

It is given that if ball lands on 29 players will get $140 otherwise casino will takes $4.

The probability of winning is 1/38. So, the probability of loss is 37/38.

Now, find the expected value of the game to the player as shown:

$E(x)=(140)\times \frac{1}{38}+(-4)\times \frac{37}{38}$

$E(x)=\frac{140-148}{38}$

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2 years ago

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Answer:

Step-by-step explanation:

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2 years ago

Please help me. I need help please.

Mice21 [21]

Answer:

The correct options are;

EFGH has 4 congruent sides

Diagonal FH bisects angles EFG and EHG

Angle FEH is congruent to angle FGH

Step-by-step explanation:

1) Given that for a reflection, we have;

The distance of the reflected preimage from the line of reflection = The distance of the reflected image from the line of reflection

Therefore;

The distance of the point E from the line HF = The distance of the point G from the line HF

Also the reflection of an preimage (x, y) about the x-axis, gives an image (x, -y)

We can show that from the length of a line given by the equation $l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$ , that the length EH ≅ GH and EF ≅ GF

Therefore since we are given that EH = EF, we have;

EH = GH = GF = EF by the definition of congruency, which gives 4 congruent sides

2) Given that EH = GH = GF = EF and HF = FH by reflective property, we have;

ΔEHF ≅ ΔGHF

∴ ∠GHF ≅ ∠EHF by Congruent Parts of Congruent Triangles are Congruent

Similarly, ∠GFH ≅ ∠EFH

Therefore, ∠GFH = ∠EFH and ∠GHF = ∠EHF

Therefore, diagonal FH bisects angles EFG and EHG

3) Given that ΔEHF ≅ ΔGHF, we have;

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2 years ago

One number is 3 more than another number. if you add 12 to 4 times the first number, the result is 5 times the second number. Fi

aleksklad [387]

Answer:

first is -3, second number is 0

Step-by-step explanation:

you have two equations x+3=y and 4*x+12=5*y

Use the first one and write y in terms of x in the second equation:

4*x+12=5*(x+3)

4*x+12=5*x+15

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2 years ago

A data set lists earthquake depths. The summary statistics are nequals300, x overbarequals5.89 km, sequals4.44 km. Use a 0.01

kirza4 [7]

Answer:

Null hypothesis $H_0:\mu=5.00km$

Alternative hypothesis $H_1:\mu\neq 5.00km$

The p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

Step-by-step explanation:

It is given that a data set lists earthquake depths. The summary statistics are

$n=300$

$\overline{x}=5.89km$

$s=4.44km$

Level of significance = 0.01

We need to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 5.00.

Null hypothesis $H_0:\mu=5.00km$

Alternative hypothesis $H_1:\mu\neq 5.00km$

The formula for z-value is

$z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}$

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$z=\frac{0.89}{0.25634351952}$

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The p-value for z=3.4719 is 0.000517.

Since the p value is 0.000517, which is less than the significance level 0.01, therefore we reject the null hypothesis and conclude that population mean is not equal to 5.00.

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2 years ago