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3 years ago

Pls help with this question please

Mathematics

1 answer:

Marina86 [1]3 years ago

5 0

Answer:

$x=8$

Step-by-step explanation:

<h3>Given:-</h3>

$RS=28$

$RT=3x+4$

Solve for x.

<h3>According to question:-</h3>

[Tangent of same circle are equal]

$=>3x+4=28$

$=>3x=28-4$

$=>3x=24$

$=>x=\frac{24}{3}$

<h3>The value of x is 8.</h3>

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Bethany needs to solve the equation -x^2 + 4x = x - 4.

notsponge [240]

Answer:

The system of equations she could write is:

y = -x² + 4x

y = x - 4

The solutions are (-1 , -5) and (4 , 0)

Step-by-step explanation:

-x² + 4x = x - 4

That means two equations one quadratic which is in the left hand side and the other is linear which is in the right hand side.

They represented graphically by a parabola and a line, the solution of it will be the points of intersection of the two graphs

To find the system of equations take each side and equate it by y

∵ y = -x² + 4x

∵ y = x - 4

∴ The system of equations is:

y = -x² + 4x

y = x - 4

Let us solve this system using -x² + 4x = x - 4

∵ -x² + 4x = x - 4

- Subtract x from both sides

∴ -x² + 3x = -4

- Add 4 to both sides

∴ -x² + 3x + 4 = 0

- Multiply both sides by -1

∴ x² - 3x - 4 = 0

Let us use the factorization to solve it

∵ x² = (x)(x)

∵ -4 = (1)(-4)

∵ (x)(1) = x

∵ (x)(-4) = -4x

∵ x + -4x = - 3x ⇒ middle term

∴ The factors of x² - 3x - 4 are (x + 1)(x - 4)

- Substitute x² - 3x - 4 by its factors

∴ (x + 1)(x - 4) = 0

Equate each factor by 0 to find the values of x

∵ x + 1 = 0

- Subtract 1 from both sides

∴ x = -1

∵ x - 4 = 0

- Add 4 to both sides

∴ x = 4

Substitute the values of x in the equation y = x - 4 to find y

∵ y = -1 - 4

∴ y = -5

∵ y = 4 - 4

∴ y = 0

The solutions are (-1 , -5) and (4 , 0)

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3 years ago

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Answer:

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3 years ago

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Snezhnost [94]

Answer:

0.2941 = 29.41% probability that it was manufactured during the first shift.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured during the first shift.

Probability of a defective item:

1% of 50%(first shift)

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Probability of a defective item being produced on the first shift:

1% of 50%. So

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$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.005}{0.017} = 0.2941$

0.2941 = 29.41% probability that it was manufactured during the first shift.

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3 years ago