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3 years ago

rhombus CDEF is shown below. If the slope of FC is 25, what must be the slope of CD in order for CDEF to be a square?

Mathematics

1 answer:

Andrew [12]3 years ago

8 0

Answer:

$-\dfrac{1}{25}$

Step-by-step explanation:

Given the rhombus CDEF, sides FC and CD are adjacent sides.

Using coordinate geometry, to proof that a quadrilateral is a square, with regards to the slope, the slope of adjacent segments must be negative reciprocals.

In fact, by definition: Two lines with slopes $m_1$ and m_2$ are perpendicular if:

$m_1=-\dfrac{1}{m_2}$

Therefore if :

FC and CD are adjacent segments
Slope of FC=25

For the rhombus to be a square:

Slope of CD $=-\dfrac{1}{25}$

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3 years ago

What is the length of the hypotenuse? 24 42

AleksAgata [21]

Answer:

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem or a^2+b^2=c^2.

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Step-by-step explanation:

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2 years ago

Read 2 more answers

10. 10. If AB bisects CAF, and m<EAF = 72°, then the m<BAF =

never [62]

The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

m∠EAF = 72° and AB bisects ∠CAF.

∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

If two lines are intersecting, then vertically opposite angles are congruent.

∠DAC ≅ ∠EAF

m∠DAC = 72°

Sum of the adjacent angles in a straight line = 180°

m∠DAE + m∠EAF = 180°

m∠DAE + 72° = 180°

Subtract 72° from both sides.

m∠DAE = 108°

∠CAF and ∠DAE are vertically opposite angles.

⇒ m∠CAF = m∠DAE

⇒ m∠CAF = 108°

AB bisects ∠CAF means ∠CAB = ∠BAF

m∠CAB + m∠BAF = 108°

m∠BAF + m∠BAF = 108°

2 m∠BAF = 108°

Divide by 2 on both sides, we get

m∠BAF = 54°

Hence the measure of ∠BAF is 54°.

4 0

3 years ago

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work pro

olchik [2.2K]

Answer:

0.756

Step-by-step explanation:

It is given that a machine has four components, A, B, C, and D.

$P(A)=P(B)=0.93, P(C)=0.95,P(D)=0.92$

If these components set up in such a manner that all four parts must work for the machine to work properly.

We need to find the probability that the machine works properly. It means we have to find the value of $P(A\cap B\cap C\cap D)$ .

If two events X and Y are independent, then

$P(X\cap Y)=P(X)\times P(Y)$

Assume the probability of one part working does not depend on the functionality of any of the other parts.

$P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)$

Substitute the given values.

$P(A\cap B\cap C\cap D)=0.93\times 0.93\times 0.95\times 0.92$

$P(A\cap B\cap C\cap D)=0.7559226$

$P(A\cap B\cap C\cap D)\approx 0.756$

Therefore, the probability that the machine works properly is 0.756.

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3 years ago

When multiplying two polynomials of degrees m and n, will the product be a polynomial? If so, explain, and state the degree.

vfiekz [6]

Yes.
The degree will be m+n

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3 years ago