Which answer describes the restrictions for the variables x+1/x-4?

Answers

Answer 1

Answer: The restriction for this is that x ≠ 4. This is because 4 - 4 = 0, and you cannot divide by zero.

An alternative way of writing this (interval notation) is (-∞, 4)U(4, ∞).

Hope this helps!

Answer 2

Answer: Hey there

The restrictions for the variables x+1/x-4 is x ≠ 4.

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Express
$2 ^( - 7)$
using a positive exponent.

Answers

Answer:

$(1)/(2^7)$

Step-by-step explanation:

To express the number 2⁻⁷ with a positive exponent, we'll make use of the properties of exponents and their relationship with reciprocals.

$\hrulefill$

Here's a list of the exponent properties:

$\boxed{\left\begin{array}{ccc}\text{\underline{Properties of Exponents:}}\n\n1.\ a^0=1\n\n2.\ a^m * a^n=a^(m+n)\n\n3.\ a^m / a^n \ ((a^m)/(a^n) )=a^(m-n)\n\n4.\ (ab)^m=a^mb^m\n\n5.\ (a/b)^m=a^m/b^m\n\n6.\ (a^m)^n=a^(mn)\n\n7.\ a^(-m)=1/a^m\n\n8.\ a^(m/n)=(\sqrt[n]{a} )^m\end{array}\right}$

In our case, we will use the reciprocal identity (#7 on the table above).

$a^(-m)=(1)/(a^m) \n\n\n\n\therefore 2^(-7)=\boxed{(1)/(2^7) }$

Thus, we can represent 2⁻⁷ as a positive exponent .

Which one is greater 2.857 or 2.87

Answers

Answer:

2.87

Step-by-step explanation:

How to solve these question?

Answers

1a) Time = Distance/Speed

t= 20/x seconds

b) d=25m
s= x+0.5 m/s
t= d/s = 25/x+0.5

c) total time = 6 seconds
therefore, 20/x + 25/x+0.5 = 6
make a common denominator of x(x+0.5):

(20(x+0.5) + 25x)/x(x+0.5) = 6
move the demoninator to the other side, and expand to form:

20x+10+25x = 6x(x+0.5)
45x+10= 6x^2 +3x
tidying it up (moving everything to one side)
6x^2 - 42x-10 = 0
divide everything by 2
3x^2-21x-5= 0 (as required)

d) use quadratic formula to solve

e) therefore, what does x equal?

hope this helps

The area of triangle ABC is 24 square centimeters. If4 cm
8 cm
16 cm
32 cm

Answers

None of the above options are true for the given area of triangle.

The area of Triangle ABC will be 27.71 if the triangle is equilateral and length of its one side is 8 cm.

Henry has 3 black shirts and 7 blue shirts in his wardrobe. Two shirts are drawn without replacement from the wardrobe. What is the probability that both of the shirts are black?

Answers

Answer:

The probability that both of the shirts are black is $(1)/(15)$

Step-by-step explanation:

Given : Henry has 3 black shirts and 7 blue shirts in his wardrobe. Two shirts are drawn without replacement from the wardrobe.

To find : What is the probability that both of the shirts are black?

Solution :

Number of black shirts = 3

Number of blue shirt = 7

Total number shirts = 3+7=10

The probability that first shirts is black is $(3)/(10)$

Two shirts are drawn without replacement from the wardrobe.

Number of black shirt left = 2

Total shirts = 9

The probability that second shirts is black is $(2)/(9)$

So, The probability that both of the shirts are black is

$P=(3)/(10)*(2)/(9)$

$P=(6)/(90)$

$P=(1)/(15)$

Since there are three black shirts and 7 blue shirts, he has a 3/10 chance of picking a black.

Which theorem proves that the triangles are congruent?A. AAS
B. ASA
C. SAS
D. SSS

Answers

Answer:

SSS

Step-by-step explanation:

We are given that the triangle has all congruent sides therefore we can prove that the triangles are similar by the SSS theorem ( side - side - side )

Answer:

D. SSS

Step-by-step explanation:

SSS (Side-Side-Side) is a proof of congruence where two triangles share three sides.

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