Find the sum. (- 7/2 z + 4) + (1/5 z - 15) HELPPP

Mathematics

1 answer:

Nonamiya [84]3 years ago

8 0

Answer:

-33/10z - 11

Step-by-step explanation:

since all of these terms are being added, there are no need for the parenthesis

-7/2z +4 + 1/5z -15

add like terms (to add the fractions, convert them to a common denominator)

-7/2z + 4 + 1/5z - 15

-35/10z + 2/10z - 11

-33/10z - 11

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Find the equation of the sphere passing through P(negative 4 comma 7 comma 6 )and Q(8 comma negative 3 comma 5 )with its center

Juli2301 [7.4K]

Answer: The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

Step-by-step explanation:

The centre of the sphere is the midpoint of the diameter, which is

1/2

[(-4,7,6) + (8,-3,5)] =(2,2,5/2)

The length of the diameter is

=sqrt |(8,-3,5) - (-4,7,6)|^2

=sqrt (12^2 + (-10)^2 + (-1)^2)

=sqrt (144+100+1)

=sqrt(245)

so the radius of

the sphere is:

1/2(sqrt(245)) = sqrt(245)/2.

The equation of the sphere is:

(x-2)^2 + (y-2)^2 + (z-5/2)^2 = sqrt(245)/2

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4 years ago

. Which category(s) does 75% belong? I. Real II. Whole III.Rational IV. Integer V. Irrational VI. Natural * A. III and IV only B

kifflom [539]

Answer: B.) 1 and 111 only.

Step-by-step explanation:

75% = 75/100 = 0.75

0.75 falls into the category of rational numbers. Rational numbers comprises of numbers which can be expressed in the form a/b where a and b are integers and B is not 0. Here, both 75 and 100 are integers, thus 75% is a rational number.

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All rational numbers and irrational numbers are REAL numbers, hence, 75% is a real number.

Natural numbers are whole digits starting from 1 e.g ( 1, 2, 3,......). Hence 75% is not a natural number

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Solve -np-80<60 for n. Show your work.<br><br> Solve 2a-5d=30 for d. Show your work.

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$-np-80 < 60\qquad\text{change the signs}\\\\np+80$

------------------------------------------------------

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