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2 years ago

What does y equal in 30+6y=7(y+6)-5

Mathematics

1 answer:

kirill [66]2 years ago

3 0

Answer:

y=-37

Step-by-step explanation:

0+6y=7(y+6)-5

0+6y=7y+42-5

6y=7y+37

-1y=37

y=-37

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If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n

andriy [413]

Answer: E. Greater than 10

Step-by-step explanation:

First, know that number to the left of a number line are negative and the square of any negative number will be positive and a perfect square.

Since the square of the unknown number is less than 1/100 i.e 0.01 then the possible unknown number 'n' can be -0.01 itself, of which the square of -0.01 will give us 0.0001 (1/10,000) i.e a value less than 0.01.

The reciprocal of 1/10000 is 10,000 which is a value greater than 10.

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2 years ago

given that 8-sqrt(18) over sqrt(2) = a + b sqrt(2) where a and b are integers find the value of a and b

Novay_Z [31]

Answer:

a = - 3 and b = 4

Step-by-step explanation:

Given

$\frac{8-\sqrt{18} }{\sqrt{2} }$

Simplify $\sqrt{18}$

= $\sqrt{9(2)}$ = $\sqrt{9}$ × $\sqrt{2}$ = 3 $\sqrt{2}$

Thus expression can be written as

$\frac{8-3\sqrt{2} }{\sqrt{2} }$

Multiply numerator/denominator by $\sqrt{2}$

noting that $\sqrt{2}$ × $\sqrt{2}$ = 2

= $\frac{\sqrt{2}(8-3\sqrt{2}) }{\sqrt{2}(\sqrt{2}) }$

= $\frac{8\sqrt{2}-6 }{2}$

Dividing each term on the numerator by 2

= 4 $\sqrt{2}$ - 3

= - 3 + 4 $\sqrt{2}$

with a = - 3 and b = 4

6 0

2 years ago

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cConsider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number,

quester [9]

Expected value = -1(1/6) + 2(1/6) + 3(1/6) - 4(1/6) + 5(1/6) - 6(1/6) = -1/6 + 2/6 + 3/6 - 4/6 + 5/6 - 6/6 = -1/6 = -0.167

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2 years ago

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Given 11, 12, and 16 as the three

Kazeer [188]

Answer:

It is an acute triangle because all the angles are less than 90 degrees.

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2 years ago

Find the length of line segment UV.

pshichka [43]

Answer:

The length of the line segment UV is 76 units

Step-by-step explanation:

In a triangle, the line segment joining the mid-points of two sides is parallel to the third side and equal to half its length

In Δ ONT

∵ U is the mid-point of ON

∵ V is the mid-point of TN

→ That means UV is joining the mid-points of two sides

∴ UV // OT

∴ UV = $\frac{1}{2}$ OT

∵ UV = 7x - 8

∵ OT = 12x + 8

∴ 7x - 8 = $\frac{1}{2}$ (12x + 8)

→ Multiply the bracket by $\frac{1}{2}$

∵ $\frac{1}{2}$ (12x + 8) = $\frac{1}{2}$ (12x) + $\frac{1}{2}$ (8) = 6x + 4

∴ 7x - 8 = 6x + 4

→ Add 8 to both sides

∴ 7x - 8 + 8 = 6x + 4 + 8

∴ 7x = 6x + 12

→ Subtract 6x from both sides

∴ 7x - 6x = 6x - 6x + 12

∴ x = 12

→ Substitute the value of x in the expression of UV to find it

∵ UV = 7(12) - 8 = 84 - 8

∴ UV = 76

∴ The length of the line segment UV is 76 units

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2 years ago