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2 years ago

Solve by factoring or finding square roots.

Mathematics

1 answer:

Sonja [21]2 years ago

3 0

Answer:

$\large{\textbf{x = 0, 3}\\}$

Step-by-step explanation:

$\large{\textup{Given}:\\$5x^2 = 15x$\\$\implies 5x^2 - 15x = 0$\\\textup{Taking $x$ common outside, we get:}\\$x\{5x - 15 \} = 0$\\\textup{Then we have two possibilities for $x $}\\$i.e., x = 0$ \hspace{5mm} \textup{or} \hspace{5mm} $5x - 15 = 0 \implies x = 3$\\$$\therefore x = 0, 3 $$}$

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Given quadrilateral EFGH at e(-4,7) f(8,4) G(t,-5) and h(-7,-1) using coordinate geometry prove EFGH is a rectangle

Tcecarenko [31]

The above question was not properly written.

Complete Question

Given quadrilateral EFGH with vertices at E(-4,8), F(8,4), G(5,-5) and H(-7,-1), prove using coordinate geometry that EFGH is a rectangle.

Answer:

Quadrilateral EFGH is a rectangle.l because:

EF = GH and FG = EH

Step-by-step explanation:

The formula for coordinate geometry is given as :

√(x2 - x1)² + (y2 - y1)² when we have coordinates: (x1, y1) and (x2 , y2)

For the quadrilateral EFGH with given coordinates above to be a rectangle,

EF = GH

FG = EH

Hence:

For side EF

E(-4,8), F(8,4)

= √(8 - (-4))² + (4 - 8)²

= √12² + -4²

= √144 + 16

= √160 units

For side FG

F(8,4), G(5,-5)

=√(5 - 8)² + (-5 - 4)²

= √-3² + -9²

= √9 + 81

= √90 units

For Side GH

G(5,-5) , H(-7,-1)

= √(-7 - 5)² + (-1 - (-5))²

= √-12² + 4²

= √144 + 16

= √160 units

For side EH

E(-4,8), H(-7,-1)

= √(-7 -(-4))² +(-1 - 8)²

= √-3² + -9²

= √9 + 81

= √90 units

From the above calculation, we can see that truly,

EF = GH

FG = EH

Therefore, quadrilateral EFGH is a rectangle.

6 0

2 years ago

The planet Venus has a mass of 4.869 ∙ 1024 kilograms. Use scientific notation to express the planet’s mass in milligrams. 1 kil

Ostrovityanka [42]

To do this you need to multiple 1,024 by 1,000,000 to get 1,024,000,000 and then convert it to scientific notation. For that you need to know how many places there are after the first number. In this case it is 9. This will be 1.024 x 10^9. You have to remember that it is to the power of however many numbers are after the first. So even though we show 3 digits after the . we still have to include those in the power.

7 0

3 years ago

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For safety reasons, 4 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills

Evgen [1.6K]

Answer:

99.93%

Step-by-step explanation:

Probability of Independent Events

Given the probability of success of each detector is 0.84 independently of the others, their combined success/failure probability can be computed with the product rule.

We can calculate the required probability by using the binomial distribution, but it's easier to calculate the probability of the negated event an subtract from 1.

We want to know the probability that a least one of the 4 systems detects the occurrence of theft. That probability is the sum of the probabilities that one of them, two of them, three of them or all of them succeed. The negated event is that NONE of them actually detects the theft. Being p the individual probability of success, p=0.84. Being q the probability of failure, q=0.16.

The probability that none of the systems detect the theft is

$P(0)=q^4=0.16^4=0.00065536$

Thus, the probability that at least one of the systems detect the theft is

$P(x\geq1)=1-P(0)=1-0.00065536=0.9993$

That means a 99.93%

3 0

2 years ago

frank rented a truck for one day. There was a base fee of 14.95, and there was an additional charge of 78 cents for each mile dr

Gemiola [76]

Answer : 153 miles

Explanation : first take 134.29 & subtract the 14.95 base fee which give you 119.34 . now divide 119.34 by 78 which gives you 1.53. so he drove 153 miles.
equation : 14.95+ 0.78x = 134.29 . to double check just multiply 153 x 0.78 and add $14.95 which gives us the total of $134.29

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2 years ago

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Does someone know this ??

Misha Larkins [42]

The scale factor is 1/5

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2 years ago

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