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3 years ago

Find the solution of this system of equations. Separate the x- and y-values with a comma. x = -11 + y and 10x - 5y = -10

1 answer:

6 0

Substitute x = -11 + y in 10x - 5y = -10
10(-11+y)-5y=10 distribute 10 with -11 and y
10(-11) + 10(y) - 5y=10 =>> -110 +10y -5y =10
combine like terms -110 +5y=10
add 110 to both sides to get the variable on one side 5y = 10+110 (120)
5y=120 divide both sides by 5 to get variable by itself 120/5=24
so y = 24
now replace the y with 24 to find x
x=-11+24 24 - 11 = 13
x=13
therefore, y=24 and x=13
hope this helps :)

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Find the distance between the points J( – 8,0) and K(1, 4).

Ksenya-84 [330]

Answer:

The answer is

$\sqrt{97} \: \: units$

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} }$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

J( – 8,0) and K(1, 4)

The distance between them is

$|JK| = \sqrt{ ({ - 8 - 1})^{2} + ({0 - 4})^{2} } \\ = \sqrt{ ({ - 9})^{2} + ( { - 4})^{2} } \\ = \sqrt{81 + 16} \\$

We have the final answer as

$\sqrt{97} \: \: \: units$

Hope this helps you

4 0

3 years ago

8 times the sum of a number and 26 is less than 304.

Jlenok [28]

Answer:

x < 12

Step-by-step explanation:

So 8 times the sum of a number and 26 is less than 304. To find the number, lets write a equation where the "number" is x.
8 times the sum of a number and 26 can be written as 8 * x+26, however since the sum of x and 26 are being multiplied, we write this as 8(x+26). Since 8 times the sum of a number and 26 is less than 304, we set 8(x+26) to < 304. This gives us our equation:

8(x+26) < 304

Lets start to solve for x by dividing by 8, giving us:

x+26 < 38

Now lets isolate x by subtracting 26 from both sides, which gives us our answer:

x < 12

So x is less than 12.

Hope this helps!

7 0

1 year ago

The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a

AlekseyPX

Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal( $\mu=460,\sigma^{2} =40^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 460 seconds

$\sigma$ = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

P(X > x) = 0.10 {where x is the required time which boy need to beat}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-460}{40}$ ) = 0.10

P(Z > $\frac{x-460}{40}$ ) = 0.10

So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;

$\frac{x-460}{40} =1.2816$

${x-460}{} =1.2816\times 40$

$x$ = 460 + 51.264 = 511.264 seconds

Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

8 0

3 years ago

A and B are independent events. P(A) = 0.40 P(B) = 0.30 What is P(A/B)

Lelechka [254]

Answer: Hello mate!

Two independent events, mean that the fact that, if the event A occurred, this has no effect in the probability of the event B to occur after.

For example, a coin flip.

The first result has no effect on the next result.

Then the notation P(A/B) is the probability of the event A when the event B occurred before, but as we know, the fact that the event B occurred before has no effect in it; so:

P(A/B) = P(A) = 0.30

6 0

3 years ago

Read 2 more answers

The product of six and the sum of a number and two had the same value as two less than the product of the same number and twenty

Minchanka [31]

<h3>The value of the unknown number is equal to 1.</h3>

6(x + 2) = 20x - 2

Distributive property.

6x + 12 = 20x - 2

Subtract 6x from both sides.

12 = 14x - 2

Add 2 to both sides.

14 = 14x

Divide both sides by 14.

x = 1

8 0

3 years ago