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3 years ago

Y=2x+3 y=3x+1 solve the system of equations using substitution

Mathematics

2 answers:

marishachu [46]3 years ago

7 0

Answer:

x= 2 and y= 7

Step-by-step explanation:

Substitution method involves getting value of one variable from one equation in terms of other variable and putting this in second equation to eliminate and find value of other variable.

Here we have

y=2x + 3

in first equation and putting this in second equation, we get

2x + 3 = 3x + 1 or

2x - 3x = 1 -3 or

-x = -2

i.e.

x = 2

Putting this Vale of x back in first equation, we get

y = 2 × 2 + 3 = 7

Hence we get x = 2 and y = 7.

Lynna [10]3 years ago

4 0

Answer:

(2, 7 )

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = 3x + 1 → (2)

Substitute y = 3x + 1 into (1)

3x + 1 = 2x + 3 ( subtract 2x from both sides )

x + 1 = 3 ( subtract 1 from both sides )

x = 2

Substitute x = 2 into either of the 2 equations for corresponding value of y

Substituting x = 2 into (1)

y = 2(2) + 3 = 4 + 3 = 7

Solution is (2, 7 )

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Tresset [83]

$513 (amount earned) / 54 (amount of hours) = $9.50 (hourly rate)

to check:
$9.50 (hourly rate) x 54 (amount of hours)
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hope this helps :)

6 0

4 years ago

Find the number of ways to listen to four CDs from a selection of eight CDs.

anzhelika [568]

Answer:

8C4=8!(8−4)!4!=70

Explanation:

This is equivalent to choosing 4 from an available 8 and is hence the combination

8C4=8!(8−4)!4!=70

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3 years ago

Which polynomial is a perfect square trinomial?

Levart [38]

Answer:

$\large\boxed{16x^2-24x+9=(4x-3)^2}$

Step-by-step explanation:

$\text{Perfect square:}\ (a-b)^2=a^2-2ab+b^2\\=======================\\\\25x^2-20x-16\to\text{NOT. Because is}\ -16=-4^2\\\\9a^2-30a-25\to\text{NOT. Because is}\ -25=-5^2\\\\25b^2-15b+9=(5b)^2-2(5b)\left(\dfrac{3}{2}\right)+3^2\to\text{NOT. Because is}\ b=\dfrac{3}{2}\ \text{and}\ b^2=3^2\\\\16x^2-24x+9=(4x)^2-2(4x)(3)+3^2=(4x-3)^2\ \boxed{YES\ :)}$

8 0

3 years 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