2а +3Ь — 5 b = a

Number of solutions to a system of equations algebraic. How many solutions does the system have? Can someone help me please....

Svet_ta [14]

Answer:

A Exactly 1 solution

Step-by-step explanation:

if we express both equations as y = mx+b

we will see that both equations have different slopes (i.e "m" values are different).

By definition, 2 straight lines of different slopes will intersect at only one location (i.e there is only one solution)

8 0

3 years ago

Read 2 more answers

What is an equation of the line that passes through (-2,3) and is parallel to y=5x + 4.Give your answer in slope intercept form

9966 [12]

Answer:

y= 5x+13

Step-by-step explanation:

Slope- intercept form

y= mx +b, where m is the gradient and b is the y-intercept.

Parallel lines have the same gradient.

y= 5x +4

Gradient of given line= 5

Thus, gradient of line= 5

Subst. m=5 into the equation.

y= 5x +b

To find the value of b, substitute a coordinate

When x= -2, y=3,

3= 5(-2) +b

3= -10 +b

b= 3 +10 (+10 on both sides)

b= 13

Thus, the equation of the line is y= 5x +13.

8 0

3 years ago

a survey amony freshman at a certain university revealed that the number of hours spent studying the week before final exams was

Marat540 [252]

Answer:

Probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

Step-by-step explanation:

We are given that the number of hours spent studying the week before final exams was normally distributed with mean 25 and standard deviation 15.

A sample of 36 students was selected.

Let $\bar X$ = sample average time spent studying

The z-score probability distribution for sample mean is given by;

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

where, $\mu$ = population mean hours spent studying = 25 hours

$\sigma$ = standard deviation = 15 hours

n = sample of students = 36

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, Probability that the average time spent studying for the sample was between 29 and 30 hours studying is given by = P(29 hours < $\bar X$ < 30 hours)

P(29 hours < $\bar X$ < 30 hours) = P( $\bar X$ < 30 hours) - P( $\bar X$ $\leq$ 29 hours)

P( $\bar X$ < 30 hours) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ < $\frac{ 30-25}{\frac{15}{\sqrt{36} } }} }$ ) = P(Z < 2) = 0.97725

P( $\bar X$ $\leq$ 29 hours) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } }} }$ $\leq$ $\frac{ 29-25}{\frac{15}{\sqrt{36} } }} }$ ) = P(Z $\leq$ 1.60) = 0.94520

So, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2 and x = 1.60 in the z table which has an area of 0.97725 and 0.94520 respectively.

Therefore, P(29 hours < $\bar X$ < 30 hours) = 0.97725 - 0.94520 = 0.0321

Hence, the probability that the average time spent studying for the sample was between 29 and 30 hours studying is 0.0321.

7 0

3 years ago

What is the equation for the line of reflection a. x= 3 b. y = 3 c. y = x d. x = 6

Stells [14]

Answer:

The answer to that question is c. y = x

8 0

3 years ago

Find the measure of <2

Yakvenalex [24]

Answer:

96

Step-by-step explanation:

Hello There!

The following figure shown is a parallelogram

If you didn't know opposite interior angles of a parallelogram are congruent

Therefore the angle that has a measure of 96 degrees and the angle labeled 2 are congruent

hence ∠2=96

8 0

3 years ago

2а +3Ь — 5 b = a – 5