This week Laura worked 40 hours regular time and 3 hours overtime. If she

The solution of a system of linear equations is where the two lines intersect....

olchik [2.2K]

Answer:

True

Step-by-step explanation:

The place where lines intersect is where the x and y values match up.

Just like this, if the lines do not intersect, there's no solution.

If the lines seem to be one line, there is all real number solutions.

Hope this helped!

5 0

3 years ago

Read 2 more answers

Would the scale factor 4.2 enlarge,reduce,or preserve

Juli2301 [7.4K]

Hey there! I'm happy to help!

Let's look at what scale factors would be able to enlarge, reduce, and preserve first. We will use the point (1,1) as an example.

ENLARGE

When we talk about scale factors, both of our numbers of the ordered pair will be multiplied by that number. To make it bigger, we will multiply it by anything larger than a one, we could have a scale factor such as 2, 100, 579395. etc.!

Dilation of 2

(1,1)⇒(2,2)

REDUCE

To reduce our ordered pair, our scale factor must be a number greater than zero but less than one because it cannot switch quadrants, which is what would happen if we used negative numbers. Our reduced number must be greater than zero. We can use 1/2, 1/4, 1/100, 0.67 etc.

Dilation of 1/2

(1,1)⇒(0.5,0.5)

PRESERVE

What would we multiply an ordered pair by to make it stay the same? One of course! This is the only number that will keep it the same!

Dilation of 1

(1,1)⇒(1,1)

Now, let's think of any scale factor as X and see what rules it has to follow to be enlarging, reducing, or preserving.

ENLARGING SCALE FACTOR: X>1

REDUCING SCALE FACTOR: 0<X<1

PRESERVING SCALE FACTOR: X=1

So, where does 4.2 fall? Well, as you can see, 4.2 is greater than one, so this scale factor would make our point larger.

Therefore, 4.2 would enlarge.

I hope that this helps! Have a wonderful day!

8 0

3 years ago

Write the equation of the line.

Oksana_A [137]

Y = 1/3x - 2.
If you sub in 0, you’ll get (0, -2) which is the y intercept.

4 0

3 years ago

Read 2 more answers

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

-------------

Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

-------------

Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

-------------

Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

------------------------------

Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

6 0

1 year ago

Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the

Black_prince [1.1K]

Answer:

a) P(2)=0.270

b) P(X>3)=0.605

c) P=0.410

Step-by-step explanation:

We know that customers arrive at a grocery store at an average of 2.1 per minute. We use the Poisson distribution:

$\boxed{P(k)=\frac{\lambda^k \cdot e^{-\lambda}}{k!}}$

a) In this case: $\lambda=2.1$

$P(2)=\frac{2.1^2 \cdot e^{-2.1}}{2}\\\\P(2)=0.270$

Therefore, the probability is P(2)=0.270.

b) In this case: $\lambda=2\cdot 2.1=4.2$

$P(X>3)=1-P(X\leq 3)\\\\P(X>3)=1-\sum_{x=0}^3 \frac{4.2^x \cdot e^{-4.2}}{x!}\\\\P(X>3)=1-0.395\\\\P(X>3)=0.605$

Therefore, the probability is P(X>3)=0.605.

c) We know that two customers came in in the first minute. That is why we calculate the probability of at least 5 customers entering the other 2 minutes.

In this case: $\lambda=2\cdot 2.1=4.2$

$P(X\geq 5)=1-P(X$

Therefore, the probability is P=0.410.

4 0

3 years ago