Lauren owns a sign company. She borrows $75 000 to purchase a laser engraver. The

Response:

We define a line L.

In a two-dimensional space, a line can be expressed as follows:

y = a*x + b

where 'a' denotes the slope and 'b' represents the y-intercept.

To determine the slope for a line passing through points (x1, y1) and (x2, y2), the formula is:

a = (y2 - y1)/(x2 - x1).

Using one of these points will help to find the value of 'b'.

Once we have the line's equation:

y = a*x + b

we can substitute in a specific point (x, y)

to verify if the equation holds true. If it does, that point lies on the line L.

Response:

6.48

Detailed explanation:

The calculation required to determine the number of tiles for the border is presented below:-

Here,

The length measures 2.02 m

And the width is 1.22

Substituting these dimensions into the formula provided above

Consequently, the total number of tiles necessary to create the border is

= 6.48

Hence, to find the tiles required for the border, we utilized the aforementioned formula.

Response:

Step-by-step explanation:

Assuming there are 100 sour candies, thus-  

since 26% of the candies are grape, it follows that 26% of 100 candies means we have 26 grape candies

Consequently, the remaining candies that are not grape amount to 100-26 = 74

Applying the multiplication principle:

P(A ∩ B) = P(A)/ P(B|A)  

 Initially, there are 26 grape candies, therefore the probability of selecting the first grape candy =  26C1 = 26

 After choosing the first one, we put the selected grape candy back, so there are still 100 candies total P(B|A) = 100C3 = 100 x 99 x 98 x 97!/3! X 97!

= 50 x 33 x 98

Thus, the probability becomes 1/ 50 x 33 x 98 x 26

= 1/4204200

I'm quite terrible at this aspect, so I'm merely making a guess.
X serves as the variable while x denotes the multiplication symbol.
X + (X x 3 - 1) + (X x 3 - 1) - 4) <span>≥ 45 is the outcome I arrived at.
The solution to that inequality is
X </span><span>≥ 7, I suppose.</span>

Answer:

A. Combining one pound of pistachios with one pound of almonds costs $20.

C. Decreasing the almond quantity by one pound leads to a total price of $40.

E. The price p (in dollars) per pound of pistachios is represented by the equation 2p + 3(p – 4) = 48.

Step-by-step explanation:

Let:

x = cost per pound of pistachios

y = cost per pound of almonds

We know that

x = y + 4 (Equation A)

2x + 3y = 48 (Equation B)

Substitute x from Equation A into Equation B:

2(y + 4) + 3y = 48

2y + 8 + 3y = 48

5y = 48 – 8

y = 8

Find x:

x = 8 + 4 = 12

Therefore, pistachios cost $12 per pound and almonds cost $8 per pound.

Verify the statements:

Case A) One pound of each equals $20.

True, since 12 + 8 = 20.

Case B) Pistachios cost twice as much as almonds.

False, because 2 × 8 = $16 ≠ $12.

Case C) Reducing almond pounds by 1 yields $40 total.

True, as 2(12) + 2(8) = 24 +16 = 40.

Case D) The almond cost modeled by 2(a – 4) + 3a = 48.

False; it should be 2(a + 4) + 3a = 48.

Case E) The pistachio cost modeled by 2p + 3(p – 4) = 48.

True, since p = a + 4 implies a = p – 4.