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astra-53 [7]
2 years ago
8

The linear equation y = −5x − 18 is written in which form?

Mathematics
1 answer:
Savatey [412]2 years ago
8 0
It’s written in slope intercept form .
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A carpenter has at most $250 to spend on lumber the inequality 8x+12y<250 represents the numbers x of 2 by 8 boards and the n
malfutka [58]

Answer:

The carpenter will not be able to buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

Step-by-step explanation:

Given:

Amount a carpenter can spend at most = $250

The inequality to represent the amount he can spend on each type of board is given as:

8x+12y

where x represents  '2 by 8 boards' and y represents '4 by 4 boards'.

To determine whether the carpenter can buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

Solution :

In order to check whether the carpenter can buy 12  '2 by 8 boards' and 14 '4 by 4 boards' ,  we need to plugin the x=12 and y=14 in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.

Plugging in  x=12 and y=14 in the given inequality

8(12)+12(14)

96+168

264

The above statement can never be true and hence the carpenter will not be able to buy 12  '2 by 8 boards' and 14 '4 by 4 boards'.

6 0
3 years ago
A javelin thrower is running at 7mph and throws her javelin at 18mph at an angle of 13o with the horizontal. Determine the resul
RUDIKE [14]
Will I get any points?
5 0
2 years ago
Helppppppppppppppppp
weqwewe [10]

Answer:

16.

Step-by-step explanation:

What does 75% Off mean? It means 75% of the price is subtracted. So find 75% of 64.

Here is our equation: 75/100 x 64 = 48.

So 48 dollars is going to be subtracted from 64, which gives us 64-48=16.

So the price of the wedding cake during the sale is 16.

3 0
3 years ago
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit
Virty [35]
Hence it is a simply rearrangement of the equation to start with, in order to make  the subject:






This is the graph in 'slope-intercept' form. From here it is easy to see that gradient  = and that y-intercept = 490.

The easiest way to draw a straight-line graph, such as this one, is to plot the y-intercept, in this case (0, 490), then plot another point either side of it at a fair distance (for example substitute  = -5 and  = 5 to procure two more sets of co-ordinates). These can be joined up with a straight line to form a section of the graph, which would otherwise extend infinitely either side - use the specified range in the question for x-values, and do not exceed it (clearly here the limit of -values is 0 ≤ x ≤ 735, since neither x nor y can be negative within the context of the question - the upper limit was found by substituting  = 0).

In function notation, the graph is:



The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.

When the profit is higher, the gradient is not changed (this is defined by the relationship between the $2 and $3 prices, not the overall profit) - instead the -intercept is higher:






Therefore we have gleaned that the new y-intercept is.

Clearly I cannot see the third straight line. However the method for finding the equation of a straight line graph is fairly simple:

1. Select two points on the line and write down their coordinates
2. The gradient of the line = 
3. Find the change in  (Δ
4. Find the change in  (Δ
5. Divide the result of stage 3 by the result of stage 4
6. This is your gradient
7. Take one of your sets of coordinates, and arrange them in the form , where your  is the gradient you just calculated
8. There is only one variable left, which is  (the y-intercept). Simply solve for this
9. Now generalise the equation, in the form , by inputting your gradient and y-intercept whilst leaving the coordinates as  and 

For example if the two points were (1, 9) and (4, 6):

Δ = 6 - 9 = -3
Δ = 4 - 1 = 3
 =  = -1
I choose the point (4, 6)
6 = (-1 * 4) + c
6 = c - 4
c = 10
Therefore, generally, 

Within the context of the question, I imagine the prices of the two lunch specials will be the same in the third month and hence the gradient will still be  - this means steps 1-6 can be omitted. Furthermore if the axes are clearly labelled, you may even be able to just read off the y-intercept and hence dispose with steps 1-8!
5 0
3 years ago
A shade of yellow light with a wavelength of 5.8×10-7 m and a frequency of 5.17 × 10-14 Hz
harina [27]

Step-by-step explanation:

We have,

The wavelength of yellow light, \lambda=5.8\times 10^{-7}\ m

Frequency of yellow light, f=5.17\times 10^{-14}\ Hz

It is assumed to find the speed of light in the yellow light.

The speed of a wave is given in terms of wavelength and frequency as :

v=f\lambda\\\\v=5.17\times 10^{-14}\times 5.8\times 10^{-7}\\\\v=2.99\times 10^{-20}\ m/s

So, the speed of light in a shade of yellow light is 2.99\times 10^{-20}\ m/s.

4 0
3 years ago
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