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gladu [14]
3 years ago
8

2. A set of two or more linear equations that contain the same variable(s) is an)_ ?

Mathematics
1 answer:
Illusion [34]3 years ago
8 0

Answer:

It is called a linear system. :)

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An architect is designing square windows with an area of(x2 + 16x +64) ft?. The dimensions of the
Darina [25.2K]

A) The dimensions are (x+10) by (x+10).

B) The perimeter is given by 4x+40.

C) The perimeter when x is 4 is 56.

The quadratic can be factored by finding factors of c, the constant, that sum to b, the coefficient of x.  Our c is 100 and our b is 20; we want factors of 100 that sum to 20.  10*10=100 and 10+10=20, so those are what we need.  This gives us (x+10)(x+10 for the factored form.  

Since the dimensions are all (x+10), and there are 4 sides, the perimeter is given by 4(x+10).  Using the distributive property we have 4*x+4*10=4x+40.

To find the perimeter when x=4, substitute 4 into our perimeter expression:

4*4+40=16+40=56.

6 0
2 years ago
Read 2 more answers
There are 20 guest at a party. The hody has 8 gallons of punch . He estimates that each guest will drink 2 cups of punch. If his
GuDViN [60]

Answer:

At the end of the party <u>5.5 gallons or 88 cups</u> of punch will be leftover.

Step-by-step explanation:

Given:

There are 20 guest at a party.

Now, to find the quantity of punch that will be leftover.

Number of guests = 20.

Total gallons of punch = 8.

Now, using conversion factor we change gallons into cups:

1 gallon = 16 cup.

So, 8 gallons = 16 × 8 = 128 cups.

<u><em>Thus, total cups of punch = 128.</em></u>

Total number of cups each guest will drink = 2.

Now, to get total number of cups the 20 guests will drink by multiplying:

20\times 2

=40\ cups.

<u><em>Total number of cups the 20 guests will drink = 40.</em></u>

So, to get the leftover punch we subtract the total number of cups the 20 guests will drink from total cups of punch:

128-40\\\\=88\ cups.

So, 88 cups = 88\div 16=5.5\ gallons.

Therefore, at the end of the party 5.5 gallons or 88 cups of punch will be leftover.

3 0
3 years ago
Read 2 more answers
The angle measures 30°, 60°, 120°, and 150° are written on
GREYUIT [131]
Therefore the probability that the angle measure are supplementary are:120,60
8 0
3 years ago
I’ll mark you brainliest, please show work!! i’ll also give more points
Nimfa-mama [501]

Answer:

414

Step-by-step explanation

80+10hrs=230

23bacteria:1hr

414bacteria:18hrs

4 0
3 years ago
Read 2 more answers
HELP PLS Given a polynomial function f(x), describe the effects on the Y-intercept, regions where the graph is increasing and de
Mashcka [7]
1. Remarks:

f(x) to f(x)-3 is the whole graph of f(x), shifted 3 units down. 

f(x) to -2f(x): 

The effect of "multiplication by -" is that the whole graph is reflected with respect to the x axis, so it is turned upside down.
 
The effect of "multiplication by 2" is that every point is "stretched vertically by a factor of 2" . So for example the point (-1, -4) in the original function, becomes (-1, -8) in the second one. Or (2, 5) would become (2, 10). 

The only points that do not change (are not streched vertically) are the roots. For example if (4,0) is an x-intercept (a root) in the original function, (4,0) is still a root in the second one because  2 times 0 is still 0.


2. Consider the polynomial function of degree n: 

f(x)= a_{n} x^{n} +a_{n-1} x^{n-1}+....+a_{2} x^{2}+a_{1} x^{1}+a_{0}

a. Y-intercept

The y - intercept is the value of the polynomial function at x=0. 
So it is f(0)=a_{0}, that is, the constant term of f(x)

in f(x)-3 the y intercept is shifted 3 units down as any other point, so it becomes  a_{0}-3

In -2f(x), the y-intercept a_{0} becomes -2a_{0}

b. Regions of f decreasing or increasing

f(x)-3 is f(x) just shifted down 3 units, so they are both increasing and decreasing in the same intervals of x

-2f(x) is f(x) turned upside down, so -2f(x) is increasing in all intervals f(x) is decreasing and it is decreasing in all intervals f(x) is increasing.

c. End behaviors

By now it is clear that end behaviors of f(x) and f(x)-3 are same, and f(x) with -2f(x) are opposite

d. Evenness, oddness

If f(x) is even, then f(x)=f(-x)

Let g(x)=f(x)-3

g(x)=f(x)-3=f(-x)-3=g(-3), so in this case f(x)-3 is even

If f(x) is odd, then f(-x)=-f(x)

g(x)=f(x)-3=-f(-x)-3,

so -g(x)=f(-x)+3

g(-x)=f(-x)-3,  

so g(-x) is not equal to -g(x). Which means f(x)-3 is not odd if f(x) is


Consider f(x)=-2f(x)

If f(x) is even, f(x)=f(-x)

g(x)=-2f(x)=-2f(-x)
g(-x)=-2f(-x)

So g(x)=g(-x), which means -2f(x) is even if f(x) is even

If f(x) is odd, f(x)=-f(-x)

let g(x)=-2f(x)=-2(-f(-x))=2f(-x)

g(-x)=-2f(-x)=-2(-f(x))=2f(x)

so g(-x) is not equal to -g(x), thus -2f(x) is not odd if f(x) is odd.

The conclusions about oddness and evenness can be also derived from the discussions about the graphs.
 

6 0
3 years ago
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