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1 year ago

Find the intercepts and graph the equation. 7x +5y=12

Mathematics

1 answer:

vazorg [7]1 year ago

3 0

Answer:

y-intercept: (0, 12/5) or (0, 2.4)

x-intercept: (12/7, 0) or (1.714, 0)

Step-by-step explanation:

The y-intercept is the point where the graph crosses the y-axis. That means, the point (0, yi). To find yi, we have to substitute x by 0 in the equation.

7x + 5y=12

7*0 + 5y = 12

y = 12/5 = 2.4

y-intercept: (0, 12/5) or (0, 2.4)

The x-intercept is the point where the graph crosses the x-axis. That means, the point (xi, 0). To find xi, we have to substitute y by 0 in the equation.

7x + 5y=12

7x + 5*0 = 12

x = 12/7 = 1.714

x-intercept: (12/7, 0) or (1.714, 0)

Finally, the graph is shown below.

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Given the polynomial 6x3 + 4x2 − 6x − 4, what is the value of the constant 'k' in the factored form? 6x3 + 4x2 − 6x − 4 = 2(x +

CaHeK987 [17]

First you graph it using a graphing calculator, you look at the table of values to find out one point in which y= 0. The first one that comes up is when x=1.
If you don't have a graphing calculator you can use trial and error by inputing some numbers into x until you get y= 0.

Once you have an x value which makes y=0, you can start factorizing it.
you divide 6x3 +4x2 -6x - 4 into (x-1) which is when y =0
to get 6x2+10x+4

This can be used to write the polynomial as (x-1)(6x2 +10x+4)
you then factorize the second bracket, 6x2 +10x+4.
you can take the 2 outside to give you 2(3x2 +5x+2)
you can factorize this to become 2(3x+2)(x+1)

Now you just substitute your factorized second bracket into your unfactorized second bracket to give you 2(3x+2)(x+1)(x-1).

From this you can deduce that k= 1

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3 years ago

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Given that √3 = 1.7321 , find correct to 3 places of decimals , the value of √192 - 1 / 2√48 - √75

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Step-by-step explanation:

the value of root three is given already so the question is asking you to round it of to the nearest 1000 which means there should be three numbers after the decimal point.

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HOW DO THE PROPERTIES OF A DILATION TRANSFORMATION DIFFER FROM THE OTHER TRANSFORMATIONS YOU HAVE LEARNED ABOUT?

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It differs because dilation changes the shape but not the orientation or place the shape is located.

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Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calcul

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Answer:

The number of calculators is 4871

Step-by-step explanation:

If we integrate dx/dt we get x, which is the number of calculators. To find the number of calculators between the beginning of third week to the end of fourth week (the beginning of fifth week), this integration must be evaluated at t between 3 and 5.

$x=\int\limits^5_3 {\frac{dx}{dt}} \, dt =\int\limits^5_3 {5000(1-\frac{100}{(t+10)^2})} \, dt$

the result of the integration is:

$x=5000(t+\frac{100}{t+10})$ to be evaluated between 3 and 5, which is:

$x=5000(5+\frac{100}{5+10})-5000(3+\frac{100}{3+10})=\frac{190000}{39}=4871.8$

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3 years ago

Suppose that a is a one-dimensional array of ints with a length of at least 2. Which of the following code fragments successfull

elixir [45]

Answer:

E)II and III only

Step-by-step explanation:

This can be seen with examples. Say a[0]=1 and and a[1]=2.

for I , the first line of code would be:

a[0]=a[1];

thus, we would get a new value for a[0]=2.

The second line of code

a[1]=a[0]; uses the new value of a[0], so we would get a[1]=2.

The end result is a[0]=2, and a[1]=2 which doesn't exchange the values of the first two elements.

For II the first line of code

int t= a[0]; saves the original value of a[0] to t, so we get t=1.

the second line of code

a[0]=a[1]; changes the value of a[0] to that of a[1]. Thus, in our example a[0]=2.

the final line

a[1]=t; changes the value of a[1] to the original value of a[0], giving us a[1]=1 and a[0]=2, what we were looking for.

For III

the first line of code

a[0]=a[0]-a[1];

gives us

a[0]=1-2

the secon line

a[1]=a[1]+a[0];

takes the new value of a[0] and replaces it in the expression

a[1]= 2+(1-2)=1

the last line

a[0]=a[1]-a[0];

takes the new value of a[0] and a[1] and replaces the in the expression

a[0]=1-(1-2)=1-1+2=2

which exchanges the values needed.

So we can see that only II and III do what we require, giving us E as the answer.

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