Which expression can be written as 4 • (3 8)?

I need to show work please i need help

stellarik [79]

Answer:

I am going to give this to someone and see if they can help!

Step-by-step explanation:

6 0

4 years ago

How do ypu slove dis? y^2(q-4) - c(q - 4)

Annette [7]

y2(q-4)-c(q-4) Final result : (q - 4) • (y2 - c)

Step by step solution :Step 1 :Equation at the end of step 1 : ((y2) • (q - 4)) - c • (q - 4) Step 2 :Equation at the end of step 2 : y2 • (q - 4) - c • (q - 4) Step 3 :Pulling out like terms :

3.1 Pull out q-4

After pulling out, we are left with :
(q-4) • ( y2 * 1 +( c * (-1) ))

Trying to factor as a Difference of Squares :

3.2 Factoring: y2-c

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =
 A2 - AB + BA - B2 =
 A2 - AB + AB - B2 =
 A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : y2 is the square of y1 

Check : c1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares

Final result : (q - 4) • (y2 - c)

4 0

4 years ago

A ladder 8m long rests against a house. If the house is 6m high and the bottom of the ladder is 2m from the house, how much of t

Alex

Answer:

15

Step-by-step explanation:

you add all of them up and you get your answer

8 0

3 years ago

Read 2 more answers

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term $x^2$ , which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression: $x_v=\frac{-b}{2a}$

Since in our case $a=1$ and $b=5$ , we get that the x-position of the vertex is: $x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

$y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}$

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the $x_v=-\frac{5}{2}$ . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

$f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0$

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0

3 years ago

a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream

Nonamiya [84]

the coordinates where the bridges must be built is $(3,-6)$ and $(6,3)$ .

Step-by-step explanation:

Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:

Basically we need to find values of x for which f(x) = g(x) :

⇒ $f(x)-g(x)=0$