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1 year ago

X2 - 4x + 4 = 0 solve following quadratic equations graphically and a table

1 answer:

6 0

Let's create a table, and use arbitrary values of x between -3 and 3 (if the solution is not in this interval, we can use another one later). If we call:

$f(x)=x^2-4x+4$

We want to find the x's for with f(x) = 0

This is the table:

And now we can evaluate f(x) in each value of x to complete the table:

$\begin{gathered} f(-3)=(-3)^2-4\cdot(-3)+4=9+12+4=25 \\ f(-2)=(-2)^2-4\cdot(-2)+4=4+8+4=16 \\ f(-1)=(-1)^2-4\cdot(-1)+4=1+4+4=9 \\ f(0)=0^2-4\cdot0+4=4 \\ f(1)=1^2-4\cdot1+4=1-4+4=1 \\ f(2)=2^2-4\cdot2+4=4-8+4=0 \\ f(3)=3^2-4\cdot3+4=9-12+4=1 \end{gathered}$

The table is:

If we use this values and plot them in the cartesian plane.

We get:

And now if we plot a line that connects the points, we get the graph of the quadratic equation:

Since the problem ask us to find the value of x for which f(x) = 0, we can see both in the table and in the graph that this value is x = 2

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Qhich are the solutions of the quadratic equation x^2=9x+6

Lera25 [3.4K]

x^2-9x-6=0

Use the quadratic formula to get (9+sqrt(105))/2 or (9-sqrt(105))/2

3 0

3 years ago

Evaluate the following integral, where R is bounded by , , and . Question content area bottom Part 1 enter your response here

Volgvan

$\iint_{R} y^{2} d A=\int_{x=-2}^{3} \int_{y=-x-2}^{3 x+6} y^{2} d x d y d x$

$\text { (taking Strip as shown). }$

$=\int_{-2}^{3}\left(\frac{y^{3}}{3}\right)_{-x-2}^{3 x+6} d x$

$=\frac{1}{3} \int_{-2}^{3}(3 x+6)^{3}-(-x-2)^{3} d x$

$\begin{gathered}=\frac{1}{3}[4375]=\frac{4375}{3} \\=1458.33\end{gathered}$

What is integral ?

Calculating an integral is called integration.
Mathematicians utilize integrals to determine a variety of useful quantities, including areas, volumes, displacement, etc.
When we discuss integrals, we often refer to definite integrals.
For antiderivatives, indefinite integrals are utilized.
Apart with differentiation, integration is one of the two main calculus subjects in mathematics (which measure the rate of change of any function with respect to its variables).
It's a broad subject that is covered in courses at the higher grade levels, such classes 11 and 12.
Broadly speaking, integration by parts and via substitution is explained.
You will discover the definition of integrals in mathematics, the integration formulae, and examples here.

So the more about integral visit.

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7 0

2 years ago

Question 2

s344n2d4d5 [400]

The work is simply the dot product of the force and displacement (which I assume are given in Newtons and meters, respectively):

W = F • d

W = (5i + 3j - 2k) N • ((4i - j + 3k) m - (j + k) m)

W = (5i + 3j - 2k) • (4i - 2j + 2k) Nm

W = (20 - 6 - 4) Nm

W = 10 J

7 0

3 years ago

Can somebody help me with this What is the value of P

leonid [27]

Answer:

p=7

∠BRG=49

Step-by-step explanation:

∠BRG and ∠YRG are on a straight line together. Therefore, they are supplementary and add to 180 degrees.

∠BRG+∠YRG=180

We know that ∠BRG is 7p and ∠YRG is 131 degrees. Substitute 7p in for ∠BRG and 131 for ∠YRG.

7p+131=180

We want to find out what p is. In order to do that, we have to get p by itself. First, subtract 131 from both sides.

7p+131-131=180-131

7p=49

Next, divide both sides by 7.

7p/7=49/7

p=49/7

p=7

Now, we have to find what ∠BRG is.

∠BRG=7p

We know that p=7, so substitute p in for 7

∠BRG=7*7

∠BRG=49

So, p=7 and ∠BRG=49

6 0

3 years ago

Read 2 more answers

If the two adjacent angles are supplementary then their outer sides are???

Ainat [17]

Answer:

If the bisectors of two adjacent angles are perpendicular to each other, are the angles then supplementary angles?

Suppose two angles ABC and CBD are x and y.

x+y = 180 deg.

The bisector of angle ABC (BE) and the bisector of angle CBD (CF) will form angle EBF = (x/2)+(y/2) = 180/2 = 90 deg.

Conclusion: If the angle bisectors of two adjacent angles are perpendicular to eaxh other, the adjacent angles are supplementary angle

Adjacent angles are when the 2 angles have a common vertex and a common arm.

if the exterior sides of 2 adjacent angles are perpendicular, then the angles are complementary angles.

Then the sum of the 2 adjacent angles is a right angle - 90°.

When 2 angles add up to 90°, they are called a pair of complementary angles.

Step-by-step explanation:

6 0

3 years ago