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Nataly [62]
3 years ago
15

Complete the square to make the binomial x^2-8x a perfect trinomial

Mathematics
1 answer:
borishaifa [10]3 years ago
3 0
The general Formula looks like this:
x^2 +bx + ( \frac{b}{2})^2
This really only involves 2 steps:
1) Take half of "x" coefficient. ----> -8/2 = -4
2) Square that number.   ---------->  (-4)^2 = 16

Perfect trinomial for this example is then:
x^2 -8x+16
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Solve the following equations<br> 1. 4(x – 2) = 6(4 – x)
Readme [11.4K]

Answer:

x = 3.2

Step-by-step explanation:

4(x – 2) = 6(4 – x)

4x - 8 = 24 - 6x

10x - 8 = 24

10x = 32

x = 3.2

3 0
3 years ago
Write an equation of the line through (-1,-5) having slope 2/3. give the answer in standard form.
jekas [21]

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{-5})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{\cfrac{2}{3}}[x-\stackrel{x_1}{(-1)}]\implies y+5=\cfrac{2}{3}(x+1)

\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y+5)=3\left( \cfrac{2}{3}(x+1) \right)}\implies 3y+15 = 2(x+1) \implies 3y+15=2x+2 \\\\\\ 3y=2x-13\implies -2x+3y=-13\implies 2x-3y=13

7 0
3 years ago
What percent of 360 is 120 <br>no links​
lesya [120]

Answer:

33.33

Percentage Calculator: 120 is what percent of 360? = 33.33.

3 0
3 years ago
Please help me with this
liubo4ka [24]

Answer:

  192.5 ft²

Step-by-step explanation:

The large sector of the circle has a central angle measure of 360° -100° = 260°, so its area will be (260°/360°) of the circle, or ...

  large sector area = (260/360)πr² = 13π/18·(8.35 ft)² ≈ 158.195 ft²

The area of the 100° triangle is ...

  triangle area = (1/2)r²·sin(100°) = (1/2)(8.35 ft)²·sin(100°) ≈ 34.332 ft²

Then the shaded area is ...

  shaded area = large sector area + triangle area

  = 158.195 ft² +34.332 ft² ≈ 192.5 ft²

The shaded area is about 192.5 square feet.

5 0
3 years ago
I really need this question someone please help ​
jasenka [17]

Answer:

\approx 15.9

Step-by-step explanation:

The length of an arc with measure \theta  and radius r is given by \ell_{arc}=2r\pi\cdot \frac{\theta}{360}. From the figure, we know that the radius of arc ADC is 4, but we don't know the measure of the arc. Since there are 360 degrees in a circle, the measure of arc ADC is equal to the measure of the arc formed by \angle AOC subtracted from 360. The measure of the arc formed by \angle AOC consists of two congruent angles, \angle AOB and \angle COB. To find them, we can use basic trigonometry for a right triangle, since by definition, tangents intersect a circle at a right angle.

In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.

We have:

\cos \angle AOB=\cos \angle COB=\frac{4}{10},\\\angle AOB=\arccos(\frac{4}{10})=66.42182152^{\circ}

Therefore, \angle AOC=2\cdot 66.42182152=132.84364304^{\circ}

The measure of the central angle of \widehat{ADC} must then be 360-132.84364304=227.15635696^{\circ}

Thus, the length of \widehat{ADC} is equal to:

\ell_{\widehat{ADC}}=2\cdot 4\cdot \pi \cdot \frac{227.15635696}{360},\\\ell_{\widehat{ADC}}=15.8585053832\approx \boxed{15.9} (three significant figures as requested by question).

6 0
3 years ago
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