find the value of x in each triangle. show your work on a separate piece of paper

We are provided with a quadratic equation , and we have to find it's roots , but let's recall some things

Where , D is the Discriminant whose value is b²- 4ac and the roots of the equation are given by a very famous formula called The Quadratic Formula , which is as follows ;

[tex]{\quad {\boxed{\pmb{\bf x = \dfrac{-b \pm \sqrt{D}}{2a}}}}}[/tex]

Now , coming back on the question ;

We are provided with the equation x² + 6x = -18 , so on comparing this equation with the standard form of quadratic equation , we have , a = 1 , b = 6 and c = 18 . Now calculating the Discriminant ;

[tex]{: \implies \quad \sf D=(6)^{2}-4\times 1 \times 18}[/tex]

[tex]{: \implies \quad \sf D=36-72}[/tex]

[tex]{: \implies \quad \sf D=-18}[/tex]

As , D < 0 , so two imaginary roots exist . Now by quadratic formula ;

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{-36}}{2\times 1}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm \sqrt{\underline{6\times 6}\times -1}}{2}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\sqrt{-1}}{2}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{-6 \pm 6\iota}{2} \quad \{\because \sqrt{-1}=\iota\}}[/tex]

[tex]{: \implies \quad \sf x=\dfrac{2(-3\pm 3\iota)}{2}}[/tex]

[tex]{\quad \qquad \boxed{\bf \therefore \: x=-3 \pm 3\iota}}[/tex]

Answer:

100%

Step-by-step explanation:

Picking a green tile from a bag with nothing with green tiles is 100%, because what else could you get

Step-by-step explanation:

JM = 27 ---- ( given )

JM = KL

so, KL = 27

Answer:

1

Step-by-step explanation:

Two ordered pairs that can be seen are (0,1) and (1,2)

Using delta y/ delta x,

(2-1)/(1-0) = slope

slope = 1/1

slope = 1

Answer:

slope = 1

Step-by-step explanation:

To find the slope of the line, use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex], in which [tex]m[/tex] represents the slope. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point, while the [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point.

Thus, locate two points on the line. We can see that the line intersects (-1,0) and (0,1), thus we can use them for the formula. (Any other two points that are also on the line will also work.) Substitute their x and y values into the appropriate places in the formula and solve:

[tex]m = \frac{(1)-(0)}{(0)-(-1)}\\m = \frac{1-0}{0+1} \\m = \frac{1}{1} \\m = 1[/tex]

Thus, the slope is 1.

Answer:

rectangular pyramid

Step-by-step explanation:

Answer:

[tex]\sin C=\frac{28}{35}[/tex]

Step-by-step explanation:

In a right triangle, [tex]\sin\theta =\frac{\text{opp}}{\text{hyp}}[/tex]. In this case, the side opposite to angle [tex]C[/tex] is 28 and the hypotenuse is 35. Therefore, the exact value of [tex]\sin C[/tex] is [tex]\boxed{\frac{28}{35}}[/tex].

Answer:6x - (6xa)/(7)

Step-by-step explanation:

Answer:

$46,800

Step-by-step explanation:

3/5 of 240 is 144

144*325 is 46,800

Answer:

b3/5of240 is144thentimesby325.00

Answer:

I agree with Mary

Step-by-step explanation:

Cone:

r = 8/2 = 4 ft

h = 16 - 12 = 4 ft

Volume = [tex]\frac{1}{3}\pi r^{2}h\\[/tex]

             [tex]= \frac{1}{3}*3.14*4*4*4\\\\=\frac{200.96}{3}\\\\= 66.98\\\\= 67 cubic feet\\[/tex]

Cylinder:

r = 4 ft

h= 12 ft

Volume = πr²h

              = 3.14*4*4*12

            = 602.88

           = 603 cubic feet

Step-by-step explanation:

the formular for finding the volume( how much it can contain in this instance) of the cone(spout) is

[tex] \frac{1}{3} \times \pi \times {r}^{2} \times l[/tex]

r is the radius of the cone l is the height of the cone π = 22/7

1/3 × 22/7 × 4 × 4 × 4

diameter divide by 2 gives the radius 8/2 = 4

the height of the whole shape - the height of the upper part(cylinder) gives the height of the cone

16 - 12 = 4

volume of spout(cone)=22/21 × 64 =67 cubic feet(f^3)

Answer:

(3i+5)+(2-6i)

⇒ 3i+5+2-6i

⇒3i-6i+5+2

⇒-3i+7

The simplified form of (3i+5)+(2-6i) will be -3i+7

Answer:ddeeececdshcbd

Step-by-step explanation:

curcirjcirvirvnr

Answer:

1. Complementary Angles.

2. x=60°

Step-by-step explanation:

Part 1:

*Note: A complementary angle is when the sum of two angles equal 90 degrees. A Supplementary angle is when the sum of 2 angles equals 180 degrees.

In this instance, the 2 angles equal 90 degrees, as indicarted by the box on the angle. Therefore, the the angles are complentary.

Part 2:

1. Since we know that the sum of the two angles (x-30 and x) is 90 degrees, we can write an equation which says: (x-30) + x=90.

2. Then we'd simplify the equation by adding the like variables, and adding 30 to both sides:

2x=120

3. Now we will divide both sides by 2

[tex]\frac{2}{2} x=\frac{120}{2} \\x=60[/tex]

4. As a result, we get x=60, now label your answer with the degree sign, and enjoy your answer.

Answer:

d

Step-by-step explanation:

Answer:

It’s a way to show how things are related. It may be a mathematical pattern.

Step-by-step explanation:

Answer:

158.3

Step-by-step explanation:

Answer:

x = 63

Step-by-step explanation:

a triangle is always 180 degrees, so you equation would be:

180 - 42 - 43 - 32 = x

180 - 42 - 43 - 32 = 63

so x = 63

Answer:

Step-by-step explanation:

a straight line  = 180 degrees

on the right side, where the angle is 32 it is vertically opposite to the right angle of the triangle then

Answer:

p=11/2

Step-by-step explanation:

there are algebra calculators

Answer:

[tex] - 3c - 8[/tex]

Step-by-step explanation:

1) Collect like terms.

[tex](6c - 9c) - 8[/tex]

2) Simplify.

[tex] - 3c - 8[/tex]

Therefor, the answer is -3c - 8.

Answer:

its less than <

Step-by-step explanation:

........

Answer:

>

Step-by-step explanation:

[tex]12 \times 1 \frac{2}{5} = 12 \times \frac{7}{5} = \frac{60}{5} \times \frac{7}{5} = \frac{420}{25} = 16 \frac{20}{25} [/tex]

Answer:

I understand you probably don't need this anymore but here is the answer anyway.

Step-by-step explanation:

So what you want to do is draw a line from a corner to the centre of enlargement (I'll use the one at (9, 10) ). Then you see that it take 2 boxes to get to that, keep the line going through for double as much as it took to reach the centre of enlargement, this is because the scale factor is two. Do this for every corner, going through the centre of enlargement for the double the length it took to get to it (plot a cross at each bit you end up). Finally, remove the lines you used and connect the crosses. This method may be a bit confusing and someone who understands it more than me would probably explain what the minus means, if I explain it will probably make this more confusing. Hope this Helps!

Answer:

para Es que yo soy español y no te entiendo

Answer:

90

Step-by-step explanation:

The missing value is 2.56 to the nearest hundredth.

Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

We have a right-angled triangle.

And cos(θ) = Adjacent leg / hypotenuse

cos(65°) = The missing value  / 6

The missing value = cos(65°) x 6

The missing value = 0.4226 x 6

The missing value = 2.56 to the nearest hundredth.

Therefore, the value is 2.56.

To learn more about the trigonometric identities;

https://brainly.com/question/24377281

#SPJ2

Answer:

The answer is C. x = 2

Answer:

d = 11 units if rounded to nearest whole number

Step-by-step explanation:

Distance formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

Your ordered pairs (-1, 1) and (4, 11)

d=√((4-(-1))²+(11-1)²)

d=√((4+1))²+(10))²)

d=√((5)²+ 100)

d = √125

d = 11.18  

d = 11 units if rounded to nearest whole number

Answer:

r ≥ -49/11

Simplified versions: r ≥ -4.45 or r ≥ -4 5/11

Answer:  [tex]r \ge -\frac{49}{11}[/tex]

r is greater than or equal to the fraction -49/11

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Work Shown:

[tex]r + 5(-2r-10) \le -4r - 1 + 6r\\\\r - 10r - 50 \le -4r - 1 + 6r\\\\-9r - 50 \le 2r - 1\\\\-9r-2r \le - 1 + 50\\\\-11r \le 49\\\\r \ge \frac{49}{-11}\\\\r \ge -\frac{49}{11}\\\\[/tex]

Note how the inequality sign flips. This happens any time you divide both sides by a negative number.

Step-by-step explanation:

[tex]1) \\ f(x) = 3x - 1 \\ f(2) = 3(2) - 1 = 5 \\ 2) \\f(x) = {x}^{2} - 1 \\ f(2) = {2}^{2} - 1 = 3[/tex]

Answer:

€18 is the answer

If you’ve been given an estimate, use that to determine how much £13.50 would be by cross multiplying

Answer:

8.0<x<8.5

Step-by-step explanation: