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3 years ago

Given: tangent to Circle O. If m C = 57°, then m BDR =

1 answer:

8 0

∠BCD = 57°
∴ ∠BDR = ∠BCD = 57° (angle that meets the chord and the tangent is equi-angular to the angle at the alternate segment)

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Find the discriminant, and determine the number of real solutions. then solve x^2 +8x+20=0

vodomira [7]

Answer:

Part 1) The quadratic equation has zero real solutions

Part 2) The solutions are

$x_1=-4+2i$ and $x_2=-4-2i$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}+8x+20=0$

$a=1\\b=8\\c=20$

The discriminant is equal to

$D=(b^{2}-4ac)$

If D=0 -----> the quadratic equation has only one real solution

If D>0 -----> the quadratic equation has two real solutions

If D<0 -----> the quadratic equation has two complex solutions

Find the value of D

$D=8^{2}-4(1)(20)=-16$ -----> the quadratic equation has two complex solutions

Find out the solutions

substitute the values of a,b and c in the formula

$x=\frac{-8(+/-)\sqrt{8^{2}-4(1)(20)}} {2(1)}$

$x=\frac{-8(+/-)\sqrt{-16}} {2}$

Remember that

$i=\sqrt{-1}$

$x=\frac{-8(+/-)4i} {2}$

$x_1=\frac{-8(+)4i} {2}=-4+2i$

$x_2=\frac{-8(-)4i} {2}=-4-2i$

8 0

3 years ago

The graph of a proportional relationship is shown. What is the

arlik [135]

Answer: B) $47/week

===========================================================

Explanation:

Because the graph goes through the origin, we can simply divide the y value over the x value. Do so for any point on the diagonal line.

For example, picking (x,y) = (2, 94) leads to k = y/x = 94/2 = 47 being the constant of proportionality and also the amount of savings per week.

You can think of it like this:

2 weeks = $94 in savings

2/2 weeks = $94/2 in savings ... divide both sides by 2

1 week = $47 in savings

leading to the savings rate of $47 per week

----------

Side note: This linear equation is y = 47x. It is in the form y = kx with k = 47. It is a direct proportion equation. The constant of proportionality is also the slope. All direct proportion equations are linear and go through the origin.

8 0

2 years ago

40 POINTS, please help

Elis [28]

First, we must understand what standard form of a line is. Standard form of a line is written like such that A,B, and C are all integers, and A must be positive. First, we must calculate the slope of the line that passes through theses coordinates.

As a refresher, this is the equation to figure out the slope of two coordinates.Now, we just simplify the numerator and denominator.

The next step is to utilize point-slope form, which is where is a point on the line. Of course, we already know that (7,-3) and (4,-8) both lie of the line. Therefore, plug in one fot he coordinates. Once converted into point-slope, we must then convert into standard form. This is what is demonstrated in the next step.

Let's multiply all sides by 3 to get rid of the fraction early.Distribute the 5 to both terms in the parentheses.Subtract 9 from both sides.Subtract 5x on both sides.We aren't done yet! The coefficient of the x-term must be positive. Therefore, divide by -1 on both sides.This is standard form now, so we are done!

8 0

3 years ago

Question 3: Find the vertex of - x2 - 4x + 12

tatuchka [14]

Answer:

A. (-2,16)

Hope this helps :)

4 0

3 years ago

The measure of an angle is 8 degrees less than three times te measure another angle. If the two angles are supplementary, what i

tatyana61 [14]

Let's solve this problem step-by-step.

First of all, let's establish that supplementary angles are two angles which add up to 180°.
Therefore:

Equation No. 1 -
x + y = 180°

After reading the problem, we can convert it into an equation as displayed as the following:

Equation No. 2 -
3x - 8 + x = 180°

Now let's make (y) the subject in the first equation as it is only possible for (x) to be the subject in the second equation. The working out is displayed below:

Equation No. 1 -
x + y = 180°
y = 180 - x

Then, let's make (x) the subject in the second equation & solve as displayed below:

Equation No. 2 -
3x - 8 + x = 180°
4x = 180 + 8
x = 188 / 4
x = 47°

After that, substitute the value of (x) from the second equation into the first equation to obtain the value of the other angle as displayed below:

y = 180 - x
y = 180 - ( 47 )
y = 133°

We are now able to establish that the value of the two angles are as follows:

x = 47°
y = 133°

In order to determine the measure of the bigger angle, we will need to identify which of the angles is larger.

133 is greater than 47 as displayed below:

133 > 47

Therefore, the measure of the larger angle is 133°.

4 0

3 years ago