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Alexus [3.1K]
3 years ago
11

Can somebody help me solve for x?

Mathematics
1 answer:
Dahasolnce [82]3 years ago
7 0

Let y = the distance between the top left corner and the bottom right corner

y^2 = 24^2 + 15^2

y^2 = 801

y = 3 * sqrt(89)

Now we can find x.

12^2 + x^2 = (3 * sqrt(89))^2

x^2 = 657

x = 3 * sqrt(73) or 25.63

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if the equation x^2 +(k+2)x+2k=0 has equal roots,then the value of k is .....a.2 b.-2 c 1/2 d.none ​
blsea [12.9K]

Answer:

k=2

Problem:

if the equation x^2 +(k+2)x+2k=0 has equal roots,then the value of k is ..

Step-by-step explanation:

Since the coefficient of x^2 is 1, we can use this identity to aid us: x^2+bx+(b/2)^2=(x+b/2)^2.

So we want the following:

[(k+2)/2]^2=2k

Apply the power on the left:

(k+2)^2/4=2k

Multiply both sides by 4:

(k+2)^2=8k

Expand left side:

k^2+4k+4=8k *I used identity (x+c)^2=x^2+2xc+c^2

Subtract 8k on both sides:

k^2-4k+4=0

Factor using the identity mentioned a couple lines above:

(k-2)^2=0

Since zero squared is zero, we want k-2=0.

Adding both sides by 2 gives k=2.

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3 years ago
Complete the equation of the line whose y-intercept is (0,6) and the slope is 3
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When finding the intersection of two lines from both Algebra 1 and geometry you first set the linear equations equal to each oth
NNADVOKAT [17]
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3 years ago
Read 2 more answers
While traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return. If
Luden [163]

Answer:

The speed driven while returning is 88 mph.

Step-by-step explanation:

We are given that while traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return.

Also, the total distance of the roundtrip was 420 miles.

Let the speed driven while returning be 'x mph' which means that the speed driven while going was '(x - 40) mph' because it has been given that while returning we have increased the speed by 40 mph.

As we know that the Speed-Distance-Time formula is given by;

                         \text {Speed} = \frac{\text{Distance}}{\text{Time}}   or  \text {Time} = \frac{\text{Distance}}{\text{Speed}}

So, according to the question;

\frac{420}{x-40} -\frac{420}{x} = 4 \text{ hours}       where Distance = 420 miles

\frac{420x-420(x-40)}{x(x-40)} = 4

\frac{420x-420x+16800}{x^{2} -40x} = 4

\frac{16800}{x^{2} -40x} = 4

4x^{2} -160x= 16800

4x^{2} -160x- 16800=0

x^{2} -40x- 4200=0

Now finding the roots of the above equation;

Here a = 1, b = -40 and c = -4200

D = b^{2} -4ac

   =  (-40)^{2} -4(1)(-4200) = 18400

Now, the roots of a quadratic equation is given by;

x = \frac{-b\pm \sqrt{D} }{2a}

x = \frac{-(-40)\pm \sqrt{18400} }{2\times 1}

So, the two roots of x are : x = \frac{40-\sqrt{18400} }{2}  and  x = \frac{40+\sqrt{18400} }{2}

Solving these two we get; x = -47.8  and  x = 87.8

Here we ignore the negative value of x, so the speed driven while returning is 87.8 ≈ 88 mph.

8 0
3 years ago
What is the equation of the line in slope intercept form
Dennis_Churaev [7]
Y=17 4/5x-1
Hope that helped
8 0
3 years ago
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