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ra1l [238]
2 years ago
9

When solved correctly, the equation 4x−8−−−−−√=x−5 has solutions of x=3 and x=11.

Mathematics
1 answer:
grigory [225]2 years ago
7 0

Answer:

x = 3 is extraneous

Step-by-step explanation:

Given

\sqrt{4x-8} = x - 5 ( square both sides to clear the radical )

4x - 8 = (x - 5)² ← expand using FOIL

4x - 8 = x² - 10x + 25 ( subtract 4x - 8 from both sides )

0 = x² - 14x + 33 ← in standard form

0 = (x - 11)(x - 3) ← in factored form

Equate each factor to zero and solve for x

x - 11 = 0 ⇒ x = 11

x - 3 = 0 ⇒ x = 3

As a check

Substitute these values into the equation and if both sides are equal then they are solutions

x = 11

left side = \sqrt{44-8} = \sqrt{36} = 6

right side = 11 - 5 = 6

Thus x = 11 is a solution

x = 3

left side = \sqrt{12-8} = \sqrt{4} = 2

right side = 3 - 5 = - 2 ≠ 2

Thus x = 3 is an extraneous solution

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The answer is 140 percent
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3 years ago
Three angles of an irregular octagon are 100 degrees, 120 degrees, and 140 degrees. The remaining angles are congruent. Find the
STatiana [176]

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° × (n - 2) ← n is the number of sides

Here n = 8 ( octagon ), hence

sum = 180° × 6 = 1080°

let the measure of 1 congruent angle be x

Then sum the 8 angles and equate to 1080

100 + 120 + 140 + 5x = 1080

360 + 5x = 1080 ( subtract 360 from both sides )

5x = 720 ( divide both sides by 5 )

x = 144

Thus each of the 5 congruent angles is 144°

7 0
3 years ago
A l-meter steel rod is bent into a rectangle so that its length exceeds quadruple its width
Dmitry_Shevchenko [17]

Answer:

The dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

Step-by-step explanation:

Given,

A 1 meter steel rod is bent into a rectangle.

That means the perimeter of the rectangle is 1 meter.

So, Perimeter = 1\ m=100\ cm

Let the width of the rectangle be 'x'.

Now According to question, length exceeds quadruple its width by 5 cm.

Hence framing the above sentence in equation form, we get;

Length=4x+5

Now we use the formula of  perimeter of rectangle,

Perimeter=2(Length+width)

On substituting the values, we get;

2(4x+5+x)=100\\\\(5x+5)=\frac{100}{2}\\\\5x+5=50\\\\5x=50-5\\\\5x=45\\\\x=\frac{45}{5}=9

Now, we substitute the value of x to get the value of length;

Length=4x+5=4\times9+5=36+5=41\ cm

Thus, Width=9 cm    Length=41 cm

Hence the dimensions of the newly formed rectangle is length is 41 cm and width is 9 cm.

6 0
3 years ago
CAN SOMEONE CHECK MY ANSWER
tigry1 [53]

Answer:

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the volume of the composite figure? Express the
Papessa [141]

Answer:

V=312\pi\ mm^{3}

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the volume of a semi-sphere plus the volume of the cone

so

V=\frac{4}{6}\pi r^{3} +\frac{1}{3} \pi r^{2} h

we have

r=6\ mm

h=14\ mm

substitute

V=\frac{4}{6}\pi (6)^{3} +\frac{1}{3} \pi (6)^{2} (14)

V=144\pi +168\pi

V=312\pi\ mm^{3}

3 0
3 years ago
Read 2 more answers
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