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3 years ago

Solve x2 − 8x + 5 = 0 using the completing-the-square method. (2 points)

Mathematics

1 answer:

RoseWind [281]3 years ago

8 0

Answer:

$x = 4 + \sqrt{11}, \: \: x = 4 - \sqrt{11}$

Step-by-step explanation:

${x}^{2} -8x + 5 = 0 \\ \\ {x}^{2} - 8x + {4}^{2} = - 5 + {4}^{2} \\ \\ {(x - 4)}^{2} = - 5 + 16 \\ \\ {(x - 4)}^{2} = 11 \\ \\ x - 4 = \pm \sqrt{11} \\ \\ x = 4 \pm \sqrt{11} \\ \\ x = 4 + \sqrt{11}, \: \: x = 4 - \sqrt{11}$

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What is the equation of the line that passes through the point (3,2) and has a slope of -5/3?

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Answer= Y=-5/3x+7

First substitute (3,2) into the equation y=-5/3x +b which gives you 2=-5/3x+b. Solve for b, then put the equation into slope-intercept form.

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3 years ago

Consider the functions f(x) = 5x – 2, g(x) = 5x² + 2 and r(x) = –2x + 4.

klemol [59]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

10.6.23

Svetach [21]

I = $ 1,200,000.00

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3%/100 = 0.03 per year,

then, solving our equation

I = 1000000 × 0.03 × 40 = 1200000

I = $ 1,200,000.00

The simple interest accumulated

on a principal of $ 1,000,000.00

at a rate of 3% per year

for 40 years is $ 1,200,000.00.

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3 years ago

16/8 would be classified as a/an?<br> A:whole number <br> B:integer <br> C:Rational Number

gregori [183]

Answer:

Whole Number

Step-by-step explanation:

Numerator. This is the number above the fraction line. For 16/8, the numerator is 16.

Denominator. This is the number below the fraction line. For 16/8, the denominator is 8.

Improper fraction. This is a fraction where the numerator is greater than the denominator.

Mixed number. This is a way of expressing an improper fraction by simplifying it to whole units and a smaller overall fraction. It's an integer (whole number) and a proper fraction.

Now let's go through the steps needed to convert 16/8 to a mixed number.

Step 1: Find the whole number

We first want to find the whole number, and to do this we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.

16/8 = 2

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (2) and multiply it by the original denominator (8). The result of that multiplication is then subtracted from the original numerator:

16 - (8 x 2) = 0

Step 3: Our mixed fraction

We've now simplified 16/8 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

2 (0/8)

You maybe have noticed here that our new numerator is actually 0. Since there is no remainder, we can remove the entire fraction part of this mixed number, leaving us with a final answer.

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3 years ago

Jake is using a horse trailer to take his horses to his new ranch. 1 Horse= 1,200 lb Trailer= 2,700 lb Jake's truck can tow a ma

Kitty [74]

Answer:

Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

Step-by-step explanation:

Given:

Weight of 1 horse = 1,200 lb

Weight of trailer = 2,700 lb

Jacks'truck can tow a maximum of 5000 pounds.

To find the maximum number of horses Jack can take in his trailer without going over the maximum weight his truck can tow.

Solution:

Let the maximum number of horses that Jack can take be = $x$

Using unitary method to find weight of $x$ horses.

If 1 horse weights = 1,200 lb

Then $x$ horses will weight in lbs = $1,200\times x = 1,200x$

Total weight of horses and trailer in lbs = $1200x+2700$

Since the maximum weight the truck can tow = 5,000 lb, so the inequality can be given as:

$1200x+2700\leq5000$

Subtracting both sides by 2700.

$1200x+2700-2700\leq5000-2700$

$1200x\leq2300$

Dividing both sides by 1200.

$\frac{1200x}{1200}\leq\frac{2300}{1200}$

$x\leq1.91$

From the inequality solution for $x$ , we can conclude that Jack can take only 1 horse on his trailer to be towed by the truck without going over the maximum weight the truck.

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3 years ago