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3 years ago

Create a list of steps, in order, that will solve the following equation. 1/ 4 ( x + 5 )^2 − 1 = 3

Mathematics

1 answer:

Art [367]3 years ago

7 0

Answer:

x= -1, -9

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

1/4x2+5/2x+21/4=3

Step 2: Subtract 3 from both sides.

1/4x2+5/2x+21/4−3=3−3

1/4x2+5/2x+9/4=0

For this equation: a=0.25, b=2.5, c=2.25

0.25x2+2.5x+2.25=0

Step 3: Use quadratic formula with a=0.25, b=2.5, c=2.25.

x=−b±√b2−4ac/2a

x=−(2.5)±√(2.5)2−4(0.25)(2.25)/2(0.25)

x=−2.5±√4/0.5

x=−1,−9

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choose the equation in point slope form for the line that is perpendicular to the given line and passing through the given point

alexdok [17]

We want to determine the equation in point slope form for the line that is perpendicular to the given line and passing through the point (5.6) .

The equation and the point is;

$y=\frac{2}{3}x+9,(5,6)$

We know that for two lines to be perpendicular, the product of their slopes should be -1.

Therefore, the slope of the perpendicular should be;

$m=-\frac{1}{(\frac{2}{3})}=-\frac{3}{2}$

The second condition is that the line must pass through the point (5,6) , to do thid, we write the equation of the line in point slope form which is;

$y-y_1=m(x-x_{1_{}})$

Inserting all values, we have,

$y-6=.-\frac{3}{2}(x-5)$

That is the final answer.

6 0

1 year ago

Bill estimates that 20 people will attend the seminar if it does not rain and 12 people will attend if it rains. The weather for

Rama09 [41]

15 people would show up

6 0

3 years ago

Find the length and width of a rectangle whose perimeter is 20 feet and whose area is 21 square feet

ipn [44]

Answer:

Length = 3

Width = 7

Step-by-step explanation:

The perimeter is 20 feet

The area is 21 feet

Let x represent the length

Let y represent the width

20 = 2(x+y)

x+y= 20/2

x+y = 10.........equation 1

x × y= 21......equation 2

From equation 1

x= 10-y

Substitute 10-y for x in equation 2

(10-y)y= 21

10y - y^2 = 21

y^2 -10y + 21= 0

After factorization the result will be

(x-3)(y-7)

x-3= 0

x= 0+3

x= 3

y-7= 0

y= 0+7

y= 7

Hence the length is 3 and the width is 7

6 0

3 years ago

How can you determine if you need to use a combination or permutation to count the number of outcomes? Which will usually have m

Nadya [2.5K]

Answer with Step-by-step explanation:

Permutation : It is an arrangement of r elements out of n elements.

Combination : it is a selection of r element out of n elements .

Suppose we have a set

S={1,2,3}

If two elements are taken at a time then

Using permutation formula

Total number of outcomes= $3P_2$

Total number of outcomes= $\frac{3!}{(3-2)!}$

Total number of outcomes=3!= $3\times 2\times1=6$

Using combination formula

$\binom{n}{r}=\frac{n!}{r!(n-r)!}$

Total number of outcomes= $\binom{3}{2}=\frac{3!}{2!1!}$

Total number of outcomes= $\frac{3\times2!}{2!}$

Hence, total number of outcomes=3

Total number of outcomes determined by permutation have more outcomes.

Because permutation is an arrangement of elements therefore, it consider order of arrangement of element but combination is a selection of elements it does no consider order of elements

Arrangements of two elements out of 3 elements

{1,2},{2,3},{2,1},{3,2},{1,3},{3,1}

By using combination if two elements taken at a time then combination

{1,2},{2,3},{1,3}

4 0

3 years ago

B)the LCM of three numbers is 24 and their G.C.D is 4. If two<br>find the other number

kicyunya [14]

Step-by-step explanation:

because 6*4=24, so the G.C.D is 4 and the other number is 6

4 0

3 years ago