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3 years ago

What value of p will make the expression below a perfect square? x^2 - x + P

Mathematics

2 answers:

pentagon [3]3 years ago

8 0

Answer:

x^2 - x + 1/4

Step-by-step explanation:

To complete the square

x^2 - x + P

Take the coefficient of x

-1

Divide by 2

-1/2

Then square it

(-1/2)^2

1/4

Add this to complete the square

x^2 - x + 1/4

shutvik [7]3 years ago

6 0

Answer:

p = $\frac{1}{4}$

Step-by-step explanation:

To make a perfect square

add ( half the coefficient of the x- term )² to x² - x, that is

x² + 2(- $\frac{1}{2}$ )x + $\frac{1}{4}$ with p = $\frac{1}{4}$ , thus

x² - x = (x - $\frac{1}{2}$ )² + $\frac{1}4}$

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Calculate a_57 for the sequence {a_n}={-6,-9/2,-3,-3/2,0}

Archy [21]

Answer:the 57th term is 78

Step-by-step explanation:

The sequence is an arithmetic sequence. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = - 6

d =3/2

n = 57

We want to determine the value if the 57th term, T57. Therefore,

T57 = - 6 + (57 - 1) ×3/2

T57 = - 6 + 56 × 3/2 = - 6 + 84

T57 = 78

3 0

2 years ago

There are 5 times as many animals at the Central zoo as there are at the Baty zoo. The Central zoo has 265 animals in all. Let b

zheka24 [161]

Answer:

It's D

Step-by-step explanation:

6 0

2 years ago

6. trapezoid ABCD shown below, AB|| DC, overline BC perp overline DC and sides have lengths as shown (aDetermine the measure of

laila [671]

Answer:

a). ∠D = 56°

b). AD = √13

Step-by-step explanation:

(a) From the figure attached, ABCD is a trapezoid with parallel sides AB and CD. We have to find the measure of ∠D from the given figure.

From triangle ADE,

$tanD=\frac{AE}{DE}$

$=\frac{3}{2}$

D = $tan^{-1}(1.5)$

D = 56.31

D ≈ 56°

Therefore, measure of ∠D is 56°.

(b). Now by applying Pythagoras theorem in ΔADE,

AD² = AE² + DE²

= 3² + 2²

AD² = 9 + 4

AD = √13

Length of AD is √13 in.

7 0

2 years ago

Please just help please

Simora [160]

Answer:

1. Yes the parentheses are necessary. To find a fourth of her regular hours you must find the total amount she works during her regular hours.

2. 6

Step-by-step explanation:

(For the second question)

4+8= 12

12 × ½ = 12 ÷ 2

12÷2 = 6

5 0

2 years ago

Anne is running on a trail at an average speed of 6 miles per hour beginning at mile marker 4. John is running on the trail at t

Sphinxa [80]

Answer:

John is running faster.

Step-by-step explanation:

Given that:

Average Speed of Anne = 6 miles per hour

Speed of John can be represented in the table below:

$\begin{center}\begin{tabular}{ c c}Time (hours) x & Mile Marker y \\ 0 & 1 \\ 0.5 & 4.5 \\ 1 & 8 \\ 1.5 & 11.5 \\\end{tabular}\end{center}$

To find:

Who is running faster of the both i.e. Anne and John?

Solution:

Here, to find the faster runner we can compare the average speed of both the runners.

We are given that, average speed of Anne = 6 miles per hour

We will have to calculate the average speed of John to find the faster runner.

<em>Average speed</em> can be calculated by dividing the total distance traveled with the total time taken.

Total distance traveled by John = 11.5 - 1 = 10.5 miles

Total time taken by John = 1.5 hours

Average speed of John = $\frac{10.5}{1.5} = 7\ miles/hr$

Clearly Average speed of John is greater than that of Anne's.

Therefore, <em>John runs faster</em>.

6 0

2 years ago