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3 years ago

Complete the square 2x^2-3x-5=0

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

2(x-3/4)^2 - 49/8 = 0

Step-by-step explanation:

2x^2 - 3x - 5 = 0

First take out the 2: 2 [x^2 -3/2x - 5/2] = 0

Now complete the square inside the square brackets: 2 [(x-3/4)^2 - 9/16 - 5/2] = 0

Simplify inside the square brackets: 2 [(x-3/4)^2 - 49/16] = 0

Now times out the square brackets: 2(x-3/4)^2 - 49/8 = 0

And we're done!

You might be interested in

What are the ordered pairs of the solutions for this system of equations

AleksAgata [21]

Answer:

(3, 6); (-3, 18)

Step-by-step explanation:

We equate the 2 expressions in x :-

x^2 - 2x + 3 = -2x + 12

x^2 - 2x + 2x + 3 - 12 = 0

x^2 - 9 = 0

(x - 3)(x + 3) = 0

So x = 3 or -3.

When x = 3, f(x) = -2(3) + 12 = 6.

When x = -3, f(x) = -2(-3) + 12 = 18.

7 0

3 years ago

The town of lantana needs 14,000 for a new playground. Lantana elementary school raised 5,258, Lantana middle school raised 2834

Pavlova-9 [17]

Answer:

about 12000 but real answer is 12224

Step-by-step explanation:

6 0

2 years ago

Nine students took the SAT. Their scores are listed below. Later on, they read a book on test preparation and retook the SAT. Th

SCORPION-xisa [38]

Answer:

t= 0.4933

t ≥ t ( 0.025 ,8 ) = 2.306

Since the calculated value of t= 0.4933 is less than t ( 0.025 ,8 ) = 2.306 therefore we accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the book had no effect on their scores.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0: ud= 0 Ha: ud≠0

The significance level is set at ∝= 0.05

The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom

The critical region is t ≥ t ( 0.025 ,8 ) = 2.306

Computations

Student Scores before Scores after Difference d²

reading book ( after minus before)

1 720 740 20 400

2 860 860 0 0

3 850 840 -10 100

4 880 920 40 1600

5 860 890 30 900

6 710 720 10 100

7 850 840 -10 100

8 1200 1240 40 1600

9 950 970 20 40

∑ 6930 8020 140 4840

d`= ∑d/n= 140/9= 15.566

sd²= 1/8( 4840- 140²/9) = 1/8 (4840 - 2177.778) = 2662.22/8= 332.775

sd= 18.2422

t= 3/ 18.2422/ √9

t= 0.4933

7 0

3 years ago

What is the volume of a cylinder of 8in by 0.5 ft in cubic inches

Naily [24]

The volume of cylinder is 1205.76 cubic inches

Solution:

We have to find the volume of cylinder

The volume of cylinder is given by formula:

$V = \pi r^2h$

Where "r" is the radius and "h" is the height of cylinder

Given dimensions are:

Radius = 8 inches

Height = 0.5 feet

Convert feet to inches

1 feet = 12 inches

Therefore,

0.5 feet = 12 x 0.5 = 6 inches

Thus, we have got,

height = 6 inches

Substitute r = 8 inches and h = 6 inches in formula:

$V = 3.14 \times 8^2 \times 6\\\\V = 3.14 \times 64 \times 6\\\\V = 1205.76$

Thus volume of cylinder is 1205.76 cubic inches

7 0

4 years ago

Can someone explain?

LekaFEV [45]

87
Because the ratio is 3:7
So we plug in 203 for 7
3:7=?:203
7 goes into 203 29 times
29*3 is
87

4 0

3 years ago

Read 2 more answers