All categories

3 years ago

X²- 6x = 7 FInd the soultion to the equation by completing the square

Mathematics

2 answers:

atroni [7]3 years ago

6 0

Answer:

x = - 1, x = 7

Step-by-step explanation:

Given

x² - 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3) x + 9 = 7 + 9

(x - 3)² = 16 ( take the square root of both sides )

x - 3 = ± $\sqrt{16}$ = ± 4

Add 3 to both sides

x = 3 ± 4, that is

x = 3 + 4 = 7 or x = 3 - 4 = - 1

Assoli18 [71]3 years ago

5 0

Answer:

x=-1 , x=7

Step-by-step explanation:

x²-6x-7=0

(x)² - 2(x)(3) +(3)² -7 - (3)²=0------------(adding and removing 9 to make it a complete square)

(x-3)² -7-9=0

(x-3)²-16=0

(x-3)² - (4)²= 0

(x-3+4)(x-3-4)=0

(x+1)(x-7)=0

(x+1)=0⇒x=-1

(x-7)=0⇒x=7

You might be interested in

An ice cream cone has a diameter of 3 inches.The distance from the top of the cone to the point at the bottom (height) is 5 inch

solong [7]

Answer:

11.781 cubic inches (round accordingly)

Step-by-step explanation:

The formula for the volume of a cone is:

$V=\frac{1}{3}\pi r^{2} h$

where r is the radius and h is the height.

For our ice cream cone:

d = 3 inches

r = 1.5 inches (the radius is half of the diameter)

h= 5 inches

So all we have to do is plug in our values and solve for the volume:

$\frac{1}{3}\pi (1.5)^{2}(5) = 11.781$

So our final answer is around 11.8 cubic inches.

3 0

3 years ago

WHAT IS 4 TIMES TWO THIRDS IN A MIXED FRACTION

Alex73 [517]

$\frac{4}{1}$ × $\frac{2}{3}$ = $\frac{8}{3}$
You then divide the numerator(top) by the denominator(bottom)
$\frac{8}{3}$ = $2 \frac{2}{3}$
Your answer is $2 \frac{2}{3}$

3 0

3 years ago

Read 2 more answers

Choose the option that best answers the question.The points A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6) form a triangle. If Angl

Sunny_sXe [5.5K]

Answer:

The correct option is 1.

Step-by-step explanation:

Given information: The coordinates of a right angled triangle ABC are A(0, 0), B(0, 4a – 5) and C(2a + 1, 2a + 6). Angle ABC = 90°.

It means AB and BC are legs of the right angled triangle ABC.

Side AB lies on the y-axis because the x-coordinate of both A and B is 0.

Two legs are perpendicular to each other. So, BC must be parallel to x-axis and the y-coordinate of both B and C is must be same.

$4a-5=2a+6$

$4a-2a=5+6$

$2a=11$

Divide both sides by 2.

$a=\frac{11}{2}$

The value of a is 2. So the coordinates of triangle ABC are

$B(0,4a-5)=B(0,4(\frac{11}{2})-5)\Rightarrow B(0,17)$

$C(2a+1,2a+6)=C(2(\frac{11}{2})+1,2(\frac{11}{2})+6)\Rightarrow C(12,17)$

The area of a triangle is

$Area=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|$

The area of triangle ABC is

$Area=\frac{1}{2}|0(17-17)+0(17-0)+12(0-17)|$

$Area=\frac{1}{2}|12(-17)|$

$Area=\frac{1}{2}|-204|$

$Area=\frac{1}{2}(204)$

$Area=102$

The area of triangle ABC is 102. Therefore the correct option is 1.

6 0

3 years ago

Textbook: Please write as an expression involving functions of Θ alone.

Setler [38]

Step-by-step explanation:

tan(Θ + 30°)

Use angle sum formula:

tan(A + B) = (tan A + tan B) / (1 − tan A tan B)

So we can write this as:

(tan Θ + tan 30°) / (1 − tan Θ tan 30°)

tan 30° = 1/√3, so:

(tan Θ + 1/√3) / (1 − 1/√3 tan Θ)

Multiply top and bottom by √3:

(√3 tan Θ + 1) / (√3 − tan Θ)

6 0

4 years ago

Different cities have different sales tax rates. Here are the sales tax charges on the same items in two different cities. Compl

tensa zangetsu [6.8K]

Answer:

What i xant understand ined pic

4 0

3 years ago

Read 2 more answers