Solve by completing the square

Answers

Answer 1

[tex]4x^2+12x=32\\\\\implies x^2+3x=8\\\\\implies x^2 +2 \cdot \dfrac 32 \cdot x+\left(\dfrac 32 \right)^2 - \left(\dfrac 32\right)^2 =8\\ \\\implies \left(x+\dfrac 32 \right)^2 = 8 + \dfrac 94 = \dfrac{41}4\\\\\implies x+\dfrac 32 = \pm\dfrac{\sqrt{41}}2\\\\\implies x = \pm \dfrac{\sqrt {41}}2 - \dfrac 32\\\\\text{The roots are}~ x = -\dfrac 32-\dfrac{\sqrt{41}}2~ \text{and}~~ x = -\dfrac 32+\dfrac{\sqrt{41}}2[/tex]

Related Questions

prove that it is congruent

Answers

Answer:

The dashes on the side lengths mean that they are equal in length
⇒ PQ = RP

The triangles share one side PS

The figure also states that m∠QPS = m∠RPS

Therefore, the triangles are SAS congruent since they have two pairs of congruent sides and a congruent included angle.

[tex]x^{2} -36\frax+5/(x+6)[/tex]

Answers

the answer is

x^{2}-31x+5b

simplify the expression 30x^6/3x^-2

Answers

Answer:

[tex]30x^{4}[/tex]

Step-by-step explanation:

Jayla just measured her pet snake and found out that it is 3.8 inches long, which is 52% longer than the last time Jayla measured. How long was the pet snake last time?

Answers

Let x be the original length.
x * (1+0.52) = 3.8
x * 1.52 = 3.8
x = 2.5 inches

Need help with this geometric question ASAP, Thank you

Answers

The error would be assuming the altitude is a bisector and divides the sides evenly.

Is ABSE- ATES? If so, identify the similarity postulate or theorem that
applies.

Answers

Hope it helps best of luck

The dimensions of triangle A are three times the dimensions of triangle B. The area of triangle B is 28 cm What is the area of triangle A?

Answers

Answer:

Below in bold.

Step-by-step explanation:

The ratio of theire areas is 1^2 : 3^2

= 1:9.

So the area of triangle A = 28 * 9

= 252 cm^2.

Answer:

[tex]252cm {}^{2} [/tex]

step by step explanation:

[tex]since \: \: dimension \: of \: traiangle \: a \: = 3 times \: dimension \: of \: triangle \: b \\ note \: that \: area \: is \: square \: of \: dimension \: \\ therefore \: area \: of \: triangle \: a \: = 3 {}^{2} \: area \: of \: triale \: \: b \\ area \: of \: trianle \: a = 9 \times 28 = 252cm {}^{2} [/tex]

If 6/10 is multiplied by a fraction less than one what will be the product?

Answers

Answer:

If 6/10 is multiple by a fraction less then one the product would be 1/2

Step-by-step explanation:

6/10 is also equal to 0.6

If 0.6 is multipled by something less then one the product would not be able to be greater then 6/10

Resulting in 1/2 being the product.

Answer: All you gotta do is multiply 6x10 and then u get 60 so the product of of 6/10 is 60

The hypotenuse of a triangle is 10 inches long. One of the legs is 6.5 inches long. what is the measurement of the missing leg? round to the nearest tenth, if necessary

Answers

Answer:

7.6

Step-by-step explanation:

a^2 + b^2 = c^2

6.5^2 + x^2 = 10^2

42.25 + x^2 = 100

isolate x by subtracting 42.25 on both sides

x^2 = 57.75

square root of 57.75 or 7.6

April is 19, Bryan is 20, Carla is 20, and Dave is 21, how old is Erica is the average of their given ages is 23?

Answers

Answer: 35

Step-by-step explanation:

The average can be found by adding their ages together and dividing by the number of ages.

Given:

[tex]\frac{19+20+20+21+x}{5}[/tex] = 23

Multiply both sides of the equation by 5:

19 + 20 + 20 + 21 + x = 115

Combine like terms:

80 + x = 115

Subtract 80 from both sides of the equation:

x = 35

Erica is 35.

Express the set using interval notation.
x≥1

Answers

Answer:

[1,∞)

Step-by-step explanation:

Brackets indicate equal to while parentheses indicate not equal to this bound.

Select the correct answer.
Which of the equations below represents a line perpendicular to the x-axis?
OA
I = 3
OB.
= = 3y
Зу
Ос.
1 = Y
=
OD
r = -3y

Answers

Answer:

0D r equals -3y

hope ts helpful

jan saw 9 full moons in 252 days write each statement as a rate

Answers

i honestly don’t know sorry

Need help Please! Quick

Answers

Answer:

please see photo for details

a family makes gumbo to serve during jazz fest.the gumbo recipe requires twice as many cups of chopped tomatoes as diced onions.Which expression can be used to represent the number of cups of diced onions based on the number of cups of chopped tomatoes,t?
A) t^2
B)2+t
C) t÷2
D)2t

Answers

Answer:

D: 2t

Step-by-step explanation:

a coefficient next to a variable is an automatic multiplication equation

The solution is Option D.

The number of cups of diced onions A to the number of cups of chopped tomatoes t is represented by the equation A = 2t

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = total number of cups of diced onions

Let the total number of cups of chopped tomatoes be = t

Now , the recipe requires twice as many cups of chopped tomatoes as diced onions

Substituting the values in the equation , we get

A = 2t

where A = number of cups of diced onions

t = number of cups of chopped tomatoes

Therefore , the value of A is 2t

Hence ,

The equation will be A = 2t where t is the number of cups of tomatoes

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Find the greatest common factor (GCF) of 12x and 18x3.

Answers

Answer:

the answer to that question is 6x squared.

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x and 18x3

first, simplify 18x3

12x and 54x

Now, cancel the x, we'll add it on in the end

12 and 54

Factor it!

(2 * 3 * 2) and (2 * 3 * 3 * 3)

2 and 3 remain common, so multiply = 6

Add on x from before.

6x is the answer.

Darren's rectangle measures 3 1/4 units by 4 1/3 units. what is its area

area = ? ?/?

Answers

Answer:

14 1/13

Step-by-step explanation:

13/4*13/3=169/12=14 1/13

axis of symmetry f(x) = −4(x − 8)^ 2 + 3

Answers

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

For an equation in the form of [tex]y=a(x-h)^2+k[/tex], the axis of symmetry is where [tex]x=h[/tex]. In this case, the axis of symmetry is the line [tex]x=8[/tex]

Which number is bigger: 0.135 or 0.14?

Answers

0.14 is the correct answer

Shahida has seen an eagle landing at the top of the tree in her backyard. She places a camera on a tripod a distance of 12 feet from the
trunk of the tree. She angles the camera to the top of the tree so she can get a picture of the eagle. The height of the tree is 31 feet. The
height of the tripod is 4 feet.

Answers

The angle of elevation from the tripod to the top of the tree is about 66 degrees

What is trigonometric ratio?

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Let Ф represent the angle of elevation. Since the tripod is at a height of 4 feet, hence:

tanФ = (31 - 4) / 12

Ф = 66 degrees

The angle of elevation from the tripod to the top of the tree is about 66 degrees

Find out more on trigonometric ratio at: https://brainly.com/question/24349828

Whcih choice best describes the group this shape belongs in, based on the kinds of sides and angles it has? Angela chose A as the correct answer. How did she get that answer?

Answers

The shape in the figure has 6 sides

The choice that describes the group the shape belongs to is (a) parallel sides, acute angles

How to determine the group of the shape?

From the figure, we have the following highlights

The shape has 6 sidesThe direct opposite sides are equalThe direct opposite sides are parallelThe measure of angles between adjacent sides are less than 90 degrees i.e. acute angles

The above highlight mean that:

The shape belongs to parallel sides, acute angles group of shapes

Hence, Angela's conclusion is correct

Answers

Answer:

B and E

Step-by-step explanation:

0.5 ÷ 0.25 = 2

A. NO because it's 20

B. Yes

C. NO because it's 0.2

D. NO because it's 1.1 repeating

E. Yes

insurance that pays for damages to houses or businesses is called

Answers

Answer:

Homeowners insurance

Step-by-step explanation:

Homeowners insurance is designed to protect your home from what are called "perils." A peril is your exposure to risk or something that causes loss or destruction. … Homeowners 2 (HO2): This policy protects your property against 18 perils (including 11 perils from Homeowners 1). Typical homeowners insurance policies offer coverage for damage caused by fires, lightning strikes, windstorms and hail. But, it's important to know that not all natural disasters are covered by homeowners insurance. For example, damage caused by earthquakes and floods are not typically covered by homeowners insurance.

Find the values of x for which the denominator is equal to zero for 2x^2+5/x^2-2x .

x = 0, x = 2

x = 1, x = 2

none

x = 2

Answers

Let's see

[tex]\\ \rm\rightarrowtail x^2-2x=0[/tex]

[tex]\\ \rm\rightarrowtail x(x-2)=0[/tex]

[tex]\\ \rm\rightarrowtail x=0\:or\:x-2=0[/tex]

[tex]\\ \rm\rightarrowtail x=0\:or\:x=2[/tex]

꧁⫷ᴀɴsᴡᴇʀ⫸꧂

[tex] \green{••••••••••••••••••••••} \blue{••••••••••••••••••••••••••}[/tex]

[tex] \sf {x^2 - 2x = 0} [/tex]

[tex] \sf {x ( x - 2) = 0} [/tex]

[tex] \sf {x = 0 \: or \: x-2 = 0} [/tex]

[tex] \sf \green{ {x = 0 \: or \: x = 2}} [/tex]

#CarryOnLearning

#LibreAngMatuto

What is the equation of a circle with center (−8, 3) and radius 8?

(x + 8)2 + (y − 3)2 = 64

(x − 8)2 + (y + 3)2 = 64

(x − 8)2 + (y + 3)2 = 8

(x + 8)2 + (y − 3)2 = 8

Answers

Answer:

(x + 8)² + (y - 3)² = 64

Step-by-step explanation:

(x - (-8))² + (y - 3)² = 8²

(x + 8)² + (y - 3)² = 64

PLEASE HELP AND EXPLAIN (WILL MARK BRAINLYIST)
Figure JKLMN is a scaled version of PQRST. The two figures are shown below.
The scale factor of figure JKLMN to figure PQRST is 3:2. If KL = 27 cm and MN = 45 cm, what is the length of side ST?
A.
30 cm
B.
40.5 cm
C.
67.5 cm
D.
18 cm

Answers

Answer: the answer is 40.5 cm

Step-by-step explanation:

first your gonna want to look at the numbers given and then solve.

hello help me with this question thanks in advance

Answers

Answer:

B. 98 ft

Step-by-step explanation:

x^2 + y^2 = z^2

z = sqrt(84^2 + 50^2) = 97.7 ft ~ 98 ft

Question #5 Answer:

B. 98 feet

Step by-step explanation:

[tex]Solution:\ From\ question\\ 84\ feet\ long\ and\ 50\ feet\ wide\\ so\ he\ will\ run\ \sqrt{{84}^2+{50}^2}\ \approx98\ feet[/tex]

6 8/10 + 1 7/10 =
please help meee

Answers

Answer:

8.2

Step-by-step explanation:

Hope this helps....

Answer:

The answer is 8 1 / 2

Step-by-step explanation:

See the Image

Option 1 is easier to understand

BCD and EFG are shown below. Which of the following statements is true? Look at picture.

Answers

Answer:

(b) ∠EGF ≅ ∠BDC

Step-by-step explanation:

Angles D and G are both marked with double arcs, indicating they are congruent:

∠EGF ≅ ∠BDC

Other choices:

BD is the short segment between the marked angles. It has no "decoration." EF is the longer segment with a single hash mark decoration. These are not corresponding parts, so are not congruent. There is no right angle in these triangles, so the Pythagorean theorem is not applicable.

CD is the longest side, with no decoration. EF is the middle-length side with a single hash mark decoration. These are not corresponding sides.

Answer:

I don't know I'm sorry soo just try to work it out if u don't know how than ask someone you know okay, ur welcome.

Help help her help help

Answers

Answer:

x = 12

Step-by-step explanation:

1. Subtract 9 from both sides:

x/6 = 2

2. Multiply both sides by 6:

x = 12

Answer:

9 + x/6 = 11

Always get rid of the constants first,

-9 -9(we subtract 9 from both sides because the inverse operation of addition is subtraction)

x/6 = 2

Isolate x by multiplying by 6 on both sides (because the inverse operation of division is multiplication)

*6 *6

x = 12

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