solve x²+5x+6=0 by completing the square​

Answers

Answer 1

Answer:

x = -2

x= -3

Step-by-step explanation:

x 2+5x+6=0

To solve the equation, factor x^2+5x+6 using formula x^2+(a+b)x+ab=(x+a)(x+b). To find a and b, set up a system to be solved.

a+b=5

ab=6

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 6.

1,6

2,3

Calculate the sum for each pair.

1+6=7

2+3=5

The solution is the pair that gives sum 5.

a=2

b=3

Rewrite factored expression (x+a)(x+b) using the obtained values.

(x+2)(x+3)

To find equation solutions, solve x+2=0 and x+3=0.

x=−2

x=−3


Related Questions

-3(2x +5) how to solve this problem

Answers

Answer:

Step-by-step explanation:

-3×2x)+(-3×5)

-6x+-15

BC is tangent to circle A. Determine the length of AC . ANSWERS: 1) 3 2) 4 3) 5 4) 6

Answers

Answer:

3) 5

Explanation:

Use Pythagoras Theorem where

a^2 + b^2 = c^2

3^2 + 4^2 = 25

C= root 25 = 5

A circle is a curve sketched out by a point moving in a plane. The length of AC in the given figure is 5 units. The correct option is

3.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

In a circle, the angle between the radius and tangent is always equal to 90°. Therefore, we can write that in the given figure ΔABC, the triangle is a right angle triangle with ∠B as the right angle.

Now, for the triangle using the Pythagoras theorem we can write,

AC² = AB² + BC²

AC² = 3² + 4²

AC² = 9 + 16

AC = √25

AC = 5

Hence, the length of AC in the given figure is 5 units.

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Find the area of the square with a side length of 8 ft.

Answers

Answer:

The area of square is 64ft².

Step-by-step explanation:

Given that all sides of a square are equal. So you have to apply the formula for area of square :

[tex]area = length \times width[/tex]

[tex]let \: length = 8 \\ let \: width = 8[/tex]

[tex]area = 8 \times 8[/tex]

[tex]area = 64 \: {ft}^{2} [/tex]

Answer:

here,

side length (l)= 8 ft.

now, area = l^2

a= 8^2

=64ft^2 is the answer..

hope i helped uh..

The number 99 is increased to 104. What is the percentage by which the number was increased, to the nearest tenth of a percent?

Answers

Answer:

5%

Step-by-step explanation:

104/99=1.05

Answer: 5%

Step-by-step explanation:

if you do the math of 99+5% you will get 103.95 and if you round that to the tenth you get 104.

At Jane's school there are 22 more girls than boys, b.

a) Write and expression for the number of girls in terms of the number of boys, b.

b) Using part a), write an equation involving b and solve it to find the number of boys at the school.

c) How many girls are there at the school?



ASAP no need to explain just the answer​

Answers

Answer:

A) girls=boys +22 .B)Boys=girls-22

Step-by-step explanation:

The answer for the question you are asking would be A. Your welcome

simplify the expression (-h^4)^5

Answers

See image below! If this is right please give me brainlest

when a number is to a power then to another power, the answer is the number to the power TIMES the other power

it should be:

-h^20.

Yash brought apples and bananas to a picnic The number of apples was three more than twice the number of beane Tach brought 11 apples to the pionie. How many bananas dd he bring?

Answers

Answer:

25 bananas

Step-by-step explanation:

11 apples doubled is 22 then plus 3 in 25 this he brought 25 bananas

The number of bananas that Yash brought is 4 bananas.

It is given that Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas.

We have to find out that how many bananas did he bring , if number of apple were 11.

What do you mean by linear equation in one variable ?

Linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are integers and x is a variable.

As per the question ;

Tach brought 11 apples to picnic.

Let's assume the number of bananas = x

Number of apple = 11 = 2x + 3

11 = 2 x + 3

⇒ 2x = 8

⇒ x = 8 ÷ 2

x = 4

Thus , the number of bananas that Yash brought is 4 bananas.

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Fill in the blanks for me

Answers

Answer:

Statement                             | Reason                                            

MNOP is a parallelogram    | Given

PM ║ ON                              | Definition of a parallelogram

∠PMO ≅ ∠MON                   | Alternate interior angles theorem

MN ║ PO                              | Definition of a parallelogram

∠POM ≅ ∠MNO                   | Alternate interior angles theorem

ΔMNO ≅ ΔPOM                   | ASA postulate

PM ≅ ON                              | CPCTC

QUICK 35 POINTS PLUS BRANLIEST. PLEASE ANSWER ALL THE QUESTIONS PROPERLY AND EXPLAIN HOW YOU GOT THEM. TRY TO ANSWER THEM BY TODAY.

THANKYOU

Answers

About 127.3(square root of 16,200, or 90√2)  Look at this problem like a right triangle.  Each leg is 90 feet, so the hypotenuse is the square root of 90^2 + 90^2About 52.3(square root of 2735.64)  Another right triangle problem!  Once again, with Pythagorean theorem (a^2 + b^2 = c^2) You can deduce that 60^2 = 29.4^2 + the width of the TV^2.About 11.6(Square root of 134.75)Another right triangle problem, you can deduce that 9.5^2 + The pool length^2 = 15^2

Hope it helps <3

(If it does, please give brainliest, only need one more for rank up :) )

Answer:

2. [tex]18\sqrt{5}[/tex]

3. [tex]52.303...[/tex]

4. [tex]11.608...[/tex]

Step-by-step explanation:

2. Using the Pythagorean Theorem, we can see that [tex]a^2+b^2=c^2[/tex]. Therefore, [tex]90^2+90^2=8100+8100=c^2[/tex]. We know that [tex]8100+8100[/tex] is [tex]16200[/tex]. The square root of [tex]16200[/tex]  is [tex]90\sqrt{2}[/tex].

3. Same as before, we use the Pythagorean Theorem. This time, we're calculating [tex]b[/tex] instead of [tex]c[/tex]. This means we have to do [tex]60^2-29.4^2=b^2[/tex], which gives us [tex]3600-864.36[/tex], which equals [tex]2735.64[/tex]. We can put this in decimal form, which would give us [tex]52.303[/tex][tex]...[/tex]

4. This one, we do [tex]15^2-9.5^2[/tex], which would give us [tex]134.75[/tex]. Simplifying this would give us [tex]11.608...[/tex].

Hope this helped! Just remember the Pythagorean Theorem.

Will give brainiest :)

Answers

Answer:

x= 116°

y= 127°

Step-by-step explanation:

x... The angle subtended at the centre is twice the angle subtended at the cicumfernce by the same arch

y.... Angle in a cyclic quadrilateral add up to 180°

hence 180-53=127

Given that 0≤β<2π, find all the solutions to the equation 2sin^2β=7sinβ+4.

Answers

Answer:

Step-by-step explanation:

2sin²β-7sinβ-4=0

2sin²β-8sin β+1 sin β-4=0

2 sin β(sin β-4)+1(sin β-4)=0

(sin β-4)(2sin β+1)=0

either sin β-4=0

sin β=4 (rejected,as |sin β|≤1)

or

2 sin β+1=0

sin β=-1/2=-sin (π/6)=sin (π+π/6),sin (2π-π/6)

β=7π/6,11π/6

PLSSS HELPPP Simplify: (2 - i) (4 +2i)

Answers

10
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Step-by-step explanation:

( 2 - 1)(4+2)

= (1)(6)

= 6

Question 5 (1 point)
(06.02 LC)
Which statement best describes the expression 3y = 8? (1 point)
O 1) 8 divided by 3 times y
O2) 8 times y divided by 3
03) 3 divided by 8 times y
O4) 3 times y divided by 8​

Answers

Answer:

Step-by-step explanation:

None of these choices is correct.  

3y = 8 is an equation, not an expression.  It states that "y is 8 divided by 3," which again is an equation.

Answer:

3 times y divided by 8

Step-by-step explanation:

Two retailers sell vanilla extract by the following price chart. When will their price be the same and how much?

Answers

Answer:

8 oz, $41

Step-by-step explanation:

For 4 oz, Chef Mate sells their's for $22 and Grocery Gourmet sells their's $25. Chef Mate sells his vanilla extract for $4.75/oz and Grocery Gourmet sells their's for $4/oz. At the 8th ounce, Chef Mate and Grocery Gourmet will charge the same amount, $41.

Chef Mate: $22 (price of 4 oz) + ($4.75 × 4) = $41

Gourmet Garden: $25 (price of 4 oz) + ($4 × 4) = $41

Image point B'(4, -8) was transformed using the translation (x-2, y + 3). What were the coordinates of B?
(2, -5)
(6,-5)
(2,-11)
(6.-11)
TURN IT IN
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Answers

Answer:

B(6 , -11)

Step-by-step explanation:

(x-2 , y+3)  = (4 , -8)

Compare the x & y co ordinates

x - 2 = 4   ; y + 3 = -8

x = 4 +2  ; y = -8 - 3

x = 6      ; y = -11

B(6 , -11)

5. Points A, B and C are all
the circle.O represents the centre.
Angle AOB = 2x+28 Angle ADB = 3x-70
Calculate the value for x​

Answers

Answer:

Step-by-step explanation:

angle acb=1/2angle aob=1/2(2x+28)------(anble subtended by an arc at centre is double the angle subtended by it at any other parts of the circle)

angle c+angle d=180....opp angles of a cyclic quad. are supplementry

hence,

x+14+3x-70=180

=>x=64

The value of x from the given figure is 59°.

Given that, points A, B and C are all the circle. O represents the center.

What is circle theorem to relate angle at circumference and central angle?

What is the circle?

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Here, Reflection of ∠AOB= 360-(2x+28)

∠ADB=1/2 (Reflection of ∠AOB)

⇒ 3x-70=1/2 (360-(2x+28))

⇒ 3x-70=1/2 (360-2x-28)

⇒ 3x-70=180-x-14

⇒ 3x-70=166-x

⇒ 3x+x=236

⇒ 4x=236

⇒ x=59

Therefore, the value of x from the given figure is 59°.

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Determine the measure of ∠F. answers: 1) 256° 2) 52° 3) 128° 4) 64°

Answers

Answer:

4) 64

Step-by-step explanation:

f = 128/2

f = 64

Answer:

4) 64°

Step-by-step explanation:

An inscribed angle has half the measure of the arc it intercepts.

m<F = (1/2)m(arc)BD

m<F = (1/2) * 128 deg

m<F = 64 deg

Question 8
Find the indefinite integral.
csc(4x) dx.

Answers

The correct answer is C. Using u-substitution: u=4x, du/dx=4, dx=du/4. So now we have to take the indefinite integral of (1/4)*csc(u). Which is (-1/4)ln|csc(u)+cot(u)|. Finally plug in 4x for u, which gives C, or the third option.

Answer:

Option C is correct.

Step-by-step explanation:

Your solution is correct. Given the integral [tex]\int \csc \left(4x\right)dx[/tex], let y = 4x, du = 4dx, respectively [tex]\frac{1}{4}[/tex]du = dx. Rewrite the given using these values of u and du.

[tex]\frac{du}{dx}[/tex] = 4 / 1 = 4,

[tex]\int csc(u)\frac{1}{4} du[/tex] - let us combine csc( u ) and 1 / 4,

[tex]\int csc(u) / 4 * du[/tex] - as 1 / 4 is a constant with respect to u, we can move it out of the integral,

[tex]\frac{1}{4} \int csc(u)du[/tex] - the integral of csc( u ) with respect to u is present in the form

" [tex]In(|csc(u) - cot(u)|)[/tex] . " Therefore,

[tex]\frac{1}{4} ( In(|csc(u) - cot(u)|) + C )[/tex] - replace all occurrences of u with 4x to receive the third solution. It can also be written as " [tex]\frac{1}{4} ( In(|csc(4x) - cot(4x)|) + C )[/tex], but only that your move the negative sign to the left of the integral.

Could someone help with this?

Answers

Answer:

30t

Step-by-step explanation:

2(15)t

30t

Answer: 30t

Step-by-step explanation:

The group earned 15t, or 15$ an hour for t hours.  Then it was doubled(15t * 2=30t)

The hypotenuse of a right triangles is 7 inches longer than the base and 14 inches longer than the height. The perimeter is 84 inches. Find its area

Answers

Answer:

294 in^2 = A

Step-by-step explanation:

Let h represent the length of the hypotenuse, b the base and h the height.  Because this is a right triangle, the Pythagorean Theorem applies.

(hypotenuse)^2 = (base)^2 + (height)^2

         h^2           =  (h - 7)^2  +  (h - 14)^2

Perimeter of the triangle is 84 inches, equal to (h) + (h - 7) + (h - 14), which in turn simplifies to 84 = h + h - 7 + h - 14, or 84 = 3h - 21, or 3h = 105.  Solving this for h, we get h = 35.

Then the base is (35 - 7), or 28, and the height is (35 - 14), or 21.

The area of the triangle is found using the formula

A = (1/2)(base)(height) = (1/2)(28)(21) = 294 in^2 = A

The graph shows data from a science experiment in which the temperature of a substance was measured over time.

What is the constant of proportionality for degrees per minute?

Answers

Answer:

The answer to this question is ---> 1/4

Step-by-step explanation:

Is 2(–2) + 6(2) equivalent to (–3)(–3) + (–1)(1)? Let negative numbers be represented with a "–" symbol and positive numbers be represented by "+" symbol. Use a pictorial model to justify your answer.

Answers

Answer:

Yes they are equivalent

Step-by-step explanation:

2(-2) = -4, plus 6(2) = 8 and

(-3)(-3) = 9, plus (-1)(1) = 8

Answer:

Yes they are equivalent

Step-by-step explanation:

the other fella right, check his reasons out, hope you guys learn from this question Stay safe everyone who sees this

PLLLLLLLLLLZZZZZZZZZ

Answers

Answer:

Hey there!

Donald would have 20x+10 dollars.

20 dollars (number of 20 dollars) + 10 dollars

Answer: 20x + 10

Step-by-step explanation:

20x in this expression means 20 * the number of dollar bills he owns.  Each bill is worth twenty dollars.  + 10 is simply 10 * 1(the number of 10 dollar bills he owns)

Hope it helps <3

Express 510 & 3/10 % as a decimal fraction.

Answers

Answer:

5.10 and 0.3

Step-by-step explanation:

510% in decimal form is 5.10 if u move the decimal to the left twice

3/10% is 30% which in decimal from is .3 if u move the decimal over to the left twice

hope this helps

HELP! A circle is inscribed in a square. A point N in the square is chosen at random. What is the probability that N lies in the shaded region? Round your answer to the nearest percent.

Answers

Answer:

30%

Step-by-step explanation:

Kathryn's school is selling tickets to a choral performance. On the first day of ticket sales the school sold 6 adult tickets and 11 student tickets for a total of $118. The school took in $156 on the second day by selling 12 adult tickets and 12 student tickets. What is the price of each adult ticket? What is the price of each student ticket?

Answers

Answer:

Adult price $5

Student price 8$

Step-by-step explanation:

Hello!

The school sells tickets for the choral performance with different prices depending on the ticket is for an adult or for a student of the school.

If X represents the price of an adult ticket and Y represent the price of a student ticket using the given information you can determine a set of two equations with two unknown values:

Day 1: 6 adult tickets and 11 student tickets for a total of $118

Symbolically: 6X + 11Y= $118

Day 2:  12 adult tickets and 12 student tickets for a total of $156

Symbolically: 12X + 12Y= $156

Step 1

From one of the formulas, clear one of the unknown values:

[tex]12X + 12Y= 156\\12Y= 156- 12X\\Y= \frac{156-12X}{12} \\Y= 13 - X[/tex]

Step 2

Replace the value obtained in step one in the second formula:

[tex]6X + 11Y= 118\\6X + 11(13 - X)= 118\\6X + (11*13) - 11X = 118\\6X -11X + 143= 118\\-5X= 118 - 143\\-5X= -25\\X= 5[/tex]

The ticket price for an adult is $5

Step 3

Using the value of X obtained in step 2, replace in the formula for Y to obtain the ticket price for students:

Y= 13 - X= 13 - 5= $8

I hope this helps!

Sign numbers, ratios & Proportion

(+10) + (+6) = ?

Answers

Answer:

16

Step-by-step explanation:

Putting a + in front of a number indicates that the number is positive. so we are just going to add it up.

10+6=16

10:6=5:3

Hope it helps:)

16 because 10 + 6 is 16

can you also answer these?!?

Answers

i cannot see the question for #33, but for

#34, im sure there are a bit more efficent ways to find surface area, but i just find the area of each square. area of top and bottom=240 square inches (120+120); area of shorter sides=60 square inches (30+30); area of longer sides= 72 square inches (36+36). add all of those together, so the total surface area is 372 square inches. So basically Charlene will need 372 square inches of wrapping paper

#35 the formula for volume is length*width*height. So do 60*45.5*14=38,220 cubic ft.

#36 first find the area of that triangle. (6*14)/2=42. Then find area of square which is 20*14=280. Add those (280+42) and get 322. So the area of the polygon is 322 square mm

what is the surface ara of a sphere with a diameter of 16cm

32pi cm^2
256 pi cm^2
1,024 pi cm^2
126 pi cm^2

Answers

Answer:

1024pi cm²

Step-by-step explanation:

4pi(16)²

4pi256

1024pi

Answer:

[tex]256\pi {cm}^{2} [/tex]

Step-by-step explanation:

surface area of a sphere=4πr^2

diametre=16

[tex]radius = \frac{diametre}{2} [/tex]

radius=8

[tex]surface \: area \: of \: sphere = 4 \times \pi \times {8}^{2} [/tex]

[tex] \: \: \: \: = 4 \times \pi \times 64[/tex]

[tex] \: \: \: \: = 256\pi {cm}^{2} [/tex]

Make a story problem for the expression below. Then solve the problem. (n + 15) ÷ 5

Answers

Answer:

Bob buys n number of cookies. He goes again and buys 15 more. After that he splits them among 5 friends.

Step-by-step explanation:

Answer:

Sandy buys a number of slices of pizzas from Pizza Hut. She then goes to Marco's Pizza and buys 15 more slices. Sandy goes to a party and splits the pizza slices evenly between 5 friends. How many slices of pizza did she buy from Pizza Hut?

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can you please help me with this one??? i need clear explanation Oral Roberts Dental Supplies has annual sales of $5,625,000. 80% are on credit. The firm has $475,000 in accounts receivable. Compute the value of the average collection period. A mass on a spring vibrates in simple harmonic motion at a frequency of 3.26 Hz and an amplitude of 5.76 cm. If the mass of the object of 0.218 kg, what is the spring constant two cars are traveling down the highway with the same speed if the first car increases its speed by 1km/hr and the other car decreases its speed by 10km/hr,then the first car will cover the same distance in 2hrs as the second car in 3 hrs, what is the speed of the cars A sample of an unknown substance has a mass of 0.158kg. If 2,520.0 j of heat is required to heat the substance from 32.0C to 61.0C what is the specific heat of the substance HELP!! Orchids are flowering plants that depend on bees for pollination. A population of orchids in a rainforest has reached its carrying capacity. The size of the rainforest's bee population is a limiting factor of the orchid population. What will happen to the orchids' carrying capacity if the rainforest's bee population decreases? Which has a preterite verb? *A. Mi mam tiene un trabajo nuevo.B. Mi hermano estaba comiendo la pizza,C. Mis amigos vinieron a visitarme anoche. I need help ASAP can some pls help me out Fructose is a molecule that can move across the cell membrane. If theconcentration of fructose is higher outside the cell than inside the cell, thenwhat will happen by the process of diffusion?O A. Fructose molecules will diffuse into the cell.B. Fructose molecules will disappear by diffusion.C. Fructose molecules will stay where they are.O D. Fructose molecules will diffuse out of the cell. if the relative density of a liquid is 0.34 what is the density of the liquid Use the Pythagorean theorem to calculate the diagonal of a TV is it's length is 36 inches and its width is 15 inches. Round your final answer to one decimal place. SOMEONE PLEASEEEEE HELLPPP !! The diameters of Breaburn apples are normally distributed with a mean of 8.2cm and a standard deviation of 2.8cm. If you had a shipment of 2000 apples, how many apples would have a diameter: a) smaller than 5.9cm? b) larger than 10.2cm? There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. How many of these sets contain any 5 numbers? k=5r-11s solve for r John couldn't recall the Serial number on his expensive bicycle. He remembered thatthere were 6 different digits, none used more than once, but couldn't remember whatdigits were used. He decided to write down all of the possible 6 digit numbers from 0 to 9. How many different possibilities will he have to create? What is the infinitive of the verb form of this word? Example: promotion--to promote (salvation _____) If the radius of a coin is 1cm than calculate its area What is the best way to improve the following code fragment? if ((counter % 10) == 0) { System.out.println("Counter is divisible by ten: " + counter); counter++; } else { System.out.println("Counter is not divisible by ten: " + counter); counter++; } Express the confidence interval 0.555 less than 0.777 in the form Modifying above p with caret plus or minus Upper E. In which quadrants do solutions for the inequality y is less than or equal to two sevenths times x plus 1 exist?