Solve x2 + 8x – 3 = 0 using the completing-the-square method.
A.x = 4+ 13
B.X= 4+13
C.x= 4+19
D.X=4 + √19

Answers

Answer 1

[tex]x = -4 \pm \sqrt{19}[/tex]

Step-by-step explanation:

Let us put 3 on the right side and rewrite the equation as

[tex]x^2 + 8x = 3[/tex]

By putting 16 on both sides, our equation becomes

[tex]x^2 + 8x + 16 = 3 + 16 = 19[/tex]

[tex]\Rightarrow (x + 4)^2 = 19[/tex]

Taking the square root of the equation, we get

[tex]x + 4 = \pm \sqrt{19}[/tex]

Finally, solving for x,

[tex]x = -4 \pm \sqrt{19}[/tex]


Related Questions

The camp cook needed 2172 ounces of juice each day each carton of juice contains 64 ounces the Cook estimated that he needed 30 cartons of juice each day which expression proves that his estimate is incorrect

Answers

Answer: 384

Step-by-step explanation:

A flagpole has a 10 foot shadow. A soldier standing next to it is 6 foot tall and has a 2 foot shadow. How tall is the flagpole?

Answers

Answer:

30 feet tall flag pole

Step-by-step explanation:

I will give crown thing
On a map of Northern Virginia, 1 inch = 4 miles. The distance from Springfield to Dulles International Airport is 5.8 inches on the map. What is the actual distance to the airport?

Answers

Answer:

23.2 miles

Step-by-step explanation:

You just need to multiply de number of inches by the number of miles that values 1 in. Therefore

4 multiplied by 5.8 = 23.2

Answer:

The actual distance to the airport is 23.2 miles.

Step-by-step explanation:

1 inch = 4 miles

5.8 · 4 = 23.2

Since the distance to the Airport is 5.8 inches, you will multiply it by 4. You do this because 1 inch = 4 miles.

An auto insurance company classifies each motorist as "high risk" if the motorist has had at least one moving violation during the past calendar year and "low risk" if the motorist has had no violations during the past calendar year. According to the company's data, a high-risk motorist has a 50% chance of remaining in the high-risk category the next year and a 50% chance of moving to the low-risk category. A low-risk motorist has a 90% chance of moving to the high-risk category the next year and a 10% chance of remaining in the low-risk category. In the long term, what percentage of motorists fall in each category? (Round your answers to two decimal places.)

high-risk category %
low-risk category %

Answers

The percentage of motorists falling in each category, in the long term, are as follows:

High-risk category = 70%

Low-risk category = 30%

Data and Calculations:

Risk Profile Categories of Motorists

                                                       High Risk      Low Risk

Probability of remaining

 in the same category                      50%              10%

Probability of moving to another

 category                                          50%              90%

Probability a motorist falling in the high-risk category = (50% x 50%) + (50% x 90%)

= 25% + 45%

= 70%

Probability a motorist falling in the low-risk category = (50% x 50%) + (50% x 10%)

= 25% + 5%

= 30%

Thus, the probability of a motorist falling in the high-risk category is 70%, while the probability of a motorist falling in the low-risk category is 30%.

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A population numbers 18,000 organisms initially and grows by 16% each year.

Answers

Answer:

The answer is 20,880

Step-by-step explanation:

This won't be a very long explanation. What I did was add 18,000 plus 16% and I got 20,880.

Hope this helps!  

Have a nice day/night/afternoon.  

(Can you mark me brainliest?)

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An angle of 90° measures (___) Pi radians.

An angle of -pi/5 radians measures ____?

°.

Answers

[tex]\huge \bf༆ Answer ༄[/tex]

Conversion from degree to radian ~

[tex] \boxed{ \sf{ \frac{\pi}{180} \times \theta }}[/tex]

[tex] \sf \dfrac{\pi}{180 } \times 90[/tex]

[tex] \sf \dfrac{\pi}{2} \: \: rad[/tex]

Conversion from radians to degree ~

[tex] \boxed{ \sf{ \frac{180}{\pi} \times \theta}}[/tex]

[tex] \sf \dfrac{180}{\pi} \times - \dfrac{ \pi}{5} [/tex]

[tex] \sf - 36 \degree[/tex]

The required measures of the angles in radians and degree are given as  π/2 radians and -36° respectively.

What are the angle?

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

here,
An angle of 90° measures
in radians,
angle = π/180 × Ф
angle = π/180 × 90 = π/2 radians

Similarly,
An angle of -pi/5 radians
in degrees,
angle = 180 / π × -π/5
angle = -36°

Thus, the required measures of the angles in radians and degree are given as  π/2 radians and -36° respectively.

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The following represents the inflation rates of foreign country X for the past 5 years:

Year 1: 35%

Year 2: 20%

Year 3: 25%

Year 4: 30%

Year 5: 15%

Which statement is correct about the selection of a functional currency for country X at the end of year 5.





a.
Country X is highly inflationary; the US dollar must be used



b.
Country X is highly inflationary; the foreign currency must be used



c.
Country X is not highly inflationary; the US dollar must be used



d.
Country X is not highly inflationary; either the US dollar or the foreign currency may be used depending on the factors to determine the functional currency





e.
Country X is not highly inflationary; the foreign currency must be used

Answers

Answer:

year 3:25 A,C,E

Step-by-step explanation:

Un
número formado por 22 centenas,
515 unidades 1765 décimas, ¿cuantas
milésimas tiene?

Answers

Hay cero milésimas en los parámetros dados.

El valor posicional se refiere al valor representado por un dígito en un número sobre la base de su posición en el número.

De los parámetros dados:

22 centenas ⇒ 2200515 unidades ⇒  5151765 décimas ⇒ 176.5

Si sumamos los valores juntos, podremos determinar la cantidad de milésimas que tenemos:

= 2200+515+176.5

= 2891.5

Por tanto, podemos concluir que hay cero milésimas en los parámetros.

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Emma says that Function A has a greater initial value. Is Emma correct? Justify your response. Function A Function B Alternative text x 2 4 6 8 10 y 2 3 4 5 6 A. Yes; Function A has an initial value of 2 and Function B has an initial value of 1. So, Function A has a greater initial value. B. Yes; Function A has an initial value of –1 and Function B has an initial value of –2. So, Function A has a greater initial value. C. No; Function A has an initial value of –2 and Function B has an initial value of 1. So, Function B has a greater initial value. D. No; Function A has an initial value of 2 and Function B has an initial value of –1. So, Function B has a greater initial value

Answers

Answer: B

Step-by-step explanation: Function A starts at 0,2 and function B starts at 2,2

Answer:

It is C

Step-by-step explanation:

"No; Function A has an initial value of 2, and Function B has an initial value of 1. So, the functions do not have the same initial value."

To indirectly measure the distance across a river, Khalil stands on one side of the river
and uses sight-lines to a landmark on the opposite bank. Khalil draws the diagram
below to show the lengths and angles that he measured. Find PR, the distance across
the river. Round your answer to the nearest foot.
N
RI
185 ft
150 ft
0
275 ft
(Diagram is not to scale.)
ft
Submit Answer
Answer:

Answers

Khalil uses the method of similar triangles to find the distance across the river, [tex]\overline{PR}[/tex]

The distance across the river is [tex]\underline{308.\overline 3 \ feet}[/tex]

Reasons:

The distances between the formed the sight-lines are;

[tex]\overline{RB}[/tex] = 185 feet

[tex]\overline{OC}[/tex] = 275 feet

The distance between the point close to the river and the next point further from the river [tex]\overline{RO}[/tex] = 150 feet

In triangles ΔPRB and ΔPOC, we have;

∠PRE = ∠POC = 90° Given

∠PER ≅ ∠PCO By corresponding angle formed between two parallel lines and a common transversal.

∴ ΔPRE is similar to ΔPOC by Angle-Angle, AA, similarity theorem

Which gives;

[tex]\displaystyle \frac{\overline {PR}}{\overline {PO}} = \mathbf{\frac{\overline {RE}}{\overline {OC}}}[/tex]

Let x represent the distance across the river, we have;

[tex]\overline{PR}[/tex] = x

[tex]\overline{PO}[/tex] = 150 + x

Which gives;

[tex]\displaystyle \frac{x}{150 + x} = \frac{185}{275}[/tex]

275·x = 185 × (150 + x) = 27,750 + 185·x

275·x - 185·x = 27,750

90·x = 27,750

[tex]\displaystyle x = \frac{27,750}{90} = \mathbf{308.\overline 3}[/tex]

Therefore, the distance across the river, x = [tex]\mathbf{\overline{PR}}[/tex] = [tex]\underline{308.\overline 3 \ feet}[/tex]

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PLS HELP!!!!!! (again! XP)
Express each of these numbers, as a product of two fractions 2/25

Answers

that is a half so divide it

If 15 out of 25 students are boys, what percent of the class is
made up of boys?

Answers

Ummmmm i think you do 25 divided by .15

Question 7
Charlie asked a random sample of both boys and girls how much time they had spent on math homework that week. Charlie displayed his data in the box plots below
Minutes Spent on Homework
Boys
Girls
10 20 30
50 60 70
Which statement is a correct inference based on this data?
А
The amount of time spent on homework is less variable for the boys than for the girls
B
The amount of time spent on homework is generally greater for the boys than for the girls
С
The percentage of boys who spent less than the median amount of time on homework is less than the percentage of girls who spent less than the median
D
The data for the boys has a greater range of values than does the data for the girls
62021 Iluminate Education, Inc

Answers

The percentage of boys who spent less than the median amount of time is less than the number of girls who spent less than the median amount of time in doing the homework.

The median is a measure of central tendency. The median of a given data set shows the middle number in a given set of scores when they arranged in ascending or descending order.

The box plots in the question shows the random sample of both boys and girls how much time they had spent on math homework in a week. We can see from the box plot that the percentage of boys who spent less than the median amount of time is less than the number of girls who spent less than the median amount of time in doing the homework.

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2/3 plus 1/4 plzzzzzzzzzzzzzzzzzz

Answers

11/12

Answer:

1. find the least common denominator (LCD) of 2/3, 1/4 in other words, find the Least Common Multiple (LCM) of 3,4

Least Common Multiple (LCM) of 3,4 LCD = 12

Least Common Multiple (LCM) of 3,4 LCD = 122.

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__3 x 4 4x3

Least Common Multiple (LCM) of 3,4 LCD = 122.Make the Denominators the Same As The LCD.2_x_4_ + _1 x 3__3 x 4 4x33. Simplify denominators are Now The Same.

8/12 + 3/12

4. join the denominators

__8+3_____

12

5. Answer 11/12

Btw the Lines are Just For Separating numbers.

What is an equation of the line with slope 6 and y-intercept -4?

Answers

Answer:

y = 6x - 4

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

Identify variables.

m = 6

y = -4

Step 2: Find Equation

Substitute in variables [Slope-Intercept Form]:                                              y = 6x - 4

can someone please explain this question

Answers

Sure thing!

So if we look at the function, it is an exponential, meaning that it is a number to the power of x
The graph can be described by the equation

y = a^x

If we look at the graph, one of the points on the line is (2, 16), the x value is 2 and the y value is 16

If we consider this along with the function for the graph, we can say that

16 = a^2

Just solve this for a and you’ll have your answer :)
So the answer is 15

Michael drove 638 miles in 11 hours.

At the same rate, how many miles would he drive in 8 hours?

Answers

she will drive 754 miles in 13 hrs.

find the equation of the line that is perpendicular to the given line and passes through the given point. CD; (-2,1). C cornet point is (2,13). D cornet point is (5,7).

Answers

Answer:

  x -2y = -4

Step-by-step explanation:

The slope of the line between points C and D is ...

  m = (y2 -y1)/(x2 -x1)

  m = (7 -13)/(5 -2) = -6/3 = -2

The slope of the perpendicular line is the opposite reciprocal of this: -1/(-2) = 1/2. The point-slope equation of the desired line is ...

  y -k = m(x -h) . . . . line with slope m through point (h, k)

  y -1 = 1/2(x -(-2))

We can rearrange this to standard form.

  2y -2 = x +2 . . . . . multiply by 2

  -4 = x -2y . . . . . . . subtract 2y+2

  x -2y = -4 . . . . . . standard form equation of the desired line

What is the answer to the question. Solve for x

Answers

Answer:

Answer:

[tex]x=\frac{75}2[/tex]

Step-by-step explanation:

Give letters, as in the attached image.

The triangles ABE and CDE are similars (AAA). In particular [tex]AE:CE=BE:DE \rightarrow 46:30=(x+20):x \rightarrow 46x=30(x+20) \rightarrow 23x=15x+300 \rightarrow 8x=300\rightarrow x=\frac{75}2[/tex]

How do you solve this??

Answers

Answer:

look it up in internet and find th right answers

Answer:

g(x)=3|x| is the first box

f(x)=1/3|x| is the second box

Step-by-step explanation:

you can solve these type of questions by looking at the slope which is in front of the x.

since 1/3 is smaller than 3 it's going to have lower slope resulting in 3 to incline faster

.I want a way to solve this question​

Answers

Check the picture below.

so then γ ≈ 180 - 69 - 43, γ ≈ 68.

For her phone service, Kala pays a monthly fee of $24, and she pays an additional $0.07 per minute of use. The least she has been charged in a month is $118.64.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.

Answers

Answer:

m=1352

Step-by-step explanation:

(118.64-24)/0.07=m

QUESTION 16 PLEASE HELP ME ASAPP

Answers

Answer: changes over time

Step-by-step explanation: it is always decreasing

Un rectángulo tiene un perímetro de 64 pulgadas y una longitud de22 pulgadas . ¿Qué ecuación puedes resolver para encontrar el ancho?

Answers

Answer:

[(P - (2 x l)] / 2

Step-by-step explanation:

[Perimeter - ( 2 x length) ] / 2

(64 - 2x22)/2 = 10 pulgadas de ancho

Help me with my math please​

Answers

Step-by-step explanation:

1 _21:00_ , _22:10_, 1:10

2. 1:20

3. 18:00

4. 21:35

1. 21:00, 22:10, 1 hr and 10 minutes

2. 20 minutes

3. 18:40

4. 21:35

х Y
2 4
4 5
7. 6.5

Write the equation of the line represented by the table

Answers

Answer:

y = 0.5x + 3

Step-by-step explanation:

Which expression is equivalent to 53p + (16p + 7p)

Answers

Answer:

u777766665655566667777777777777

76p is the equivalent expression of 53p + (16p + 7p)

What is Expression?

An expression is combination of variables, numbers and operators.

The given expression is 53p + (16p + 7p)

Fifty three times of p plus sixteen p plus seven p.

In the given expression p is the variable and plus is the operator.

We need to find the equivalent expression.

Equivalent expressions are expressions that work the same even though they look different.

53p + (16p + 7p)

76p

Hence, 76p is the equivalent expression of 53p + (16p + 7p)

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A golfer takes an uphill shot towards the hole, and they make the shot. The path of the ball can be modeled by the equation y=-5^2– 40x– 10, where x is the horizontal distance and y is the vertical distance traveled by the ball in meters. How much higher is the hole than the spot from where the shot was taken? The hole is meters higher What was the maximum height above the hole that the ball reached while it was in the air? meters The maximum height that the ball reached above the hole was What was the horizontal distance that the ball traveled from the point that the shot was taken to the hole? Round your ai the nearest tenth of a meter. meters. The horizontal distance covered by the ball was​

Answers

Answer:

Solve for n

n=log5  (− 2 /y  −20x−5),y<−40x−10

Step-by-step explanation:

plz help me to answer

Answers

Answer:

for 3, 4 or both?

4. is probably zero

Step-by-step explanation:

Wait is 4 a question?

[tex]cos^2 x + \cos^2 y = \cos(2x + 2y)\\\\\implies \dfrac{d}{dx} (\cos^2 x + \cos^2 y) = \dfrac{d}{dx} \cos(2x+2y)\\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-\sin(2x+2y) \left(2+2\dfrac{dy}{dx} \right) \\\\\implies -2\cos x \sin x -2 \cos y \sin y \dfrac{dy}{dx}=-2\sin(2x+2y) -2\sin(2x+2y)\dfrac{dy}{dx} \right) \\\\\implies 2 \sin(2x+2y) \dfrac{dy}{dx} - 2 \cos y \sin y \dfrac{dy}{dx} = 2 \cos x \sin x-2\sin(2x+2y)[/tex]

[tex]\implies \sin(2x+2y) \dfrac{dy}{dx} - \cos y \sin y \dfrac{dy}{dx} = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} [\sin(2x+2y) - \cos y \sin y] = \cos x \sin x-\sin(2x+2y)\\\\\implies \dfrac{dy}{dx} = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}\\\\\implies y'(x) = \dfrac{\cos x \sin x-\sin(2x+2y)}{\sin(2x+2y) - \cos y \sin y}[/tex]

its suppolsy the hardest question in math

Answers

Answer:

E

Step-by-step explanation:

[tex]\sqrt{\dfrac{64}{49}} = \dfrac{\sqrt{64}}{\sqrt{49}} = \dfrac 87[/tex]

Answer:

E

Step-by-step explanation:

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