Solve the following equation by completing the square.
x(x-5)=14

Answers

Answer 1

Answer:

[tex]x_1=-2,\: x_2=7[/tex]

Step-by-step explanation:

[tex]x(x-5)=14\\\\x^2-5x=14\\\\x^2-5x+(\frac{-5}{2})^2 =14+(\frac{-5}{2})^2\\\\x^2-5x+\frac{25}{4}=14+\frac{25}{4}\\\\x^2-5x+\frac{25}{4}=\frac{81}{4}\\ \\(x-\frac{5}{2})^2=\frac{81}{4}\\ \\x-\frac{5}{2}=\pm\frac{9}{2}\\ \\x=\frac{5}{2}\pm\frac{9}{2}\\ \\x_1=-2,\: x_2=7[/tex]


Related Questions


Hi I really need help on 4 pls help

Answers

Answer:

a. Draw a column for each ticket sold. (For 0-9, draw a bar upto 2. For 10-19, draw a bar upto 4. For 20-29, draw a bar upto 3. And for 30-39, draw a bar upto 1.

b. 10 students sold tickets

c. 40% of students sold 20 or more tickets

Answer:

a) attached image below

b) 10 studentssold tickets

c) 40% of students sold 20 or more tickets

Step-by-step explanation:

good job on number 3 !

Hope this helps, let me know if you have any questions :)

Which is a reasonable conclusion from the information presented in the bar graph? A. Germany won the fewest number of Olympic medals in the Summer Games of 2004. B. Russia won the most number of Olympic medals in the Summer Games of 2004. C. Australia won 20 Olympic medals in the Summer Games of 2004. D. Australia won more Olympic medals than the United States in the Summer Games of 2004.

Answers

It's really hard to see on the graph but the answer should be A. Germany won the fewest number of Olympic medals in the Summer Games of 2004.

If you read the other options, it doesn't make sense at all so through the process of elimination, A is the answer.

Answer:

A.Germany won the fewest number of Olympic medals in the Summer Games of 2004.

Step-by-step explanation:

because i took the quiz

Find if line M is a tangent line to circle B.

Answers

Answer:

No

Step-by-step explanation:

The tangent line must form a right angle with the radius

No, 4 5 6 isn't a right triangle

Answer:

Line m is not a tangent line to circle B.

Step-by-step explanation:

The tangent line to a circle is always perpendicular to the radius.

The line segment measuring 4 units is the radius of Circle B, therefore if line m is a tangent line to the circle, the angle between this segment and the segment measuring 5 units will be a right angle (90°).

We can use Pythagoras' Theorem to check if the triangle is a right triangle.

Pythagoras’ Theorem:  [tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Therefore, the legs are the line segments measuring 4 and 5, and the hypotenuse is the line segment measuring 6 units.

Substituting the values for the legs into the formula:

[tex]\implies 4^2+5^2=c^2[/tex]

[tex]\implies 16+25=c^2[/tex]

[tex]\implies 41=c^2[/tex]

[tex]\implies c=\sqrt{41}[/tex]

Therefore, as the hypotenuse of the triangle is not √41, the triangle is not a right triangle, and therefore line m is not a tangent line to circle B.

The tire's diameter is 1 meter, and it made 8000 rotations during the trip. How far did the bus travel?

Answers

The circumference of the tire = pi x diameter = 3.14 x 1 = 3.14 meters


every rotation the tire travels 3.14 meters


3.14 x 8000 = 25120 meters


1 kilometer = 1000 meters


25,120 meters /100 = 25.12 kilometers


answer: 25.12 kilometers

A professional painter knows that it takes 0.29 ounces of the paint he prefers to cover 1 square foot of wall. If he calculates that he will need 92.8 ounces of paint to cover an 8-foot wall, then how wide is the wall he is planning to paint?

Answers

Answer:

The wall is 40 feet wide.

Step-by-step explanation:

92.8 / 0.29 = 320 square feet

320 / 8 = 40 feet

HELP ME PLS IM THIS CLOSE TO LOOSING ALL OF MY SANITY

Answers

Answer:

INSPIRING

Step-by-step explanation:

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, the triangle is acute. However, if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse. And if the sides satisfy the Pythagorean theorem, it is a right triangle.

PLS HELP WILL GIVE BRAINLYEST!!! WHOEVER ANSWERS IN THE NEXT 2 HRS WILL GET 100 PTS.
(08.05;08.06 HC)

The box plot below shows the total amount of time, in minutes, the students of a class surf the Internet every day:

A box plot is shown. The left-most point on the plot is 20 and the right-most point is 95. The box is labeled 37.5 on the left edge and 60 on the right edge. A vertical line is drawn inside the rectangle at the point 50.

Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)

Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)

Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)

Answers

Answer:

it shows that the least amount is 37.5 minutes           it shows the most amount of time is 60 minutes         one thing it does not show is how many students where in the class

Step-by-step explanation:

Answer:

this is for A Part A: it shows that the least amount is 37.5 minutes

         it shows the most amount of time is 60 minutes

       one thing it does not show is how many students where in the class

Step-by-step explanation:

Well, you need to know the aton mic weight of Platinum (Pt) and the number of atoms per mole. The answer to the former is 195.084 g/mole and the latter is 6.023 * 10^23 atoms/mole. Then, multiply everything as shown below:

Number of atoms = (1 g) * (1/195.084 g/mole) * 6.023 * 10^23 atoms/mole

Number of atoms = 3.087 * 10^21 atoms

Note, I’ve included units on everything and you can see that they all cancel except for atoms. Dragging the units along can be a pain but it is a great way to check that they way the numbers are being combined is

In an archery competition, each archer shoots 3 arrows at a target. An archer’s score is calculated by measuring each arrow’s distance from the center of the target and finding the mean. One archer has a mean distance of 1.6 inches and a MAD of 1.3 inches in the first round. In the second round, this same archer’s arrows are farther from the center but more consistent. What values for the mean and MAD would fit this description for the second round?

Answers

Answer:

Mean: 3 Mad: 1/3

Step-by-step explanation:

First we need to find out the numbers, so to get a mean of 3 we have to get to 9 ebcause there are 3 arrows.

We have to make sure that the arrows are not too close to the centerYou can have decimals

2nd: Once you find the numbers which are 2.5, 3, and 3.5 you add them together and divide it by 3 to get 3 the mean

3rd: Find the MAD but adding .5 and .5 to get 1 then divide it by 3 and you get 1/3 as the MAD.

Hope this helps!

The archer's mean distance in the second round is 1.6 inches and the MAD is 0.83 inches.

What is a mean?

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Let's first recall that MAD stands for Mean Absolute Deviation, which is a measure of the variability of a set of data.

The MAD is calculated by taking the absolute value of the difference between each data point and the mean, and then finding the average of those absolute values.

Let the mean distance of the archer's arrows in the second round be m, and let the MAD be d.

In the first round, the archer's mean distance was 1.6 inches and the MAD was 1.3 inches.

This means that the absolute difference between each arrow's distance from the mean was, on average, 1.3 inches.

In the second round, the archer's arrows were farther from the center, so we expect the mean distance to be larger than 1.6 inches.

However, the arrows were more consistent, so we expect the MAD to be smaller than 1.3 inches.

To find the new value for the mean distance, we can use the fact that the sum of the distances from the mean is equal to zero. This means that:

3(m - mean) = 0

Solving for m, we get:

m = mean

Therefore, the mean distance in the second round is equal to the mean distance in the first round, which is 1.6 inches.

To find the new value for the MAD, we can use the fact that the variance (the square of the standard deviation) is equal to the average of the squared differences between each data point and the mean.

This means that:

Var = (1/3)(d²)

Since the arrows in the second round are more consistent, we expect the variance to be smaller than in the first round.

Therefore, we can set the new variance to be some fraction f of the old variance, and solve for the new value of d:

f(Var) = (1/3)(d²)

d² = 3f(Var)

d = √(3f(Var))

We don't know the exact value of f, but we do know that it is less than 1 since the variance is decreasing.

Let's assume that f = 0.5 for simplicity.

Using this value of f and the given values for the mean and MAD in the first round, we get:

Var = (1/3)(1.3³) = 0.56

d = sqrt(30.50.56) = 0.83

Therefore,

The archer's mean distance in the second round is 1.6 inches and the MAD is 0.83 inches.

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Question 8 of 25
A new auditorium is being built for a college. The balcony has 400 seats. The
floor has 50 rows with x seats in each row. The number of people in the
auditorium must be under 1300 to meet safety regulations.
What is the solution of this inequality, and what is its, meaning?
O A. 50x< 1300; The new auditorium must have fewer than 26 seats in
each row on the floor to meet fire safety regulations.
20
21
22
23
24
25
26
27
28
29
30

Answers

Inequalities help us to compare two unequal expressions. The number of seats in each row on the floor must be less than 18.

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Given the balcony has 400 seats, and the floor has 50 rows with each row having x number of seats. Therefore, the number of seats on the floor will be,

Number of seats on floor = 50 × x = 50x

Since the total number of seats in the auditorium should be less than 1300, therefore, the inequality can be written as,

Number of seats in balcony + Number of seats on floor < 1300

400 + 50x < 1300

50x < 1300-400

50x < 900

x < 18

Hence, the number of seats in each row on the floor must be less than 18.

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Maisy got a score of 80% correct on an quiz. There were 30 questions on the quiz. How many questions did Maisy get correct?​

Answers

Answer:

24 Questions answered correctly

Step-by-step explanation:

So as we know, 30/x = 100/80

100/80 = 1.25

Now we have 30/x = 1.25

Multiply both sides of the equation by x - (30/x)x = (1.25)x

Now we have 30 = 1.25x

Divide both sides by 1.25 - 30/1.25 = 1.25x/1.25

24 = x

Marcia is using the rule “Heart, Star, Star to make a repeating pattern. she wants the pattern to repeat 6 times. How many stars will be in Marcia’s pattern?

Answers

If the repeating pattern is “Heart, Star, Star". Then the number of the stars is 12 in Marcia's pattern.

What is multiplication?

It is also known as the product. If the object n is given to m times then we just simply multiply them.

Marcia is using the rule Heart, Star, Star to make a repeating pattern. she wants the pattern to repeat 6 times.

Then the number of the stars will be

→ 6 × 2

→ 12

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What is the length of the equal sides of an isosceles right-angle triangle, with a hypotenuse of 15cm?

Answers

Answer:

8.66

Step-by-step explanation:

15/sqrt(3) = 8.66 (to nearest hundreth)

Find the length of XV for Rectangle WXYZ.

PLEASE HELP!!!!

Answers

Answer: 20.5

Step-by-step explanation:

PLEASE ANSWER!!

A quadratic function is shown on the graph.

A. Write an equation to represent the function in vertex form.

B. Write an equation to represent the function in standard form.


Answers

Answer:

see explanation

Step-by-step explanation:

A

the equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

here (h, k ) = (1, - 4 ) , then

y = a(x - 1)² - 4

to find a substitute the coordinates of any other point on the graph into the equation.

using (0, - 3 )

- 3 = a(0 - 1)² - 4 ( add 4 to both sides )

1 = a(- 1)² = a ⇒ a = 1

y = (x - 1)² - 4 ← in vertex form

B

the equation of a quadratic in standard form is

y = ax² + bx + c ( a ≠ 0 )

using the result from A

y = (x - 1)² - 4 ← expand the factor using FOIL

  = x² - 2x + 1 - 4

y = x² - 2x - 3 ← in standard form

If a polynomial has three terms, x2 12x 36, which factoring method can be considered? perfect-square trinomial difference of squares sum of cubes difference of cubes

Answers

The best factoring method that can be considered for the polynomial is (a) perfect-square trinomial

How to determine the factoring method?

The polynomial is given as:

x² + 12x + 36

The above polynomial has three terms,

This means that the sum or the difference of cubes and squares cannot be applied (because it has more than two terms)

Hence, the best factoring method that can be considered for the polynomial is (a) perfect-square trinomial

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Answer:

A

Step-by-step explanation:

Got it right on Edge 1922

In order to select new board members, the French club held an election. 20% of the 40 members of the club voted. How many members voted?

Answers

The number of members is an illustration of proportions, and there are 200 members in the club

How to determine the members that vote?

The given parameters are:

French = 20%

French = 40

Let the number of members be x.

So, we have:

20% * x= 40

Divide both sides by 20%

x = 200

Hence, there are 200 members in the club

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in 1965, the population of country A was 2 714 000. in 2015 the population was 3 663 900. write the population in 2015 correct to 3 significant figures?​

Answers

BEST ANSWER :

(iv) a) 3.66 × 10^6

b) 2.714 × 10^6

(iii) 35%.

by question known :

(i) a) 3663900 = 3.6639 × 10^6

= 3.66 × 10^6

{ keep three significant digit }

b) 2714000 = 2.714 × 10^6

(iii) (3663900 - 2714000) ÷ 2714000 × 100%

= 949900 = 2714000 × 100%

= 0.35 × 100%

=35%

.°. the percentage increase in the population from 1965 to 2015 is 35%

Find the equation of the line that passes through the points (12, 9) and (2,7)

Answers

Answer:

see photo below for analysis

Step-by-step explanation:

PLEASEEE HELPPPPP

Triangle A and Triangle B are similar triangles that have corresponding angle measures of 98 degrees and 43 degrees . What is the angle measure of the third angle in Triangle A and Triangle B?

Answers

Answer:

47 degrees

Step-by-step explanation:

Similar just means they may be different sizes but have the same angle measure. That means the angles will be identical in both triangles A and B.

All angles must add up to 180 degrees. We already have two angles, so we just need to find the last one. 90+43= 133.

180-133=47.

A circular railroad-crossing sign has a diameter of 30 inches.
Which measurement is closest to the area of the sign in square inches?

Answers

Diameter = 30

30/2 = 15 15 is the radius

To find area:

3.14 x 15 x 15 = 706.5

706.5 is the answer

Help me with this please giving brainlist

Answers

Answer: 6 pounds is the mode

Step-by-step explanation: 6 is the most common number

what is the opposite of -26? how many units away from 0 is its location on a horizontal number line,and in which direction ?

Answers

I’m not sure but I think I don’t know I just really need points

How much times is 1,700,000,000 greater than 400,000,000

Answers

Answer:

4.25(Divided) or 1,300,000,000(subtracted)

The measure of AB is 126º. What is the measure of ABC, the tangent- chord angle?​

Answers

Ans:  B 63 degree

Step-by-step explanation:


Chord
to find the chord
1/2 or either 0.5

0.5 x 126 = 63
Mark me as Brainliest
Ty , hope it helped

Answer:

B

Step-by-step explanation:

is is correct 63 degrees , Hope this helps !!

i need helpppppp!!!!

Answers

Answer:

The first one

Step-by-step explanation:

neritic zone, shallow marine environment extending from mean low water down to 200-metre (660-foot) depths, generally corresponding to the continental shelf. Neritic waters are penetrated by varying amounts of sunlight, which permits photosynthesis by both planktonic and bottom-dwelling organisms.

please help!! hurry! thank you

Answers

Answer:

108 degrees

Hope this helps!!

Here are pairs of equivalent expressions, one in standard form and the other in factored form. Find
the missing numbers.
1. x2 +
+
and (x – 9) (x - 3)
2. 22 – 9x + 20 and (x – 4) (x +

Answers

The first equation will be x²-12x+27=(x-9)(x-3). The second equation will be x²-9x+20=(x-5)(x-4).

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1. For the first equation to be complete, we need to expand the factors, therefore, we can write,

(x-9)(x-3)

= x² - 9x - 3x + 27

=x²-12x+27

Hence, the first equation will be x²-12x+27=(x-9)(x-3).

2. For the second equation to be complete, we need to factorise the left side of the equation, therefore, we can write,

x²-9x+2

= x²-5x-4x+20

= x(x-5)-4(x-5)

=(x-5)(x-4)

Hence, the second equation will be x²-9x+20=(x-5)(x-4).

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Answer:

Step-by-step explanation:

lern it yourself

Joe has a cube shaped box that needs to be filled with packaging material If the length of one side 2 feet, then what is the volume of the box?

Answers

answer: 8 cubic feet

explanation:
given: cubic box of length=2 ft
to find: volume

solution: a= 2 ft
volume= a^3
=2^3
=8 ft^3

(06.04)
Determine the solution to the system of equations graphed below and explain
your reasoning in complete sentences.

WILL MARK BRAINLIEST

Answers

0,2 because that is where the lines meet.

Feng is starting a running plan to train for a race. In the first week of his running plan, Feng will run 15 miles. The plan calls for Feng to increase his weekly milage by 1.5 miles every week. If Feng sticks to the plan, how many miles would he be expected to run during his 15th week of the training plan?

Answers

Answer:

37.5 miles

Step-by-step explanation:

y = 1.5x + 15

1.5 * 15 = 22.5

22.5 + 15 = 37.5

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