Consider this question:

-2x=x^2-6

1) Rewrite the question by completing the square. Your equation should look like (x+c)^2=d or (x-c)^2=d.

2) What are the solutions to the equation?

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

(1)

Given

- 2x = x² - 6 ( subtract x² from both sides )

- x² - 2x = - 6 ( multiply through by - 1 )

x² + 2x = 6

To complete the square

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

x² + 2(1)x + 1 = 6 + 1

(x + 1)² = 7

(2)

Take the square root of both sides

x + 1 = ± [tex]\sqrt{7}[/tex] ( subtract 1 from both sides )

x = - 1 ± [tex]\sqrt{7}[/tex]

Solutions are x = - 1 - [tex]\sqrt{7}[/tex] , x = - 1 + [tex]\sqrt{7}[/tex]


Related Questions

What is the image of the point (-9, -8) after a rotation of 90° counterclockwise
about the origin?

Answers

Answer:

-x,y

Step-by-step explanation:

The coordinates of the image (9, -8) after a rotation of 90° counter-clockwise about the origin.

What is a graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

What is a scale image?

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object

A rotation of 90° counter-clockwise about the origin is defined as the x-coordinate and y-coordinate change places, and the line y = x is the coordinates (-x , y).

To determine the image of the point (-9, -8) after a rotation of 90° counterclockwise about the origin

Suppose, the coordinates are (a,b)

A point (a,b) reflected across the line y = -x will become (-a,b).

Let a = -9 and b = -8

Substitute the values of a and b,

So the coordinates of image (9, -8)

Hence, the coordinates of the image (9, -8) after a rotation of 90° counter-clockwise about the origin.

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Toni can carry up to 18 lb in her backpack. Her lunch weighs 1 lb, her gym clothes way 2 lb, and her books (b) weigh 3 lb each. how many books can she carry in her backpack?

Answers

Answer:

Toni can carry a total of 5 books.

Step-by-step explanation:

[tex]1+2+3b\leq18[/tex] - Write the inequality out .

[tex]3+3b\leq 18[/tex] - Combine like terms.

 

[tex]3b\leq 15[/tex]  - Subtract 3 from both sides .

[tex]b\leq 5[/tex] -  Divide both sides by 3.

She can carry a max of 5 books.

Hope this helps!

Help please!!! 15 points!

Answers

(3,8) should be plotted on the 1st quadrant.

Hope this can help.

On approximately what percent of the days was the rainfall more than 15 mm?


Answers

Answer: monday aug 13

Step-by-step explanation:

write the prime factorization of the following
(A) 27
(B) 64
(C) 125

Answers

Answer:

A) 27 = 3 × 3 × 3

B) 64 = 2 × 2 × 2 × 2 × 2 × 2

C) 125 = 5 × 5× 5

Step-by-step explanation:

Answer:

(A) 27 = 3 by 3 by 3

(B) 64 = 2 by 2 by 2 by 2 by 2 by 2

(C) 125 = 5 by 5 by 5

Step-by-step explanation:

congruence transformation pls help me thanks

Answers

Answer:

X,6,1

Step-by-step explanation:

i mean thats what i think the answer is.

it flips down over the x axis. (x)

then it moves right 6 (x+6)

then it moves up one (y+1)

please solve the following question​

Answers

Answer:

5

Step-by-step explanation:

15(8/(8+16))

15(8/(24))

15(1/3)

5

Answer:

4.95

Step-by-step explanation:

15(8÷(8+16))

= 15(8÷24)

= 15×0.33

Reason for this answer↑: It was written as “8÷24” not “24÷8”

= 4.95

PLEASE HELP IM TRYING TO CATCH UP!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

hello guys images not coming

Step-by-step explanation:

please send the image clearly

Find the perimeter of triangle PQR if the vertices are P(3,0), Q(-1,3) and R(11,6).​

Answers

Answer :

[tex]\dag\bf\:P(x_1,y_1)=(3,0)[/tex]

[tex]\dag\bf\:Q(x_2,y_2)=(-1,3)[/tex]

[tex]\dag\bf\:R(x_3,y_3)=(11,6)[/tex]

Distance between P and Q :

[tex]\sf\:PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\sf\:PQ=\sqrt{(-1-3)^2+(3-0)^2}[/tex]

[tex]\sf\:PQ=\sqrt{(-4)^2+(3)^2}[/tex]

[tex]\sf\:PQ=\sqrt{16+9}[/tex]

[tex]\sf\:PQ=\sqrt{25}[/tex]

[tex]\bf\:PQ=5\:unit[/tex]

Distance between Q and R :

[tex]\sf\:QR=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}[/tex]

[tex]\sf\:QR=\sqrt{(11-(-1))^2+(6-3)^2}[/tex]

[tex]\sf\:QR=\sqrt{(12)^2+(3)^2}[/tex]

[tex]\sf\:QR=\sqrt{144+9}[/tex]

[tex]\sf\:QR=\sqrt{153}[/tex]

[tex]\bf\:QR=12.37\:unit[/tex]

Distance between P and R :

[tex]\sf\:PR=\sqrt{(x_1-x_3)^2+(y_1-y_3)^2}[/tex]

[tex]\sf\:PR=\sqrt{(3-11)^2+(0-6)^2}[/tex]

[tex]\sf\:PR=\sqrt{(-8)^2+(-6)^2}[/tex]

[tex]\sf\:PR=\sqrt{64+36}[/tex]

[tex]\sf\:PR=\sqrt{100}[/tex]

[tex]\bf\:PR=10\:unit[/tex]

Perimeter of Triangle :

➝ perimeter = PQ + QR + PR

➝ perimeter = 5 + 12.37 + 10

Perimeter = 27.37 unit

Evaluate this expression for b= 3, and a=2. b-a

Answers

substitute the values in the expression
b-a=3-2=1
answer b-a=1

Answer: 1

Explanation: In this problem, b - a is equal to 3 - 2 which gives us 1.

find an equation of the line passing through the point (5 4) and parallel to the line whose equation is y= 2x-6

Answers

Answer:

[tex]y = 2x - 6[/tex]

Step-by-step explanation:

Given

Equation: [tex]y = 2x - 6[/tex]

Required

Determine the equation of Point: (5,4)

First, we need to determine the slope of [tex]y = 2x - 6[/tex]

The general form of an equation is [tex]y = mx + b[/tex]

Where m represents the slope;

Hence; [tex]m =2[/tex]

Since the equation and the point are parallel. then they have the same slope (m).

[tex]m = 2[/tex]

Next, is to determine the equation of the point, using the following formula:

[tex]m = \frac{y - y_1}{x - x_1}[/tex]

Where

[tex](x_1,y_1) = (5,4)[/tex]

So, the equation becomes

[tex]2 = \frac{y - 4}{x - 5}[/tex]

Cross Multiply

[tex]y - 4 = 2(x - 5)[/tex]

Open Bracket

[tex]y - 4 = 2x - 10[/tex]

Make y the subject of formula

[tex]y = 2x - 10 + 4[/tex]

[tex]y = 2x - 6[/tex]

Hence, the equation is [tex]y = 2x - 6[/tex]


Part I: Describe how the account balance of a savings account earning simple interest is determined.

Part ll: Explain the difference between a savings account earning simple interest and a savings account earning compound interest.

Part Ill: Which type of savings account would you open and why?

Answers

Answer:

part 1: You start with an annual "simple interest rate," which is the percentage of the principal balance your money earns each year. ... Add the daily interest earned to the balance.

part 2: Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.

part 3: a compound interest account and here's why. When it comes to investing, compound interest is better since it allows funds to grow at a faster rate than they would in an account with a simple interest rate

Step-by-step explanation:

The frequency table shows the results of tossing a ball 24 times into the four coloured sections on a carnival game Section | number of | Tosses Blue | 3 Green | 5 Red | 12 Yellow | 4 Based on the data on the table, how many times will the ball most likely land in the yellow section when it is tossed 200 times? A. 35 B. 40 C. 50 D. 65

Answers

Answer:

50

Step-by-step explanation:

you toss the ball 24 times, and of those 24 times, it lands 12 times on the yellow section, so 12/24= 0.5

Answer: 50

Step-by-step explanation:

name the part of the circle​

Answers

Answer:

radius

Step-by-step explanation:

i believe it is radius because in my point of view it looks like the line travels up to the half of the circle.

JZ is a line to the middle of the circle , which would make it the RADIUS. If it when’s all the way such as ZG it is the diameter. The circumference is the outside of the circle.

Segment AB has a midpoint M. If A is located at (4, 2) and M is located at (7, -3), what are the coordinated of B?

Answers

(

8
,
3
)

Explanation:
The coordinates are ordered pairs with the
x
value listed first.
The change in the
x
position is
4


2
=
6

The change in the
y
position is
7

5
=
2

Since the midpoint is halfway between A and B, the change will stay the same, so
x
is

2

6
=

8
and
y
is
5

2
=
3

Describe the 4 cases to look out for when dealing with adding or subtracting integers

Answers

Answer:

Step 1: Take the absolute value of each number. Step 2: Subtract the number with a smaller absolute value from the number with bigger or larger absolute value. Step 3: Copy the sign of the number with the bigger or larger absolute value.

Step-by-step explanation:

Steve is cutting out decoration stars for his neighbors Labor day celebration. Steve has to cut out 9 stars in the last 10 minutes. How many stars should Steve expect to cut in one hour?​

Answers

Answer:

54 Stars

Step-by-step explanation:

Step 1:

60 mins = 1 Hour

Step 1:

10 × 6 = 60

Step 2:

9 × 6 = 54

Answer:

54 Stars

Hope This Helps :)

Answer:

54

In 1min star cutted= 9÷10

So in 1 hr or in60 min star cutted =60×9÷10

=54

what is sin 63°? round your answer to the nearest hundredth

Answers

Answer:

0.89

Step-by-step explanation:
it was right

The value of the trigonometric function sin 63° is 0.89. So option C is correct.

What is trigonometry?

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

Given that,

the trigonometric function is sin63°

the value of sin63° = ?

One of the way to calculate the value of sin63° is by using calculator

And from the calculator its value can be estimated as 0.89100

After round figure up-to two  digit

we can write the value sin63° is 0.89.

Hence, the value of the function from the calculator is comes out as 0.89.

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what are the two ways that rational numbers are written as decimals

Answers

Answer:

Repeating Decimals and Terminating Decimals

Step-by-step explanation:

Any number that can be written in fraction form is a rational number.

Hope This Helps :)

ax + by = c
Solve for b

Answers

Answer:

[tex]b = \frac{c - ax}{y}[/tex]

Step-by-step explanation:

[tex]ax + by = c \\ by = c - ax \\ b = \frac{c - ax}{y} [/tex]

Given f(x)= 18x + 12, find f(5).

Answers

Answer:

102

Step-by-step explanation:

Given f(x) =18x+12

F(5)=18(5)+12

=90+12

=102

102 no explanation why

Steve weighs 18 more pounds than Ryan. If their weight totals 144 pounds, how much does Ryan weigh?

Answers

Answer:

A) Steve = Ryan +18

B) Steve + Ryan = 144

A) Steve -Ryan = 18 then adding B

B) Steve + Ryan = 162

2 Steve = 162

Steve weighs 81 pounds

Ryan weighs (81 -18) pounds 63 pounds

Step-by-step explanation:

X = Ryan’s weight
X + 18 = Steve’s weight
144 = total weight for both

X + X + 18 = 144 ( equation)
2X = 144 -18 (group your equation)
2X/2 = 126/2 (divide both sides by 2)
X = 63 ( Ryan’s age)
X + 18 = 81 ( Steve’s age)

(7x^3)(3x^7) your answer should be a monomial in standard form

Answers

Answer:

i think its 21x^10

Step-by-step explanation:

Hotah and his 3 friends are each running 1/4 of a 2-mile relay race. How far is each person running?

Answers

Answer:

Each friend is running a half mile.

They are running 1/2 mile.

What are arithmetic operations?

The operations of addition, subtraction, multiplication, division, exponentiation, and modulus are carried out by the arithmetic operators.

They cover the study of numbers, including the order of operations, which are useful in algebra, data handling, and geometry, among other areas of mathematics.

Given Hotah and his 3 friends are each running 1/4 of a 2-mile relay race

total distance covered by them out of 2 miles is

2 x 1/4 = 1/2 miles

Therefore each person runs at 1/2 a mile.

Learn more about arithmetic operations;

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olivia can run 100 yards in 15 seconds. what is her speed in miles per hour?

Answers

14 mph

Step-by-step explanation:

13.636364

is what you get by doing

100/15 then you get 6.6666......7

after that you multiply that by 3600 because thats how many seconds in that hour.

Then you get 24000 and transfer it to miles and get 13.636364 and you round it and get 14mph

PLEASE MARK MY ANSWER BRAINLIEST

How many total necklaces can Maria own?

Answers

Answer:

49

Step-by-step explanation:

She can buy 46 more and she has three, so she can own 49

Answer:

Maria can own 15 necklaces.

Step-by-step explanation:

Sorry if i'm wrong but i hope this helps : )

what is the difference between equality and inequailty

Answers

Answer:

Step-by-step explanation:

Inequality and equality is that inequality is an unfair, not equal state while equality is (uncountable) the fact of being equal.

What is the simplified form of this expression (8x^2-3x+1/3) - (2x^2-8x+3/5)

Answers

Answer:=6x2+5x + −4/15

Step-by-step explanation:Let's simplify step-by-step.

8x2−3x+13−(2x2−8x+3/5)

Distribute the Negative Sign:

=8x2−3x+13+−1(2x2−8x+3/5)

=8x2+−3x+13+−1(2x2)+−1(−8x)+−1(3/5)

=8x2+−3x+13+−2x2+8x+−3/5

Combine Like Terms:

=8x2+−3x+1/3+−2x2+8x+−3/5

=(8x2+−2x2)+(−3x+8x)+(1/3+−3/5)

=6x2+5x+−4/15

1. Describe two ways the numbers in each proportion are related.
a) 5:20 = 125:500 b) 10:1 = 120:12 c) 75:25 = 300: 100
d) 1:3 = 16:48
2. Multiply between ratios to determine each value of n.
a) 2:5 = 8:n b) 2:n = 6:9 c) n:5 = 12:20
d) 8:n = 4:15
Need
Read
the lo
3. Multiply within ratios to determine each value of z.
a) 4:8 = 3:2 b) 5:2 = 6:18 c) z: 14 = 10:20
d) 3:21 = z:56​

Answers

Answer:

Each value has been identified below.

Step-by-step explanation:

(1) We have to describe two ways the numbers in each proportion are related;

(a) 5 : 20 = 125 : 500

One way of describing that the given ratios are in proportion is;

Product of means = Product of extremes

20 [tex]\times[/tex] 125 = 5 [tex]\times[/tex] 500

2500 = 2500

This shows that the given proportion is related.

Another way of describing that the given ratios are in proportion is;

As 5 : 20 = 125 : 500

We will check that; [tex]\frac{5}{125}[/tex] is equal to [tex]\frac{20}{500}[/tex] or not.

[tex]\frac{5}{125} = \frac{20}{500}[/tex]

[tex]\frac{1}{25} = \frac{1}{25}[/tex]

This shows that the given proportion is related.

(b) 10 : 1 = 120 : 12

One way of describing that the given ratios are in proportion is;

Product of means = Product of extremes

1 [tex]\times[/tex] 120 = 10 [tex]\times[/tex] 12

120 = 120

This shows that the given proportion is related.

Another way of describing that the given ratios are in proportion is;

As 10 : 1 = 120 : 12

We will check that; [tex]\frac{10}{120}[/tex] is equal to [tex]\frac{1}{12}[/tex] or not.

[tex]\frac{10}{120} = \frac{1}{12}[/tex]

[tex]\frac{1}{12} = \frac{1}{12}[/tex]

This shows that the given proportion is related.

(c) 75 : 25 = 300 : 100

One way of describing that the given ratios are in proportion is;

Product of means = Product of extremes

25 [tex]\times[/tex] 300 = 75 [tex]\times[/tex] 100

7500 = 7500

This shows that the given proportion is related.

Another way of describing that the given ratios are in proportion is;

As 75 : 25 = 300 : 100

We will check that; [tex]\frac{75}{300}[/tex] is equal to [tex]\frac{25}{100}[/tex] or not.

[tex]\frac{75}{300} = \frac{25}{100}[/tex]

[tex]\frac{1}{4} = \frac{1}{4}[/tex]

This shows that the given proportion is related.

(d) 1 : 3 = 16 : 48

One way of describing that the given ratios are in proportion is;

Product of means = Product of extremes

3 [tex]\times[/tex] 16 = 1 [tex]\times[/tex] 48

48 = 48

This shows that the given proportion is related.

Another way of describing that the given ratios are in proportion is;

As 1 : 3 = 16 : 48

We will check that; [tex]\frac{1}{16}[/tex] is equal to [tex]\frac{3}{48}[/tex] or not.

[tex]\frac{1}{16} = \frac{3}{48}[/tex]

[tex]\frac{1}{16} = \frac{1}{16}[/tex]

This shows that the given proportion is related.

(2) Now we have to determine each value of n in the following given ratios;

(a) 2 : 5 = 8 : n

As we know that Product of means = Product of extremes

5 [tex]\times[/tex] 8 = 2 [tex]\times[/tex] n

40 = 2n

[tex]n=\frac{40}{2}[/tex] = 20

Hence, the value of n is 20.

(b) 2 : n = 6 : 9

As we know that Product of means = Product of extremes

n [tex]\times[/tex] 6 = 2 [tex]\times[/tex] 9

6n = 18

[tex]n=\frac{18}{6}[/tex] = 3

Hence, the value of n is 3.

(c) n : 5 = 12 : 20

As we know that Product of means = Product of extremes

5 [tex]\times[/tex] 12 = n [tex]\times[/tex] 20

60 = 20n

[tex]n=\frac{60}{20}[/tex] = 3

Hence, the value of n is 3.

(d) 8 : n = 4 : 15

As we know that Product of means = Product of extremes

n [tex]\times[/tex] 4 = 8 [tex]\times[/tex] 15

4n = 120

[tex]n=\frac{120}{4}[/tex] = 30

Hence, the value of n is 30.

(3) Now we have to determine each value of z in the following given ratios;

(a) 4 : 8 = 3 : z

As we know that Product of means = Product of extremes

8 [tex]\times[/tex] 3 = 4 [tex]\times[/tex] z

24 = 4z

[tex]z=\frac{24}{4}[/tex] = 6

Hence, the value of z is 6.

(b) 5 : z = 6 : 18

As we know that Product of means = Product of extremes

z [tex]\times[/tex] 6 = 5 [tex]\times[/tex] 18

6z = 90

[tex]z=\frac{90}{6}[/tex] = 15

Hence, the value of z is 15.

(c) z : 14 = 10 : 20

As we know that Product of means = Product of extremes

14 [tex]\times[/tex] 10 = z [tex]\times[/tex] 20

140 = 20z

[tex]z=\frac{140}{20}[/tex] = 7

Hence, the value of z is 7.

(d) 3 : 21 = z : 56​

As we know that Product of means = Product of extremes

21 [tex]\times[/tex] z = 3 [tex]\times[/tex] 56

21z = 168

[tex]z=\frac{168}{21}[/tex] = 8

Hence, the value of z is 8.

Will you brainliest!!! Only question 10-14!

Answers

Answer:

10. <PTR = 80

11. < PTQ = 45

12. <QTS = 130 - 45 = 85

13. Luis didn't subtract 80 by 40

14. 180

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