Solve x2 + 2x = 4 for x by completing the square. x equals plus or minus square root of 5 plus 1 x equals plus or minus square root of 5 minus 1 x = 1 x = 3

Answer:

The ratio of 1 by 5 is to 1 by 6​  is   Rs 176  :   Rs 146.67

Step-by-step explanation:

The given amount here = Rs 880

Now let us assume the 1 by 5 of Rs 880 = m

and assume 1 by 6 of the amount Rs 880 =n

To Find  m : n

Now, [tex]\frac{1}{5}  \times 880 = m\\\implies m =176[/tex]

or, 1 by 5  = 176

Similarly: [tex]\frac{1}{6}  \times 880 = n\\\implies n =146.6666[/tex]

or, 1 by 6  = 146.67

⇒ m  : n  = 176  : 146.67

Hence, the ratio of 1 by 5 is to 1 by 6​  = Rs 176  :  Rs 146.67

Answer:

12.22

Step-by-step explanation:

I don't know if 12.22 is an answer for you but if it's not I would round to 12. What you do is multiply 9.32 by 16 3/4 which gives you 156.11. Take 156.11 and subtract 150 since Garth is putting that in the bank which leaves you with 6.11. Lastly you will divide 6.11 by .5 which will give you 12.22. So Garth can buy 12 raffle tickets.

Answer:

Garth can buy 12 raffle tickets.

Step-by-step explanation:

This is because when you multiply 9.32 with 16, it is 149.12.

Then, each quarter an hour, or 15 minutes, he earns 2.33 dollars.

Multiply by 3 and you get 6.99.

Add 6.99 with 149.12 and you get 156.11

Get rid of 150$ and you have 6.11

Each dollar you can get 2 raffle tickets.

So 6 dollars or 6, multiplied by 2 is 12.

Hope this helps you!

P.S If I may, can I please have brainliest, I would greatly appreciate it.

Answer:

Part A) The reasonable domain to plot  the growth function is the interval [0,5]

Part B) The average rate of change is [tex]0.21\ \frac{cm}{day}[/tex]

see the explanation

Step-by-step explanation:

Part A)

Let

f(n) -----> the height of the plant in cm

n ----> the number of days

we have

[tex]f(n)=10(1.02)^n[/tex]

This is a exponential function of the form

[tex]f(x)=a(b)^x[/tex]

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

[tex]a=10\ cm[/tex] ----> initial value or y-intercept

[tex]b=1.02\\r=b-1=1.02-1=0.02\\r=2\%[/tex]

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

[tex]11.04=10(1.02)^n\\11.04/10=(1.02)^n\\1.104=(1.02)^n[/tex]

Apply log both sides

[tex]log(1.104)=(n)log(1.02)\\n=log(1.104)/log(1.02)\\n=5\ days[/tex]

so

The reasonable domain to plot  the growth function is the interval -----> [0,5]

[tex]0 \leq x \leq 5[/tex]

Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

the average rate of change is equal to

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

In this problem we have

[tex]f(a)=f(1)=10(1.02)^1=10.2\ cm  f(b)=f(5)=10(1.02)^5=11.04\ cm\\a=1\\b=5\\[/tex]

Substitute

[tex]\frac{11.04-10.2}{5-1}=0.21\ \frac{cm}{day}[/tex]

The average rate of change is the change of the function values (output values) divided by the change of the input values.

That represent ----> The plant grew an average of 0.21 cm per day during that time interval

"Part A) The reasonable domain to plot  the growth function is the interval [0,5]

Part B) The average rate of change is

see the explanation

Step-by-step explanation:

Part A)

Let

f(n) -----> the height of the plant in cm

n ----> the number of days

we have

This is a exponential function of the form

where

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

In this problem we have

----> initial value or y-intercept

For f(n)=11.04 cm

Find the value of n

substitute in the exponential function

Apply log both sides

so

The reasonable domain to plot  the growth function is the interval -----> [0,5]

Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?

the average rate of change is equal to

In this problem we have

Substitute

The average rate of change is the change of the function values (output values) divided by the change of the input values.

That represent ----> The plant grew an average of 0.21 cm per day during that time interval"quoted from

(3, 6) can replace the missing value and create a function

Step-by-step explanation:

Given relation is:

{(8,5), (2, 3), (1,6), (7,4), _?_}

In order for a relation to be a function, the first condition is that there should be no repetition in domain of the function i.e. same input cannot map to multiple outputs.

In the form of ordered pairs, the first element of each ordered pair represents the elements of domain set

So,

From all the option given, only (3,6) is suitable to be put in the blank space as it will create no repetition in the domain while other ordered pairs will cause repetition.

Hence,

(3, 6) can replace the missing value and create a function

Keywords: Relations, functions

Learn more about functions at::

#LearnwithBrainly

Answer:

x = 1/4 when y = 8/3

Step-by-step explanation:

Divide both by 1/4

x = 1 when y = 32/3

When x = 1 1/8 = 9/8  

y = 32/3 x 9/8

y = 12

Answer:

25/12 or 2 1/12

Step-by-step explanation:

4 3/4=19/4

2 2/3=8/3

19/4-8/3=57/12-32/12=25/12

Answer:

D: is the answer  

Step-by-step explanation:

A. +   add

B. −   subtract

C. ×   multiply

D. ÷  divide (can also be written with a "/") as in 3/2 vs 3÷ 2

The symbol used to write an algebraic expression for "three divided by a number" is the division symbol, ÷. We write this based off the description as '3 ÷ n' or '3/n' in fractional form.

To write an algebraic expression for "three divided by a number," you would use the division symbol which is represented as ÷. So, if our unknown number is represented by the letter 'n', the algebraic expression would be written as "3 ÷ n" or "3/n" in fractional form.

In an algebraic expression, each symbol represents a specific mathematical action. The '+' symbol is for addition, '-' is for subtraction, 'x' is for multiplication, and '÷' is for division. In this case, since the problem specifies division, the correct symbol to use would be '÷'.

https://brainly.com/question/34192827

#SPJ11

Answer:

Divide by 13, you will get 10x - 1

To factor the expression 130x - 13, find the greatest common factor, which is 13, and factor it out. The factored form is 13(10x - 1).

To factor the expression 130x - 13, you need to look for a common factor in both terms. In this case, both terms can be divided by 13, which is the greatest common factor of the two numbers. By factoring out 13, you get:

13(10x - 1)

This process is known as factoring by common factor or GCF factoring. It simplifies the expression to a product of a constant (13) and a binomial (10x - 1). This method is very useful in solving equations, simplifying expressions, and can be a first step in more complex factoring processes.

Answer:

Adults= 250 tickets

Children= 400 tickets

Step-by-step explanation:

Answer

250 adult tickets were sold and 400 children tickets were sold

Step by Step Explanation:

Given

Saturday Sales: $3675

Total tickets: 650

Cost of adult tickets = $7.50

Cost of children tickets = $4.50

Let A represent the adult tickets and C represent the children tickets,

if there's a total of 650 tickets, then

A + C = 650

Also,

if an adult ticket cost $7.50 and a child ticket cost $4.50 then

7.5A + 4.5C = 3675

From these, we have a simultaneous equation

A + C = 650 ------- (1)

7.5A + 4.5C = 3675 ----------(2)

Make A the subject of formula in (1)

A + C = 650  becomes

A = 650 - C

Substitute 650 - C for A in (2), we have

7.5(650 - C) + 4.5C = 3675

Open the bracket

4875 - 7.5C + 4.5C = 3675

4875 - 3C = 3675

Collect like terms

-3C = 3675 - 4875

-3C = -1200

Divide through by -3

[tex]\frac{-3C}{-3} = \frac{-1200}{-3}[/tex]

C = 400

Recall that

A = 650 - C

So, A = 650 - 400

A = 250

Hence, 250 adult tickets were sold and 400 children tickets were sold

Answer:

The sign of the product is negative because a positive multiplied by a negative is a negative.

Step-by-step explanation:

Since you asked for evidence I will multiply even though the question asks you to solve without multiplying.

1×-1=-1

-1×-1=1

1×1=1

A negative multiplied by a positive is always negative. Doesn't matter which order you put it in. Meaning a positive multiplied by a negative is also always negative.

A positive multiplied by a positive is always positive.

A negative multiplied by a negative is always positive.

356,864 × −194,758 = negative sign answer

Answer:

The measure of the diagonal is [tex]3\sqrt{6}\ units[/tex]

Step-by-step explanation:

Let

c -----> the diagonal of a square in units

a ----> the length side of a square

Remember that a square can be divided into two congruent right triangles

see the attached figure to better understand the problem

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+a^{2}[/tex]

we have

[tex]a=3\sqrt{3}\ units[/tex]

substitute

[tex]c^{2}=(3\sqrt{3})^{2}+(3\sqrt{3})^{2}[/tex]

[tex]c^{2}=54[/tex]

[tex]c=\sqrt{54}\ units[/tex]

simplify

[tex]c=3\sqrt{6}\ units[/tex]

Answer:

The length of the mat is 60 in.

Step-by-step explanation:

Given :

Mats are inclined to form a triangle.

two sides of the mat are right triangles.

Hence the triangle formed is right angled triangle.

Let the length  be x.

Now,The height of the mat is 28 inches shorter than the length of the mat.

Height of mat = x - 28

Also, the hypotenuse is 8 inches longer than the length of the mat.

Hypotenuse = x + 8

Hence by using Pythagoras theorem we get ,

[tex]Hypotenuse^2= lenght^2+height^2\\[/tex]

[tex]x^2+(x-28)^2=(x+8)^2\\x^2+x^2-56x+784=x^2+16x+64\\x^2-72x+720=0\\x^2-60x-12x+720 = 0\\x(x-60)-12(x-60)=0\\(x-12)(x-60) = 0\\x-12=0\\x=12\\x-60=0\\x=60[/tex]

Now we get 2 values of length 12 and 60.

But height is 28 in less than length.

And when we take length value as 12 the height will be negative hence it can't be true.

Hence the Length of mat = 60 in.  

Answer:

The value of positive integers are 21.22 and 12.11

Step-by-step explanation:

Given as :

The sum of squares of two integer = 698

Let The one positive integer be x

And The other positive integer be y

According to question

one positive integer = 3 less than twice the other positive integer

So, x = 2 × y - 3

I.e x = 2 y - 3

And x²  +  y² = 698

So, Put the value of x

I.e  ( 2 y - 3 )² +  y² = 698

or, 4 y² + 9 - 12 y +  y² = 698

Or, 5 y² - 3 y - 698 = 0

Now solving this quadratic equation

y = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]

Or, y = [tex]\frac{3\pm \sqrt{-3^{2}-4\times 5\times -698}}{2\times 5}[/tex]

Or, y = [tex]\frac{3\pm \sqrt{13969}}{10}[/tex]

Or, y = [tex]\frac{3\pm 118.19}{10}[/tex]

∴ y = 12.11 , - 11.51

So , The value of y = 12.11

And the value of x = 2 × 12.11 - 3

I.e x = 21.22

Hence The value of positive integers are 21.22 and 12.11 Answer

To find the two integers, we can set up two equations based on the given information. By substituting the value of x from the first equation into the second equation, we can solve for y. Then, substituting the value of y back into the first equation, we can find the value of x.

To solve this problem, we can set up two equations based on the given information. Let's say the first integer is x and the second integer is y. We are given that x is 3 less than twice y, so we can write the equation: x = 2y - 3. We also know that the sum of their squares is 698, so the equation becomes x^2 + y^2 = 698. Now we can substitute the value of x from the first equation into the second equation and solve for y.

Substituting x = 2y - 3 into the equation x^2 + y^2 = 698, we get (2y - 3)^2 + y^2 = 698. Expanding this equation, we get 4y^2 - 12y + 9 + y^2 = 698. Combining like terms, we have 5y^2 - 12y + 9 = 698. Rearranging this equation and simplifying, we get 5y^2 - 12y - 689 = 0. Now we can solve this quadratic equation to find the value of y.

Using the quadratic formula, y = (-(-12) ± sqrt((-12)^2 - 4(5)(-689))) / (2(5)). Simplifying the equation further, we have y = (12 ± sqrt(144 + 13780)) / 10. Taking the positive value, y = (12 + sqrt(13924)) / 10. Evaluating this expression, we find y ≈ 9.7394. Now we can substitute this value back into the first equation to find x.

Using x = 2y - 3, we have x = 2(9.7394) - 3. Simplifying this equation, we get x ≈ 16.4788. Therefore, the two integers are approximately 16.4788 and 9.7394.

500

Step-by-step explanation:

The median is always the middle line in the box of the data set even if the data set is uneven.

Answer: 20/27

Step-by-step explanation:

multiply numerators and denominators

1/3 x 20/9 = 20/27

you can not simplify further

Answer:6i-6

Step-by-step explanation:

9i-3i=6i

1+5=6

Answer:

The sum of 50 and 6 is the total of 56

Answer:

Fifty plus six equals fifty-six.

4x+8=7.8+5x

Subtract 4x from both sides:

8 = 7.8 +x

Subtract 7.8 from both sides:

x = 0.2

Answer:

This cannot be done, but it can be factored as: 6(5x + 1)

Step-by-step explanation:

This expression cannot be distributed any further.

The distributive property is used when multiplying polynomials (multiplying one or more terms by two or more terms). In which case, each term in multiplied by each of the terms in the bracket, for example: .

5(x + 2)  =  5x + 10

We can factor this expression however to go the opposite direction:

30x + 6

Since 30 and 6 are both divisible by 6, we can factor it out of each term.

Divide 30x by 6 and divide 6 by 6.

6(5x + 1)

Answer

○ A. [tex]\displaystyle y - 5 = 2(x - 10)[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 7}{-10 + 4} = \frac{-12}{-6} = 2[/tex]

Then, according to the Point-Slope Formula, [tex]\displaystyle y - y_1 = m(x - x_1),[/tex]all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT signs:

[tex]\displaystyle y - 5 = 2(x - 10)[/tex]

I am joyous to assist you anytime.

Answer:

The number is -5.

Step-by-step explanation:

x+x=x-5

2x=x-5

x-2x=5

-x=5

x=-5

Final answer:

The student's question involving a system of equations can be solved to find that the two numbers are 17 and -5. By setting up a system of equations based on the given conditions and solving it using the elimination method, we obtain the values for the two unknown numbers.

Explanation:

System of Equations to Find Two Numbers

Let's define the first number as x and the second number as y. The problem states that x plus twice y equals 7 and twice x plus y equals 29. These statements can be turned into a system of linear equations:

x + 2y = 7

2x + y = 29

Using the substitution or elimination method, we can solve these equations for x and y. First, multiply the first equation by 2 to align the coefficients of x:

(2)(x) + (2)(2y) = (2)(7)

The equations now become:

2x + 4y = 14

2x + y = 29

Subtracting the second equation from the first gives us:

3y = -15

Divide both sides of this new equation by 3 to get the value of y:

y = -5

Now that we have a value for y, substitute it back into one of the original equations to find x:

x + 2(-5) = 7

x - 10 = 7

x = 17

The two numbers that solve the system are x = 17 and y = -5.

Answer:

y = 42x

Step-by-step explanation:

Answer:

The answer is y=42x

Answer:

error pecentage is 5.5% i think because 1.8 divde by 32.7 is 0.5504... * 100 is 5.504

Step-by-step explanation:

The percent error in Charlie's guess regarding his dog's weight is 5.5%, calculated using the difference between the actual and estimated values divided by the actual value, times 100%.

To calculate the percent error in Charlie's guess, we use the formula for percent error which is:

Percent Error = (|Actual Value - Estimated Value| / Actual Value) × 100%

Substitute the values into the formula:

Percent Error = (|32.7 - 34.5| / 32.7) × 100%

Percent Error = (1.8 / 32.7) × 100%

Percent Error = 0.054983922826 × 100%

Percent Error = 5.5% (rounded to the nearest tenth)

Therefore, the percent error in Charlie's guess is 5.5%.

Answer:

$293.6

Step-by-step explanation:

Here is the complete question: A cell phone is on sale for 30% off. Find the original price if the sale price of the cell phone is $205.50.

Given: Sale price of cell phone is $205.50

           Discount= 30%

As 30% discount is given on original price or we can say 70% of original price is $205.50.

∴ Let the original price be x.

⇒ [tex]\frac{70}{100} \times x= 205.50[/tex]

Now, cross multiplying both side.

⇒ [tex]x= \frac{100}{70} \times 205.5[/tex]

∴ x= $293.6

The original price of cell phone is $293.6.

Answer:

40%

Step-by-step explanation:

30/75 = 0.4

Move decimal point back 2 places to convert to percent.

0.4 = 40%

Answer: 40%

Step-by-step explanation:

let x equal the percent

75x=30

x=2/5=40%

Answer:

4*6+8*6=48

Step-by-step explanation:

Answer:

The number is 4.

Step-by-step explanation:

4x+8x=48

12x=48

x=48/12

x=4

angle = 125 degree because it is Vertically Opposite to the angle 1.

Answer:

x = 2y

x + 4 = 3y + 1

2y + 4 = 3y + 1

y = 3, x = 6