A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it’s width. The total area of the rug ( in square inches) based on the width W of the rug (in inches ) is given by A(w) = w (2+w) If the desired area of the rug is 15 square inches, what is the width of the rug, in inches?

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:

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

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:

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:

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:

x=-1189/36, y=242/9. (-1189/36, 242/9).

Step-by-step explanation:

-8x-16y=-166

8x+7y=-76

----------------

-9y=-242

9y=242

y=242/9

8x+7(242/9)=-76

8x=-76-1694/9

8x=-2378/9

x=(-2378/9)/8

x=-1189/36

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:

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]

4x+8=7.8+5x

Subtract 4x from both sides:

8 = 7.8 +x

Subtract 7.8 from both sides:

x = 0.2

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

Final answer:

It will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.

Explanation:

To determine the number of weeks it will take for the stock's price to reach $20.00 per share, we need to find the number of weeks it will take for the price to decrease from $62.50 to $20.00. Since the price is declining at a rate of 5% per week, we can set up an equation:

$62.50 - ($62.50  imes 0.05  imes  ext{number of weeks}) = $20.00

Simplifying the equation, we have:

$62.50 - (0.05  imes 62.50  imes  ext{number of weeks}) = $20.00

$42.50 = (0.05  imes 62.50  imes  ext{number of weeks})

Dividing both sides by 0.05 and 62.50, we get:

ext{number of weeks} =  rac{42.50}{0.05  imes 62.50}

Calculating this, we find that it will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.

Answer:

- 0.183

Step-by-step explanation:

Given that [tex]\sin \theta = \frac{1}{3}[/tex]

and [tex]\frac{\pi }{2} < \theta  < \pi[/tex]

We have to find the exact value of [tex]\sin (\theta + \frac{\pi }{6} )[/tex].

Now, [tex]\sin \theta = \frac{1}{3}[/tex]

⇒ [tex]\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47[/tex]

Now, since  [tex]\frac{\pi }{2} < \theta  < \pi[/tex],

So, [tex]\theta  = 180 - 19.47 = 160.53[/tex]

{Since [tex]\sin \theta = \sin (180 - \theta)[/tex]

Now, [tex]\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52[/tex]

Hence, [tex]\sin (\theta + \frac{\pi }{6} )[/tex].

= [tex]\sin 190.52[/tex]

= - 0.183 (Approximate) (Answer)

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:

x = 2y

x + 4 = 3y + 1

2y + 4 = 3y + 1

y = 3, x = 6

Answer:

The second city is 54 miles behind the first city

Step-by-step explanation:

The first bus is assumed to go ahead of the second bus and is moving at 54 mph. The second bus is moving at a speed such as 54 mph is 60% (0.6) of its speed.  

The speed of the second bus is then 54/0.6 = 90 mph

When 1 and a half hour has passed, the first bus has moved a distance of

[tex]X_1=54\times 1.5[/tex] = 81 miles

The second bus (behind the first bus) has moved

[tex]X_2=90\times 1.5[/tex] = 135 miles

The problem states they both meet in that time, it can only be possible if the second bus departed a distance 135 - 81 = 54 miles behind the first city

So, the second city is 54 miles behind the first city

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 number is -5.

Step-by-step explanation:

x+x=x-5

2x=x-5

x-2x=5

-x=5

x=-5

Answer: 30

Step-by-step explanation:

1:7

x:210

find x

210 is 30 times bigger than 7 so 30 is 30 times bigger than 1

30 is the answer

Answer:

30 blueberries

Step-by-step explanation:

divide the total by the 7, it's a lot simpler since it's a 1:7 but yeah so it's 30:210 blueberries to strawberries

Answer:

w(-15-w)= 0

w= 0 or (-15-w) = 0

Now,

-15-w =0

w= -15

So,The solution of w(-15-w) = 0

w= 0, -15

Answer:

w=-15,0

Step-by-step explanation:

w(-15-w)=0

-15w-w^2=0

-(w^2+15w)=0

w(w+15)=0

w=-15,0

Answer:6i-6

Step-by-step explanation:

9i-3i=6i

1+5=6

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

Answer: 20/27

Step-by-step explanation:

multiply numerators and denominators

1/3 x 20/9 = 20/27

you can not simplify further

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:

$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.

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:

31.5 hours

Step-by-step explanation:

time * speed = distance

speed=400/6=66.67 miles per hour

2100/(400/6)=31.5 hours

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:

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:

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.