How much change does he need to receive back

The width of the rug is 3 inches

Step-by-step explanation:

A knitter wants to make a rug for a dollhouse

We need to find the width of the rug

∵ The area of the rug is A(w) = w(2 + w)

- Simplify the right hand side

∴ A(w) = 2w + w²

∵ The desired area of the rug is 15 square inches

- Equate A(w) by 15

∴ 2w + w² = 15

- Subtract 15 from both sides

∴ 2w + w² - 15 = 0

- Its a quadratic equation arrange its terms from the greatest power of x

∴ w² + 2w - 15 = 0

Factorize it into two binomial factors

∵ w² = w × w

∵ 15 = 3 × 5

∵ 5w - 3w = 2w

∴ w² + 2w - 15 = (w -3)(w + 5)

∴ (w - 3)(w + 5) = 0

- Equate each factor by 0

∴ w - 3 = 0 OR w + 5 = 0

∵ w - 3 = 0

- Add 3 to both sides

∴ w = 3

∵ w + 5 = 0

- Subtract 5 from both sides

∴ w = -5 ⇒ rejected because no dimension with -ve value

∴ w = 3 only

The width of the rug is 3 inches

Learn more:

You can learn more about the quadratic equation in brainly.com/question/9328925

#LearnwithBrainly

Answer:

one hundred million seven thousand and one

Answer:

One hundred million seven thousand and one

Step-by-step explanation:

Answer: Yes it is irrational

Step-by-step explanation:

Answer:

Yes.

Step-by-step explanation:

sqrt(3)=1.73205080...

Therefore, it's irrational.

Answer:

see explanation

Step-by-step explanation:

Sum the parts of the ratio, 2 + 3 + 3 = 8

Divide the sum to be shared by 8 to find the value of one part of the ratio

£96 ÷ 8 = £12 ← value of 1 part of the ratio, thus

David gets 2 × £12 = £24

Stephen gets 3 × £12 = £36

June also gets £36

Answer: n=45 degrees, m=20 degrees

Step-by-step explanation:

the smaller triangle is isosceles

since one of the angles is 90 degrees that the other have to be 45 degrees each

so n=45 degrees

the big triangle is also isosceles meaning that m+n=(180-50)/2

m+n=65

we know n=45

so m=20

The amount he will be spending now is : 0.65q

Using the information given ;

The amount which would be reduced from his spending would be :

Now we have ;

q × 35%

= 0.35q

The amount he will be spending now is :

Now we have;

q - 0.35q = 0.65q

Hence, the amount he will be spending now is : 0.65q

It's a bit of a trick question.  The principal square root of a real number, as indicated by the radical sign, is never negative. So if p is negative we'll get -p as the result.  We write this with absolute value:

[tex]\sqrt{p^2} = |p|[/tex]

Answer:

Step-by-step explanation:

[tex](5x^2)(-4x^3)=\bigg(5\cdot(-4)\bigg)(x^2x^3)\\\\\text{use}\ a^na^m=a^{n+m}\\\\=-20x^{2+3}=-20x^5[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{2}{3}}[/tex]

Step-by-step explanation:

[tex]4^{3x}=4^2\iff3x=2\qquad\text{divide both sides by 3}\\\\x=\dfrac{2}{3}[/tex]

Answer:

C is the answer

Step-by-step explanation:

just took the assignment, and got 100%

-38(-3) = 114

-72/(-12) = 6

-9 x 23 = -207

-150/5 = -30

564 / -4 = -141

Given that, we have to find each product or quotient

-38(-3)

It is a product, so we have to find product value

[tex]-38(-3)=38 \times 3=114[/tex]

-72 / (-12)

It is division, so we have to find the quotient

[tex]\frac{-72}{-12}=\frac{72}{12}=6[/tex]

-9 x 23

It is a product, so we have to find product value

[tex]-9 \times 23=-207[/tex]

- 150 / 5

It is division, so we have to find quotient

[tex]\frac{-150}{5}=-30[/tex]

564 / -4

It is division, so we have to find the quotient

[tex]\frac{564}{-4}=-141[/tex]

Answer:

2(2x+4)=6x+10

2x=2

x=2/2

x=1

y=2(-1)+4

y=-2+4

y=2

Answer:

6/14 or 0.43 it depends from a question

Final answer:

After 64 sessions, the cost of both of Kendall's plans would be the same, which would be $2149.

Explanation:

Kendall's two pricing plans can be represented by linear equations. Plan 1 is $37 + $33 per session, while Plan 2 is $101 + $32 per session. To find out after how many sessions the cost would be the same, we set the two equations equal to each other:

37 + 33x = 101 + 32x

This simplifies to:

33x - 32x = 101 - 37

x = 64

So, after 64 sessions, the cost of both plans would be equal. To find that cost, we substitute x back into either equation:

Total cost for Plan 1 = 37 + 33(64) = $2149

Therefore, the cost for 64 sessions is $2149 using either plan.

Answer:

-4(i+9)

Step-by-step explanation:

(4+5i)(-4+sqrt(-16))

(4+5i)(-4+4i)

-16-20i+16i+20i^2

-16-4i+20(-1)

-16-4i-20

-4i-16-20

-4i-36

-4(i+9)

Answer:

Slope: -10

Y-intercept: 50

X-intercept: 5

Step-by-step explanation:

y-mx+b

y=-10x+50

Answer: 3

Step-by-step explanation: We found the factors and prime factorization of 21 and 27. The biggest common factor number is the GCF number. So the greatest common factor 21 and 27 is 3.

The greatest common factor of 21 and 27 is 3.

A set's greatest common factor (GCF) is the largest factor that all of the numbers share.

For example, 12, 20, and 24 have two common factors: 2 and 4. The largest is 4, so we say that the GCF of 12, 20, and 24 is 4.

We have the number 21 and 27.

Now, factories 21 and 27 as

21 = 3 x 7

27 = 3 x 3 x 3

So, the common factor of 21 and 27 is 3.

Learn more about Greatest Common Factor here:

https://brainly.com/question/11221202

#SPJ2

Answer:

your answer would be X>-4

Answer:

A

Step-by-step explanation:

if you multiply the top by 2 the coefficients for x will be the same in both equations

4*2=8

The equations have equal x-coefficients is to A. Multiply both sides of the top equation by 2.

Multiplying both sides of the top equation by 2 results in:

8x + 4y = 8

This makes the x-coefficients equal in both equations, as they are both now 8x.

Option B would not work, as dividing both sides of the top equation by 4 would result in an x-coefficient of 1x in the first equation and 8x in the second equation.

Option C would also not work, as dividing both sides of the top equation by 2 would result in an x-coefficient of 2x in the first equation and 8x in the second equation.

Option D would work, as multiplying both sides of the top equation by 4 would result in an x-coefficient of 8x in both equations. However, option A is the simplest and most direct way to achieve the desired result.

Therefore, the correct answer is A. Multiply both sides of the top equation by 2.

You invested 11000 in in 2st fund and 9000 in 2nd fund

Given that, You invested money in two funds.  

Last year, the first fund paid a dividend of 8% and the second a dividend of 5%, and you received a total of $1330.  

This year, the first fund paid a 12% dividend and the second only 2%, and you received a total of $1500.

Let the amount in Fund I be $x and amount in Fund II be $ y

Then, for last year ⇒ 0.08x+0.05y=1330 ----- eqn (1)  

And for this year ⇒ 0.12x+0.02y=1500 ------- eqn (2)  

Multiply (1) by 2 ⇒ 0.16 x + 0.1 y = 2660  

Multiply (2) by 5 ⇒ 0.6 x + 0.1 y = 7500

Subtract the two equations  

(2) ⇒ 0.6x + 0.1y = 7500

(1) ⇒ 0.16x + 0.1y = 2660

(-) --------------------------------

0.44x + 0 = 4840

x = 11000

Now, from eqn (2)  

0.12(11000) + 0.02y = 1500  

0.02y = 1500 – 1320  

0.02y = 180  

y = 9000

Hence, he invested 11000 in in 2st fund and 9000 in 2nd fund

Answer:

b

Step-by-step explanation:

the answer is b , x= 2 and y= 8, observe: 3.2+ 4.8= 6+32=38 , second ecuation 5.2-5.8= 10-40= -30

Answer:

Domain of set of given ordered pair is { -1, 0, 5, 10}

Step-by-step explanation:

All of the values that can go into a relation or function (input) are called the domain.

The domain is the set of all first elements of ordered pairs (x-coordinates).

     In the given question,

                 ordered pairs are (-1,1) , (0,-1) , (5,-11) , (10,-21)

     Therefore,

       Domain is the set of all first elements of ordered pairs.

       i.e -1, 0, 5, 10

       Hence the required set is   { -1, 0, 5, 10}.

The domain of the set of ordered pairs is {-1, 0, 5, 10}.

The domain of a set of ordered pairs represents all the x-values in the set. In this case, the set of ordered pairs is (-1,1), (0,-1), (5,-11), and (10,-21). The x-values in this set are -1, 0, 5, and 10. Therefore, the domain of the set of ordered pairs is A. {-1, 0, 5, 10}.

Step-by-step explanation: To find the slope of a line with a negative slope, we would use the ratio rise/run between any two points that are on that line.

Let's look at an example which I have provided in the image attached. I have labeled two points which are points A and B.

Notice however that to get from point A to point B, we must first go down 3 units so we say that our rise is -3. From there we move 4 units to the right so our run is 4. So our slope or rise over run is -3/4.

The equality used is Subtraction property of equality

Option A is correct

Step-by-step explanation:

We need to identify which option best explains or justifies Step 1.

Step 1 is: [tex]-c = ax^2 + bx[/tex]

The given equation is: [tex]0 = ax^2 + bx + c[/tex]

To get the equation for step 1 we need to subtract c on both sides of equation i.e using subtraction property of equality

[tex]0-c = ax^2 + bx + c-c[/tex]

[tex]-c = ax^2 + bx [/tex]

So, The equality used is Subtraction property of equality

Option A is correct.

Keywords: Solving Quadratic Equations

Learn more about Solving Quadratic Equations at:

#learnwithBrainly

The expression for how far Marcia ran on Tuesday is 1.18m miles.

To find the expression for how far Marcia ran on Tuesday, we can start by noting that she ran 18% farther than she did on Monday. Since she ran m miles on Monday, we can express the distance she ran on Tuesday as m + 18% of m.

To calculate the 18% of m, we need to multiply m by 18/100 or 0.18. Therefore, the expression for how far Marcia ran on Tuesday is m + 0.18m, which simplifies to 1.18m.

So, Marcia ran 1.18m miles on Tuesday.

https://brainly.com/question/12281459

#SPJ11

Answer:

3 stamps for $5

Step-by-step explanation:

$5 times 3 is $15

Answer:

1500 students

600 boys

Step-by-step explanation:

40% are boys, so 60% are girls.

Writing a proportion:

900 / 60% = x / 100%

x = 1500

There are 1500 students in the school, which means there are 600 boys in the school.

Answer:

c

Step-by-step explanation:

let the number be n then multiplied by itself gives n², thus

n² + 7 = 16 ( subtract 7 from both sides )

n² = 9 ( take the square root of both sides )

n = [tex]\sqrt{9}[/tex] = 3

Final answer:

The positive number that when squared and increased by 7 equals 16 is 3, which corresponds to option (c).

Explanation:

The student is asking to find a positive number which, when multiplied by itself (squared), and then 7 is added, equals to 16. To find this number, we can set up a simple equation where x is the positive number we are looking for: x2 + 7 = 16. To solve for x, subtract 7 from both sides to get x2 = 9. Taking the square root of both sides gives us x = 3, since 32 = 9. Therefore, the correct answer is (c) 3.

Answer:

(-4, 0)

Step-by-step explanation:

range applies to the y values.

The lowest y value it hits is -4, while the highest is 0.

Therefore, range is (-4, 0)