The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle.

Answers

Answer 1

Step-by-step explanation:

Let the width=x

Length =6x-4

As we know that in a rectangle

[tex]{\boxed{\sf Area=LB}}[/tex]

Substitute the values

[tex]\hookrightarrow\sf x (6x-4)=20 [/tex]

[tex]\hookrightarrow\sf 6x^2-4x=20 [/tex]

[tex]\hookrightarrow\sf 6x^2-4x-20=0 [/tex]

Here a=6, b=-4, c=-20.use quadratic formula

[tex]\hookrightarrow\sf x=\dfrac {1}{3}+\dfrac {1}{3}\sqrt {31} \quad or \quad \dfrac {1}{3}+\dfrac {-1}{3}\sqrt {31}[/tex]


Related Questions

What is the prime factorization of 48?

Answers

Answer:

2x2x2x2x3

Step-by-step explanation:

Andrea runs a fruit store. She started Sunday with 20 cherries in stock. During the day, she sold 17 cherries and got a shipment of fresh cherries. The shipment contained 4 times as many cherries as she started the day with. How many cherries does Andrea have in stock at the end off the day?


answer:


example ​

Answers

Answer:

Um.

Step-by-step explanation:

Could you give an example of what? Or no.?

If f(x)=|x−5|+2, find f(3)

Answers

Answer:

f(3) = 4

Step-by-step explanation:

The absolute value, |X|, is defined as the magnitude of a number without regard to its sign. For example, absolute value of 1 is 1 and absolute value of -1 is 1.

Thus, based on the function:

f(x)=|x−5|+2

f(3) = |3−5|+2

f(3) = |-2|+2

-Absolute value of -2 = 2-

f(3) = 2+2

f(3) = 4

2 3/4 2 11/12 in simplist form

Answers

Answer:

2 9/12 and 2 11/12

Step-by-step explanation:

if that is what u are asking. simplist form is 2 3/4 and 2 11/12.

Hope that helps and good luck :)

What is the answer to this?

Answers

Answer:

65 reaminder  85  

Step-by-step explanation:

u divided it and theres a big remainder so i did the two first reinders i found

.........................

Answers

Answer:

Good thanks for points hehe

How is the space between consecutive whole numbers divided on the number line?
O into halves
O into fifths
O into sixths
O into sevenths

Answers

Answer:

I think it’s is into fifths if I’m correct

Step-by-step explanation:

What is an equation of the line that passes through the point (−5,2) and is parallel to the line 4x-5y=5

Answers

4x - 5y = 5
4x - 5 = 5y
y = 4/5x - 1
Parallel = same slope
Y = 4/5x + b
2 = 4/5(-5) + b, b = 6
Solution: y = 4/5x + 6

cos(0)=square root 3/3, sin 0<0. what is the value of sin0​

Answers

Answer:

sin θ = [tex]\frac{\sqrt{6} }{3}[/tex]

Step-by-step explanation:

Given that,

cos θ = [tex]\frac{\sqrt{3} }{3}[/tex]

From the trigonometric functions,

cos θ = [tex]\frac{adjacent}{hypotenus}[/tex]

⇒ adjacent = [tex]\sqrt{3}[/tex], and the hypotenuse = 3

Let the opposite side be represented by x, applying the Pythagoras theorem we have;

[tex]/hyp/^{2}[/tex] = [tex]/adj/^{2}[/tex] + [tex]/opp/^{2}[/tex]

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

9 = 3 + [tex]x^{2}[/tex]

[tex]x^{2}[/tex] = 9 - 3

   = 6

x = [tex]\sqrt{6}[/tex]

Thus, opposite side = [tex]\sqrt{6}[/tex]

So that,

sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

        = [tex]\frac{\sqrt{6} }{3}[/tex]

Therefore,

sin θ = [tex]\frac{\sqrt{6} }{3}[/tex]

7x+8y=-23
3x - 16y= 29

Answers

Answer:

(-1, -2)

Step-by-step explanation:

Find – 8-(-3). -8-(-3) =​

Answers

Answer:

-5.5

Step-by-step explanation:

the answer would be -24 if it is -8-(-3)

Plz help plz I’m begging I will give brainliest

Answers

Answer:

B is the answer.

Step-by-step explanation:

Answer:

The second one

Step-by-step explanation:

-2 and 1/4 is the same as -9/4 bec -9/4 is just in the improper form.

(can i get brainliest now)

Question 3
And question 4 pleaseeee help!!

Answers

Answer:

see pdf

Step-by-step explanation:

Find the value of x in each figure. B 9. - 15 2x A C​

Answers

The answer is 2 because it says 2x
The answer is 2 I believe

Solve for y: 18x + 3y = 24​

Answers

Answer: y=8-6x

Step-by-step explanation:

How would you write 0.7 repeated as a fraction

Answers

Answer:

7/9

Step-by-step explanation:

7/9 = 0.777777777777777777...

0.7 repeated can be written as a fraction [tex]\frac{7}{9}[/tex].

What are Fractions?

Fractions are defined as a part or portion in a whole. There are two parts for a fraction, numerator which is the upper part and the denominator, which is the lower part.

Fractions are generally written in the form [tex]\frac{p}{q}[/tex], where p and q are real numbers. Here, the number p is called the numerator and the number q is called the denominator.

Fractions can be simplified as decimals.

We have to find the fraction representing the number 0.7 repeated.

0.7 repeated is actually the number 0.77777.....

The quotient of 5/8 = 0.625

The quotient of 6/7 = 0.857...

The quotient of 7/9 = 0.777.......

The quotient of 7/100 = 0.07

So, the quotient of 7/9 is the required number.

Hence the fraction which on simplification gives 0.7 repeated is 7/9.

To learn more about Fractions, click on the link given below:

https://brainly.com/question/10354322

#SPJ2

Please help I'll give brainlest

Which of the following is 1,215 divisible by? Select all that apply.
A.3
B.2
C.9
D.10
E.5
F.8
G.4
H.6

Answers

Answer: A,C,E

Step-by-step explanation:

All of the other answers give you a decimal.

Answer:

ACE

Step-by-step explanation:

A

1215 divided by 3 = 405

B

1215 divided by 9 = 135

C

1215 divided by 5 = 243

*The other answers can give a decimal answer.

Kaitlyn is sharpening a pencil that is 19 cm. Each time she sharpens it goes down 2.5 cm. If she sharpens her pencil 4 times. How many centimeters of pencil does she have left?

Answers

Answer:

9 cm

Step-by-step explanation:

2.5x4=10

which of the following is a quadratic function?

Answers

Answer:

A

Step-by-step explanation:

Y = ax2 +bx + c

trapped in a cell that contains 3 doors. The first door leads to a tunnel that returns her to back tothe cell after 2 days of travel. The second door leads to a tunnel that returns her back to the cell after 4days of travel. The third door leads her freedom after 1 day of travel. If it is assumed that Ally will alwaysselect doors 1, 2, and 3 with probabilities 0.5, 0.3, and 0.2 (respectively), what is the expected number ofdays until she reaches freedom

Answers

Answer:

The expected number of days until prisoner reaches freedom is 12 days

Step-by-step explanation:

From the given information:

Let X be the random variable that denotes the number of days until the prisoner reaches freedom.

We can evaluate E(X) by calculating the doors selected, If Y be the event that the prisoner selects a door, Then;

E(X) = E( E[X|Y] )

E(X) = E [X|Y =1 ] P{Y =1} + E [X|Y =2 ] P{Y =2} + E [X|Y =3 ] P{Y =3}

[tex]E(X) = (2 + E[X])\dfrac{1}{2}+ (4 + E[X])\dfrac{3}{10}+ 1 (\dfrac{2}{10})[/tex]

[tex]E(X) = (2 + E[X])0.5+ (4 + E[X])0.3+ 0.2[/tex]

Solving for E[X]; we get

E[X] = 12

Which function could be represented by the graph on the
coordinate plane?

Answers

The last option f(x)=(x-8)^2 -6

The reason is that whatever is in the parenthesis is always opposite. So since the graph is on the right side that means it’s -8 not positive 8. And the -6 represents a vertical translation and the graph is placed below zero.

Answer:

f(x)=(x-8)^2 -6

Step-by-step explanation:

A cylindrical soup can has a radius of 8.4 cm and a height of 13.2 cm. What is the volume of the soup can to the nearest tenth of a cubic centimeter?
A= 110.9 cm3

B= 348.3 cm3

C= 673.8 cm3

D= 2926.1 cm3

Answers

Answer:

Option D: 2926.1 cm³

Step-by-step explanation:

Dimensions of the cylidrincal soup can are given as;

Radius; r = 8.4 cm

height; h = 13.2 cm

Formula for area of cylinder is;

A = πr²h

Plugging in the relevant values gives;

A = π × 8.4² × 13.2

A = 2926.05 cm³

Approximating to the nearest tenth gives;

A = 2926.1 cm³

At her birthday party, marcie's guests ate 2/3 of her birthday cake and her family ate 1/4 of the cake. How much cake was left after her party?

Answers

Answer:

1/12

Step-by-step explanation:

So you start with an equation. 2/3 plus 1/4= ?.

Step 1: Find a common donominator.

Count by each number until they meat up.

3 6 9 12

4 8 12

Step 2: Multiply.

Basically, make sure that if you do something to the bottom you do the same to the top. You have

[tex]\frac{2}{3}[/tex]  = [tex]\frac{?}{12}[/tex]. 3 times 4 is 12. 2 times 4 is 8. Your new fraction is [tex]\frac{8}{12}[/tex].

[tex]\frac{1}{4}[/tex] = [tex]\frac{?}{12}[/tex]. 4 times 3 is 12. 1 times 3 is 3. Your new fraction is [tex]\frac{3}{12}[/tex].

Step 3: Just Add!

[tex]\frac{8}{12} + \frac{3}{12}= \frac{11}{12}[/tex]

Step 4: Answer the question! The question asks "How much cake is left. You know that a whole cake is [tex]\frac{12}{12}[/tex]. So, [tex]\frac{12}{12} -\frac{11}{12} = \frac{1}{12}[/tex]

I will give brainliest
Find x and y, there is no given info, and the line that is 8 units long is not a midsegment, but it is parallel to the line that is ten units long

Answers

Answer:

x = 1.25

y = 1.75

Step-by-step explanation:

Since, the line that is 8 units long is parallel to the line that is ten units long.

Therefore, both the triangles are similar by AA postulate.

Corresponding sides of of the similar triangles are in proportion.

Therefore,

[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]

Which of the following fractions is equal to the repeating decimal 0.555

Answers

Answer:

5/9

Step-by-step explanation:

5/9 is 0.5 recurring

it should be 5/9. so pick the first one !

just say something so that you can have my points :)

Answers

Answer:

thanks !!

Step-by-step explanation: have a wonderful day :)

Answer:

Thank you!!

Step-by-step explanation:

Have a great day:)

Use a matrix to solve the system:

Answers

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

[tex]2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\[/tex]

Rewrite these equations in matrix form

[tex]\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\[/tex]

we can write it like this,

[tex]AX=B\\X=A^{-1}B[/tex]

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

[tex]A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\[/tex]

now multiply the matrix with B

[tex]X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\[/tex]

Can anyone solve this.

Answers

Answer:

x-1+5x+1=180, 6x=180, x=30

Step-by-step explanation:

5. [Statistical independence] Consider a month consisting of exactly 28 days, split into four weeks of seven days each, such that the first of the month is a Monday. One of the 28 days will be selected uniformly at random (so that each day has probability 1/28 of being selected). Event A is that the selected day is a Monday or Wednesday. Event B is that the selected day falls either in the first or third weeks of the month. Are A and B independent or not? Show your work.

Answers

Answer:

They are independent events

Step-by-step explanation:

For independent events;

Pr(A & B) = Pr(A) × Pr(B)

Given that:

A = day is Monday or Wednesday

Since we have four weeks and each week will have one Monday and Wednesday each,

Pr(A) = (8/28)

B = day falls in the first or third week

Since, first and the third week has a total of 14 days,

Pr(B) = 14/28

Therefore;

Pr(A) × Pr(B) = 8/28 * 14/28

Pr(A) × Pr(B)  = 1/7

Now, A and B = day is either Monday or Wednesday, and it is in the first or third week

There are four such days, Thus Pr(A and B) = 4/28 = 1/7

Since, Pr(A and B) = Pr(A) * Pr(B),

A and B are independent events

Cheesy Chicken and Rice has 430 kcals per serving. How many grams of protein are in one serving of the meal if 31% of the kcals come from protein?

Answers

Answer: 133,300

Step-by-step explanation:

Given that:

Number of kcals per serving = 430

Percentage of protein in the kcal = 31%

To obtain the number or amount of protein in one serving :

31% of 430

= 0.31 * 430

= 133.3 kcal

I kcal = 1000 gram calories

Hence,

133.3 kcal = (1000 * 133.3) = 133,300 gram calories

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