The length of a rectangle is 7 inches
more inan its width. the area of
the rectangle is eqaul to 4 inches less
than 4 times the perimeter. Find the
length and width of the rectangle

Answers

Answer 1

Answer:

length = 20 inches

width = 13 inches

Step-by-step explanation:

l = length

w = width

area = l×w

perimeter = (2×l) + (2×w)

l = w + 7

l×w = 4×(2×l + 2×w) - 4

(w+7)×w = 4×(2×(w+7) + 2×w) - 4

w² + 7w = 4×(2w + 14 + 2w) - 4

w² + 7w = 8w + 56 + 8w - 4 = 16w + 52

w² - 9w - 52 = 0

the solution for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

here we use now w instead of x.

and a=1

b=-9

c=-52

w = (9 ± sqrt(81 - -208))/2 = (9 ± sqrt(81+208))/2 =

= (9 ± sqrt(289))/2 = (9 ± 17)/2

w1 = (9+17)/2 = 26/2 = 13

w2 = (9-17)/2 = -8/2 = -4

and a negative length does not make any sense for a geometric shape.

so, only w1 = 13 applies.

l = w + 7 = 13 + 7 = 20


Related Questions

This shape is broken up into rectangles. What is the area of the
entire shape?

Answers

Answer:

38inch2

Step-by-step explanation:

3inch*2inch+8inch*4inch

=6inch2+32inch2

=38inch2

-35.9=y/0.1+0.1 please help me with this.

Answers

Answer:

358.9 I think

Step-by-step explanation:

A store is having a sale on trail mix and jelly beans. For 5 pounds of trail mix and 3 pounds of jelly beans, the total cost is $17. For 2 pounds of trail mix and 12 pounds of jelly beans, the total cost is $23. Find the cost for each pound of trail mix and each pound of jelly beans.

Answers

Answer:

Trail Mix costs $2.50 per pound, and Jelly Beans cost $1.50 per pound.

Step-by-step explanation:

Using x for trail mix and y for jelly beans, we have a system of equations being

[tex]\left \{ {{5x+3y=17} \atop {2x+12y=23}} \right.[/tex]

We can solve this system using substitution

5x+3y=17

Divide by 5 to have a coefficient of 1 before x

[tex]x+\frac{3}{5} y=\frac{17}{5}[/tex]

Subtract [tex]\frac{3}{5} y[/tex] from each side to single out one variable to one side

[tex]x=\frac{17}{5} -\frac{3}{5} y[/tex]

Now, we can plug in our value for x into the given equation

[tex]2(\frac{17}{5} -\frac{3}{5} y)+12y=23[/tex]

Open the parentheses

[tex]\frac{34}{5} -1\frac{1}{5} y+12y=23[/tex]

Merge Y values

[tex]6.8+10.8y=23[/tex]

Separate numerical values from variables

[tex]10.8y=16.2[/tex]

Divide by 10.8 in order to have a coefficient of 1

[tex]y=1.5[/tex]

Now that we have one of the values, we know that a pound of jelly beans costs $1.50. We can now plug in 1.5 for y into one of our equations to find x.

[tex]5x+3(1.5)=17[/tex]

Open parentheses

[tex]5x+4.5=17[/tex]

Single out the variable

[tex]5x=12.5[/tex]

Divide by 5 to have a coefficient of 1 before x

[tex]x=2.5[/tex]

[tex]y=1.5[/tex]

What is the slope of the line that passes through the points (6-8) and (10,-8)?

Answers

Answer:

The slope of the line that passes through the points would be 0

Step-by-step explanation:

Lets use the formula : y2-y1/x2-x1

In this case lets let y2 be -8 and y1 be -8

And lets let x2 be 6 and x1 be 10, that would look like..

-8-(-8)/6-10

which equals...

0/-4 = 0

We know that the slope of the line is 0

Solve 2/5 - 1/7
Help pls this is timed!!!!

Answers

Answer:

9/35

Step-by-step explanation:

Answer:

9/35

Step-by-step explanation:

ok so find the lcm of 2/5 and 1/7: this is 35

then convert them

2/5 = 14/35

1/7 = 5/35

14/35 - 5/35 is 9/35

How much would you make for the YEAR at $25.02 per hour,
worked 51 hours and do get paid overtime? Round to the nearest
cent.

Answers

Answer:

1276.02

Step-by-step explanation:

25.02*51=(25*51)+(.02*51)=1275+1.02=1276.02

solve 557+3 using number disks

Answers

557+3=560 cuz 57+3 = 60 and 60+500= 560

PLEASE HURRY! WILL MARK BRAINLIEST IF CORRECT!! (Screenshot)

Answers

The correct answer is 6 2/3

Evaluate the expression 5xy+ -2xy+y^2 when x=4 and y=-5

Answers

Answer:

-35

Step-by-step explanation:

5(4)(-5) + -2(4)(-5) + (-5)²

= -100 + 40 + 25

= -35

Answer: -35

Step-by-step explanation:

5(4)(-5)+(-2)(4)(-5)+(-5)^2

-100+40+25

-35

Find x round. your answer to the nearest tenth of a degree

Answers

Answer:

x = 55.6

Step-by-step explanation:

Recall the 3 main trig functions

Sin = opposite / hypotenuse

Cos = adjacent / hypotenuse

Tan = opposite / adjacent

Note that hypotenuse = longest side length

We want to find angle "x".

We are given its opposite side length ( 19 ) as well as the adjacent side length

When dealing with the opposite and adjacent we use tan

Tan = Opp / Adj

Opp = 19 and Adj = 13

Tan(x) = 19/13

* take the inverse tan of both sides *

x = 55.6

Maplewood Furniture Store is having a sale on dining room furniture. When a customer purchases a set of dining chairs, a one-time discount of $55 is applied to the total. During the sale, Rhianna buys a set of 6 chairs that match the table she inherited from her grandmother. Rhianna pays $455 in all. Which equation can you use to find the regular cost, c, of each chair? ( ANSWERS 6c - 55 = 455, 55(c - 6) = 455, 55c - 6 = 455, 6(c - 55) = 455,) What is the regular cost of the chair

Answers

The equation used to model the regular cost of each chair at Maplewood Furniture store is given by 6c - 55 = 455

A linear equation is in the form:

y = mx + b;

where y, x are variables, m is the rate of change and b is the y intercept.

Let c represent the regular cost for x chairs. Hence:

c = mx + b

Given that a discount of $55 is applied to the total, hence, b = -55.

Rhianna buys a set of 6 chairs and pays 455, hence:

6c - 55 = 455

6c = 510

c = 85

The equation is given by 6c - 55 = 455 and the regular cost of each chair is $85

Find out more at: https://brainly.com/question/25737132

The automobile drove 50 mph and had gone 200 miles when the airplane set out in pursuit. It took 4 hours to overtake the car. What was the speed of the airplane?

Answers

100 mph per hour

Step-by-step explanation:

solution

speed of auto mobile=50mph

distance already traveled when the airplane took out in pursuit=200miles

time taken to overtake the car=4 hours

Now,

let the speed of airplane be X

X=50×4+200

or,X=200+200

or,X=400

or, X=400÷4

Therefore, X=100

Can u help me with my homework

Answers

Ur dad Ur dad Ur dad

Eva and Jamir like to bake cookies. Eva baked 24 chocolate chip cookies, and Jamir baked ppp peanut butter cookies. Together they baked a total of 56 cookies.

Answers

Jamir baked 32 peanut butter cookies

3+3=6! Easy for kids to learn!

Answers

Answer:

indeed

Step-by-step explanation:

3+3=6

HELP ME PLEASEEEEEEE I WILL GIVE POINTS AND BRAINLIEST

Answers

The answer is < A hope this helps

8/9 write simplified​

Answers

The fraction is already simplified.

Find the measure of the angle marked and indicated in bold.

Answers

Answer:

105° your answer

Step-by-step explanation:

parrallel line = gongruent angles

16x - 7 = 15x

16x - 15x = 7

x = 7

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

7 * 15 = 105° your answer

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

16 * 7 - 7 = 15 * 7

105 = 105

the answer is good

Write the first five terms of the geometric sequence whose first terns 6, and whose common ratio is 3.

Answers

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Geometric progression is given by:

[tex]nth\ term=ar^{n-1}[/tex]

where a is the first term, r is the common ratio

Given that first term is 6, and common ratio is 3, Hence a = 6, r = 3

[tex]First\ term=6\\\\Second \ term=6(3)^{2-1}=18\\\\Third \ term=6(3)^{3-1}=54\\\\Fourth \ term=6(3)^{4-1}=162\\\\Fifth \ term=6(3)^{5-1}=486[/tex]

The first five terms of the geometric sequence is 6, 18, 54, 162 and 486

Find out more on geometric sequence at: https://brainly.com/question/24355584

explain how you your answer

Answers

Answer:

1.43 = x

Step-by-step explanation:

Math in the picture attached. Hope it helps!


Francis owns a cake shop. She is currently preparing cupcakes (x) and cookies (y) for two birthday
parties. The first birthday party ordered 20 cupcakes and 40 cookies and their total cost was $61. The second birthday party ordered 30 cupcakes and 30 cookies. Their total cost was $64.50.

Answers

The cost of cupcakes is $1.25 and cookies costs $0.90.

Two equations that would be used to determine the required values can be derived from this question:

20x + 40y = 61 equation 1

30x + 30y = 64.50 equation 2

In order to determine the value of y, the following steps would be taken: Multiply equation 1 by 3 and equation 2 by 2.

60x + 120y = 183 equation 3

60x + 60y = 129 equation 4

Subtract equation 4 from 3

60y = 54

Divide both sides of the equation by 60

y = $0.90

Substitute for y in equation 1

20x + 40(0.9) = 61

20x + 36 = 61

20x = 61 - 36

20x = 25

x = 25 / 20

x = $1.25

To learn more about simultaneous equations, please check: : https://brainly.com/question/25739929


I’m genuinely confused on this, can someone explain how to do this problem?

Answers

Answer:

[tex]n \times 12[/tex]

.......

Q.

x ÷ 2 = 1.000.000.000
x = ?​

Answers

x÷2=1.000.000.000

x=1.000.000.000×2

x=2.000.000.000

Check:

2.000.000.000÷2=1.000.000.000

♪Answer :

let's find the value of x

x ÷ 2 = 1.000.000.000x = 1.000.000.000*2x = 2.000.000.000

Hello hello helppppppppppppp

Answers

Answer:
5 units left and 2 units down

Answer:

the person anove is correct

Step-by-step explanation:

Jill bought 7 pounds of melon and 0.9 pounds of cherries. How much fruit did she buy in all

Answers

Answer:

7.9 pounds of fruit

Step-by-step explanation:

In all means to add, so 7 + .9 = 7.9 pounds

If b= 62 degrees and c=24, find b.

Answers

Answer:

21.2

Step-by-step explanation:

b = sin of angle B times length of c

b = 24*sin(62) = 21.1907

Answer A

21.2

Step-by-step explanation:

Help help help help help

Answers

Answer:

100°

Step-by-step explanation:

Answer:

∡5=100°

Step-by-step explanation:

∡5 is perpendicular to the 100° above, therefore your answer is ∡5=100°.

Brainliest would be appreciated! :-)


Explain why and show how the expression -x might represent a positive number, a negative
number, or even 0.

Answers

If the variable is a negative you get -(-1) and minus a negative is positive. If the variable is a positive number the - makes it negative. If the variable is 0 we’ll it equals 0.

Help me plz it’s number 11 I need this urgent

Answers

Answer:

f = -9

Step-by-step explanation:

3(x)

3(-9)

-27

HELP ME PLS
Ursula has fraction 1 over 2 cup of butter. She uses fraction 1 over 4 cup of butter to make a batch of brownies.

Part A: How many batches of brownies can Ursula make with fraction 1 over 2 cup of butter? (4 points)

Part B: On your own paper, draw a fraction model that shows the total number of batches of brownies that Ursula can make with fraction 1 over 2 cup of butter. Make sure to label the model. Below, explain your model in detail to describe how this model visually shows the solution for Part A. (6 points)

Answers

Answer:

i think its 1/2

Step-by-step explanation:

Answer:

A. 1/2

1 over 2 is equal to 1/2

B. 1/2 Batch

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