Emily wants to hang a painting in a gallery. The painting and frame must have an area of 31 square feet. The painting is 5 feet wide by 6 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?4x2 + 22x − 1 = 0
4x2 + 22x + 31 = 0
x2 + 11x − 1 = 0
x2 + 11x + 31 = 0

Answers

Answer 1

Answer:

Option c) x² + 11x - 1 = 0 is the correct quadratic equation that can be used to determine the thickness of the frame.

In this problem, Emily wants to hang a painting in a gallery, and she needs to determine the thickness of the frame, denoted by "x," surrounding the painting. The painting and frame together should have an area of 31 square feet. The dimensions of the painting are given as 5 feet in width and 6 feet in length. To find the equation that will help us determine the thickness of the frame, we need to set up a quadratic equation based on the given information.

Let's start by visualizing the problem. The painting is a rectangle, and the frame around it will also form a rectangle. So, we can find the area of the frame by subtracting the area of the painting from the total area of the painting and the frame.

The area of a rectangle can be calculated by multiplying its length and width. For the painting, we have:

Painting's area = Length * Width

= 6 feet * 5 feet

= 30 square feet

Now, we know that the total area of the painting and frame together is 31 square feet. So, we can set up the following equation:

Total area (painting + frame) = Painting's area + Frame's area

31 square feet = 30 square feet + Frame's area

Frame's area = 31 square feet - 30 square feet = 1 square foot

The frame's area is given by the product of its width (which is the thickness "x") and the length of the painting (6 feet):

Frame's area = x * 6 feet

Since the frame's area is equal to 1 square foot, we can write:

x * 6 = 1

Now, let's rearrange the equation to set it to zero on one side:

6x - 1 = 0

We have now derived the quadratic equation that represents the problem:

6x - 1 = 0

The correct answer is not directly provided among the options. However, let's manipulate the equation to put it in standard quadratic form (ax² + bx + c = 0):

Multiply the equation by -1 to change the sign of each term:

-6x + 1 = 0

Now, it matches option c) x² + 11x - 1 = 0.

Thus, option c) is the correct quadratic equation that can be used to determine the thickness of the frame, "x," for the given problem.

To know more about Quadratic Equation here

brainly.com/question/17177510

#SPJ2

Answer 2

Answer:

The correct answer is 4x2 + 22x − 1 = 0

That's what you get when you (5 + 2x)(6 + 2x) = 31

And you get to expand that based on the data that is already provided in the question.

Related Questions

Please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Round 71195.4277573 to 2 decimal places.
Purchase computer of 30000
When a number is increased by 39, the resultis 47. What equation fits this statement?
Two angles of a quadrilateral are 79° and 154°. What is the sum of the other two angles?

How do you solve:

x-y=3
x-y=7

Answers

$\left\{\begin{array}{ccc}x-y=3\nx-y=7&/\cdot(-1)\end{array}\right\n\n+\left\{\begin{array}{ccc}x-y=3\n-x+y=-7\end{array}\right\n---------\n.\ \ \ \ \ \ \ \ 0=-4\ -\ FALSE\n\nAnswer:no\ solution;\ x;\ y\in\O$

If you are trying to solve those equations using the equal values method, you would first turn both the equations to equal y. So for x-y=3, you would add y to each side to get x=3+y and then subtract 3 from each side to get x-3=y. When you do the same thing to the equation x=y=7, you get x-7=y. When you plug them together you take away the y's and put an equal sign in between:
x-3=x-7 -then you would subtract x from any side and do that to the other side. You get -3=-7 which isn't correct so you would get a "no solution" problem.

The length of the shadow of a tree is 24 feet, the tan P = .7.
Write an equation involving a trigonometric ratio that can be used to find the height x of the tree. Explain why your equation is correct.

Find the height x of the tree by using your equation.

Answers

You do not included the picture. I can guess that p is the angle formed by the shadow and the hypotenuse of the right triangle.

The the trigonometric ratio is tan(p) = x/s

Where x is the height of the tree and s is the length of the shadow.

Then, x =s*tan(p) = 24 feet * 0.7 = 16.8 feet

Which prefix means one hundredth?

milli
deci
centi
deca

Answers

The answer to that is centi.

Answer: The answer to that is centi.

Write a explicit formula for the sequence 10, 9.5, 9, 8.5, 8 then find ^a8

Answers

Answer:

Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

Step-by-step explanation:

Given: Sequence = 10, 9.5 , 9 , 8.5 , 8

To find: Explicit Formula for the sequence and 8th term of sequence

1st term of sequence = 10

2nd term of sequence = 9.5

3rd term of sequence = 9

4th term of sequence = 8.5

5th term of sequence = 8

Difference between 2nd and 1st term = 9.5 - 10 = -0.5

Difference between 3rd and 2nd term = 9 - 9.5 = -0.5

Since, Difference is same in both cases

⇒ It is Arthematic Progression

⇒ First term, a = 10 and Common term, d = -0.5

using formula of AP for nth term we get,

$a_n=a+(n-1)d$

$a_n=10+(n-1)(-0.5)$

$a_n=10-0.5n+0.5$

$a_n=10.5-0.5n$

⇒ 8th Term of AP, $a_8=10.5-0.5*8=10-4=6$

Therefore, Explicit formula for the sequence is $a_n=10.5-0.5n$ and $a_8=6$

Answer:

The term number eight is 6.5

$a_(8)=6.5$

Step-by-step explanation:

The given sequence is an arithmetic sequence, because each term can be found by applying a difference.

In this case, you can observe that such difference is -0.5, because each term is going down by 0.5 units.

The formula that describes an arithmetic sequence is

$a_(n)=a_(1)+(n-1)d$

Where $a_(n)$ is the last term, $a_(1)$ is the first term, $n$ is the position of the last term and $d$ is the difference.

Each variable is

$a_(1) =10\nd=-0.5\nn=8\n$

Where we are gonna find $a_(8)$ the term number eight. So, replacing values, we have

$a_(n)=a_(1)+(n-1)d\na_(8)=10+(8-1)(-0.5)\na_(8)=10+7(-0.5)=10-3.5\na_(8)=6.5$

Therefore, the term number eight is 6.5.

A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the caris 30 mph slower than twice the speed of the motorcycleIn two hours, the car is 20 miles ahead of the motorcycle. Find thespeed of both the car and the motorcycle, in miles per hour.

Answers

speeds are s_c for car, s_m for motorcycle.

time is 2

distance of car is:
d_c = d_m + 20, d_m is distance of motorcycle.

speed is defined as:
s = d/t, distance over time.

hence:
d_c/2 = s_c = d_m/2 + 10
s_c = s_m + 10

from problem statement we know:
s_c = 2s_m - 30

so we have 2 simultaneous equations:
s_c = s_m + 10
s_c = 2s_m - 30

multiply second by -1 and sum them both:
s_c = s_m + 10
-s_c = -2s_m + 30
-------------------------
0 = -s_m + 40
s_m = 40
that is the speed of the motorcycle

s_c = s_m + 10
s_c = 40 + 10
s_c = 50

that is the speed of car, both speeds in miles per hour

Solve (if you can (ha ha ha)).

$x^7-128=0$

Answers

Step 1: Add 128 to both sides.
x^7−128+128=0+128
x^7=128
Step 2: Take root.x=(128)^(1/7)
x=2
Answer:
x=2

x^7 -128= 0
⇒ x^7 -2^7= 0 (because 2^7= 128)
⇒ x^7= 2^7
⇒ x= 2

The final answer is x=2~

Other Questions

Find the area of a regular hexagon with an apothem 11.4 yards long and a side 13 yards long. Round your answer to the nearest tenth.

Helpppp i’ll give that crown thing

The ratio of the number of CARS to SUVs in a parking lot is 5:2. There are 70 total Vehicles in the parking lot. How many SUVs are there

Factorise 15x + 35y - 40 z