Solve the problem using a system of equations: Donnette found a widescreen TV at a garage sale, but she isn't sure if it will fit in her entertainment center. The TV is 50". The size of a TV is measured on the diagonal of the screen, and a widescreen has a length that is larger than the width. The screen also has an area of 1,200 square inches. What are the length and width of the TV screen?
length=_inches, width=_ inches

Answers

Answer 1

Check the picture below.

[tex]\begin{cases} L^2+w^2=50^2\\ Lw = 1200\\[-0.5em] \hrulefill\\ L^2+w^2=2500\\ L=\sqrt{2500-w^2} \end{cases}\qquad \stackrel{\textit{substituting on the 2nd equation}}{\sqrt{2500-w^2}~w=1200} \\\\\\ \stackrel{\textit{squaring both sides}}{w^2(2500-w^2) = 1200^2}\implies 2500w^2-w^4=1440000 \\\\\\ 0=w^4-2500w^2+1440000\implies 0=\stackrel{\textit{tis a quadratic}}{(w^2)^2-2500w^2+1440000}[/tex]

[tex]0=(w^2-900)(w^2-1600)\implies \begin{cases} 0=w^2-900\\ 900=w^2\\ \sqrt{900}=w\\ \boxed{30=w}\\[-0.5em] \hrulefill\\ 0=w^2-1600\\ 1600=w^2\\ \sqrt{1600}=w\\ \boxed{40=w} \end{cases} \\\\\\ \stackrel{\textit{we know that}}{L = \sqrt{2500 - w^2}}\implies \begin{cases} L=\sqrt{2500-30^2}\\ \boxed{L=40}\\[-0.5em] \hrulefill\\ L=\sqrt{2500-40^2}\\ \boxed{L = 30} \end{cases}[/tex]

Solve The Problem Using A System Of Equations: Donnette Found A Widescreen TV At A Garage Sale, But She

Answer 2

The length of the given TV is 40 inches and width of the given TV is 30 inches.

What is the area of a rectangle?

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

The area of rectangular shape TV is 1,200 square inches.

The TV is 50".

Now, L²+W²=50² ----------(I)

L×W=1200 ----------(II)

L²+W²=2500

⇒ L²=2500-W²

⇒ L=√(2500-W²)

Substitute L=1200/W in L=√(2500-W²), we get

1200/W=√(2500-W²)

Squaring on both the sides we get

1440000/W² =2500-W²

⇒ 1440000=2500W²-[tex]W^4[/tex]

⇒ [tex]W^4[/tex]-2500W²+1440000=0

⇒ (W²)²-2500W²+1440000=0

⇒ (W²)²-900W²-1600W²+1440000=0

⇒ W²(W²-900)-1600(W²-1600)=0

⇒ (W²-1600)(W²-900)=0

⇒ W²-1600=0 and W²-900=0

⇒ W²=1600 and W²=900

⇒ W=±40 and W=±30

So, W=40, -40, 30, -30

Length =1200/W =40 or 30

Therefore, the length of the TV is 40 inches and width is 30 inches.

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Related Questions

A car travelling at a constant speed covers 585 km in 9 hours. In how much time will it cover in 520 km? I want the answer in direct or inverse proportion.

Answers

Answer:

It took eight hours to travel 520km

Step-by-step explanation:

-4= 6 + b I need help in this question

Answers

-4=6+b

Subtract 6 on both sides.

-10=b

The final answer is b=-10.

Hope this helped!! :)

HELP ASAP

In math class, the girl to boy ratio is 8 to 6. If there are 24 girls in the class, how many boys are there?
A
20
B
30
C
18
D
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Answers

Answer:

C 18

Hope this helps

SOLVE PLZ I give brainlest
17+ -9

A. 26

B. 8

C. -8

D.-26

Answers

Answer:

B: 8

Step-by-step explanation:

When you add a negative number, it means you subtract that number.

[tex]17+-9=17-9=8[/tex]

Y=4x+8 y=-x-7 solve by substitution

Answers

Step-by-step explanation:

Alrighty! here you go image.

Answer:x=15

Step-by-step explanation:

What four digit number an i? The sum of my digits is 4. The product of my digits is 1

Answers

Answer:

4, 2, 1, 1

Step-by-step explanation:

Instruction
Active
Constructing Parallel Lines through a Given Point
ty
Construct a line through P that is parallel
to the given line by following these steps.
1. Construct a line through points
Q and P

Answers

make two pair of line segment of PQ andQP and construct use of a scale and the parallel line give the point name

Help help help
Help hep help

Answers

Answer:

-2

Step-by-step explanation:

-4x-2x ≤ 17-5

-6x ≤ 12 | /(-6)

x ≥ -2

group the first two terms by underline the first two terms 16x^3-4x^2-4x+1

Answers

Answer:

Terms are the things that are separated by a (+) or a (-).

Step-by-step explanation:

16x^3 - 4x^2 -4x+1

I don't think I'm right...

Food A 150 calories in 3/4 of a serving. Food B 250 calories in 2/3 of a serving. Find each unit rate. Which food has fewer calories per serving?

Answers

Food A 112.50
Food B 166.50
Food A has less calories

What is the area of a square if the Perimeter is 36 inches and each side is X -1

Answers

Answer:

Area= 100 inches square.

Step-by-step explanation:

4(x-1)=36

4x-4=36

4x=40

x=10

10×10=100

A set of house plans is made in the ratio 30:1. if a room is 6m long,how long is this room on the plan

Answers

Answer:

0.2

Step-by-step explanation:

30: 1

6:?

cross multiply

(6*1)/30

ans:0.2cm

paki sagot po kailangan na kasi..

thank you in advance ☺

Answers

1. 5

2.2

3.2,5

4.2,5

5.2

HOPE IT HELPS:)

PLS FOLLOW:)

#BRAINLIEST:)

____________is the exact average deviation of data values from the mean in squared units, and ____________ is the approximate average deviation of data values from the mean in regular units.

Answers

Variance is the exact average deviation of data values from the mean in squared units and the Standard deviation of data values from the mean in regular units.

Variance is a statistical measure of the dispersion of numbers in a data collection. Variance estimates how much more each number in the set deviates from the mean, and from each and every other number in the set.

The variance is a measure of the degree of variability. It is determined by averaging the squared deviations out of the mean.

The greater the spread of the data, the greater the variance in proportion to the mean.

The standard deviation is determined as the square root of variance by calculating the departure of each data point from the mean. The standard deviation represents the average level of variation in your dataset. It informs you how far each number deviates from the mean on average.

Learn more about Variance here:

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0.94 written as a fraction in simplest form

Answers

Its simplest form in fraction is 47/50

Construct a linear equation for the linear data presented in the table.
A) y = x + 3
B) y = 2x + 3
C) y=x-3
D) y = 2x - 3

Answers

Answer: A) y = x + 3

Step-by-step explanation:

Use two points given in the table and plug them into slope-intercept form y = mx + b.

In order to solve for m, the slope, by plugging them into [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex].

(0, 3) (2, 5)

[tex]\frac{5-3}{2-0}[/tex] = [tex]\frac{2}{2}[/tex] = 1

Use one of the points and plug it into the slope-intercept form y = mx + b.

3 = 1(0) + b

3 = 0 + b

3 = b

The linear equation to the table would be y = x + 3.

Find the dimensions of a rectangle (in m) with area 1,000 m2 whose perimeter is as small as possible. (Enter the dimensions as a comma separated list.)

Answers

The perimeter of the rectangle is the sum of its dimensions

The dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]

The area is given as:

[tex]\mathbf{A = 1000}[/tex]

Let the dimension be x and y.

So, we have:

[tex]\mathbf{A = xy = 1000}[/tex]

Make x the subject

[tex]\mathbf{x = \frac{1000}{y}}[/tex]

The perimeter is calculated as:

[tex]\mathbf{P = 2(x + y)}[/tex]

Substitute [tex]\mathbf{x = \frac{1000}{y}}[/tex]

[tex]\mathbf{P = 2(\frac{1000}{y} + y)}[/tex]

Expand

[tex]\mathbf{P = \frac{2000}{y} + 2y}[/tex]

Differentiate

[tex]\mathbf{P' = -\frac{2000}{y^2} + 2}[/tex]

Set to 0

[tex]\mathbf{ -\frac{2000}{y^2} + 2 = 0}[/tex]

Rewrite as:

[tex]\mathbf{ -\frac{2000}{y^2} = -2}[/tex]

Divide both sides by -1

[tex]\mathbf{\frac{2000}{y^2} = 2}[/tex]

Multiply y^2

[tex]\mathbf{2000 = 2y^2}[/tex]

Divide by 2

[tex]\mathbf{1000 = y^2}[/tex]

Take square roots of both sides

[tex]\mathbf{y = \sqrt{1000 }}[/tex]

[tex]\mathbf{y = 10\sqrt{10 }}[/tex]

Substitute [tex]\mathbf{y = \sqrt{1000 }}[/tex] in [tex]\mathbf{x = \frac{1000}{y}}[/tex]

[tex]\mathbf{x = \frac{1000}{\sqrt{1000}}}[/tex]

[tex]\mathbf{x = \sqrt{1000}}[/tex]

[tex]\mathbf{x = 10\sqrt{10 }}[/tex]

Hence, the dimensions that minimize the perimeter are [tex]\mathbf{10\sqrt{10 },10\sqrt{10 }}[/tex]

Answers

Based on the information given, the value of the two numbers will be 2 and 1 respectively.

Let the first number be aLet the second number be b

The equation to solve the question will be:

7a + 8b = 22 .... i

5a + 8b = 18 ..... ii

Subtract equation ii from I

2a= 4

a = 4/2

a = 2

Therefore, 7a + 8b = 22

7(2) + 8b = 22

14 + 8b = 22

8b = 22 - 14.

8b = 8

b = 8/8 = 1

Therefore, the numbers are 2 and 1.

Read related link on:

https://brainly.com/question/25701830

What is the slope of the line on the graph?

Answers

Answer:

slope: 4/12

Simplified to: 1/3

Negative slope so: -1/3

Y intercept:4

Form: Y=mx+b

Y=-1/3x+4

jessie works in an electronics store and earns a 7.5% commission on every item that she sells. How much commission would she earn for selling a computer that costs $1,580?

Answers

Answer: $118.50

Work Shown:

7.5% = (7.5)/100 = 0.075

7.5% of $1580 = 0.075*1580 = 118.50

pls help mee I dont k ow this and if anyone is smort enough can you help me with the 9ther questions (5 i total my last redo)

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Answer:

Step-by-step explanation:

I think that is the answer

Answer:

Step-by-step explanation:

it is equal to.

Which value for x makes the following equation true?

−2x−4=−6

Answers

Answer:

Step-by-step explanation:

−2x − 4 = −6

−2x − 4 + 4 = −6 + 4

−2x = −2

−2x/-2 = −2/-2

x = 1

The equation is,

→ -2x - 4 = -6

Let's solve for the value of x,

→ -2x - 4 = -6

→ -2x = -6 + 4

→ x = (-2)/(-2)

→ x = 2/2

→ [ x = 1 ]

Thus, the value of x is 1.

I need help please please whoever gets it correct I’ll give bairnlast

Answers

Answer:

(-1,-1)A

B (1,-3)

C (-2,-4)

Julie withdrew $64 from her savings account. After the withdrawal she has $127. How much money did julie have before she made the withdrawal?

Answers

Answer:

191

Step-by-step explanation:

All you have to do is 127+64 to get the total before the withdrawal.

If 5 measures 110 what is the measure of 2?

A) 55
B) 70
C) 110
D)160

Answers

The answer is C) 110. This is because they are corresponding angels which means they are congruent

A banker estimated a customer's worth to be $127,000. The customer was actually worth $120,000.

Find the percent error.

A. 5.5%

B. 5.6%

C. 5.7%

D. 5.8%

Please explain and get 100 points+ Brainlyist

Answers

Answer:

the answer is

5.6 I think

If sin theta < 0 and cot theta < 0, which quadrant(s)

could the terminal side of theta lie?

Answers

Answer:

Step-by-step explanation:

sinθ < 0 means below the x axis

cotθ = cosθ/sinθ < 0

As sinθ is already < 0 means cosθ has to be > 0 meaning right of the y axis.

Right of y and below x is the IV quadrant.

The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).

What is meant by Trigonometric Identities?

Trigonometric Identities are equality conditions that hold for all possible values of the variables in the equation and use trigonometry functions. There exists numerous unique trigonometric identities that relate a triangle's side length and angle.

here, we have,

Sine, cosine, and tangent are the fundamental three operations in trigonometry. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical notions exists built.

Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence. These exists identities that, geometrically speaking, involve certain functions of one or more angles.

we have,

sinθ < 0 means below the x axis

cotθ = cosθ/sinθ < 0

As sinθ is already < 0 means cosθ has to be > 0 meaning right of the y axis.

Right of y and below x is the IV quadrant.

Hence, The quadrant in which angle theta lie if sin theta < 0 and cot theta < 0 exists Quadrant IV (4).

To learn more about trigonometric identities refer to:

brainly.com/question/7331447

#SPJ2

.79 % of what number of horses is 29 horses

Answers

Answer: 37

Cross multiply 100x29 over 79

I need help with number 5 please

Answers

Answer:

-4[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

I hope this helps!

I make $20 an hour but I love 30% to taxes. How much do I take home each hour after taxes?

Answers

Answer:

$14

Step-by-step explanation:

We can make an equation

30%. . . . . .X

--------- = ---------

100. . . . . . .20

Now we cross multiply

100x = 600

x = 6

Now we subtract to find how much we will take home.

20 - 6 = $14 every hour will be made

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