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
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]
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
Can someone help with question #3
Answers
Answer:
y = –12x –300 that will help you
.Sort the numbers based on the number of significant figures they have.
Drag each tile to the correct location.
1,230
155.6
200
1,245
8.88
22
136
8.880
0.01
20
20.
Answers
Let's check the significant figures one by one
[tex]\\ \sf\longmapsto 1,230=3[/tex]
[tex]\\ \sf\longmapsto 155.6=4[/tex]
[tex]\\ \sf\longmapsto 200=1[/tex]
[tex]\\ \sf\longmapsto 1245=4[/tex]
[tex]\\ \sf\longmapsto 8.88=3[/tex]
[tex]\\ \sf\longmapsto 22=2[/tex]
[tex]\\ \sf\longmapsto 136=3[/tex]
[tex]\\ \sf\longmapsto 8.880=3[/tex]
[tex]\\ \sf\longmapsto 0.01=1[/tex]
[tex]\\ \sf\longmapsto 20=1[/tex]
One Significant figure - 200, 0.01, 20
Two Significant figures- 22, 20.
Three Significant figures- 1,230, 8.88, 136
Four Significant figures- 155.6, 1,245, 8.880
PLATO
The perimeter of a triangle is 71 cm. If the longest side of the triangle is 8 cm longer than five times the shortest side and the third side is 7 cm less than four times the shortest side. How long is the longest side of the triangle?
Answers
Answer:
43 cm
Step-by-step explanation:
If the longest side of the triangle is 8 cm longer than five times the shortest side
5s + 8
the third side is 7 cm less than four times the shortest side
4s - 7
The perimeter of a triangle is 71 cm
s + (4s - 7) + (5s + 8) = 71
Combine like terms
10s + 1 = 71
Subtract 1 from both sides
10s = 70
divide both sides by 10
s = 7
---------------------------------
How long is the longest side of the triangle
5s + 8
5(7) + 8
35 + 8
43
Use the figure below to find the values of x and y
Answers
Answer:
x=68 and y = 112
Step-by-step explanation:
angles of a triangle must equal 180, so
52°+60°+x°=180
112+x=180 <-- subtract 112 to get x on one side.
x=68
To solve for y, a straight line = 180 so
68+y=180 --> just subtract 180-68
y=112
Write 12 as a product of primes. Use index notation when giving your answer
Answers
or
[tex]12 = {2}^{2} \times 3[/tex]- BRAINLIEST answerer
after how many years will £6,000.00 yield a simple interest of £900.00 at 3%
Answers
Answer:
add 1 Century to divide £6 000 000
Answer:
the answer to your question is 105 I think sorry if it's not
A car was valued at 380,000 in the year 2014. By 2019, the value had depreciated to 110,000. If the cars value continues to drop by the same percentage,what will it be worth by 2017?
Please help thanks and Godbless
Answers
Answer:
160000
Step-by-step explanation:
3. The value of x varies directly with y,
and when x = 21, y=3.
Find the value of x if y= 10.
Answers
Answer:
70
Step-by-step explanation:
First you want to find the amount of x per 1 y so you divide 21 by 3 to get when x = 7 y = 1. Now you can just multiply 10 by 7 to get 70.
I hope this helps!
Maria finds a local gym that advertises 44 training sessions for $1393. Find the cost of 136 training sessions.
Answers
Answer:
$4305.60
Step-by-step explanation:
1393 divided by 44 = 31.6590909
that's how much for one training session
so to find the pay for 136 sessions you need to do 31.6590909 x 136
which is 4305.63636
if you round that, you get $4305.60
Can somebody please help this is honestly due tomorrow
Answers
Answer:
I am almost completely sure its 4.
Step-by-step explanation:
I dont mind brainiests by the way
Which equation represents the data in the table shown?
A) y = -2x
B) y = 2x + 3
C) y = -2x + 3
D) y = -2x - 3
Answers
Answer:
C
Step-by-step explanation:
the y-axis is getting smaller by 2 so its -2 and the x-axis is getting bigger by 1 so its -2 times 1 which is -2 but then 0=3 so the equation would be y = -2 + 3 :)
6 short questions 50 POINTS
Answers
Answer:
KN be better
sons of if his
WILL GIVE YOU BRILLIANT
State whether the graph of the linear relationship is a solid line or a set of unconnected points. Complete the explanation of your reasoning. The relationship between the number of $5 lunches you buy with a $145 school lunch card and the money remaining on the card because you select ) The relationship is a select ) buy a (select
Answers
Answer:
The relationship will be a solid line.
Step-by-step explanation:
The relationship between the number of $4 lunches you buy with a $100 school lunch card and the money remaining on the card.
The relationship will be a solid line as it is a linear and common slope. Each time you buy lunch, the amount in the card will decrease by $4.
Let the number of lunches you buy be = x
Let the amount remaining in the card be = y
So, equation forms:
When you buy 1 lunch, or x = 1
When x = 2
When x = 3
We can see that the decrease is gradual and same.
You can also see the graph attached that a straight line is formed.
a ratio is a comparison between two or more numbers or quantities
a. True
b. False
Answers
A 6-pack of ice cream sandwiches costs $3.86. What is the unit price, rounded to the nearest cent?
Answers
Answer: so either .64 or , .66,
Step-by-step explanation:
divide 3.86 by 6
A large drink dispenser used at a school field day holds 640 ounces of lemonade. How many glasses of lemonade can be poured from the dispenser if each glass holds 8 ounces?
Answers
Answer:
80 glasses
Step-by-step explanation:
640/8 = 80
Answer: 80 glasses
There are 80 glasses of lemonade can be poured from the dispenser if each glass holds 8 ounces.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
A large drink dispenser used at a school field day holds 640 ounces of lemonade.
Now,
Find the number of glasses of lemonade can be poured from the dispenser if each glass holds 8 ounces as;
= 640 ÷ 8
= 80
Thus, There are 80 glasses of lemonade can be poured from the dispenser if each glass holds 8 ounces.
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Triangle ABC has coordinates A(-2, -3), B(1, 1), and C(2, -1). If the triangle is translated 1 unit right and 3 units up, what are the coordinates of A'?
Answers
Answer:
answeris: C.(-6,-9)➡(6-9)
WHAT IS THE EQUATION IN SLOPE INTERCEPT FORM FOT THE LINE THAT PASSES THROUGH THE POINTS (2,-2) AND (-3,-17)
Answers
Answer:
y = 3x - 8
Step-by-step explanation:
to find slope the equation (y2 - y1) / (x2 - x1) is used
this means change of y over change of x
[-17 - (-2)] / (-3 - 2)
(-17 + 2) / -5
-15 / -5 = 3
the slope is 3
to find slope intercept form you must find the y intercept
using y = 3x + b and plugging things in we can find it
we can plug in the first point
-2 = 2(3) + b
b is your y intercept
-2 = 6 + b
b = -8
Answer:
y = 3/1x - 8
steps:
(2,-2) (-3, -17)
x1. y1. x2. y2
y2-y1
x2-x1
-17 - -2 = -15. = 3
-3-2. -5. 1
(2,-2)
y= mx + b
-2 = 3/1(2) + b
-2 = 6 + b
-6 -6
-8 = b
y = 3/1x - 8
An arrow is shot vertically upward from a platform 45 feet high at a rate of
132 ft/sec. Use the quadratic function h(t)=−16t2+132t+45 to find how long it will take the arrow to reach its maximum height, and then find the maximum height. Round to the nearest tenth.
Answers
Answer:
486 feet will reached after 5.25 seconds, when rounded to nearest tenth would be 5.3
Step-by-step explanation:
Find the GFC of 72 and 64
Answers
Answer:
8
Step-by-step explanation:
GCF of 64 and 72 is 8.
I hope it helps you..
Please help! Asap.
I suck at this.
I need to find y
Answers
x = 180 - 115
x = 65
180 = 65 + 90 + y
180 - 65 - 90 = y
25 = y
Answer:
y° = 25°
Step-by-step explanation:
Given the diagram of a triangle, where it shows an exterior angle with a measure of ∠115°, and that an angle bisector bisects the triangle into two right triangles.
According to the Exterior Angle Theorem, the measure of the exterior angle is equal to the sum of the measures of two non-adjacent interior angles. In other words, the given exterior angle, m∠115° is equal to m∠y° + m∠90°.
Solve for y:Hence, we could simply solve for the value of y algebraically:
m∠y° + m∠90° = m∠115°
y° + 90° = 115°
Subtract 90° from both sides:
y° + 90° - 90° = 115° - 90°
y° = 25°
Double-check:Verify whether we have the correct value for y by solving for x:
Since the exterior angle, ∠115°, and ∠x° are supplements, then it means that:
m∠115° + m∠x° = 180°
115° + x° = 180°
Subtract 115° from both sides:
115°- 115° + x° = 180° - 115°
x = 65°
According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180°.
Hence:
m∠x° + m∠y° + m∠90° = 180°
65° + 25° + 90° = 180°
180° = 180° (True statement).
Therefore, the correct answer is: y = 25°. This measure represents either one of the ∠y.
This is a glucose molecule. How many hydrogen atoms are in a molecule of glucose? A) 10. B) 11. C) 12. D) 13
Answers
Answer:
12 for sure
Step-by-step explanation:
I just know
Find all factors of 27.
Answers
Answer:
all the factors of 27 is 1, 3 ,9,and 27
6-4x=12+2x
Solve for x
Answers
+4X. +4X
6= 12 + 6X
-12. -12
-6 = 6X
X EQUALS -1!
Original price of a puppy $159.95 Discount 15% Tax 8.725%?
Answers
Answer:
$124.095
Step-by-step explanation:
Discounted Price= $159.95- 15%of $159.95=$135.9575
Final Price= Discounted price + Tax
= $135.9575+ 8.725% of $135.9575
= $135.9575-$11.8622
=$124.095
Which of the following is equal to the expression below
(8 - 32014
A 40
B. 30
C 835
D. 1035
Answers
Answer:
C 835Which of the following is equal to the expression below
This morning, Megan and her dad had smoothies for breakfast. Megan made her smoothie with 1 cup of mango and 3 cups of strawberries. Her dad made a giant smoothie with 2 cups of mango and 6 cups of strawberries. Did the smoothies have the same ratio of mango to strawberries?
Answers
Answer:
Yes.
Step-by-step explanation:
What is the algebraic expression for the following word phrase: "the product of x and the sum of 2 and y"?
Answers
Answer:
x(2+y)
Step-by-step explanation:
sum of 2 and y=2+y
product of x=x times expression
:. Answer =x(2+y)
determine if you can use the hypotenuse-leg congruency property to prove the triangles are congruent
Answers
Answer:
4. We don't know if they're right triangles
Step-by-step explanation:
If you could assume that the triangles are right triangles, then you would be able to prove congruency with HL. In this case however, the angles are not given so you can't assume anything.
A
Triangle ABC is right-angled at A, and AD is the altitude from A to the hypotenuse BC.
Find x
Answers
Answer:
Step-by-step explanation:
5 x 6:30