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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group the first two terms by underline the first two terms 16x^3-4x^2-4x+1
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Answer:
Terms are the things that are separated by a (+) or a (-).
Step-by-step explanation:
16x^3 - 4x^2 -4x+1
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Answer:
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Step-by-step explanation:
We can make an equation
30%. . . . . .X
--------- = ---------
100. . . . . . .20
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100x = 600
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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]
Instruction
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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
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A
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C
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Answer:
C 18
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Answer:
slope: 4/12
Simplified to: 1/3
Negative slope so: -1/3
Y intercept:4
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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:
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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]
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[tex]\mathbf{x = \frac{1000}{\sqrt{1000}}}[/tex]
[tex]\mathbf{x = \sqrt{1000}}[/tex]
[tex]\mathbf{x = 10\sqrt{10 }}[/tex]
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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.
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Answer:
c
Step-by-step explanation:
I think that is the answer
Answer:
c
Step-by-step explanation:
it is equal to.
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Step-by-step explanation:
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Step-by-step explanation:
Alrighty! here you go image.
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Step-by-step explanation:
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Answer:
Step-by-step explanation:
−2x − 4 = −6
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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.
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Answers
Answer:
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Step-by-step explanation:
30: 1
6:?
cross multiply
(6*1)/30
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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).
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Answer:
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Step-by-step explanation:
4(x-1)=36
4x-4=36
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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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)
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3 = 1(0) + b
3 = 0 + b
3 = b
The linear equation to the table would be y = x + 3.
What four digit number an i? The sum of my digits is 4. The product of my digits is 1
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Answer:
4, 2, 1, 1
Step-by-step explanation:
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
Work Shown:
7.5% = (7.5)/100 = 0.075
7.5% of $1580 = 0.075*1580 = 118.50
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Answers
Answer:
191
Step-by-step explanation:
All you have to do is 127+64 to get the total before the withdrawal.
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Answer: 37
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There are two mystery numbers. The sum of 7 times the first number and 8 times the second number is 22. The sum of 5 times the first number and 8 times the second number is 18. What are the two numbers?
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 bThe 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.
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Food B 166.50
Food A has less calories