Answers
Answer:
C
Step-by-step explanation:
Y=2(-1)+3
y=-2+3
y=1
true
Related Questions
What is standard deviation?
Group of answer choices
The difference in the maximum and minimum valudes of the data set.
measure of how dispersed the data is in relation to the mean.
The difference in Quartile 3 and Quartile 1.
the center of the data
Answers
Answer:
The difference in Quartile 3 and Quartile 1.
x= -1/8y2
The focus of the parabola is:
O (0, -2)
O (2, 0)
O (-2, 0)
Answers
x=-1/8y²
Interchange x and y
y=-1/8x²Compare to Vertex form y=a(x-h)²+k
a=-1/8Now
1/4a1/4(-1/8)-2.So
Focus (-2,0)
Answer:
(-2, 0)
Step-by-step explanation:
Standard form of a parabola with a horizontal axis of symmetry:
[tex](y-k)^2=4p(x-h)\quad \textsf{where}\:p\neq 0[/tex]
[tex]\textsf{Vertex}=(h, k)[/tex]
[tex]\textsf{Focus}=(h+p,k)[/tex]
Given equation:
[tex]x=-\dfrac18y^2[/tex]
Rewrite in standard form:
[tex]\implies (x-0)=-\dfrac18(y-0)^2[/tex]
[tex]\implies -8(x-0)=(y-0)^2[/tex]
[tex]\implies (y-0)^2=-8(x-0)[/tex]
Comparing with the general standard form:
k = 0h = 04p = -8 ⇒ p = -2Therefore:
[tex]\textsf{Vertex }(h,k)=(0,0)[/tex]
[tex]\textsf{Focus }(h+p,k)=(0-2,0)=(-2,0)[/tex]
A politician wants to estimate the proportion of constituents favouring a controversial piece of proposed legislation. Suppose that a 99% confidence interval that extends at most 0.05 on each side of the sample proportion is required. How many sample observations are needed?
Answers
Answer:
I pressed this by an accident
Use the expression 4(8 + 3x) to answer the following: Part A: Describe the two factors in this expression. (4 points) Part B: How many terms are in each factor of this expression? (4 points) Part C: What is the coefficient of the variable term? (2 points)
Answers
Given : 4(8 + 3x)
To Find : Describe the two factors in this expression
How many terms are in each factor of this expression
coefficient of the variable term
Solution:
4(8 + 3x)
two factors in this expression are
4 and ( 8 + 3x)
terms in each factor of this expression
1 term in 4
2 terms in (8 + 3x)
coefficient of the variable term is 3 in factorized form
4(8 + 3x) = 32 + 12x
and coefficient of the variable term is 12 in expanded form
Learn More at brainly.com/in:
find the value of x by factorization, x2-8x+1280=0 - Brainly.in
https://brainly.in/question/7343350
Using factor theorem, factorize each of the following polynomial ...
https://brainly.in/question/15904651
Factorise: 1. a3 – 4a2 + 12 – 3a 2. a3x – x4 + a2x2
https://brainly.in/question/13142738
by selling an article for #2500 a trader made a profit of #200.find the percentage profit of the article.
Answers
Answer:
I'm going to assume the # is meant $, if that is the case then the trader made 8% profit
Step-by-step explanation:
200 out of 2500 is basically 200/2500. 200 divided by 2500 is 0.08, and to find the percent of a number you have to multiply it by ten (or just move the decimal two places to the right) 0.08 multiplied by 10 would give you 8, so the answer is 8 percent. Hope this helps!
50 POINTS AND BRAINLIEST IF IT INCLUDES STEPS
Create and solve a multi-step equation WORD PROBLEM that includes at least THREE STEPS (three or
more mathematical operations), that will have a final answer of 12. THE EQUATION MUST INCLUDE A
VARIABLE
Answers
Answer:
3(x-6)+9=27
Step-by-step explanation:
1. Multiply 3 to x-6
3x-18+9=27
2. add -18 and 9
3x-9=27
3. add 9 to 27
3x=36
4. Divide 36 and 3
x=12
Find the area of the figure.
Answers
Answer:
[tex]\huge\boxed{\sf 9300\ m\²}[/tex]
Step-by-step explanation:
The figure is made up of:
A rectangle A triangleFormula for area of rectangle:
Length × WidthFormula for Area of triangle:
[tex]\displaystyle =\frac{1}{2} (Base)(Height)[/tex]Area of rectangle:
Length = 90 m
Width = 70 m
= Length × Width
= 90 × 70
= 6300 m²
Area of Triangle:
Base = 170 - 70 = 100 m
Height = 90 - 30 = 60 m
[tex]\displaystyle =\frac{1}{2} (Base)(Height)\\\\= \frac{1}{2} (100)(60)\\\\= (50)(60)\\\\= 3000 \ m^2[/tex]
Total Area of the figure:
= Area of the rectangle + Area of the triangle
= 6300 + 3000
= 9300 m²
[tex]\rule[225]{225}{2}[/tex]
A triangle has side lengths 25, 15x and 20x. The longest side is 25. What value for x proves that this triangle is a right triangle?
Answers
To prove that this triangle is a right triangle, we need to check the side lengths using pythogoras theorem.
Given:
Longest side = 25 unitsTriangle side lengths: 25, 15x, and 20xPutting the side lengths into pythogoras theorem:
⇒ [tex]25^{2} = 15^{2} + 20^{2}[/tex]⇒ [tex]625 = (10x + 5x)^{2} + (20x + 0x)^{2}[/tex]Using the formula "(a + b)² = a² + 2ab + b²
⇒ [tex]625 =[(10x)^{2} + 2(10x)(5x) + (5x)^{2} ] + [(20x)^{2} + 2(20x)(0) + (0)^{2} ][/tex]⇒ [tex]625 = [(10x)(10x) + 2(10x)(5x) + (5x)(5x)] + [(20x)(20x)][/tex]⇒ [tex]625 =[100x^{2} + 100x^{2} + 25x^{2} ] + [400x^{2} ][/tex]⇒ [tex]625 = 100x^{2} + 100x^{2} + 25x^{2} + 400x^{2}[/tex]⇒ [tex]625 = 625x^{2}[/tex]Divide both sides by 625:
⇒ [tex]\frac{625}{625} = \frac{625x^{2}}{625}[/tex]⇒ [tex]1 = x^{2}[/tex]⇒ [tex]\sqrt{1} = \sqrt{x^{2} }[/tex]⇒ [tex]\sqrt{1 \times 1} = \sqrt{x \times x }[/tex]⇒ [tex]1 = x[/tex]The value of x that proves this triangle a right triangle is 1.
x = 1
If it is a right angle triangle
→ (short side)² + (short side)² = (long side)²
given long side is 25====================================
(15x)² + (20x)² = 25²225x² + 400x² = 625625x² = 625x² = 1x = √1x = ±1as distance is positive
x = 11) Debbie bought 8 oranges and 7 apples for $10.20. Katrina bought 5 oranges and 14 apples for $12.15. How much did one apple and one orange cost?
2) Joel and Janie are selling fruit. Joel sold 2 small boxes of fruit and 5 large boxes for $31. Janie sold 4 small boxes of fruit and 7 large boxes for $47. How much does one small box of fruit and one large box of fruit cost?
3) Carmen is trying to decide which jet ski rental plan to use. Plan A charges a one-time fee of $40 and $25 per hour. Plan B charges a one-time fee of $60 and $15 per hour. After how many hours will the plans cost the same?
4) Julie and Wendi purchased cell phones. Julie’s phone cost $50 and she pays $0.35 per minute. Wendi’s phone cost $70 and she pays $0.15 per minute. After how many minutes of use will Julie’s phone cost more than Wendi’s?
5) 78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
6) 168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
7) Christina spent $81.25 on books. Comic books cost $2.25 each and novels cost $7.00 each. If she bought 15 books, how many comic books did she buy?
8) Tina bought 8 pieces of clothing for a total of $164. Jeans cost $22 each and shirts cost $18 each. How many shirts did Tina buy?
9) Farmer Brown had 25 cows and chickens. They had a total of 72 legs. How many cows and how many chickens did Farmer Brown have?
10) Farmer Brown had 28 cows and chickens. They had a total of 96 legs. How many cows and how many chickens did Farmer Brown have?
What you need to do:
Please WRITE both equations for each problem, identify what your variables represent, and solve the system.
I don’t know what to do, so please help me understand by explaining how you got the answer.
I WANT TO LEARN FROM YOU! :)
- Will give BRAINLIEST if it gives me the option -
Answers
78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
Solution:Let the number of cars be "x" and the number of vans be "y".
According to question,
x + y = 10 5x + 12y = 78 -->(ii)
=> 5(x + y) = 10 × 5
=> 5x + 5y = 50 -->(i)
By Elimination method,
Equation (i) - (ii) we get,
(5x + 5y) - (5x + 12y) = 50 - 78
=> 5x + 5y - 5x - 12y = - 28
=> - 7y = - 28
=> 7y = 28
=> y = 28/7
=> y = 4
Putting the value of "y" in Equation (i)
5x + 5y = 50
=> 5x + 5 × 4 = 50
=> 5x + 20 = 50
=> 5x = 50 - 20
=> 5x = 30
=> x = 30/5
=> x = 6
Therefore,The total number of cars went = 6
The total number of vans went = 4
====================================================
Question no.6:168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
Solution:
Let the number of buses be "x" and the number of vans be "y".
According to question,
x + y = 10 42x + 6y = 168 -->(ii)
=> 42(x + y) = 10 × 42
=> 42x + 42y = 420 -->(i)
By Elimination method,
Equation (i) - (ii)
(42x + 42y) - (42x + 6y) = 420 - 168
=> 42x + 42y - 42x - 6y = 252
=> 36y = 252
=> y = 252/36
=> y = 7
Putting the value of "y" in Equation (ii)
42x + 6y = 168
=> 42x + 6 × 7 = 168
=> 42x + 42 = 168
=> 42x = 168 - 42
=>42x = 126
=> x = 126/42
=> x = 3
Therefore,Total number of buses went = 3
Total number of vans went = 7
what is the mode median mean and range of 4,5,0,2,3,1
Answers
Answer:
Mode = none, Median = 2.5, Mean= 2.5
Step-by-step explanation:
Hope this helps! :)
Step-by-step explanation:
the mode is the data item that occurres the most often.
but in 4, 5, 0, 2, 3, 1 every number appears only once. so, the mode is 0, 1, 2, 3, 4, 5 (as special case this average number can have more than one value - like in our case here).
the median is the value in the data set that lies directly in the middle between the other values (half of them are higher, the other half is lower).
if our data set has an even number of data points, or there is no unique middle value for other reasons, then the median is the mean value of the 2 middle values.
in our case 2 and 3 are the 2 middle values, so the median is (2+3)/2 = 2.5
the mean value is directly the average value across the whole data set : the sum of all values divided by the number of values.
(0+1+2+3+4+5)/6 = 15/6 = 2.5
the range is the difference between the highest and the lowest value in the data set : 5 - 0 = 0
50 POINTS NO LINKS
An object is launched at 39.2 meters per second (m/s) from a 42.3-meter tall platform. The equation for the objects height s at time t seconds after launch is s(t)=-4.9t^2+39.2t+42.3, where s is in meters. Create a table of values and graph the function. Approximately what is the maximum height of the object?
Answers
Convert into vertex form y=a(x-h)²+k
y=-4.9t²+39.2t+42.3After calculating
y=-4.9(x-39.2)²+42.3Vertex at
(39.2,42.3)Max height=42.3m
Graph attached
solve the following absolute value
Answers
Answer:
x < 2
Step-by-step explanation:
|-7x+4| < 18
7x + 4 < 18
7x + 4 - 4 < 18 - 4
7x < 14
7x/7 < 14/7
x < 2
im not sure if this is right but this is what i got.
Question 26 of 27
Find the value of x that makes ABCD a parallelogram.
Answers
Answer:
60°
Step-by-step explanation:
→ Find the sum of the angles
70 + 70 + x + 50 + x + 50 = 2x + 240
→ Equate the expression to 360
2x + 240 = 360
→ Minus 240 from both sides
2x = 120
→ Divide both sides by 2
x = 60
please help me find the answer
Answers
Answer:
the angle is equal to 60 degree
Please solve and show work!!! Need by tomorrow look at attached photo!!<44
Answers
Answer:
1.
First, I would solve for ACB.
Calculations:
63° = y?
I would do that because I know that angle 'y' is vertical to 63°, which is given. (Also vertical angles are congruent, meaning that the measure the same degrees).
2.
Second, I would solve for BAC.
Calculations:
x + 63 + 85 = 180
x + 148 = 180
-148 -148
x = 32°
I would do that because I know that there are two given angles so I could easily solve for the leftover angle, 'z', using the a + b + c = 180° formula.
3.
Next, I would solve for CED.
Calculations:
x + 130 = 180
-130 -130
x = 50°
I would do that because I know finding this angle will help me find angle CDE.
4.
Finally, I would solve for CDE.
Calculations:
x + 63 + 50 = 180
x + 113 = 180
-113 -113
x = 67°
I would do that because I know there are now two given angles so I could easily solve for the leftover angle, x, using the a + b + c = 180° formula.
Given rectangle WSDV, WD = 5−31 and SV = 2+11. Find the measurement of diagonal SV
Answers
Answer:
wheres tha rectangle
Step-by-step explanation:
Year Speed 1 38 2 46 3 52 4 57 5 61 3) During which time period was the ANNUAL rate of increase of the speed the GREATEST? HELP FAST
A) from year 1 to year 2
B) from year 1 to year 3
C) from year 1 to year 4
D) from year 1 to year 5
Answers
Answer: A) from year 1 to year 2
Step-by-step explanation: subtract 46-38=8, I also just took the K12 test and got it right.
Answer:
A) from year 1 to year 2
Step-by-step explanation:
2/5+3/8 5th grade Math. Please help.
Answers
Answer:
31/40
Step-by-step explanation:
Given expression:
[tex]\dfrac{2}{5} + \dfrac{3}{8}[/tex]
Note: Both fractions must have same denominators if we want to perform addition, subtraction, multiplication, or division.
The only way to simplify this expression is to have a common denominator, which can be determined by the LCM of 5 and 8.
⇒ Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45...⇒ Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72...Multiply the denominators with such a number that is equivalent to 40.
Note: The number you are multiplying should also be multiplied to the numerator.
[tex]\rightarrow \dfrac{2 \times 8}{5 \times 8} + \dfrac{3 \times 5}{8 \times 5}[/tex]
[tex]\rightarrow \dfrac{16}{40} + \dfrac{15}{40}[/tex]
Finally, simplify the expression to determine the solution.
[tex]\rightarrow \dfrac{31}{40}[/tex]
Since 31 is a prime number, we can't simplify this fraction. Thus, the final answer is 31/40.
Ah yes, adding fractions! Adding fractions can be a bit of a pain.
So, we have [tex]\frac{2}{5} + \frac{3}{8}[/tex].
To add fractions, the bottoms, or denominators, must be the same number. So we must multiply the fractions by certain numbers to make the denominators the same number. So let's go easy and make the denominator 40, because 8 goes into 40 and so does 5. So, to make 8 become 40, we'll multiply the whole fraction by 5. For 5, we'll multiply by 8.
[tex]5 * \frac{3}{8} = \frac{15}{40}[/tex]
[tex]8 * \frac{2}{5} = \frac{16}{40}[/tex]
Now we'll add the two fractions. When we add fractions we only add the tops, the numerators.
[tex]\frac{15}{40}+\frac{16}{40} = \frac{31}{40}[/tex]
Then we must reduce (or try to reduce). This fraction cannot be reduced, so the answer is simply [tex]\frac{31}{40}[/tex].
I hope this helps you understand.
-Toremi
what is the distance between these two numbers -3 1/4 and 4 1/2
Answers
Answer:
7 3/4
Step-by-step explanation:
Method 1:
Step 1: Instead of subtracting you distribute the minus sign to the number in the parenthesis
4 1/2 - (-3 1/4) = 4 1/2 + 3 1/4
Step 2: Then you can just add
4 1/2 + 3 1/4= 7 3/4
Method 2:
If you dont know fractions transfer them into decimals. 1/2 = 0.5 and 1/4 = 0.25
Step 1: Instead of subtracting you distribute the minus sign to the number in the parenthesis
4.5 - (-3.25) = 4.5 + 3.25
Step 2: Add the numbers
4.5 + 3.25= 7.75
Step 3: Convert the decimal back into a fraction
7.75= 7 3/4
A camera has a listed price of 643.99 before tax. If the sales tax rate is 9.75%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answers
Answer: $1,271.88
Step-by-step explanation:
The total cost of the camera with sales tax included will be 100% plus our sales tax:
100% + 9.75% = 109.75%
Dividing a percent (%) by 100 gives us a decimal:
109.75% / 100 = 1.975
We can multiply this decimal by the listed price of the camera to find our answer
643.99 * 1.975 = $1,271.88
The camera will cost $1,271.88 with sales tax.
What is the perimeter?
Answers
Answer:
i believe your answer is 41,
Step-by-step explanation:
because to find perimeter, you simply have to add up all of the sides unlike area where you have to multiply, giving you 18+18+2+2=41 for your answer
Answer:
41
Step-by-step explanation:
add up all the sides total to 41
You deposit all of your graduation money, $2,560, into an account earning 3.5% interest, compounded annually. You want to let it sit, no deposits or withdraws, while you are in college for 4 years. How much will you have at the end of 4 years? Round to the nearest cent.
Answers
Answer:
To calculate compounded interest, use the compound interest formula.
A(t)=P(1+rn)n⋅t
Recognize the information given in the problem.
P=2560,r=0.035,n=1,t=4
Substitute the values into the appropriate position in the formula.
A(4)=2560(1+0.0351)1⋅4
Simplify by multiplying and dividing by 1.
A(4)=2560(1+0.035)4
Simplify using the order of operations.
A(4)=$2,937.66
The balance at the end of 4 years would be $2,937.66.
Step-by-step explanation:
Solve the equation below by factoring:
Answers
[tex]\huge\fcolorbox{blue}{aqua}{Answer:}[/tex]
═════════════════════
Answer: =A.[tex]x = - 3[/tex] [tex]x = - 4[/tex]
Solution:
[tex]x ^ { 2 } +7x=-12[/tex]
[tex]x^{2}+7x+12=0 [/tex]
[tex]a+b=7 ab=12 [/tex]
[tex]1,12 2,6 3,4 [/tex]
[tex]1+12=13 2+6=8 3+4=7 [/tex]
[tex]a=3 b=4 [/tex]
[tex]\left(x+3\right)\left(x+4\right) [/tex]
[tex]x = -3[/tex] , [tex]x = -4[/tex]
so the answer is = A.════════════════════
Explanation:
#Carry on learning
7 and multiply to 12?
3 and 4
Rewrite the expression using the above.
(x+3)(x+4) = 0
x+3=0 or x+4=0
So x = -3 or x= -4
1. Children must be at most 36 inches tall to ride the kiddie roller
coaster. Let h = the height required to ride the kiddie roller coaster.
2. The gym can seat a maximum of 1200 people.
Let n = the number of people who can sit in the gym.
3. Children must be at least 13 to go to a PG-13 rated movie.
Let a = the age you must be to attend a PG-13 movie.
Answers
Answer:
Step-by-step explanation:
1.) H (greater than or equal to) 36in
2.) N (Less than or equal to) 1200
3.) A (greater than or equal to) 13
Write an equation to find the value of x and solve it. Round your answer to the nearest tenth if necessary.
x =
Write your equation and explain how you came up with your equation and how you solved it. What concepts apply to this problem? How do you know your answer is correct?
Answers
Answer: x = 14
Step-by-step explanation:
estimate 259+372 by rounding each number to the nearest 10
Answers
Answer: ok well the answer is 631 if it were rounded it would be 630
Now if u mean those 2 numbers they would be 259:260 and 372:370 there hope it helps bye!
The table of values represents a continuous function. Which type of function describes g(x)?
Rational
Polynomial
Logarithmic
Exponential
Answers
A logarithimic function is a function of the sort; loga(a^x) = x. The function that is described by g(x) is a logarithmic function.
What is a lograithimic function?A logarithimic function is a function of the sort; loga(a^x) = x. We now have to look at this table to ascertain of this condition is met.
Given this condition, we can see that each of the entries in the table satisfies this basic criterion of a logarithmic function hence, the function that is described by g(x) is a logarithmic function.
Learn more about logarithmic function: https://brainly.com/question/14356798
Answer:
Exponential
Step-by-step explanation:
The function g(x) described by the given table of values is most likely an exponential function because x increases by a constant factor and the values of g(x) increase or decrease by a consistent factor. This behavior aligns with the characteristics of an exponential function, where the variable x appears in the exponent. I put polynomial as my answer on the test and got it incorrect and then realized the answer was exponential.
The Payans have just learned that the bank will approve them for a mortgage at an APR of 4.3% for 30 years if they meet the back-end ratio requirement. To determine whether they’ll meet the requirement, the back-end ratio needs to be calculated with the actually monthly payment rather than the estimate used in part A. Use this monthly payment formula to calculate the Payans’ monthly mortgage payment.
Answers
The annual percentage rate (APR) for the Payans is the yearly interest rate that's generated by a sum charged to borrowers.
What is APR?Your information is incomplete as the values aren't given. Therefore, an overview will be given. Here, the APR is the cost that one has to pay to borrow money and it's expressed as a percentage.
Also, the mortgage payment is made up of the principal and the interest payments. It's how one will pay back their home loan.
Learn more about APR on:
https://brainly.com/question/1686286
Answer:
1237.18
Step-by-step explanation:
A class is made up of 54% women and has 21 women in it. What is the total number of students in the class?
Answers
Answer:
39
Step-by-step explanation:
percentage=part/total x 100
54= 21 / total x 100
total=38.88 = 39
A homebuyer is building a home and has sat down with an architect. The buyer tells the architect the perimeter of the house must be 200
feet. The dimensions of the house that would give the buyer the maximum area would be which of the following?
A 10 x 90 feet
B 20 x 80 feet
C 30 x 70 feet
40 x 60 feet
E 50 x 50 feet
Answers
Answer:
[tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area for a rectangle with the given circumference of [tex]200\; {\rm ft}[/tex]. (Note, that a circle of the same circumference would have an even larger area.)
Step-by-step explanation:
Assume that the base of the house is a rectangle. Let the length of the two sides be [tex]x\; {\rm ft}[/tex] and [tex]y\; {\rm ft}[/tex], respectively. The goal is to find the [tex]x[/tex] and [tex]y[/tex] that:
[tex]\begin{aligned} \text{maximize} \quad & x\, y \\ \text{subject to} \quad & 2\, (x + y) = 200 \\ & x > 0 \\ & y > 0 \end{aligned}[/tex].
Using the equality constraint [tex]2\, (x + y) = 200[/tex] (or [tex]x + y = 100[/tex]), the variable [tex]y[/tex] could be replaced with [tex](100 - x)[/tex] to obtain an equivalent problem of only one variable:
[tex]\begin{aligned} \text{maximize} \quad & x\, (100 - x) \\ \text{subject to} \quad & x > 0 \\ & (100 - x) > 0 \end{aligned}[/tex].
Simplify to obtain:
[tex]\begin{aligned} \text{maximize} \quad & -x^{2} + 100\, x \\ \text{subject to} \quad & x > 0 \\ & x < 100 \end{aligned}[/tex].
The objective function of this problem is [tex]f(x) = -x^{2} + 100\, x[/tex]. Derivatives of this function include
[tex]f^{\prime}(x) = -2\, x + 100[/tex] and[tex]f^{\prime\prime}(x) = -2[/tex].Since [tex]f^{\prime\prime}(x)[/tex] is constantly less than [tex]0[/tex], [tex]f(x)[/tex] is concave and would be maximized when [tex]f^{\prime}(x) = 0[/tex].
Setting [tex]f^{\prime}(x) = -2\, x + 100[/tex] to [tex]0[/tex] and solving for [tex]x[/tex] gives:
[tex]-2\, x + 100 = 0[/tex].
[tex]x = 50[/tex].
Notice that [tex]x = 50[/tex] satisfies both constraints: [tex]x > 0[/tex] and [tex]x < 100[/tex]. Therefore, [tex]x = 50[/tex] is indeed the solution that maximizes the area [tex]f(x) = -x^{2} + 100\, x[/tex] while at the same time meeting the requirements.
With the length of one side being [tex]x = 50[/tex] ([tex]50\; {\rm ft}[/tex],) the length of the other side would be [tex]100 - x = 50[/tex] ([tex]50\; {\rm ft}\![/tex].) Hence, a rectangular house of dimensions [tex]50\; {\rm ft} \times 50\; {\rm ft}[/tex] would maximize the area under the given requirements.