Answer:
[tex]Area=25\,\,in^2[/tex]
Step-by-step explanation:
The length of the rectangle is unknown and is defined with the letter "x". Notice that the width of the rectangle is also unknown, so we can name it 'y".
Recall the formula for the area of a rectangle (length times width), and notice that it is this quantity the one we need to maximize (find the maximum possible value).
We use the other information provided to represent the rectangle's with (y) in terms of "x" :
length + width = 10 inches
x + y = 10
Therefore, y = 10 - x
Now we use this expression for "y" in the product for the area;
[tex]Area= x\,*\,y\\Area=x\,(10-x)\\Area=10x-x^2\\Area=-x^2+10x[/tex]
Notice that this quadratic expression corresponds to a parabola with branches pointing down (negative leading term), so its maximum value would be given at the vertex of the parabola.
Now recall that the formula for the x-value of a parabola's vertex when its function is of the form [tex]f(x)=ax^2+bx+c[/tex]
is given by:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]
which in our case where "a" = -1 and "b" = +10, gives:
[tex]x_{vertex}=-\frac{b}{2a}\\x_{vertex}=\frac{-10}{2(-1)}\\x_{vertex}=\frac{-10}{-2}\\x_{vertex}=5[/tex]
Then the maximum value for the Area can be obtained by replacing "x" with "5" in the area formula:
[tex]Area=-x^2+10x\\Area=-(5)^2+10\,(5)\\Area=-25+50\\Area=25\,\,in^2[/tex]
Therefore, the area of the rectangle is [tex]25\,\,in^2[/tex]
Why do some quadratic graphs move left or right and others do not? Is there a correlation between this and them moving up and down? How would you demonstrate your reasoning is correct?
Answer:
(x + 3)^2 is left 3 because it becames 0 at -3
(x - 3)^2 is right 3 because it becames 0 at 3
x^2 +3 is up 3 because your just adding 3 units up
x^2 - 3 is down 3 because your just subtracting 3 units down
Step-by-step explanation:
Which of the following is most likely the next step in the series Z3Y6X9W 12
Answer:
V
Step-by-step explanation:
This series is a letter, followed by a number where the letter is the previous letter in the alphabet and the number is increasing by 3
Answer:
12 V 15 U 18 T 21 S 24 R 27 Q
Step-by-step explanation:
Letters going backwards, numbers increasing by 3
Which of the following choices best describes the behavior of the light rays when they pass through the lens:
A)The rays will refract and bend away from each other.
B)The rays will refract and bend toward each other.
C)The rays will move through the lens without changing direction.
D)The rays will bounce off the surface of the lens.
i would C because it the lights didnt bend
it went through
If you spin a spinner with 3 equal parts, how many possible outcomes are there? A. 1 B. 2 C. 3 D. 4
potatoes are 50p a pound . how much for 24oz
Answer:
25p
Step-by-step explanation:
IM NOT SURE IF ITS RIGHT BUT THAT WHAT I THINK. HAVE A NICE DAY!
Answer:
Hi...
The correct ans is 25 p
Hope this helps.....
Pls mark my ans as brainliest....
Sry dude the calculations r longggggggggggg
Be sure to mark my ans as brainliest
NUMBERS THAT ARE GONNA BE ROUNDED TO: 1/2, 1, 0
1. 1/8 + 2/5
2. 13/14 - 1/10
3. 1/12 + 1/20
Answer:
1. 1/2
2. 1
3. 0
Step-by-step explanation:
do supplementary angles form right angles? yes or no
Answer:
Yes i
Step-by-step explanation:
A supplementary angle can be two angles that sum up to 180 if you want you can have 2 angles that are 90 degrees that add up to 180 so therefore that would make a right angle.
Lance is tracking the progress of his plant's growth. Today the plant is
5 cm high. The plant grows 1.5 cm per day. Which equation below
represents the height of the plant (h) after d days?
Answer:
h = 5 + 1.5d
Step-by-step explanation:
Need Help ASAp will give brainliest!!!
Answer:
0.05
Step-by-step explanation:
3.25 divided by 9 is 0.35 and 2.4 divided by 8 is 0.3 (0.30)
theres a 0.05 gap
if im wrong im sorry
Which of the following is a characteristic of hyperbolic geometry?
A. There are an infinite number of lines parallel to a given line
through a given point.
B. There is exactly one line perpendicular to a given line through a
given point.
C. There is exactly one line parallel to a given line through a given
point.
D. There are an infinite number of lines perpendicular to a given line
through a given point.
Answer:
A
Step-by-step explanation:
Hyperbolic geometry is defined as a non-Euclidean geometry.
(invalidating the fifth postulate of Euclid's five fundamental postulates)
Choice B and D can be eliminated because this has nothing to do with perpendicular lines.
Choice C should be eliminated as well since that's exactly the fifth postulate of Euclid's five fundamental postulates
We are left with A by the process of elimination
Answer:
A. There are an infinite number of lines parallel to a given line through a given point.
Hope this Helps!
HELPPPPP PLEASE IT'S URGENT!!!!!!
What is the volume of the composite figure? Express the
answer in terms of .
A) 1447 mm
B)1687 mm
C) 3121 mm
D) 4567 mm
Answer:
Step-by-step explanation:
Volume of the hemisphere
V = 2/3π x r^3
= 144π cu. mm
Volume of the cone
V = 1/3π x r^2 x h
V = 168π cu. mm.
Volume of the composite figure
= 144π + 168π
= 312π cu. mm.
Under the Objective Theory of Contacts, the Reasonable Person Select one: a. May determine the existence of a contract if there is a dispute. b. May determine the terms of a contract if there is a dispute. c. Both of the above. d. Neither of the above.
Answer:
ayo this was posted the day after my birthday
Step-by-step explanation:
Also why u here during summer?
The answer is C though, its explaing it very well
What is the total amount of material
needed for the entire birdhouse?
Answer:
This question is incomplete ... plz complete the question so that you may get better help.
Step-by-step explanation:
From: Brainy services
f (x) = x² + 10x + 24.
Help plzz !!
Answer:
Consider the form
x
2
+
b
x
+
c
x2+bx+c
. Find a pair of integers whose product is
c
c
and whose sum is
b
b
. In this case, whose product is
−
24
-24
and whose sum is
−
10
-10
.
−
12
,
2
-12,2
Write the factored form using these integers.
(
x
−
12
)
(
x
+
2
)
(x-12)(x+2)
Answer:
[tex]f(x)=x+5x^{2} -1[/tex]
A chemist is adding pure (100%) acid to a 12 liter solution that is 15% acid in order to increase it to 49% acid. How much pure acid must she add?
How many ounces of 35% ethanol must be added to a 23 ounce mixture that contains 26% ethanol in order to obtain a mixture of 30.86% ethanol?
How many liters of 30% acid must be added to 10 liters of 53.66% acid in order to obtain a mixture that is 43% acid?
Answer:
1) 8 liters of pure acid
2) 27 liters of 35% ethanol
3) 8.2 liters of 30% acid
Step-by-step explanation:
The inicial amount of acid is 15% of 12 L, and the inicial volume is 12L.
Adding 'x' L of 100% acid, we have the amount of acid equal to 12 * 0.15 + x * 1, and the volume of 12 + x. The concentration is the amount of acid over the volume, so we have that:
(12*0.15 + x) / (12 + x) = 49/100
(1.8 + x)*100 = (12 + x) * 49
180 + 100x = 588 + 49x
51x = 408
x = 8 liters of pure acid
Similar to the solution above, for the second question we have:
(23*0.26 + 0.35*x) / (23 + x) = 30.86/100
(5.98 + 0.35*x)*100 = (23 + x) * 30.86
598 + 35x = 709.78 + 30.86x
4.14x = 111.78
x = 27 liters of 35% ethanol
For the third question, we have:
(10*0.5366 + 0.3*x) / (10 + x) = 43/100
(5.366 + 0.3x)*100 = (10 + x)*43
536.6 + 30x = 430 + 43x
13x = 106.6
x = 8.2 liters of 30% acid
Need answers to both large and small cups plez
Answer:
4 large and 5 small
Step-by-step explanation:
$1.50×4= $6.00
$0.90×5= $4.50
$6.00+$4.50= $10.50
Which ordered pair is a solution of the equation y=2x+5
A. (3,11)
B. (2,7)
C. (1,6)
Answer:
A(3,11)
Step-by-step explanation:
[tex]y = 2x + 5[/tex]
[tex]2×3 = 6[/tex]
[tex]6 + 5 = 11[/tex]
Pls help me it’s emergency plzz fast
Answer:
67.3%
Step-by-step explanation:
Calculate profit = selling price - cost price
cost price = 50 × $28 = $1400
38 × $49 = $1862
12 × $40 = $480
selling price = $1862 + $480 = $2342
Profit = $2342 - $1400 = $942
% profit = [tex]\frac{profit}{cost}[/tex] × 100%
= [tex]\frac{942}{1400}[/tex] × 100% ≈ 67.3% ( to 1 dec. place )
What is the volume, in terms of π, for a cylindrical
container with a radius of 3.25 centimeters and a
height of 10 centimeters? (use the formula V
= I1r2 h)
Answer:
[tex]105.625\pi cm^3[/tex]
Step-by-step explanation:
[tex]V=\pi r^2h=\pi *3.25^2*10=331.83072\\=331.83[/tex]
Answer in terms of [tex]\pi[/tex]
[tex]105.625\pi cm^3[/tex]
Harry likes to grow his own vegetables. He wants to harvest at least 129 squashes during the summer season. If he has already harvested 61 squashes and plans to pick 8 squashes every week, how many weeks will it take him to harvest at least 129 squashes?
Answer:
8.5 weeks
Step-by-step explanation:
to solve, you can start by subtracting 61 from 129 because he has already picked 61.
129 - 61 = 68
then, just divide 68 by 8 to find how many weeks it will take him.
68/8 = 8.5
it will take Harry 8 and a half weeks to harvest at least 129 squashes.
Harry needs 9 weeks to harvest at least 129 squashes.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Let, The number of weeks it will take Harry to harvest at least 129 squashes be 'w'.
Therefore, The inequality that represents the given situation is,
8w + 61 > 129.
8w > 68.
w > 68/8.
w > 8.5.
So, It will take him at least 9 weeks.
learn more about inequalities here :
https://brainly.com/question/30228778
#SPJ2
Determine the surface area of this cone if the radius is 4 cm and the height is 12 cm . Round your answer to the nearest tenth . Help please because it says 209.22 is not the answer
Please help me with 3 more questions ill give good ratings please!
Answer:
(- 32, - 16 )
Step-by-step explanation:
Since the dilatation is centred at the origin, multiply the original coordinates by the scale factor, that is
(- 8, - 4 ) → (4(- 8), 4()- 4)) → (- 32, - 16 )
I NEAD HELP ASAP The Lewis family dined at a restaurant. Their bill came to $52, and they plan on leaving a 19% gratuity. This means that the total amount they will pay is 119% of the bill. Which calculation results in the best estimate of the total amount they will pay in dollars? Assume there is no tax. (50) (110 percent) = (50) (100 percent + 10 percent) = (50) (100 percent) + (50) (10 percent) = (50) (1.0) + (50) (0.1) = 50 + 5 = 55 (50) (120 percent) = (50) (100 percent + 20 percent) = (50) (100 percent) + (50) (20 percent) = (50) (1.0) + (50) (0.2) = 50 + 10 = 60 (60) (110 percent) = (60) (100 percent + 10 percent) = (60) (100 percent) + (60) (10 percent) = (60) (1.0) + (60) (0.1) = 60 + 6 = 66 (60) (120 percent) = (60) (100 percent + 20 percent) = (60) (100 percent) + (60) (20 percent) = (60) (1.0) + (60) (0.2) = 60 + 12 = 72
Answer:
Step-by-step explanation:
multiply 52 times 90% +52
Answer:
Option B is the correct answer.
Explanation:
The image below is the correct answer.
he;p me please i am losing my points please anyone can you help at least one of you please please please! :(
[tex]answers \\ 1. \: \: c \\ 2. \: a \\ 3. \: d \\ 4. \: b \\ explantion \\ 1. \: \: r \: rotated \: 270.the \: r \: lies \: on \: {3}^{rd} \\ quadrant. \\ 2. \: \: r \: reflected \: to \: x. \: the \: r \: mirroring \\ to \: {1}^{st} quadrant. \\ 3. \: r \: moves \: 12 \: units \: upward. \\ 4. \: r \: scaled \: \frac{1}{5} . \: therefore \: the \: sides \: \\ scaled \: \frac{1}{5} also. \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment..[/tex]
please solve
thanks
Answer:
1) 250°, 2) 44°
Step-by-step explanation:
1) See attached
If we add a line ⊥ to both AB and DE, we can find x as a sum of 2 internal angles of right triangles and 180°
∠D internal = 360°-312°=48°
x=180°+(90°-62°)+(90°-48°)= 180°+28°+42°= 250°
x=250°
2)
∠ADC= ∠ABC= 180°- ∠ADE= 180°- 110°= 70°
∠DBC= ∠ABC- ∠ABD= 70°-26°= 44°
∠DBC= 44°
A newspaper conducted a survey to find out how many high school students play video games. The two-way table below displays the data from the survey. Based on these data in the table, which statement is true? *
A. There were 2,451 boys surveyed, and about 29% of them play video games.
B. There were 2,996 girls surveyed, and about 45% of them play video games.
C. There were 5,447 students surveyed, and about 54% of them do not play video games.
D. There were 2,493 students surveyed, and about 34% of them are girls who do not play video games.
Answer:
Correct option is:
B. There were 2,996 girls surveyed, and about 45% of them play video games.
Step-by-step explanation:
Let us calculate the percentage step by step as per the options.
We are given the following:
1. Boys who do play video games = 1593
2. Boys who do not play video games = 858
3. Total boys = 2451
4. Girls who do play video games = 1361
5. Boys who do not play video games = 1635
6. Total boys = 2996
7. Total number of candidates = Total boys + Total girls = 5447
8. Total number of students, who play video games = 2954
9. Total number of students, who do not play video games = 2493
Percentage of boys who play video games:
[tex]\dfrac{1593}{2451} \times 100 = 64.99\%[/tex]
So, option A is not correct.
Percentage of girls who play video games:
[tex]\dfrac{1361}{2996} \times 100 = 45.43\%[/tex]
The percentage is near about 45%, so option B is correct.
Percentage of Total number of students, who do not play video games:
[tex]\dfrac{2493}{5447} \times 100 = 45.77\%[/tex]
So, option C is not correct.
Hence, correct answer is option B.
Answer:
Its b
Step-by-step explanation:
B , it just makes sense
F(x)=x^2 What is g(x)?
Answer:
answer is D
Step-by-step explanation:
Andy's savings account pays 0.3% more interest than Marty's. What is 0.3% written as a decimal number?
A. 0.003
B. 0.3
C. 0.0003
D. 0.03
Answer:
A. 0.003
Step-by-step explanation:
When using decimals to represent a percentage it goes as follows:
100% = 1
75% = 0.75
50% = 0.5
25% = 0.25
1% = 0.01
And in the case of this problem: 0.3% = 0.003
Alaine has 1 gallon of paint. She is going to pour it into
paint tray that measures 10 inches wide, 12 inches long, and 5 cm deep.
(1 gallon = 231 in?, 1 inch = 2.54 cm)
Which of the following scenarios will happen?
The paint will not fill the tray by 369 cm
The paint will not fill the tray by 5.22 in
The paint will fill the tray exactly
The paint will overfill the tray by 5.22 in?
Answer:
First, solve for the volume of the tray by the equation V = L x W x H. Convert first all the dimensions to inches. The operation gives an answer of volume equal to 236.22 in³. Converting the amount of paint available to in³. This gives an answer of 231 in³. Hence, the answer is letter B.
Step-by-step explanation:
A jar contains 5 red, 4 blue, and 3 yellow marbles. What is the probability of pulling a red marble, then pulling a blue marble, without
replacement? Calculate to the nearest tenth.
O 15.2 %
O 13.9%
14%
O 17.1%
Answer:
15.2%
Step-by-step explanation:
The total number of marbles in the jar is:
5 + 4 + 3 = 12 marbles
The jar contains 5 red, 4 blue, and 3 yellow marbles.
The probability of pulling a red marble is 5/12
There are now 11 marbles in the jar.
The probability of pulling a blue marble is 4/11
Therefore, the probability of pulling a red marble, then, pulling a blue marble, without replacement is:
5/12 * 4/11 = 5/33
Converting to percentage:
5/33 * 100 = 15.2%
