Solution :
Maximize, S = xy
subject to 2x + 2y = 996
So,
2x + 2y = 996
2(x + y) = 996
x + y = 498
y = 498 - x
Therefore,
S = x (498 - x)
S = 498x - [tex]x^2[/tex]
S = [tex]-x^2 + 498x[/tex]
[tex]$S = -(x^2-498x + 249^2) + 300^2$[/tex]
[tex]$S= -(x-249)^2 + 249^2$[/tex]
S = x (498 - x)
S = 498x - [tex]x^2[/tex]
[tex]$\frac{dS}{dx}= 498 - 2x$[/tex]
[tex]$\frac{dS}{dx}= 0$[/tex]
498 - 2x = 0
2x = 498
x = 249
∴ y = 498 - x
y = 498 - 249
= 249
Answer:
A = 249 x 249 = 62001 square meter.
Side is L = 249 m
Step-by-step explanation:
Total length of the fence is 996 m.
Let the length is L and the width is W.
Perimeter = 2 (L + W)
996 = 2 (L + W)
498 = L + W
L = 498 - W ...... (1)
Let the area is
A = L W
A = (498 - W) W
A = 498 W - W^2
Differentiate with respect to W.
dA/dW = 498 - 2 W
Put it equal to zero.
498 - 2 W = 0
W = 249 m
Now, L = 498 - 249 = 249 m
Differentiate with respect to W again
[tex]\frac{d^2A}{dW^2} = - 2[/tex]
As it is negative so the area is maximum.
The maximum area is
A = 249 x 249 = 62001 square meter.
Side is L = 249 m
There are 3200 students at Lake High School and 310 of these students are sophomores. If 38 of the sophomores are in favor of the school forming a crew team and 34 of the remaining students (not sophomores) are also in favor of forming a crew team, how many students are opposed to this idea?
Answer: 3128 students
Step-by-step explanation:
Total no of students in the school : 3200
No of sophomores in favor of the school forming a crew team : 38
No of the remaining students in favor of forming a crew team : 34
Total students in favor of forming a crew team = 38+34= 72
No of students against it : Total students - Students in favor
= 3200-72 = 3128 students
Find the arc length of the partial circle.
Answer: C=10.99
Step-by-step explanation:
It can be seen that the arc has an angle of a=90 degrees, respectively, the length of the arc can be found by the formula[tex]\bf C=\dfrac{2\bf {\pi} r}{360} \cdot \alpha=> \dfrac{2\cdot 3,14\cdot 7 }{360} \cdot 90=\boxed{\bf 10.99}[/tex]5 a + 3 b + 2 a b + 4 a -7 b
Answer:
5a+4a=9a
3b-7b=-4b
2ab
=9a-4b+2ab or 2ab+9a-4a
Step-by-step explanation:
Calculate liked terms
Will Mark Brainnlest Please help me
Answer:
sory
Step-by-step explanation:
soryuuuiuuuiiiiiiijjjjkkkkkj
HELP!!
Resolve into factors:
8 – 6а – 9a^2 + 27a^3
[tex]\\ \sf\longmapsto 8-6a-9a^2+27a^3[/tex]
[tex]\\ \sf\longmapsto 27a^30-9a^2-6a+8[/tex]
Take 3a common[tex]\\ \sf\longmapsto 3a(9a^2-3a-2)+8[/tex]
Hence doneUse the Diagram to find BC.
Answer:
Step-by-step explanation: you have to ask your parents for help
solve A = 1/2bh, for b
Answer:
b=2A/h
Step-by-step explanation:
First I throw everything else to another side with A by dividing them
(A = b)/2h
then I get
b=2A/h
Step-by-step explanation:
A = 1/2 bh
divide by 1/2
2A = bh
divide by h
2A/h = b
F(x) = 3x + 2 what if f(5)
What is the volume of the cylinder?
•576 cm3
•2887 cm3
•96 cm3
•192 cm3
[tex] \large\begin{gathered} {\underline{\boxed{ \rm {\red{Volume \: \: of \: \: cylinder \: = \: \pi \: {r}^{2} \: h }}}}}\end{gathered}[/tex]
r represents radius of cylinder.h represents height of cylinder.So ,r = 6 cmh = 16 cmπ = 3.14Substuting the values⇥Volume of the cylinder = π r² h
⇥Volume of the cylinder = 3.14 × 36 × 16
⇥Volume of the cylinder = 113.04 × 16
⇥Volume of the cylinder = 1808.64
Hence , the volume of cylinder is 1808.64 cm²
can someone help me with this one ....
Answer:
-5, - 2, 3
Step-by-step explanation:
y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3
Based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why AABC= ALMN?
Check all that apply
O A. LL
O B. ASA
I C. LA
D. HL
E AAS
3 Answers:
Choice A. LLChoice D. HLChoice F. SAS==========================================================
Explanation:
Let's go through the answer choices one by one.
A) This can be used because LL = leg leg, and this means we have two pairs of congruent legs. Those pairs are AC = LN and CB = NM. The LL theorem only applies to right triangles.B) This cannot be used. We don't have info about two pairs of angles. We only know that one pair of angles are the same (those 90 degree angles). So we can't form the second "A" in "ASA". This idea will come up again in choice C and choice E.C) This cannot be used. Why not? Because the "A" of "LA" refers to "acute angle". But unfortunately we don't know anything about the acute angles (whether they are congruent or not). The LA theorem can only be applied to right triangles.D) This can be used. We can use the HL (hypotenuse leg) theorem because we see that AB = LM are the pair of congruent hypotenuses, and you can use any of the congruent leg pairs to form the L of HL. Similar to LL and LA, the HL theorem only works for right triangles.E) This cannot be used. Like with choice B, we can't form the second "A" of "AAS".F) This can be used because we have two pairs of congruent sides, with a pair of congruent angles between those sides. Those angles being the marked 90 degree angles. It turns out that LL theorem is a special case of the SAS theorem.In short, we can use choice A, choice D, choice F. We can't use the other three choices because we lack the info about any other pairs of angles.
The congruence theorem or postulate that we can use to show that triangle ABC is congruent to triangle LMN is LL (Side-Side-Side), the correct option is A.
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]
(|AB| denotes length of line segment AB, and so on for others).
We are given that;
Sides are equal
Now,
Based only on the information given in the diagram, we can use the following congruence theorems or postulates to show that triangle ABC is congruent to triangle LMN:
A. LL (Side-Side-Side): This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. In this case, we know that AB = LM, AC = LN, and BC = MN, so we can use LL to show that triangle ABC is congruent to triangle LMN.
B. ASA (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent. In this case, we do not know any angle measures, so we cannot use ASA to show that the triangles are congruent.
Therefore, by the congruent triangles the answer will be LL (Side-Side-Side).
Learn more about congruent triangles here:
https://brainly.com/question/16921692
#SPJ7
(4a)^2 without the exponents
Answer:
16 a*a
Step-by-step explanation:
(4a)^2
(4a) (4a)
16 a*a
Answer:
16a²
Step-by-step explanation:
(4a)²
=>(4)² x (a)²
=> 16 x a²
=>16a²
Problem 3 Find the value of x.
value of x should be 3.2 units
Answered by Gauthmath must click thanks and mark brainliest
Find the surface area of each figure. Round your answers to the nearest tenth, if necessary
Answer: 109m^2
Step-by-step explanation:
(5)(8.4)/2 = 21 m^2
(4 ) (21) = 84 m^2
Base = 5^2 = 25 m^2
84 + 25 = 109 m^2
what is the gcf of 36, 126, and 210?
Answer:
Greatest common factor (GCF) of 36 and 210 is 6.
Step-by-step explanation:
Answer:
6
Brainliest, please! (Almost an Ace!)
Step-by-step explanation:
Look at the smallest factor, 36. Find its factors.
36: 1, 2, 3, 6, 12, 18, 36
Out of all of them, which is the biggest one that 126 and 210 are also divisible by?
We see that they're divisible by 1, 2, 3, and 6.
Our answer is 6.
A. 4√29/ 7 feet
b. 4√5 feet
c.√164 feet
d. 2√41
Answer:
These two triangles are similar triangles. This means that their side lengths are proportional to each other.
Thus, making line segment EC equal to "x", and BC equal to "y" we can write:
8/y = 28/(10+y)
The next step is to get rid of the fractions, which can be done by cross multiplying.
So we have:
8(10+y) = 28(y)
After distribution and some simplification, you should get the value of y.
80+8y = 28y
80 = 20y
80/20 = 20y/20
4 = y
y = 4
Knowing that y = BC, and y = 4, it is clear that BC = 4.
Since BC = 4, one can use the Pythagorean Theorem to solve for segment EC.
Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths of a right triangle, and c is the hypotenuse (in other words the longest side)
In our case, a and b are 8 and 4 (the order doesn't really matter here).
So we have: 8^2 + 4^2 = c^2
64 + 16 = c^2
80 = c^2
c = sqrt 80
c = 4 sqrt 5
And we arrive at the answer- EC = 4 sqrt 5, making B the correct choice.
Hope this helps!
Please help me find which expression is correct
Answer:
IN MY OPINION D NO IS THE CORRECT ANSWER OF YOUR QUESTION.
Answer:
in my opinion d is the correct answer of your questions.
Step-by-step explanation:
Because subtract subtract sign is always add.
hope this will help you
thanks
Find the least number by which the following number must be multiplied so that the product are perfect cube one number 72 to number 128 number 288 phone number 675
Answer:
Well this question is actually a piece of cake. Just pick your favorite number. Multiply it by 10. Then do whatever operation you want with the 2,300. For the exponent part of this. Lets say we do it this way y times z equals 2,300. Exponents are letters used in mathematical terms. So any letter can be used to represent any number.
Step-by-step explanation:
I have 5 digits.My eight is worse 8000. One of my sixes is worth 60.The other is worth 10 times as much.My other digit is a zero
Answer:
i think its 58,660
Step-by-step explanation:
Answer:
58,660
Step-by-step explanation:
please help in indices
[tex] \frac{ {5}^{m + 2} - {5}^{m} }{ {5}^{m + 1} + {5}^{m} } \\ \\ \frac{ {4}^{m} + {4}^{m + 1} }{ {4}^{m + 2} - {4}^{m} } [/tex]
Step-by-step explanation:
Hey there!
Please see your required answer in picture.
Hope it helps!
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
Plz solve question 12
Answer: C
Step-by-step explanation:
To solve for 12, we can use eliminate or substituion to solve our system of equations. Let's use elimination method.
[tex]\left \{ {{3f-2k=10} \atop {-3f-2k=14}} \right.[/tex]
Let's add the equations together. This way, 3f+(-3f)=0
[tex]-4k=24[/tex] [divide both sides by -4]
[tex]k=-6[/tex]
Now that we know k, we can plug it into either equation to find f.
[tex]3f-2(-6)=10[/tex] [multiply]
[tex]3f+12=10[/tex] [subtract both sides by 12]
[tex]3f=-2[/tex] [divide both sides by 3]
[tex]f=-\frac{2}{3}[/tex]
Now that we have f and k, we know that C is the correct answer.
Explain the process due to which rain falls ? Class 4 - EVS
Answer:
As you may already know, water drops that fall from the cloud are considered "rain".
The Sun's heat turns the moisture or water from leaves, plants, rivers, lakes, and oceans - and turns it into gas or also called, vapor. This water vapor then turns into gas and disappears into the air. When it gets mixed with the air, it cools down. When it cools down, it changes into small water drops, which then form a cloud. These small water drops join together with other water drops to create larger and bigger water drops.
You may know this now because this is the easiest part. What happens when something gets heavy or is over-filled? It falls down, right?
So, the large drops from water fall down as they get too heavy for the cloud to carry. These big droplets falling down on us are called Rain.
Which is the best estimate of -14 1/9 (-2 9/10)
Answer:
Step-by-step explanation:
-14 1/9 is close to - 14
-2 and 9/10 is close to - 3
The best estimate would be 42 (14 * 3)
Estimate means you put your calculator on the kitchen counter until you've done this question.
Let's see what the actual answer is. 40.92222 which is close to 41.
42 is a pretty good estimate.
Please help me with this anyone
Answer:
Step-by-step explanation:
Begin by combining like terms and then factoring. Combining like terms will give you
[tex]10p^2-17p-20=0[/tex] Using the "old-fashioned" way of factoring, the a times c method, our a = 10, b = -17 and c = -20.
a * c = 10(-20) = -200 and now we need the factors of 200 (don't worry about the negative) that combine to give us that middle term, -17p (here is where the negative matters). The factors of 200 are:
1. 200; 2, 100; 4. 50; 5, 40; 8, 25; 10, 20
The combination of those numbers that can be manipulated to give us a -17p is the 8, 25 as long as we say that the 25 is negative and the 8 is positive. Rewrite the original polynomial to reflect those factors:
[tex]10p^2-25p+8p-20=0[/tex] and then factor by grouping:
[tex](10p^2-25p)+(8p-20)=0[/tex] and factor out from each set of parenthesis what is common:
[tex]5p(2p-5)+4(2p-5)=0[/tex] again factor out what is common:
(2p - 5)(5p+ 4) = 0. These are the factors; therefore the solutions are
2p - 5 = 0 so
2p = 5 and
p = 5/2 and
5p + 4 = 0 and
5p = -4 so
p = -4/5
Jimmy is saving money to buy a concert ticket for $155. He has $42 so far and he can save $20 per week. In how many weeks will he have enough money to buy the ticket? Select an equation that could be used to answer the question above. Let W represent the number of weeks. A. 20w + 42 = 155 B. 20w - 155 =42 C. 42w + 20 = 155 D. 155w - 20 = 42
Answer:
The answer for this question is A
write as a sentence in words 7.8 > 3.4
Answer:
seven and eight tenths is greater than three and four tenths
Hope it helped youMohamad bought a remote control car and paid $70.20. The price before tax was $65.00. What percent sales tax did he pay?
Answer:
Mohamad payed 8% of sales tax.
Step-by-step explanation:
First, we need to find the additional amount he paid to find the tax percentage.
70.20 - 65.00 = $5.20
Now, we divided that answer by the original price to find the actual percentage.
5.20/65.00 = 0.08 = 8%
9) Assume that the random variable X is normally distributed, with mean = 90 and standard deviation o = 12. Compute the probability P(57 < X < 105).
A) 0.7888 B) 0.8944 C) 0.8914 D) 0.8819
Answer:
Step-by-step explanation:
The mean, [tex]\bar{x}[/tex], is 90 and the standard deviation, [tex]\sigma[/tex], is 12. We are looking for the probability that the variable X will fall between 57 and 105. We use the z-score table for this, AFTER we find the z scores. The formula to find the z-scores for us is:
[tex]P(\frac{57-\bar{x}}{\sigma}\leq z\leq \frac{105-\bar{x}}{\sigma})[/tex] and we fill in accordingly:
[tex]P(\frac{57-90}{12}\leq z\leq \frac{105-90}{12})[/tex] which simplifies to
[tex]P(-2.75\leq z\leq 1.25)[/tex] and we will break them up into 2 different sets as follows:
P(-2.75 ≤ z ≤ 0) + P(0 ≤ z ≤ 1.25)
and based on the fact that z scores are given from 0 on up, we are going to convert the first one by using the logic that if z is greater than -2.75 but less than 0, by symmetry, z is greater than 0 but less than 2.75:
P(0 ≤ z ≤ 2.75) + P(0 ≤ z ≤ 1.25) and we go to the z-score table.
Locate 2.7 down along the left side and move over til you're under the .05; that gives us the z-score for 2.75 which is .4970. Do the same for 1.25 to get a z-score of .3944. Add them together to get a final z-score that covers the range of values for X:
.4970 + .3944 = 0.8914
Pls help me I will mark your answer as brainliest!
Answer:
9
Step-by-step explanation:
if we divide it my 9 we will get 927,998.666667
Answer: greatest number which should be replace m= 8
Except number 9, ; 2,5.and 8 can replace m so that the number 5567m92 is divisible by 6( Here greatest among all is 8 so 8 is your answer)
Step-by-step explanation:
5567292 is divisible by 6.
5567592 is divisible by 6.
5567892 is divisible by 6.
Will Mark Brainlest Helppp please
Answer:
1
Step-by-step explanation:
a pair of coordinates defines a first number x, and as second number y (or the functional result).
so, we need to find the value of x that leads to 2 as functional result.
2 = x² + 1
1 = x²
x = 1
